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This thesis has been examined and approved for acceptance by the Department of Physics and Geophysical Engineering, Montana College of Mineral Science and Technology, on this 27th day of October, 1987.

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THREE DIMENSIONAL GRAVITY MODELING TECHNIQUES WITH APPLICATION TO THE ENNIS GEOTHERMAL AREA

by Dave Semmens

A thesis submitted to the Department of Physics and Geophysical Engineering Montana College of Mineral Science and Technology in partial fulfillment of the requirements for the degree of Master of Science in Geophysical Engineering

Montana College of Mineral Science and Technology Butte, Montana

October , 1987

LIBRARY OF MONTANA COLLEGE OF MINERAL SCIENCC AND TECHNOLOGY, BOTTE


UMI Number: EP32241

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ABSTRACT

3-D gravity modeling is done in the area of the Ennis hot spring in an attempt to determine controlling structure of the Ennis hot spring.

The modeling is done in a two-step process

where: 1) The topography is modeled by modeling the valley fill from the highest elevation in the modeling area to some elevation below the lowest station elevation using Talwani and Ewing's (1960) method of modeling with vertically-stacked, horizontal, n-sided polygons. Once the gravity contributions of the valley fill included in this "topographic model" are calculated, they were removed from the original gravity data. 2) The remaining valley fill is modeled using blocks where the 3-D algorithm for modeling with blocks results from integrating the gravity formula in the X and Z directions and approximating the integration in the Y-direction using a quadrature formula. Finally, an inverse 3-D gravity modeling program was written to automatically adjust the bedrock topography output from this two-step modeling process.

The gravity data calculated from the

adjusted bedrock topography, output from the inverse modeling program, should match the observed gravity data within the error of the survey.


m

This two-step forward gravity modeling procedure, used sequentially with the inverse gravity modeling program, was applied to modeling of the gravity data collected in Ennis hot spring area.

The resulting bedrock topography model produces

calculated gravity data that matches the observed gravity data, collected in the area of the Ennis hot spring, within the 0.5 mgal assumed error of the survey.

In addtion, this bedrock

topography model matches reasonably with drilling and seismic refraction data. Interpretation of this bedrock topography model indicates the presence of a wrench fault across which structural trends and/or bedrock depths change noticeably.

This wrench fault is

located approximately 500 meters north of the hot spring along a N-S line. A drill site, located approximately 750 meters NE of the hot spring and contained in the interpreted location of the wrench fault, is proposed based on an interpretation of the inverse 3-D gravity modeling results.

If a well is drilled at

this suggested site, a crude estimate indicates that 99 C water might be intercepted in the bedrock if the interpreted wrench fault controls the ascending geothermal water.


ACKNOWLEDGEMENTS

There are several people who, without their involvement or cooperation, this thesis project could not have been done. First of all, I would like to thank the U.S. Department of Energy who funded this project under contract number DE-FG07-84ID12525.

I would also like to thank Dr. Charles

Wideman and Dr. William Sill; two professors who worked with me on a daily basis. Without Dr. Wideman's encouragement I would not have gone to graduate school, and without Dr. Sill I would not have had the skill (or desire) to do 3-D gravity modeling. Finally, I would like to thank the landowners in the area of the Ennis hot spring. Without their cooperation our study of the Ennis hot spring would have been impossible.

These landowners

include:

Dan Leadbetter,

Rich MacMillan, William Goggins

Miles Bob, William Thexton, and

Glen Rinehart.


TABLE OF CONTENTS INTRODUCTION Purpose and Scope Geothermal Resources in SW Montana Study Area and the Ennis Hot Spring A Note on Figures

I 1 2 3 7

PREVIOUS WORK Drilling Fracture Zone in Wells TX-12, MAC-1 Heat Flow and Thermal Gradients Geothermometry of the Ennis Geothermal System Structural Geology of the Ennis Geothermal System .. Faults of the Northern Madison Valley Spanish Peaks Fault Jack Creek Fault Tear Faults Madison Range Front Fault North Meadow Creek Fault Dating of Faults Precambrian Movement Cretaceous-Eocene (Laramide) Movement .... Tertiary (Basin and Range) Movement Formation and Chronology of Laramide Structure . Inferred Faults Buried in the Northern Madison Valley Geophysics Seismic Refraction Seismic Reflection Audio-Magnetotellurics Controlled Source Audio-Magnetotellurics ...... Gravity Burfeind Montana Tech Senterfit

9 9 12 14 20 25 27 27 29 29 30 30 31 31 31 32 32 34 36 36 38 42 45 45 45 46 48

GRAVITY DATA Additional Gravity Data Modeled Gravity Data

50 50 50

3-D GRAVITY MODELING 54 Assumptions and Modeling Decisions 54 Gridding of Gravity Data 54 Density Determination for Modeling 56 Modeling with Blocks 59 Modeling of Topography 60 Determination of Depth to Bedrock using Inversion Theory 65 3-D Gravity Modeling Theory 66 Forward Modeling Theory 66 Inverse Modeling Theory 70 Linear Algebra 72


vi

Scaling Matrix 73 Determining the Marquardt Damping Factor .. 73 Determining the Error 74 Weighting 74 Constraining the Solution Path 76 Gravity Models of the Ennis Geothermal Area 78 Topographic Model 78 Fo rwa rd Mode1 84 Inverse Model 86 Reliability of the Inverse Model 94 Comparison with Seismic Refraction 94 Comparison with Drilling 96 Comparison with Seismic Reflection 97 STRUCTURAL INTERPRETATION OF THE 3-D GRAVITY MODELING RESULTS Interpretaion Considerations Interpre tation Interpretation Implications

102 102 105 110

SUMMARY

114

REFERENCES CITED

119

APPENDICES A - GRAVITY DATA AND CORRECTIONS

123

B - FORTRAN CODE OF PROGRAMS GRAVBL, GINDEP, AND 3D . 128 B.l CODE FOR PROGRAM GRAVBL 129 B.2 CODE FOR PROGRAM GINDEP 138 B. 3 CODE FOR PROGRAM 3D 159 C - PREPARING OBSERVED GRAVITY DATA FOR USE WITH PROGRAMS GRAVBL AND GINDEP

165

D - INPUT TO AND OUTPUT OF PROGRAMS GRAVBL AND GINDEP 175 D.l INPUT TO AND OUTPUT OF PROGRAM GRAVBL .... 176 D.2 INPUT TO AND OUTPUT OF PROGRAM GINDEP 179 E - MODELED GRAVITY DATA ITS PREPARATION FOR USE WITH PROGRAMS GRAVBL AND GINDEP E.l LOCATIONS AND GRAVITY VALUES OF THE MODELED GRAVITY DATA E.2 X-POSITION, Y-POSITION, GRIDDED GRAVITY VALUE OF THE GRIDDED OBSERVED GRAVITY DATA E.3 GRAVITY CONTRIBUTIONS OF THE VALLEY FILL INCLUDED IN THE TOPOGRAPHY MODEL E.4 GRIDDED OBSERVED "TOPOGRAPHY CORRECTED" GRAVITY DATA

184 185 189 193 197

F - FORWARD AND INVERSE 3-D GRAVITY MODELING RESULTS FOR THE ENNIS GEOTHERMAL AREA 201 F.l FORWARD MODELING RESULTS 202


vi i

F.1.1

F.2

FORWARD MODEL OF THE ENNIS GEOTHERMAL AREA 203 F.1.2 INPUT FILE (GRAVBL.DAT) FOR PROGRAM GRAVBL 206 F.1.3 CALCULATED GRAVITY OUTPUT FROM PROGRAM GRAVBL 209 INVERSE MODELING RESULTS 213 F.2.1 INPUT FILE (FILE G.DAT) FOR PROGRAM GINDEP 214 F.2.2

OUTPUT OF PROGRAM GINDEP (FILE GINDEP.OUT)

217

F.2.3

GRAVITY VALUES CALCULATED USING THE RESULTS OF PROGRAM GINDEP

240

G - TEST CASES FOR PROGRAMS GRAVBL, GINDEP

244


LIST OF ILLUSTRATIONS LIST OF FIGURES: Figure 1. Hot springs of SW Montana. to Chadwick and Leonard (1979)

Figure according

2 Figure 2. Study area (inner square, app. 9 Km ) shown as it would appear on the Ennis 15' quadrangle...

4 6

Figure 3. Test wells (wells starting with TX), shot holes (wells starting with SH), and selected domestic wells in the area of the Ennis hot spring....

10

Figure 4. Thermal gradient profiles of selected wells located in the area of the Ennis hot spring. Figure according to Leonard (written communication)

16

Figure 5. -Contours of conductive heat flux values (mW/m ). The data was taken from wells located in the area of the Ennis hot spring.

18

Figure 6. Regional geology of a portion of SW Montana. Figure adapted from Schmidt and Garihan (1983)........

26

Figure 7. Major documented faults located in the northern Madison valley. Mapping according to Swanson (1950), Garihan and others (1983), and Young (1984)

28

Figure 8. Location of NE and NW trending seismic refraction lines. The seismic refraction data was collected by the physics/geophysics department of Montana Tech under the direction of Dr. Charles Wideman

37

Figure 9. Seismic refraction data and accompanying bedrock depth interpretation for the NE trending seismic refraction line (see Figure 8). Interpretation according to McRae (unpublished senior report)

39

Figure 10. Seismic refraction data and accompanying bedrock depth interpretation for the NW trending seismic refraction line (see Figure 8 ) . Interpretation according to McRae (unpublished senior report) *

40


IX

Figure 11. Placement of 8 seismic reflection lines located in the northern Madison valley. Young interpreted the following structure from this seismic refraction data: a) The Jordan Creek graben, b) The Shelhamer Ranch graben, and c) The axis of the northern Madison valley. The dotted lines connect the deepest points along these interpreted structures

41

Figure 12. Contours of apparent resistivities (ohm-meters) based on AMT data collected by Long and Senterfit (1979) along NS and EW oriented dipoles at the 19 stations shown. This data is displayed at 100 and 300 meter skin depths for the EW and NS dipole orientations based on interpretations by Semmens and Emilsson

43

Figure 13. Locations of the 67 gravity stations collected by the physics/geophysics department of Montana Tech under the supervision of Dr. Charles Wideman (unpublished data)

47

Figure 14. Locations of the 33 gravity stations collected by Senterfit (1980)

49

Figure 15. Locations of the 63 gravity stations collected by Semmens and Emilsson in September, 1985 and January, 1986

51

Figure 16. Locations of the 158 gravity stations used in the gravity modeling. Data includes stations collected by Montana Tech, Senterfit (1980), and Semmens and Emilsson. The contours shown are contours of the gravity data (c.i. = lmgal) drawn by hand, and the inner rectangle represents the area containing the gridded gravity data

55

Figure 17. Locations of the 120 (15 columns x 8 rows) gridded gravity stations. Contours are gravity contours (c.i.=lmgal) drawn by computer using the Surface II contouring package (Sampson, 1978). The values assigned to the grid nodes were interpolated from the hand contoured gravity data (see Figure 16)

57

Figure 18. Modeling a block-faulted valley with blocks of earth

60


Figure 19. A) Representation of a cross section along a row of gravity data in a block-faulted valley. Sediments from the highest elevation in the modeling area to some elevation below the lowest station elevation are included in the topography model. B) Schematic showing how the valley fill included in the topography model might be modeled using vertically stacked, horizontal polygons according to the gravity modeling method of Talwani and Ewing ( 1960)

62

Figure 20. Once the contributions of the valley fill in the topography model have been removed, the remaining valley fill can be modeled efficiently using blocks. Note that with the removal of the gravity contributions of the valley fill included in the topography model it is not as if the gravity stations have been dropped to the plane at the base of the topography model

63

Figure 21. Coordinate system with a unit volume located at (x',y',z') and an observation point at (x,y,z)

67

Figure 22. Modeling area (outer square) relative the gridded observed gravity data area (inner square) as they would appear on the Ennis 15' quadrangle

79

Figure 23. Selected contour elevations (meters above sea level) taken from the Ennis 15' quadrangle map. These contours are assumed to give an adequate representation of the topography in the modeling area

80

Figure 24. A) A plan view of the 5 polygons which comprise the topography model. These polvgons are digitized representations of the 5 contours shown in Figure 23. B) Schematic showing the individual polygons

82

Figure 25. A) Contours (c.i.=lmgal) of the gridded gravity data with the gravity contributions of the gravity data included in the topography model removed. B) Contours (c.i.=0.2mgals) of the gravity contributions from the valley fill included in the gravity model

83

Figure 26. Plan view of the spatial locations of the blocks used in the gravity modeling. The blocks are numbered as they were in the actual modeling

85


XT

Figure 27. Plan view of the final model output from the forward modeling process. The numbers in the blocks represent the depths (in meters) below a 1475 meter elevation datum to the bedrock

87

Figure 28. A) Contours (c.i.=lmgal) of the "topography corrected" gridded observed gravity data. B) Contours (c.i.=lmgal) calculated using the forward modeling program with the model shown in Figure 27 input

88

Figure 29. Contours of the absolute value of the differences between the gridded observed "topography corrected" gravity data (c.i.=0.5mgals) - Figure 28a and the calculated gravity from the forward model - Figure 28b. The average root mean square misfit between the observed and calculated data is app. 1.0 mgal

89

Figure 30. Plan view of the model output after 3 iterations using the inverse gravity modeling program. The numbers in the blocks represent the depth (in meters) below a 1475 meter elevation datum to the bedrock

91

Figure 31. A) Contours (c.i.=lmgal) of the "topography corrected" gridded observed gravity data. B) Contours (c.i.=lmgal) calculated from the model shown in Figure 30 output after 3 iterations of the inverse modeling program

92

Figure 32. Contours of the absolute value of the differences between the gridded observed "topography corrected" gravity data (c.i.=0.5mgals) - Figure 28a and the calculated gravity from the forward model - Figure 28b. The average root mean square misfit between the observed and calculated data is app. 0.49 mgal

93

Figure 33. Comparison of the bedrock depths determined from the seismic refraction work and the inverse gravity modeling results. The dotted line shows the depth to bedrock interpreted (McRae, unpublished senior report) from the seismic refraction data, and the straight line segments represent the depth to bedrock +/- a standard deviation determined from the inverse gravity modeling

95


xn Figure 34. The upper picture shows "distinctive reflector horizons" picked and traced from seismic reflection line #2 by Young (1984). The lower picture shows Young's interpretation of the data in the upper picture. Superimposed on both of these pictures are the depths to bedrock indicated from the inverse gravity modeling results

98

Figure 35. Explanation of symbols shown in Figures 36 and 37

103

Figure 36. Plan view of the 54 blocks of the inverse gravity model included for interpretation. These blocks are shown as they would appear on the Ennis 15' quadrangle, and the numbers in these blocks indicate the depth (in meters) below the 1475 meter elevation to the bedrock

104

Figure 37. Interpretation of the inverse gravity modeling results shown in Figure 36 (see Figure 35 for an explanation of symbols)

106

Figure 38. Location of the cross section lines placed north and south of the wrench fault

108

Figure 39. Comparison of modeled bedrock topography located north and south of the wrench fault. See Figure 38 for the locations of the cross section lines

109

Figure 40. A) B)

249

The "correct model". Input model for program GINDEP

LIST OF TABLES: Table 1. Location, elevation, maximum depth, maximum temperature and depth in the well at which the maximum temperature was recorded, and depth to bedrock information for test wells and shot holes in the area of the Ennis hot spring. Well MAC-1 was drilled for Richard MacMillan and other investors

11

Table 2. Drawdown effects on well TX-11, and TX-12 during a pump test of the MAC-1 well. Data taken from Pump Test of the MacMillan Well (Sonderegger, unpublished MBMG report)

14

Table 3.

19

Conductive heat flow calculations

Table 4. Equations for temperature estimations using various geothermometers. Table taken from Fournier (1981)

21


XT

Table 5. Hydrogeochemical data for wells in the Ennis hot spring area. The data is taken from Leonard (written communication) and Project Milestone Report prepared for the Montana Department of Natural Resources and Conservation by GeoProducts Corporation (June, 1984)

24

Table 6. Greatest depth of Jordan Creek and Shelhamer Ranch grabens, Madison Range front fault, and North Meadow Creek fault as interpreted from seismic reflection data. Depths (in meters) according to Young, 1984 3 Table 7. Saturated densities (gm/cm ) of the valley fill sediments taken from cores of wells located near the Ennis hot spring according to Leonard (written communication)

58

Table 8. Comparison of bedrock depths determined from gravity modeling and drilling

99

Table 9. Interval velocities determined by Young (1984) using the Dix equation for seismic line #2. Time represents two way travel time

42

100


INTRODUCTION

Purpose and Scope Because of the search for alternate energy sources in the 1970's, the Ennis hot spring was the focus for an extensive amount of geophysical and hydrogeological work.

This previous

work provides a solid foundation on which new efforts are built, and this paper contains a discussion of the information gathered in the previous studies.

In the summer and fall of 1985 new

data was collected including controlled source audiomagnetotelluric (CSAMT) and gravity data.

Collection, modeling,

and interpretation of the CSAMT data are covered in a thesis presently being written by Gunnar Emilsson, and his final conclusions were not available at the time of this writing. Collection, modeling and interpretation of the gravity data are described in this paper. The purpose of the gravity modeling is to map the bedrock topography in an attempt to locate faults, offsetting the bedrock, which might control the path of the geothermal water ascending to eventually emerge as the Ennis hot spring.

The

purpose of the gravity modeling, then, might be construed as an attempt to locate promising areas for a drilling program developed to use the geothermal resource.

To satisfy this

purpose, I wrote a 3-D forward gravity modeling program and also an inverse gravity modeling program which when used sequentially are designed to find a bedrock topography model


2 from which calculated gravity data will match the observed within the error of the gravity survey.

I also devised a

modeling sequence which increases the efficiency and accuracy of the modeling process. The funding for this project was contingent on finding information pertaining to the Ennis hot spring.

For this

reason, the modeling programs and process discussed in this paper were applyed to the gravity data collected near the Ennis hot spring.

However, in general, these modeling techniques

could be used to solve geological and hydrogeological (as well as geothermal) problems in any valley where a valley fill over bedrock geologic setting exists.

Geothermal Resources in SW Montana There are 27 hot (> 38째C) springs in Montana (NOAA-Key to Geophysical Records Documentation No. 12, 1980), and 25 (92%) of these hot springs are located in southwest Montana.

Southwest

Montana is defined as the area south of 47 N latitude and west of 110째W Longitude (Chadwick and Leonard, 1979).

Of these 25

hot springs 19 (79%) issue either from crystalline rock adjacent to valley fill or from the valley fill itself (Chadwick and Leonard, 1979) as shown in Figure 1.

The heat content of the

springs in SW Montana appears to be controlled by deep circulation along fault and fracture zones in areas with average to above average thermal gradient.

Heat derived from young

magma bodies is not considered responsible for those thermal springs outside of the Yellowstone geothermal area because


47°P~

110°

114°

46°

45°

PARK

Cenozoic sedimentary rocks in principal block-faulted valleys. Cenozoic to Precambrian crystalline ': y <y rocks.

O

Hot spring

Ennis hot spring

Figure 1. Hot springs of southwestern Montana. Chadwick and Leonard (1979).

Figure according to


4 "residual heat from all but the largest magma bodies is dissipated within one to two million years" (Williams, 1975). The youngest volcanism in southwest Montana (1-2 million years old) is associated with the Yellowstone Park area (Chadwick, 1978).

In southwest Montana the crystalline rocks have an

average thermal gradient of 30 C/Km, while the sediments average approximately 60 C/Km (Nathenson and others, 1983; Blackwell and Chapman, 1977).

The approximate minimum depth of circulation

necessary to attain the hot spring's surface temperature is found using the formula:

D = (TR - TS) / G where:

D

= Depth of Circulation

T

R = Reservoir Temperature

T

S = Mean Annual Surface Temperature Thermal Gradient

Study Area and the Ennis Hot Spring The Ennis hot spring is located in southwest Montana in the Madison Valley approximately 2 kilometers north of the town of Ennis, Montana along U.S. Highway 287 (see Figure 1). The spring issues from valley fill near the western edge of the Madison Valley at the base of a river terrace composed of fluvial cobbles and clay.

The area studied for this paper


5

includes approximately 9 square kilometers surrounding the Ennis hot spring (see Figure 2 ) . Ever since the mid-1970's the Ennis hot spring has been studied intensively.

This work has been focused on the Ennis

hot spring for 3 general reasons: 1) At 83 C (NOAA-Key to Geophysical Records Documentation No. 12, 1980) the Ennis hot spring has the hottest surface temperature of any spring in Montana; 2) The Ennis hot spring is easily accessible in that it is located near highway #287 and the town of Ennis; and 3) The physical setting of the Ennis hot spring typifies the majority of hot springs in southwest Montana in that it issues from valley fill adjacent to crystalline rock.

The previous work in the area of the Ennis hot spring includes drilling, temperature and heat flow studies, hydrogeochemical, and geophysical surveys discussed in the section to follow.

which will be

I warn the reader here that

the previous work section to follow is rather long because much of the previous work is incorporated (directly or indirectly) either in the gravity modeling or the interpretation of the gravity modeling results.

If the modeling techniques and

results are all that is of interest, skip directly to the gravity modeling section.


â&#x20AC;˘ttf.

111.75

111.72

i ^ \13 Si VL

< '

111.69

N 18

lll.6o

LONGITUDE (DEG.) Figure 2.

Study area (inner square, app. 9 Km2) shown as i t would appear on the Ennis 15' quadrangle.


7

A Note on the Figures In the figures of this text which display the locations of the observed gravity data and the gravity modeling results, spatial location units of both latitude and longitude and meters east and north of an assumed origin are used.

I used units

of meters north and east of an assumed origin because the gravity modeling programs I wrote require this orientation of the gravity stations; consequently, those figures which depict the modeling results contain spatial location units of meters. For those figures not showing the gravity modeling results, I followed the common convention of using spatial units of latitude and longitude. The figures which display the locations of the gravity data and the gravity modeling results are not all shown at the same scale.

Scale reductions or enlargements were necessary because

I desired to keep all the figures within the text, rather then in plates located at the back of the thesis.

I realize that

these changes in scale make it difficult for the serious reader to compare results from figure to figure.

However, I think it

is generally more desirable to keep the figures within the text for ease of readability. To reduce orientation problems which may arise because of unit and scale changes from figure to figure, on all figures containing units of latitude and longitude, I have also included a meter scale.

Also on all figures showing spatial locations of

features within the modeling area, I have included the


8

location of Ennis hot spring and the benchmark to which the gravity data has been referenced.

The Ennis hot spring is shown

as a ball with a tail while the benchmark is labeled as BM.


PREVIOUS WORK

Drilling From October, 1977 to August, 1982, eleven test wells were drilled by the U.S. Geological Survey (TX-1 to TX-11) while one test well (TX-12) was drilled by the Montana Bureau of Mines and Geology in the area of the Ennis hot spring.

A thirteenth

well, MAC-1, was drilled in 1982 for Richard MacMillan and other investors.

Along with these test wells, 4 shot holes (SH-1, 3,

4, and 5) and several domestic wells are also located in the area.

See Figure 3 and Table 1 for the location of these wells.

The shot holes were used for a seismic refraction survey, the results of which will be discussed in the geophysics subsection. In each of the shot and test holes, variation of temperature with depth information was gathered.

See Table 1

for maximum temperature with depth in each well.

Three of the

test wells, TX-9, 11, and 12, one shot hole, SH-3, and well MAC-1 penetrated the bedrock.

Depth to bedrock information for

these wells is also contained in Table 1.

Drilling logs for the

wells indicate that the valley fill is composed of a surficial layer of alluvium, five to ten meters thick, consisting of boulders and cobbles.

Below this layer "poorly consolidated,

commonly calcareous, tuffaceous clay, silt, and argillaceous sand â&#x20AC;&#x201D;

all interbedded with lenticular layers of coarse sand

and gravel" (Leonard, written communication) is found to compose the cores.

In wells TX-9 and 11 a "well consolidated" silt and


10

o TX8 BM •

(0 N in.

*

m"

i

TOTH

O TX6

,

ORIFFEN

«-»

PRAY

o

o

°

MACI

SH4 O

(9 Ul

o

TXII.SHI

CYPRUS A

111

i

a

TXI

3

LATI .366

o

TXI2

o

TX2

V

o

o YENNY

TXT O

£

0

i\™5 ^

N N | S

HOT SPRING

o

TX9 TX4 O O TX3

O SH3 SCALE I

0

i

i

300

i

i

i

600

i

900 maters

<o w IO iri 111.74

111.73 LONGITUDE (DEG.)

111.72

Figure 3. Test wells (wells starting with TX), shot holes (wells starting with SH), and selected domestic wells in the area of the Ennis hot spring.


Well

Elev.(m.)

TX-1

1500

TX-2

Lat.u

Max. Temp

Long.

Max. Depth(m.)

45.3675

1 11.7281

89.5

/

1500

45.4675

1 11.7300

73.0

/ 116.1

TX-3

1495

45.3616

1 11.7228

10.4

/

54.6

TX-4

1495

45.3622

] 11.7275

17.9

/

83.5

TX-5

1492

45.3669

] 11.7247

60.4

/

98.1

TX-6

1496

45.3736

] 11.7381

103 116 55 84 99 60

19.1

/

60.4

TX-7

1502

45.3636

]111.7367

TX-8

1489

45.3803

]111.7275

29.8

/

91.0

TX-9

1502

45.3642

]L11.7333

42.0

/ 120.0

TX-10

1480

45.3811

1111.6969

26.9

/ 258.0

TX-11

1489

45.3706

]111.7244

94.0

/ 183.0

161

TX-12

1499

45.3678

]111.7247

92.3

/ 152.4

142

MAC-1

1489

45.3702

]L11.7253

97.0

/ 335.0

216

SH-1

1489

45.3690

1111.7213

62.1

/

15.4

SH-3

1503

45.3567

1L11.7377

11.7

/

9.0

SH-4

1498

45.3678

1

11.9

/

14.0

SH-5

1488

45.3702

91 120 258 183 291 372 15 15 14 14

18.9

/

14.0

111.7337 111.7185

C/Depth (m.)

Pep, to Bedrock (m.)

51.8

107

26

Table 1. Location, elevation, maximum depth, maximum temperature and depth in the well at which the maximum temperature was recorded, and depth to bedrock information for test wells and shot holes in the area of the Ennis hot spring. Data according to Leonard (written communication).


12

clay layer 10 to 15 meters thick is described in the well logs. Leonard (written communication) suggests that this clay layer is a "potentially extensive confining layer."

In well TX-12 there

is also a clay layer, 15 meters thick, above a 5 meter thick layer of cobbles and pebbles situated at the base of the valley fill.

The driller's log for MAC-1 was not personally viewed by

this author.

The "bedrock" according to cores taken from wells

SH-3, TX-9, 11, and 12 is composed of quartz-feldspathic hornblende and biotite gneiss.

Fracture Zone in Wells TX-12, MAC-1 The geologist's log of well TX-12 indicates that there is a zone of considerable fracturing in the gneiss at a depth of 150-187 m below the surface or approximately 8 meters below the base of the valley fill.

The driller's log for well MAC-1 was

not viewed by this author; nevertheless, Sonderegger and Zaluski (1983) indicate that well MAC-1 intercepted a fracture zone in an interval from 335 to 365 meters.

The fracture zones in wells

TX-12 and MAC-1 appear to be interconnected based on drawdown effects in TX-12 during a pump test of MAC-1 (Pump Test of the MacMillan well, Montana Bureau of Mines and Geology in-house report) as shown in

Table 2.

TX-12 is located 308 m south of

MAC-1 on a nearly north-south line; consequently, if the fracture zone is assumed to be a linear feature of unknown strike between the two wells, then a dip component of 31 N is indicated for the fracture zone in this area.

Well TX-11


13

intersected the bedrock yet did not cross a fracture zone. As TX-11 is located 80 meters southeast of MAC-1, it is possible that if TX-11 were deepened past its present 185 meters maximum depth, the fracture zone would be penetrated.

During the pump

test of MAC-1, the drawdown on TX-11 (80 meters away) was not as great as in well TX-12 (308 meters away).

See Table 2.

The fact that drawdown in well TX-12 occurred during pumping of well MAC-1 indicates a lack of water supply from additional aquifers to well TX-12.

Or, in other words, the

fracture zone is possibly the major conduit by which water is supplied to well TX-12.

Unfortunately the 3-D geometry of the

fracture zone is unknown because a third well has not penetrated this zone.

Nevertheless, the 2-D results of the pump test

indicate a general northerly direction of supply to well TX-12 and possibly the Ennis hot spring. In well MAC-1 a sustained 3 flow of .0242 m /s was achieved during the pump test of the MAC-1 well (Sonderegger, MBMG in-house report).

For comparison

3 surface flow at the Ennis hot spring was measured at .0012 m /s (Leonard, written communication). These numbers indicate the flow rate of the Ennis hot spring is ~20 times less than the pumped flow rate in the fracture zone below well MAC-1. For this reason the Ennis hot spring is assumed to represent only a minor portion of the Ennis geothermal system.

Below the fracture zone

flow drops off and the bedrock is described as "tight" to the bottom of well TX-12 at 291 meters according to the drilling log.


14

Table 2. Drawdown effects on wells TX-11, and TX-12 during a pump test of the MAC-1 well. Data taken from Pump Test of the MacMillan Well (Sonderegger, unpublished MBMG report). Well TX-11

Drawdown (m./lOOOminutes) 0.83

TX-12

1.19

Heat Flow and Thermal Gradients Heat in the earth may be transported in the following three ways: 1)

radiation, 2) conduction, and 3) convection.

In

geothermal systems radiative heat flow is negligible because of the temperature range pertinent to known geothermal systems (Rybach, 1981).

Conductive heat flow/area (flux) is described

by Fourier's Law (Rybach, 1981):

q = -k V T where: 2 q = heat flux (mW/m ) k = thermal conductivity (mW/ C'm) VT = temperature gradient ( C/m)

The negative sign is used in Fourier's Law because heat flow is in a direction opposite to the thermal gradient. Convective heat flow in a geothermal system (water is the medium by which heat is transferred) is given by the equation:


15

Qconv = CPH20(AT)(F) where: Q = Convective heat flow (mW) conv Cp _

= heat capacity of water [4.19 xlO mW-s/(°Cm3)]

AT

= difference between mean annual temperature

F

and temperature of the flow ( C) 3 = flow rate (m /sec)

In Figure 4, profiles of thermal gradients of selected shot holes and test wells are shown.

This figure illustrates that in

the high temperature wells (TX-1, 2, 5, and 11) large near surface gradients diminish to become near isothermal at depth. High thermal gradients which diminish to near isothermal at depth are common thermal profile features of many geothermal systems in the Basin and Range province (Chapman and others, 1978).

To model these thermal profiles, Chapman and others

(1978) achieved reasonable results by assuming the large near surface temperature gradients indicate a relatively large component of conductive heat flow while the deeper near isotherms suggest convective heat flow as the primary mechanism of heat transfer.

Therefore, using Chapman and other's (1978)

logic, an estimate the total heat flow (Qâ&#x20AC;&#x17E;) of the Ennis geothermal system, based on a sum of the convective and conductive heat flows, was determined.

Q

T

Q

conv

+ Q

cond

For example,


16

TEMPERATURE - Deg. C. 80 20 40 60

0

100

1500

1475

11450 TX-3

i

z o LÂąJ _)

UJ

1425

1400 T*I0

26.9 at 1221.5 m

1375 Figure 4. Thermal gradient profiles of selected wells located in the area of the Ennis hot spring (EHS). Figure according to Leonard (written communication).


17

where:

Q

= total heat flow.

Qcond = conductive heat flow (found by multiplying the heat flux values by the area which they occupy). Qconv = convective heat flow.

To determine the thermal gradients for conductive heat flow calculations, slopes on the temperature gradient profiles for wells TX-1, 2, 5, and 11 were estimated in the near surface region of high temperature gradients.

For the lower temperature

wells, values for thermal gradients were taken from information given by Leonard (written communication). Some of the wells (SH-1, SH-5, CYPRUS 1 and 2,and GRIFFEN) had only bottom hole temperatures, and for these wells temperature gradients were estimated by the difference between mean annual surface temperature (6.6 C) and the bottom hole temperature.

For the

valley fill in the Ennis geothermal area an average thermal conductivity, determined from core samples of the valley fill (Leonard, written communication) of 1465 milliwatts/m^ C (3.5 mcal/cm-s- C) was used . Contours were then drawn for heat flux values of 200, 500, 1000, 5000, and 10,000 (mW/m2).

The area

enclosed in each of these heat flux value contours was then estimated using a planimeter, and finally conductive heat flow values were estimated by multiplying the average heat flux value in each contour interval (trapezoidal rule) by the area contained in each contour interval.

These results are

summarized in Table 3, and the contours of heat flux values are shown in Figure 5.

The total conductive heat flow (Q

),


18

111.74

W.73

111.72

LONGITUDE (DEG.) Figure 5.

Contours of conductive heat flux values (mW/m 2 ). The data was taken from wells located in the area of the Ennis hot spring.


19

estimated for the Ennis geothermal area in the area of drilling, is 33.764 kilowatts (see Table 3 ) . For the determination of convective heat flow in the Ennis geothermal system the following values were used: c

Puor,

=

4.19 x 109 mW-sec/(째C-m3)

=

83째C - 6.6째C = 76.4째C

rlZU AT F

=

1.2 x 10~3 m3/sec.

The flow rate and temperature of the Ennis hot spring are those cited by Leonard (written communication). Because the flow rate used for these calculations is that of the Ennis hot spring, which apparently represents only a minor portion of the Ennis geothermal system, the conductive heat flow results represent a low-end value.

Using these numbers, a value for convective heat

flow of 384.139 KW is reached.

Therefore, the low end

approximation for the total heat flow (Q ,+ Q ) for the cond conv Ennis geothermal system in the area of drilling is approximately 420 kW (0.42 MW).

The estimated "safe yield" (above this yield

it is assumed the resource will be mined) of the Ennis Table 3. 2 Heat flux (mW/m )_ 200

Conductive Heat Flow Calculations. 2 2 Area(m _)_ Avg. Heat Flux(mW/m _)_

q(mW)

25460

350

8.911 106

12261

750

9.196 106

6231

1250

7.789 106

3685

7500

2.764 106

469

10822

5.104 106 33.764 kW

500 1000 5000 10000


20

geothermal system is 3.15 x 10 communication).

m /sec (Sonderegger, personal

Using this value for the flow rate, a "safe

yield" total heat flow value for the Ennis geothermal system is 10.5 MW.

Geothermometry of the Ennis Geothermal System Geothermometers are "tools" used to estimate reservoir (maximum) temperatures in a geothermal system from geochemical measuring of geothermal waters.

Their effectiveness is based on

the fact that "the compositions of geothermal fluids are controlled by temperature-dependent reactions between minerals and fluids" (Fournier, 1981).

There are several types of

geothermometers each given a name based on the geochemical constituent(s) of the geothermal waters being used to estimate subsurface temperature conditions (see Table 4).

All

concentrations of cations for the equations given in Table 4 are in units of parts per million.

The C on the right hand side of

the equations for geothermometers a-f in Table 4 represents the concentration of silica in parts per million.

Because

temperature estimates for geothermometers a-f depend on the concentration of silica, they are collectively termed silica geothermometers.

To determine the value of 3 to use for the

Na-K-Ca geothermometer (equation i in Table 4), Fournier and Truesdell (1973) suggest the following: 1) Using 3 = 4/3 find the temperature using equation i of Table 4;


21

Table 4.

Equations for temperature estimations using various geothermometers. Table taken from Fournier (1981). Equation

Geothermometer

Restrictions

-27315 a. Quartz-no steam loss t ° C = . . . 1 3 0 9 5 19 - log C b. Quartz-maximum steam loss

f°C

c. Chalcedony

«

d. a-Cristobalite

4-69 - log C ,°C = - - i M _ - 2 7 3 . . 5 4-78-log C

e. /?-CristabaIite

t°C-

i = 0-250°C

1522 -27315 5-75-log C

f = 0-250°C

•« .„,.„

781

f=0-250°C J = 0-250°C

27315

r = 0-250°C

f. Amorphous silica

731 t°C = 4-52 ^ — -; log C - - 2 7 3 15

t = 0-250°C

g. Na/K (Fournier)

t°C =

'

h. Na/K (Truesdell) i. Na-K-Ca

451 -log C

27315

1217 :-27315 log (Na/K) +1-483 „~ 855-6 t°C = .log (Na/K)+ 27315 ; r ^- r -— :0-8573 t°C =

j. A I 8 0 ( S O ; - H 2 0 )

1000 + ^,BO(HSO4-) " = 1000+*>*O(HaO)'

2)

1647

log (Na/K) + /?pog(v/Ca/Na) + 206] + 2-47 -27315 1000 In a = 2-88(106 7"-2)-4-l and

r =

r>150°C r>150°C f<100°C, 0 = 4/3 f>100°C, 0=1/3

°K

If this calculated temperature is less than 100 C and the log [(/Ca/Na) + 2.06] is positive, then keep the temperature indicated in step 1; or

3)

If the indicated temperature is greater than 100 C or_ log [(/Ca"/Na) + 2.06] is negative, then use 3 = 1/3 and recalculate the temperature.

Various assumptions are made when using any geothermometer. These assumptions are summarized by Fournier and others, 1974, as follows:


22

1) Temperature dependent reactions occur at depth; 2) All constituents involved in a temperature-dependent reaction are sufficiently abundant (that is supply is not a limiting factor); 3) Water-rock equilibration occurs at the reservoir temperature; 4)

Little or no re-equilibration or change in composition occurs at lower temperatures as water flows from the reservoir to the surface; and

5)

The hot water coming from deep in the system does not mix with cooler shallow groundwater (if this assumption is violated, "mixing models" as described later can be used).

The theory behind each of these geothermometers is amply discussed in the literature, and useful references include the following: 1) Silica Geothermometer: - Theory: Arnorsson (1975), Muffler (1979), Brook and others (1979). - Mixing model corrections: Fournier and Truesdell (1974) ,Truesdell and Fournier (1977). 2) Na/K and Na-K-Ca Geothermometers: - Theory: Fournier and Truesdell (1973) - Mg Correction: Fournier and Potter (1978) 3) Oxygen Isotope, Sulfate-Water Geothermometer: - Theory: Lloyd (1968) - Mixing model corrections: McKenzie and Truesdell (1977) 4) For an overall view of the applicability of each geothermometer to a given geothermal area and the assumptions involved in the use of each geothermometer, Fournier (1981) is an excellent reference.


23

Hydrogeochemical data for test wells (TX-1 to TX-12), shot holes (SH-1, 3, 4, and 5), and several domestic wells (see Figure 3 for locations of these wells) in the Ennis geothermal area are shown in Table 5.

This hydrogeochemical data is taken from

Leonard (written communication) and Project Milestone Report which was prepared for the Montana Department of Natural Resources and Conservation by Geoproducts Corporation (June, 1984).

Leonard (written communication) determined reservoir

temperature estimates using the silica geothermometers, the Na-K-Ca geothermometer modified by the addition of a magnesium correction, and the oxygen isotope, sulfate-water geothermometer.

Based on the geothermometry results, Leonard

assumes a reservoir temperature of approximately 165 c for the Ennis geothermal system.

Juncal (Project Milestone Report) also

used quartz and chalcedony (with mixing model corrections), and Na-K-Ca geothermometers to determine the reservoir temperature of the Ennis geothermal system.

Juncal (Project Milestone

Report) concludes that reservoir temperatures calculated using the Na-K-Ca geothermometer are the most reliable, and these temperatures average approximately 160 c.

It should be noted

that Juncal and Leonard used the same data set: therefore, similar temperature estimates by Juncal and Leonard should be viewed as a confirmation of each others work rather then as unique results. Using the 160 c reservoir temperature, end-value estimates of the depth of this reservoir can be attempted based on what is known of the Madison Valley near Ennis and applying the 30 c/km


Well

Sampling Depth

ÂŁ"

Ca++

Mg++

Nat

K+

ck

EHS

0.0 (m.)

8.4 7.8 8.4 8.2 8.3 7.2 7.4 8.9 9.4 8.9

5.5 5.0 3.5 3.7 3.3 2.1

0.1 0.2 0.3 0.9 0.2 0.4

15.0

120.0

14.9

111.0

15.0

120.0

17.0

5.1 4.3 9.4 7.4 4.7 7.3 2.0

10.0

58.0

320 314 340 75 130 180 25 110 110 10 340 331 330 21 26 290 140 240 330 310 75

MAC-1

371.9

TX-1

104.2

TX-4

86.6

TX-5

98.5

TX-6

60.4

TX-7

15.2

TX-8

64.0

TX-9

122.8

TX-10

33.5

TX-11

157.0

TX-12

152.4

SH-1

16.1

SH-3

15.2

SH-4

14.0

CYPR.l

24.7

CYPR.2 GRIFF.

11.6 54.9

PRAY

41.2

TOTH

63.1

YENNY

37.8

7.7 7.1 7.8 7.5 7.6 8.9 8.2 7.5 7.8 7.4

9.6 5.1

0.8 0.4

44.0

16.0

4.8 5.2 5.8

0.0 0.2 0.6

32.0

11.0

66.0

20.0

4.4 5.6 9.1 5.0 9.3

0.5 1.3 0.9 1.0 2.0 5.6

28.0

20.0 54.0 16.0

8.5 18.0

6.7

16.a

120.0

15.2

116.0

18.0

110.0

8.2 6.6

21.0

13.0

73.0

7.1 7.8

24.0

12.0

110.0

9.3 5.8

100.0

15.0

68.0

32.0

Si02

B-tot

TDS

100 108 45 42 44 .43 39 34 43 19 160 107 90 30 28 72 23 46 75 .47 43

0.62

0.17

992 966 945 246 374 516

0.09

...

0.10 0.03

348 340 242

0.61

1120

0.68

1030

0.64

985 226 371 845 398 712 945 859 342

0.62 0.71 0.05 0.20

0.13

0.08 0.07 0.39 0.09 0.38 0.54 0.38 0.12

Table 5. Hydrogeochemical data for wells in the Ennis geothermal area. Data according to Project Milestone Report prepared for the Dept. of Natural Resources and Conservation by Geoproducts Corporation (June, 1984). Concentrations in parts per million.


25

bedrock gradient and the 60 C/km thermal gradient for the valley fill.

For example, by drilling it is known that the depth of

valley fill below the Ennis hot spring is approximately 150 meters while the maximum depth of valley fill in the Madison Valley near Ennis is approximately 2 kilometers (Young, 1984). Using these valley fill depths and bedrock and valley fill thermal gradients, end values for the depth to the reservoir are 5 and 3.3 kilometers, respectively. reservoir is

The actual depth of the

probably somewhere between this range of 3.3 to 5

kilometers.

Structural Geology of the Madison Valley Near Ennis Because the gravity modeling for this paper was done to determine controlling structure of the Ennis geothermal system, only the structural geology of the Madison Valley near Ennis will be discussed in this section.

For information on the

geomorphology and stratigraphy of the Madison Valley, see, for example, Paul and Lyons (1960), Shelden (1960), Montagne (1960), and Young (1984).

Unfortunately, there are no mapped structures

discussed in the literature to date (see, for example, Vitaliano and Cordua (1979) and Figure 6) which obviously control the present location of the spring.

Because of this, major

structures, apparently important in the structural development of the Madison Valley near Ennis, located a few to tens of kilometers away from the Ennis hot spring will be discussed. The purpose of this section, therefore, is to examine the


III" so

45째 00'

EXPLANATION Quaternary Tertiary sediments Terliory volcanic rocks Deformed Lole Cretaceous and Paleocene sedimentary rocks Tertiary and Cretoceous intrusive rocks Mesozoic rocks Paleozoic rocks Proterozoic BeH Supergroup rocks Archeon melamorphic rocks

Lilhologic boundaries 4BoS0'

Normal fault along previous reverse fault Mapr range-boundary normal fault

58

Thrust fault bounding fold and thrust belt Thrust fault with significant lateral movement Thrust fault in Rocky Mountain forelond Oblique tleft reverse) slip foutt Oblique (nghl reverse) slip fault Axial I race (and plunge direction) of anticline Overturned anticline Synclme Overturned syncltne

4 5 째 00'

Monocline

FAULTS IN THE AREA OF ENNIS, MONTANA I Modnon Range front fault

Figure 6.

2 Jack Creek fault

3 Spahltn Peak* fault

4 North Meadow Creek fault

Regional geology of a portion of SW Montana, (1983b).

Figure adapted from Schmidt and Garihan

CM


27

structural history of the Madison Valley near Ennis. Based on this structural setting, the controlling structure of the Ennis geothermal system, indicated by the 3-D gravity modeling, can be interpreted. The Madison Valley is a north-south trending basin and range style depression (Pardee, 1950) located approximately 75 kilometers east of the frontal fold and thrust zone of southwest Montana (see Figure 6 adapted from Schmidt and Garihan, 1983b). Near Ennis, the Madison Valley is bounded to the west by the Tobacco Root Mountains, to the east by the Madison Range, and to the north by the Norris hills. Major documented faults in the Madison Valley are exposed to the east of the Ennis hot spring in the Madison Range.

These faults include the Spanish Peaks

fault (Figure 6, number 3), the Jack Creek thrust fault (Figure 6, number 2) and the Madison Range front fault (Figure 6, number 1).

Bounding the northern edge of the upper Madison Valley is

the North Meadow Creek fault (Figure 6, number 4 ) .

Faults of the Madison Valley Near Ennis:

Spanish Peaks Fault The Spanish Peaks fault is a reverse fault trending N55-60 W and dipping steeply to the northeast (see Figure 7). Archean metamorphic rocks have been uplifted northeast of the fault, and Young (1984) estimates a minimum vertical displacement of 2200 meters for the portion of the Spanish Peaks Fault shown in Figure 7.

Slikenside data indicate approximately


^%v

Mill Creek Syncline

&

A

' 2439 m.

â&#x20AC;˘305

EHS

Ennis

Figure 7. Major documented faults located in the N. upper Madison valley. to Swanson (1950), Garihan and others (1983), and Young (1984).

Mapping according CO


29

equal reverse-dip-slip and left-lateral motion resulting in a net slip of 3100-4200 meters along the fault plane (Young, 1984).

Jack Creek Fault The Jack Creek fault is a gently westward (~30 ) dipping thrust fault that has placed archean metamorphic rock on top of overturned Paleozoic rocks (see cross section A-A', Figure 7). These overturned Paleozic rocks are contained in the overturned limb of a syncline called the Mill Creek Syncline.

This

syncline is discussed by Swanson (1950), Schmidt and Garihan (1983), and Young (1984).

It is uncertain whether the Jack

Creek thrust continues west of the Madison Range front fault and into the Madison Valley.

However, Young (1984) and Garihan and

others (1983) propose that seismic reflection data shot in the Madison Valley indicates a 30-35

west-dipping reflection which

they interpret as the Jack Creek thrust system continuing west into the valley.

Tear faults Three west-northwest trending left-lateral tear faults associated with the Jack Creek fault and the Spanish Peaks fault are located in the Jack Creek thrust area (Swanson, 1950; Young, 1984).

Two of these tear faults are shown in Figure 7. Young

(1984) gives left lateral displacements on these faults as follows:


30

1)

Northernmost tear fault (not shown in Figure 7 but located parallel to the SPf and approximately a kilometer north of the middle tear fault) - 25 meters offset;

2) Middle tear fault (shown as northernmost tear fault in Figure 7) - 300 meters offset; and 3)

Southernmost tear fault (shown as southernmost tear fault in Figure 7) - at least 200 meters offset.

The two northernmost faults are defined by offset of the Paleozoic rocks. The southernmost fault is described by Young (1984) as "a series of enechelon faults identified by shear zones in the Archean rocks and juxtaposition of Archean and Cambrian rocks."

Madison Range Front Fault The Madison Range front fault bounds the uplifted Madison Range to the east from the valley floor to the west (see Figure 7).

This fault is a major normal fault with displacement on the

fault in the range of 1830 meters (Pardee, 1950; Shofield, 1981) for this area of the Madison Valley.

North Meadow Creek Fault The North Meadow Creek fault is roughly parallel to, though offset to the north from, the Spanish Peaks Fault (see Figure 7).

The fault dips steeply to the southwest and is downthrown

on the southwest side (Garihan and others, 1983).

From seismic


31

reflection and gravity data, Young (1984) estimates dip slip movement along the fault plane at 640 to 680 meters.

Schmidt

and Garihan (1983) also determine a component of left-lateral motion along the fault plane based on slikenside data.

Dating of Faults:

Precambrian Movement Schmidt and Garihan (1983) have suggested that many of the northwest trending faults in southwest Montana which document substantial movement in the Cretaceous, because of Laramide tectonic activity, are reactivated Precambrian faults. Young (1984) states that the Spanish Peaks fault possibly had a Precambrian ancestry based on a change in metamorphic fold and foliation trends along the Spanish Peaks fault.

Cretaceous-Eocene (Laramide) Movement Young (1984) brackets the age of the Spanish Peaks fault (with Precambrian ancestry) and the Jack Creek fault between mid-Cretaceous and Late Eocene.

This dating according to Young

(1984) is based on the following: 1)

Andesite sills, 86 million years old, are not localized along the fault surfaces and, therefore, predate them;

2)

The Scarface thrust fault, of the same system as the Jack Creek Thrust but 30 kilometers south,


32

offsets the Sphinx conglomerate (late Paleocene to early Eocene); and 3)

Approximately 40 kilometers southwest of the Jack Creek thrust fault, the Spanish Peaks fault is overlain by middle Eocene pyroclastics.

This mid-Cretaceous to late Eocene dating indicates the association of the Spanish Peaks and Jack Creek fault systems with Laramide deformation.

Tertiary (Basin and Range) Movements Young (1984) states that the presence of fresh water diatoms in deposits southwest (down side) of the North Meadow Creek fault indicates that this fault is Miocene or younger. Carl (1970) says that this late Cenozoic movement (down to the southwest) on the North Meadow Creek fault "ponded somewhat" the ancestral Madison river.

This is based on approximately 30

meters of unconsolidated gravels deposited in the mouth of the Beartrap canyon where the Madison River leaves Ennis Lake. The Madison Range front fault documents a history of movement from Miocene to present (Paul and Lyons, 1960; Shelden, 1960).

The

most recent movement of documented displacement along the fault was from the August 17, 1959, Hebgen Lake earthquake.

Formation and Chronology of Laramide Structure: Swanson (1950) gives a Laramide chronology of: "Initial folding of the (Mill Creek) syncline, with stress from the west, was followed by folding and faulting along the Gardiner fault zone (Spanish


33

Peaks Fault of today), with stress from the northeast, and that in turn was followed by renewed stress from the west and the development of the Madison fault zone (Jack Creek thrust zone of today)".

He based this chronology on structures developed along a northeast trending tear fault mapped near the western edge of the Spanish Peaks fault. Garihan and others (1983) give the following Laramide structural sequence: 1)

Development of the Mill Creek syncline;

2)

Reverse movement along the Spanish Peaks Fault;

3)

Jack Creek thrust faulting; and

4)

Renewed Spanish Peaks fault movement.

They place development of the Mill Creek syncline before reverse movement along the Spanish Peaks fault because in plan view, the overturned west limb of the syncline is cut off by the Spanish Peaks Fault.

They explain the tear faults as resulting from the

eastern movement of rocks, carried by the Jack Creek thrust, being blocked by the rigid buttress of Archean rocks brought up along the northwest trending Spanish Peaks fault.

This requires

movement along the Spanish Peaks Fault to predate thrusting. Finally, renewed movement along the Spanish Peaks Fault is used to explain numerous small, east trending folds in the allochthonous sedimentary rocks. Young (1984) believes that displacement on the Jack Creek thrust and Spanish Peaks faults "occurred contemporaneously", and that the Mill Creek syncline is "formed by the intersection


34

of the N-S trending foreland fold of the Jack Creek thrust system and the west-northwest trending foreland fold of the Spanish Peaks fault"

(A foreland fold is a basement-involved,

fault-related fold located in the foreland of the frontal fold and thrust zone).

She bases contemporaneous movement of the

faults on the fact that neither fault "can be shown to cut the other."

In fact, according to Young, displacement on the Jack

Creek thrust diminishes near the Spanish Peaks fault because the Spanish Peaks fault accommodated the east-directed stress of the Jack Creek Fault by acting as a tear fault.

This would explain

the left-lateral movement along the Spanish Peaks fault according to Young.

Inferred Faults Buried in the Madison Valley Near Ennis: After the Laramide compressional events, a tensional environment, producing the basin and range tectonic activity, presumably resulted in the creation of the Madison Valley.

The

question to address here is: Based on its structural history, what probable structure is hidden beneath the valley fill of the Madison Valley? As shown in Figure 7, the tear faults and the Jack Creek fault terminate against the Madison Range front fault.

As these

faults predate the Madison Range front fault, it is possible that they extend west into the Madison Valley underneath the valley fill.

If the tear faults are the product of some

interaction between the Spanish Peaks fault and the Jack Creek fault as Young (1984) and Garihan and others (1983) suggest, it


is not probable that they would be propagated a great distance west into the Madison Valley.

This is because the mapped

displacements of the tear faults, close to the intersection of the Spanish Peaks and Jack Creek faults, are in the range of hundreds of meters (Young, 1984). In addition, stress was also apparently relieved by strike slippage along the fault planes a the intersection of the Jack Creek and Spanish Peaks faults. As for the Jack Creek fault, Young (1984) and Garihan and others (1983) interpret seismic reflection data as indicating the Jack Creek fault continues west of the Madison Range front fault and into the Madison Valley.

In my opinion it is

certainly possible that the Jack Creek and/or related thrusts extend across the Madison Valley.

Even though there are no

mapped thrusts in the bedrock exposed west of the Ennis hot spring (see Figure 6 ) , the fact that Archean bedrock is present at the surface west of the hot spring indicates the possibility of thrusting (at least some sort of tectonic activity) in this area. Another possible fault inferred by Young (1984), but not discussed previously because of the tenuous nature of its existence, has a bearing on the structural development of the Madison Valley near Ennis. Young's evidence for this W-NW trending fault is the linearity and extent of erosion through the Archean rock carried by the Jack Creek fault and the underlying Mesozoic and Paleozoic rocks. This erosion has created the Jack Creek Canyon located roughly E-NE of the town of Ennis in the western slope of the Madison Range.

This


36

inferred fault would have to predate the Laramide faulting (Young assumes it is a Precambrian fault), and the relatively rapid erosion along the strike of the fault may be related to a shear zone developed along the W-NW trending fault during the Laramide events.

It is not certain if this inferred fault

extends west into the Madison Valley.

Geophysics

Seismic Refraction: In February, 1979, two seismic refraction lines were shot by students of the physics/geophysics department under the direction of Dr. Charles Wideman.

Shot holes (SH-1, 3, 4, and

5) were drilled for a dynamite source, and the data was collected at stations 33.5 meters apart using a 36 trace analog recording system.

One line trends in a northeast direction and

wells SH-3, TX-7, TX-2, SH-1, and SH-5 were used as shot holes, the other line trends to the northwest and wells TX-6, SH-4, TX-2, and TX-3 were used as shot holes (see Figure 8). Double coverage (reversed shot and receiver orientations) was obtained for each profile along each of the lines except between wells TX-2 and TX-3 and TX-6 to SH-4 on the northwest line.

Because of cable problems "the time break was lost on

several shots" (Mcrae, unpublished senior report).

In this

instance approximate arrival times were recovered by adding a correction time calculated by dividing the depth of the shot by the velocity of the nearest known low velocity layer.

Mcrae's


37

O TX8 BM 10 TOTH

0째 GRIFFEN

SH5

o u

II,SHI

Q 111

o TX2

a

58

TXI O

TXI2 째 Ho

YENNY

w

\

H m s

HOT SPRING

TX3

SH3 SCALE l

0

1

1

300

1

1

600

1

1

900 maters

w

10 in

111.74

r111.73 LONGITUDE (DEG.)

111.72

Figure 8. Location of NE and NW trending seismic refraction lines. The seismic refraction data was collected by the physics/ geophysics department of Montana Tech under the direction of Dr. Charles Wideman.


38

(unpublished senior report) interpretation of the seismic refraction information is shown in Figures 9 and 10.

Seismic Reflection: East of the Madison River in the upper Madison Valley, eight seismic reflection lines were shot by Grant Geophysical, Ltd. for Canadian Hunter, Ltd. in February, 1982. Young (1984) was able to obtain this proprietary data and from this data interpreted structures which she has termed the Jordan Creek and Shelhamer Ranch grabens. Figure 11 shows the location of the seismic lines, and Young's (1984) structural interpretation including subsurface locations of the Jordan Creek and Shelhamer Ranch grabens, the Madison Range front fault, and the axis of the Madison Valley.

The dotted lines shown on Figure 11 connect

the deepest points along each structure, and Table 6 contains these maximum depth values for each structure.

The lines with

balls located along the seismic lines indicate interpreted normal faulting with the balls on the downthrown side of the fault.

A velocity analysis was done along each seismic line,

and based on this analysis interval velocities were computed by Young using the Dix equation.

Using this velocity information

Young converted two way times to depth. shown in Table 6 were calculated.

This is how the depths

Young estimates a maximum

error of + 10 percent in the depth estimates based on improper velocity picks.


••_ 300

-

200

-

« •

. •"•

m

e

•'

u 100

z

'•

1-

0

-200

"

,

0

TX7

SH3

TX2

,*•.., ~

\

T

\

0

*

SHI

SH5

^

*

\-r-^1-r-m \

a

.

* S H 0 T DEPTH

SCALE

\

250

5 0 0 METERS

\ \

Figure 9. Seismic refraction data and accompanying bedrock depth interpretation for the NE trending seismic refraction line (see Figure 8 ) . Interpretation according to McRae (unpublished senior report). CO


•••_

•. 300

• • 200

• '•

si i ^

•' 100

"

p

0

"

'

"T

, , , , , ,111111

i ii

1

~

SH4

TX6

\

1

TX3

TX2

i i • i • • • i"

i "•'

' "

"""l

200 # SHOT DEPTH

ui 4 0 0

SCALE 0

250

3 5 0 0 METERS

J t /"7—rrr r 7 7 t J r? TIT

( NO VERT. EXAGO )

Figure 10. Seismic refraction data and accompanying bedrock depth interpretation for the NW trending seismic refraction line (see Figure 8). Interpretation according to McRae (unpublished senior report).

-P>


41

Figure 11. Placement of the 8 seismic reflection lines located in the northern Madison valley. Young interpreted the following structure from this seismic reflection data: a) The Jordan Creek graben, b) The Shelhamer Ranch graben, and c) The axis of the northern Madison valley. The dotted lines connect the deepest points along these interpreted structures.


42

Table 6:

Seismic Line 2 3 4 5 6

Greatest depth of Jordan Creek and Shelhamer Ranch grabens, Madison Range Front Fault, and North Meadow Creek fault as interpreted from seismic reflection data. Depths (in meters) according to Young, 1984. N.M.Cr. F

Jordan Cr.G. 640

Sh.R.G. 1066 1066

M. R. F.F. 1763 2348 722 800 1600

Audio-Magnetotellurics (AMT): Long and Senterfit (1979) collected data from 20 AMT stations surrounding the Ennis hot spring area (see Figure 12). The data was collected using north-south and east-west oriented dipoles at frequencies of 7.5, 27, 285, 6700, and 18600 hertz. Electromagnetic waves decay exponentially into the earth, and the depth of penetration of these waves for interpretation purposes is given by the formula: 1/2 a

f

where pa is an apparent resistivity (ohm-meters) given by Pa = _1_|E 5f 'B where: f

=

frequency (Hertz)

6a

=

Apparent Skin Depth (meters)


43

Reciever Orientation

111.78

III 74

111.70

LONGITUDE (DEG.)

Reciever Orientation N-

Ill 74

III 70

LONGITUDE (DEG.)

Figure 12. Contours of apparent resistivities (ohm-meters) based on AMT data collected by Long and Senterfit (1979) along NS and EW oriented dipoles at the 19 stations shown. This data is displayed at 100 and 300 meter skin depths for the EW and NS dipole orientations based on interpretations by Semmens and Emilsson.


44

E

=

Magnitude of the Electric Field (volts/meter)

B

=

Magnitude of the Magnetic Induction (gammas)

Long and Senterfit (1979) interpret the AMT data as indicating that thermal water alters the alluvium over an area of 1.5 by 4 kilometers surrounding the Ennis hot spring.

They

also state that a northwest trend in the scalar resistivities may delineate a northwest trending fault and conclude that the geothermal potential of the spring may extend 1 kilometer to the northwest and 3 kilometers southeast of the surface location of the Ennis hot spring. Long and Senterfit's (1979) data was also studied by Gunnar Emilsson, a fellow student, and myself.

An example of our work

is shown in Figure 12 which contains contours of apparent resistivities for east-west and north-south dipole orientations at apparent skin depths of 100 and 300 meters.

Contours in

Figure 12 are shown at 20, 60, 100, 200, 300, and 400 ohm-meters because of the large range of apparent resistivities.

These

data clearly show a broadening of the low resistivity contours in all directions except west of the hot spring for the 300 meter skin depth relative to the 100 meter skin depth data. Also a north-south trend through the Ennis hot spring is shown for the low resistivity data in the modeling. Without modeling this data, interpretations are tenuous; nevertheless, I believe the broadening of the low resistivity data with depth indicates


45

the surface flow of the Ennis hot spring represents only a minor portion of the geothermal system, and the north-south trend of the less than 20 ohm-meter data indicates a possible north-south oriented fault or aquifer controlling the geothermal water.

Controlled Source Audio-Magnetotellurics (CSAMT): In the summer of 1985, an extensive set of CSAMT data was collected by Gunnar Emilsson and myself under the direction of Dr. William Sill.

Frequencies of 1, 2, 4, 8, 16, 32, 64, 128,

256, and 1024 hertz were used.

The data was collected at 50 or

100 meter intervals along east-west lines of data from 900 meters south to over a kilometer north of the hot spring.

These

lines extended approximately one kilometer west of the hot spring and east to the Madison River.

Emilsson, for a thesis in

progress, is interpreting this data using 1-D inversion and 2-D forward modeling programs.

His final interpretations of these

data are not yet available.

Gravity:

Burfeind One of the first geophysical studies in the Ennis area was done by Walter Burfeind (1967).

For a doctoral thesis Burfeind

undertook a large scale gravity survey covering the Jefferson, Beaverhead, Three Forks, north Boulder, Madison, Prickley Pear, and Ruby-Gravelly basins and some of the intervening mountain


46

ranges.

The accuracy of this survey is considered by Burfeind

to be from 1 to 3 milligals in general and at worst 15 milligals in the mountain ranges. In the Madison Valley, Burfeind modeled an E-W line, placed approximately 900 meters south of the town of Ennis, through his gravity data.

Burfeind's 2-D modeling indicated that the

Madison Valley near Ennis is an asymmetric, deep to the east, valley with a maximum depth of approximately 1.5 kilometers. Because the eastern valley wall has a much steeper slope than the western wall, Burfeind concluded that "the Madison Valley is the result of block faulting that has tilted the area eastward." Burfeind noted that the more negative gravity values to the south probably indicated deepening of the valley to the south.

Montana Tech In September and October, 1978, students of the physics/geophysics department of Montana Tech collected 67 gravity stations (unpublished data) north of the Ennis hot spring under the direction of Dr. Charles Wideman (see Figure 13).

The gravity data was referenced to a Department of Defense

gravity base station located at Three Forks, Montana, and a United States Geological Survey gravity base station located in Helena, Montana.

A secondary base, United States Coast and

Geodetic Survey bench mark Y145 (elevation 1,492.4 meters), was used as the local reference point for the gravity data collected in this survey. The gravity stations were surveyed for


47

BM •

o

o

o

«•»

in o

»

O O

O o

O

o «> o

O

CD ©

o

Q *~*

a

•X3 3

0 0 0 >

0

0

0

0

0

° 0 o

o

o

o

o

o

o

o

o o

0 o

o

0

o

t>

O -°

o

o

O

o

o

ENNIS HOT SPRING

° • Station location.

SCALE 300

600

900 METERS

•© om

mjA

HI73 Longitude (Depp

111.72

Figure 13. Locations of the 67 gravity stations collected by the physics/geophysics department of Montana Tech under the supervision of Dr. Charles Wideman (unpublished data).


elevation, and closure on the survey loop was within 3 hundredths of a meter. Elevation (free air and Bouguer), drift, latitude, and terrain corrections were applied.

The assumed accuracy for this

survey is in the several tenths of a milligal range (Wideman personal communication).

Senterfit On November 4, 1978, Senterfit (1980) established 33 gravity stations on two east-west lines south of the Ennis hot spring (see Figure 14). The gravity data were collected using a LaCoste-Romberg gravity meter (G-235) and is referenced to the Department of Defense gravity base station located at Three Forks, Montana, and the United States Geological Survey (USGS) gravity base station in Helena, Montana.

Elevations were

surveyed and an error of +_ .03 mgals is assumed to result from elevation uncertainty.

Drift, elevation, latitude, and terrain

corrections were applied.

Senterfit offered no interpretation

of these two lines in his 1980 USGS Open File report.


ft

BM •

0

= Station location SCALE O

©

300

600

900 METERS

Q

^ •

o

2 * = oJ

ENNIS HOT

SPRING

o

o

o

o

o

.

o

o

o

o

o

o

o

o

o

o

o

o

o o

JI75

1 \\\J4

o

1 111.73

o

o

r 11172

o

1117

Longitude (Deg.) Figure 14. Locations of the 33 gravity stations collected by Senterfit (1980).


GRAVITY DATA

Additional Gravity Data In September, 1985, 32 gravity stations, spaced 50 meters apart, were set up on 2 east-west lines approximately 500 meters north of the Ennis hot spring.

These lines begin just east of

highway 287 (see the Ennis 15 minute quadrangle map) and extend 850 meters east into the Madison Valley.

Another 15 gravity

stations, spaced 100 meters apart, were located in a loop of roads approximately 1.5 kilometers northeast of the hot springs, east of the Madison River.

Finally, in January, 1986, an

additional 16 gravity stations were set up on a loop of roads east of the Madison River approximately 1.5 kilometers southeast of the hot spring.

These 16 stations were spaced at

approximately 300 meter intervals along the road.

See Figure 15

for the location of these 63 gravity stations. This gravity work was done using a LaCoste-Romberg (model D) gravity meter accurate to tens of micro-gals.

The data is referenced to the U.S. Coast

and Geodetic Survey benchmark Y145, and as Senterfit's (1980) data was also referenced to this benchmark, his value for the benchmark was added to all 63 of the new gravity stations. In

*

This gravity data was collected by Gunnar Emilsson, a fellow

student, and myself.


o o o o o o

45.38 BM

•oooooooooooooooo oooooooooooooooo

o o o o o o o

b. 45.37

<u

•a

o

Id

o

o

Q

ID <

~* 45.36 o = gravity station I km.

45.35 .75

X

111.73

111.71 LONGITUDE (deg)

111.69

Figure 15. Locations of the 63 gravity stations collected by Semmens and Emilsson in September 1985 and January 1986.

en


52

this way the new gravity data was referenced to the Department of Defense gravity base station in Three Forks, Montana and the USGS gravity base station in Helena, Montana. The station elevations were determined by surveying and each of the survey loops for the three gravity surveys discussed previously closed within 6 hundredths of a meter.

During each of

the three gravity surveys, benchmark Y145 was reoccupied in a time period of under two hours to determine drift (tidal effects were considered to be included in the drift correction).

In the

two surveys east of the Madison River, drift in the gravity readings based on reoccupation of benchmark Y145 was under 5 hundredths of a milligal, and drift for each station on these loops is considered negligible.

For the survey west of the

Madison River, closure was in the tenth of a milligal range and drift corrections were applied.

All stations had latitude,

elevation, and terrain corrections (covering an area out to 21.95 kilometers) applied.

Accuracy for these surveys is assumed to be

in the range of half a milligal. The raw data and gravity corrections are contained in Appendix A.

Modeled Gravity Data The gravity data used for the 3-D gravity modeling includes Senterfit's (1980) gravity data, gravity data collected by Montana Tech (unpublished), and the 63 gravity stations collected by Gunnar Emilsson and myself in September, 1985, and January, 1986 (see Appendix E.l).

All of the gravity stations used for


53

the modeling were surveyed for elevation control, and all of the gravity data is referenced to benchmark Y-145 of the U.S. Coast and Geodetic Survey.

Terrain corrections for the stations

collected by Senterfit and students of Montana Tech were calculated using a USGS computer program written to correct for an area inside a radius of 166.7 kilometers around each station. The stations collected by Emilsson and myself were terrain corrected by hand using Hammer charts, and the area surrounding each station, contained in a radius of 21.9 kilometers, was included in the corrections.

Terrain corrections (using the

166.7 kilometer radius) values for two USGS gravity stations contained in the state gravity data file differed by only two and three tenths of a milligal from similarly located stations for which the terrain corrections were calculated by hand. Considering an error of not greater than .15 milligals for elevation uncertainties and several tenths of a milligal for terrain correction and operator errors, an average error in the range of .5 milligals is assumed for the gravity data used in the gravity modeling.


3-D GRAVITY MODELING

Assumptions and Modeling Decisions

Gridding of the Gravity Data: For 3-D gravity modeling, spatial (x,y) location of the observation points must be considered.

To limit the amount of

input and simplify the programming, I chose to write the programs using gravity stations confined to a rectangular grid. Therefore, a rectangular window (confining the grid) in the data has to be defined, and the gravity values assigned to the grid nodes have to be interpolated from the original field data (if the gravity data was not collected on a grid).

In my work, I

contoured the observed gravity data by hand, and the values assigned to the grid nodes were interpolated (by eye) from the hand contoured gravity data.

To graphically display the gridded

observed gravity data, I used the SURFACE II contouring package of Robert B. Sampson (1978). Figure 16 shows the locations of the 158 gravity stations included as data points for the gravity modeling, and the gravity contours (c.i. = 1 mgal.) drawn by hand through this gravity data.

The bold inner box of Figure 16 outlines the area 2 (approximately 8.5 km ) chosen to contain the modeling grid. A

grid of 15 columns and 8 rows (120 grid nodes) was selected for this area because this grid provides even coverage in the north and east directions (with approximately 300 meters between columns and rows).

The location of these grid nodes together


45 .38 -

73

111

1 11 .69

LONGITUDE (DEG)

Figure 16.

Locations of the 158 gravity stations used in the gravity modeling. Data includes stations collected by Montana Tech, Senterfit (1980), and Semmens and Emilsson. The contours shown are contours of the gravity data (c,i. = 1 mgal) drawn by hand and the inner rectangle represents the area containing the gridded gravity data.

en en


56

with the gravity contours (c.i. = 1 mgal.) drawn by computer using the SURFACE II contouring package (Sampson, 1978) are shown in Figure 17. The gravity contours of Figure 17 were drawn using values assigned to the grid nodes that were interpolated from the original hand contoured gravity data set. It is these 120 interpolated gravity values that are used in the modeling, and as these values are only weighted averages of the original data set, I will use the phrase "gridded observed gravity data" when referring to the gridded gravity data set.

See Appendix E.2 for

the actual gravity values and station locations in this gridded gravity data set.

Density Determination for Modeling: Leonard (written communication) cites an average density of 3 2.1 gm/cm for the valley fill in the area of the Ennis hot 3 spring and a 2.6 gm/cm density for the bedrock of gneiss and 3 schist.

The 2.1 gm/cm

average density assigned to the valley

fill is determined from averages of measured saturated densities taken from cores samples in wells TX-2,4,5,6, and 11 as is shown 3 in Table 7. The 2.6 gm/cm density of the bedrock is based on a measured density from a core originally situated in an interval located 190.5-191.4 meters below the land surface (approximately 30 meters below the base of the valley fill) in well TX-11. As is indicated in Table 7, there is a range of densities which display no systematic correlation with depth because of the inhomogeneity of the valley fill.

This inhomogeneity of the

valley fill is also emphasized in the drillers logs for wells


2000 0

1 000

3000

2000

400D

METERS EAST â&#x20AC;&#x201D; â&#x20AC;˘ Figure 17. Locations of the 120 (15 columns x 8 are gravity contours (c.i. = 1 mgal) contouring package (Sampson, 1978), interpolated from the hand contoured

rows) gridded gravity stations. Contours drawn by computer using the Surface II The values assigned to the grid nodes were gravity data (see Figure 16).

en


58

Table 7.

Saturated densities (gm/cm ) of the valley fill sediments taken from cores of wells located near the Ennis hot spring according to Leonard (written communication).

Test Well

Cored interval below land surface (m)

Saturated Density

TX-2

128.9-129.8

1.79 g/cnT

TX-4

85.3-86.2

2.21 2.06

TX-5

97.5-98.4

1.94 2.02

TX-6

41.4-42.4

2.11 2.11

Lithlogic Description Clay: silty ,tuffaceous, mottled grayishgreen and pink. Sand: quartzose,argillaceous , finegrained,olive with welded and nonwelded tuffaceous material; about 50% argillaceous matrix. Sand: argillaceous, micaceous,finegrained,angular to subangular grains, quartzose,tan to dark gray. Gravel: subrounded pebbles to 2 cm. diameter predominantly biotite gneiss and quartz, calcareous, tuffaceous. Sand: argillaceous,dark gray to olive, micaceous, arkosic. Clay: hard,tuffaceous, gray. Silt: sandy,brown, tuffaceous,with scattered lithic grains.


59

TX-11 and TX-12 (both relatively deep wells which penetrate the bedrock) which record the presence of alternating layers of clay, silt, shales, and unconsolidated to well consolidated sands. Clearly, the density variations between these alternating layers of varing composition will contribute to the observed gravity values, but because the geometry and lateral extent of these layers is unknown, it is impossible to include these layers in a model. Therefore, I modeled the valley fill using the -0.5 3 density contrast between the 2.1 gm/cm average density for the 3 valley fill and the 2.6 gm/cm bedrock density measured from the core of well TX-11.

Using this -0.5 density contrast, I am

assuming that the observed gravity data results solely from the density difference between "average" valley fill and the metamorphic bedrock.

Modeling With Blocks: Block faulting and step-like normal faulting of the bedrock in the Madison Valley near Ennis is indicated from interpretations of seismic and gravity data (McRae, unpublished senior report; Young, 1984; and Burfeind, 1967). Based on these interpretations, I assumed that the gravity data of the Madison Valley could be efficiently modeled by summing the gravity contributions of blocks of earth of variable depth and surface area.

Figure 18 shows a schematic of a block-faulted valley and

how it might be modeled with blocks assuming an average density contrast between the bedrock and the valley.


60

Figure 18. Modeling a block-faulted valley with blocks

Modeling of Topography: It is often assumed that once elevation and terrain corrections have been applied, the gravity stations have been reduced to a plane. However, this is generally not the case because the assumptions inherent in the corrections are not totally accurate.

Therefore, for more reliable results

(especially in areas of steep terrain), the gravity stations should retain their elevations in the modeling process; and this involves modeling of the topography.

Because blocks generally

can not be used to efficiently model the topography, I used a 3-D


61

gravity modeling program (program 3D), written by Richard Allan Payne (1986) and myself.

This modeling program is based on

Talwani and Ewing's (1960) algorithm which sums the gravity contribution of vertically stacked, horizontal, n-sided polygons. These polygons can be used to accurately describe irregular 3-D bodies and are ideally suited to the modeling of topography. Coding for program 3D is contained in Appendix B and information on input to and output of program 3D is contained in Appendix C. To model the topography, I modeled the valley fill from the surface down to some convenient elevation below the lowest station elevation then, using program 3D, the gravity contribution attributed to each of the gridded gravity stations from this topographic model was calculated and removed from the gridded observed gravity values.

Once this removal of the

gravity contributions from the valley fill in the topographic model was accomplished, the remaining valley fill (below the valley fill contained in the topographic model) was modeled using blocks. This modeling procedure is illustrated in Figures 19 and 20. Figure 19a shows a schematic of a cross section along a row of the gridded gravity data located in a block faulted valley. Gravity stations along the row of the gridded gravity data are indicated by the circles on the surface of the valley, and the cross-hatched area, extending from the surface to the shallowest bedrock, represents the valley fill included in the topographic model.

Figure 19b shows an example of how the valley fill in the

topographic model might be modeled using program 3D.

The


Gravity station

O

Valley fill included in the v> topography model

Gravity station O V)

Polygons in cross section

"Q-o--e-o-Q--Q Figure 19.

A) Representation of a cross-section along a row of gravity data in a block faulted valley. Sediments from the highest elevation in the modeling area to some elevation below the lowest station elevation are included in the topography model. B)) Schematic showing how the valley fill included in the topography model ight be horizontal might be modeled modeled using using vertically vertically stacked, stacked, horizontal polygons polygons according to u _ â&#x20AC;&#x17E; * . . . . . . : 4... m A / l n l ^ n n m n t h n f l n f T a l u a n i a n d P w i n n M Qfifl I . the gravity modeling method of Talwani and Ewing (I960).

en


Original topography \~. ^ True valley fill bedrock O - O - Os contact O ~

o

^o-o-o-o-o-cr

Figure 20.

/

o.o O

Once the gravity contributions of the valley fill in the topography model have been removed, the remaining valley fill can be modeled efficiently using blocks. Note that with the removal of the gravity contributions of the valley fill included in the topography model, it is not as if the gravity stations have been dropped to the plane at the base of the topography model. en eo


64

horizontal lines in Figure 19b are cross sectional representations of five vertically-stacked, horizontal polygons. An effective way to determine the shape and vertical location of these polygons is to digitize elevation contours (a sufficient number to "adequately" reflect the topography) in the modeled area relative to the origin of the gridded observed gravity data. Using this method each of the polygons is assigned a vertical location based on the contour elevation and an outline determined by the contour shape. Once the gravity contributions of the topographic model are removed, it is (ideally) as if all the sediments in the topographic model have been removed as is shown in Figure 20. Figure 20 shows that once the gravity contributions of the valley fill in the topographic model have been removed from the gridded observed gravity data, the gridded gravity stations have not been dropped to the plane representing the base of the topographic model. However, with this correction, forward modeling with blocks is now reasonable because the upper edge of each block can be assigned a uniform depth representing the base of the valley fill in the topographic model.

Figure 20 also

shows an example of how the remaining valley fill could be modeled with blocks assuming the blocks were assigned some average density contrast between the valley fill and the bedrock. It should be noted that both program 3D and program GRAVBL (the forward modeling program using blocks) allow for individual densities to be assigned to each polygon or block so that vertical and lateral density distributions can be modeled.


65

As noted before, the topography was not modeled using blocks because blocks, in general, can not be used to model the topography efficiently.

Therefore, a separate modeling program

was used to model the topography from the highest elevation to a convenient elevation below the lowest station elevation.

Another

reason for using this two-step modeling procedure is that the removal of the valley fill in the topographic model increases the distance between the upper edge of the blocks and the gravity stations (see Figure 20) and this numerically stabilizes the forward modeling algorithm (equation 3, Forward Modeling Theory section).

For example, it was found that

modeling of blocks buried a depth of 5 meters or less often resulted in taking the logarithm of a near zero number. By removing the topography to a depth greater than five meters below the lowest station elevation, this numerical instability can be eliminated.

Determination of Depth to Bedrock Using Inversion Theory: The gravity data in the area of the Ennis hot spring was collected with the purpose of finding offsets in the bedrock which might be fault controlled and therefore might possibly control the path of the ascending geothermal water. Consequently, the principal goal of my gravity modeling was to accurately map the topography of the bedrock hidden beneath the valley fill in the modeling area.

For this reason, I wrote an

inverse modeling program to adjust the bedrock depths, output from the forward modeling program, in an attempt find a model of


66

the bedrock surface that reproduced the gridded observed gravity data within the assumed survey error.

It should be reiterated

that I assumed the observed gravity data to be solely the result of a density contrast between "average" valley fill and bedrock; and therefore, I modeled using blocks extending from the base of the topography model to the assumed bedrock depth.

Consequently,

the inverse modeling program I wrote adjusts the lower depth of each block where I assume the base of each block represents the depth to bedrock.

3-D Gravity Modeling Theory

Forward Modeling Theory: In cartesian coordinates the vertical component of gravity in three dimensions is given in the following formula (see Figure 21):

[ J

g (x,y,z) = jf z J

where

( J

Gp(x',y',z')(z-z')dx'dy'dz' r(x-x')2 + (y-v')2 + (z-z')2] 3/2

x,y,z

=

coordinates of the observation point

x',y',z'

=

coordinates of the source

p(x',y',z')

=

density of the source

G

=

universal gravity constant

x ,xâ&#x20AC;&#x17E;

=

x limits of the block

Yi >y? z ,z

=

=

y limits of the block z limits of the block

(1)


67

With no loss in generality, the observation point may be assumed to be at the origin:

â&#x20AC;&#x17E; ,n n n\ = r z {0'">0) J

g

Yi

C Jz l

f Jx

Gp(x',y',z')z'dx'dy'dz' [(x 1 ) 2 + ( y 1 ) 2 + (z')2]3/z

(2)

i

Integration of (2) is not difficult if the exact integration is carried out in two directions and the final integration is approximated.

Because an inverse modeling program was to be

written to invert on depths, I chose to approximate the integration in the y-direction to keep z involvement at a minimum. The resulting formula after integration of (2) in the x and z directions for block i is:

Figure 21. Coordinate system with a unit volume located at (x',y',z') and an observation point at (x,y,z).

-Âť X .(x,y,z)

(x',y;z' dx'

'2

Vdy

dz'


68

g (i)(0,0,0) = G p ( i ) / 2 {Ln[x.(i)+(x.(i)) +(z_(i)) +(y') ] i

Yi

1

z

-

Ln[x2(i)+(x2(i))2+(z2(i))2+(y')2]

+

Ln[x2(i)+(x2(i))2+(Zl(i))2+(y')2]

-

Ln[x1(i)+(x1(i))2+(z1(i))2+(y')2]}dy'

This is an integral of the form: ,y2 gz(i)(0,0,0) = Gp (i)/ A1(y')dy'

(3)

(4)

Yi

where:

A.(y') are varying constants (mgals/meter) dependent on the value of y' of block i.

I approximated the integration in (4) by using a quadrature formula proposed by Talwani and Ewing (1960).

With a quadrature

formula, the gravity anomaly from a 3-D body is approximated by summing a number of anomalies from thin rectangular laminae defined by x.(i), xâ&#x20AC;&#x17E;(i), z.(i), zâ&#x20AC;&#x17E;(i), and a thickness Ay. In order for the quadrature formula approximation to be accurate, enough laminae must be chosen to keep Ay "small." In the forward program I wrote, laminae are equally spaced along the block and a minimum of 10 are inserted.

The actual number of

laminae (>10) is controlled by the following formula:

NUMLAM(i) = YLEN(i) x (MIN[XLEN(i),YLEN(i)] / MAX[XLEN(i)/YLEN(i)]) x IM where: NUMLAM(i) = number of laminae in block i. MIN,MAX[XLEN(i)/YLEN(i)] = Minimum, Maximum of x,y lengths of block i. IM = input multiplier.


69

If the number of laminae is even another will be inserted because the chosen quadrature formula requires an odd number of laminae. For example, if a block has an x-length of 100 meters and a y-length of 200 meters with an input multiplier of 1, then 101 laminae will be placed at equally spaced intervals along the block. The number of laminae used in the quadrature formula approximation is partly responsible for the amount of computer time involved in reaching a solution.

Therefore, the increased

accuracy of the quadrature formula approximation resulting from the use of more laminae must be weighed against the increase in computer time for a result.

Because the quadrature formula sums

anomalies from vertical rectangular laminae, less laminae need be inserted for blocks (assuming constant density) which are broad in the x and z directions and thin in the y-direction.

Blocks

which approach an infinite, thin horizontal slab take the most laminae to achieve an accurate result.

In my modeling with

blocks 500 meters wide, (x-direction), 400 meters long (z-direction) and hundreds of meters deep, the 17-80 laminae I used in modeling with a -0.5 gm/cc density contrast appear to give reliable results (within the .5mgal assumed accuracy for the observed gravity data). As noted before, I chose to confine the gravity stations to a rectangular grid in the modeling.

Therefore, the number of

gridded gravity stations (and the number of times the forward problem must be done) is determined by the number of columns and rows in the grid.

The number of gridded gravity stations, number


70

of observation points, number of blocks in the model, and the number of laminae per block largely determine the amount of computer time necessary for the program to run.

For a model with

80 blocks, having 17-80 laminae per block, and 120 observation points a CPU time of approximately 1.5 minutes was necessary for the forward modeling program to run using a VAX 8500 mainframe computer.

Coding of the 3-D forward gravity modeling program

(GRAVBL) is contained in Appendix B.l while examples of preparing the gravity data for use with program GRAVBL is contained in Appendix C.

Inverse Modeling Theory: As stated before, the inverse 3-D gravity modeling program was written to better determine the depth to bedrock in the modeled area of the Madison Valley.

Because blocks of uniform

density contrast which extend from the surface to the bedrock were used in the modeling, the parameter defining the maximum depth of each block represents the depth to bedrock.

This is

parameter z„ in equation (3), and as equation (3) indicates, g (i)(0,0,0) is not linear with respect to parameter z„. Therefore, to solve for parameter z , using least squares generalized inverse techniques, equation (3) had to be linearized with respect to parameter z„. This linearization was accomplished by rewriting equation (3) using a Taylor series expansion and including only the linear terms (see for example Marquardt, 1963).

Once equation (3) has been approximated with

the Taylor series expansion, parameters must be updated using an


71

iterative solution technique which requires an initial guess for each of the parameters.

Because equation (3) has been

approximated in the linearization process, a "bad" initial parameter guess may cause a parameter to lay outside of the area of assumed local linearity.

If this occurs, successive

iterations will result in divergence of this parameter from the "true" solution.

Therefore, a judicious choice of the initial

parameters is necessary to achieve reliable results.

The initial

parameters (maximum depths of each block) I supplied to the inversion program were those which, when output from the forward modeling program, resulted in a reasonable results based on matches with the drilling and geophysical data. Once the initial parameters have been supplied, new parameters are determined by parameter jumps; the magnitude and direction of which control the path to the solution, for example:

m . , . , , = m. . + dm. . l'.l + l l.i ii where:

m. , . = Parameter i i n i t e r a t i o n

i.

dm.. = Parameter jump i n i t e r a t i o n j . m.,.

= New p a r a m e t e r s for i t e r a t i o n j + 1 .

To c a l c u l a t e t h e s e parameter jumps, I used a w e i g h t e d ,

scaled,

damped l e a s t s q u a r e s s o l u t i o n (Menke,1984) u s i n g M a r q u a r d t ' s (1963,1970) maximum neighborhood method.

This l e a s t

squares

s o l u t i o n i s of the form:

dm = D(DATW AD + e

AI)

1

DATW Ad e

(5)


72

where:

dm = Mxl (M = number of blocks in the model) matrix containing the parameter jumps used to alter zâ&#x20AC;&#x17E; (depth to bedrock parameter) in a direction which ideally reduces the error between the observed and calculated data. D = M x M diagonal scaling matrix. A = N xM (N= number of observed gravity data points) matrix of partial derivatives of parameter z with respect to the observed gravity data. W = N x N data (noise) weighting matrix. e X = Constant, updated with each iteration according to Marquardt's algorithm. Ad = N x 1 matrix of differences between the observed and calculated gravity data.

Linear Algebra All of the matrix multiplications and manipulations in the inverse gravity modeling program (program GINDEP) were determined using subroutines of the IMSL (1982) library.

To invert the the

T matrix (DA W AD + XI) in equation (6), an IMSL subroutine called e LINV2F was selected.

In this subroutine the matrix x is solved

for column by column in the following equation: Ax = B where B is set to the identity matrix.

The IMSL manual does not

explicitly describe the technique used to determine x; however, a possible solution method is to upper triangularize the A matrix and then solve for x using a back-solving procedure (Menke, 1984).


73 Scaling Matrix The diagonal scaling matrix D is used to better condition the MxM matrix to be inverted.

The values of D were determined

as follows: If i = j , then: 1,3

V(ATWeA) . i >J

otherwise: D. . = 0.0

Determining the Marquardt Damping Factor To determine the Marquardt damping factor, A , the following algorithm proposed by Marquardt (1970) was used:

-3 1) Let X = 10 for the initial parameters. 2) Calculate the new parameters, and if these new parameters reduce the error between the observed and calculated data: set

X = X/10

â&#x20AC;&#x201D; > iterate again,

otherwise: set

A = A x 10 â&#x20AC;&#x201D; > keep the previous parameters,

recalculate the parameter jumps. 3) Repeat step 2. A solution is found once the parameters of a given iteration reduce the error between the observed and calculated data below some input value.


74

Determining the Error Of the multitude of ways to estimate the error between the observed and calculated data, I chose the following formula:

E

1/_i_ N-M

x

(g

observed

g

calculated)

(6)

As formula (6) indicates, if the number of blocks (M) used in the model approaches the number of gridded gravity stations (N), the error approaches infinity.

This formula, therefore, tends to

keep the modeler "honest" by not entertaining complicated models unless they are substantiated with a large amount of data.

Weighting My choice of a noise weighting matrix was of the form described by Last and Kubik (1983).

In their article Last and

Kubik discuss noise and parameter weighting matrices used in a 2-D inverse gravity modeling program which inverts on densities assigned to a model formed of a grid of rectangles.

The noise

weighting matrix they use (assuming normally distributed noise) is:

W .J = (G..W (Density)..G..T).. eii lj m ' JJ ij n

i = 1 to N j = 1 to M

where: G = N x M data kernal matrix mapping densities to the observed gravity data.


75

W (Density) = M x M diagonal density weighting matrix, m

By using Last and Kubik's form of a noise weighting matrix each time the parameters (densities) are updated, the noise weighting matrix is also updated.

This is a reasonable approach in my

opinion because, in my modeling, with every parameter (depth to bedrock) change, "geologic noise" inherent in the model is also changed.

"Geologic noise" being defined as gravity sources which

contribute to the observed gravity yet which are not accounted for in the modeling (i.e. gravity contributions produced from density contrasts in the valley fill).

In my modeling I assumed

that geologic noise increased in direct proportion to the depth of the block.

In other words, I assume the deeper the valley

fill the greater the probability of encountering gravity sources not accounted for in the modeling. As stated before, I chose a weighting matrix of the form of that used by Last and Kubik (1983).

My noise weighting matrix

being:

We., = (A..Wm(Depth)AT..).. li IJ IJ n where: A = N x M matrix of derivatives of observed gravity with respect to the depth of bedrock (parameter z2).

Wm (Depth) = Diagonal depth weighting matrix.

(7)


76

The depth weighting matrix I chose to use is:

Wm(Depth).. = 1./[ABS(zâ&#x20AC;&#x17E;) . )] JJ 2 j

This noise weighting matrix (equation 7) is a preferentially shallow depth weighted matrix in that shallow blocks are assigned a greater weight.

The individual values of this matrix map the

magnitude of the sensitivity to which the jumps in parameter zâ&#x20AC;&#x17E; match the differences between the observed and calculated data.

Constraining the Solution Path I constrained the solution path taken in my modeling program in three ways in an attempt to get physically possible and geologically reasonable results.

First of all if during an

iteration, a parameter jump caused z

(the bottom of a block) to

have a value less than z. (the top of a block) then this parameter jump was divided by 10 until z z .

had a value less than

Secondly, maximum and minimum (zmax and zmin) values of

bedrock depths estimated for the modeling area may be input in the program. If during an iteration a block ends up out of this range of values, the depth of the block is set either to zmax or zmin (whichever extreme was crossed), and this block is damped so that during the next iteration the block is essentially fixed at zmax or zmin.

The damping is done based on Marquardt's finding

that parameter jumps will decrease as the damping variable is increased.

This constraining method is implemented as follows:


77

If the depth of a block (zâ&#x20AC;&#x17E;) is less than zmin then: 1)

Set z.(j) = zmin

2)

Set

A = 15

= Marquardt's damping factor

If the depth of a block is greater than zmax then: 1)

Set zâ&#x20AC;&#x17E;(j) = zmax

2)

Set

A = 15

If during the next iteration, the parameter jumps for the heavily damped blocks are in the direction that brings the depth back into the allowable range, the damping variable is reset to the current Marquardt damping value.

Damping the blocks with a value

of 15 is based on my modeling experience which showed that this value was sufficiently large to constrain the blocks.

I found

that if the Marquardt damping factor reached 100 (the Marquardt damping variable increasing by a factor of 10 each time an iteration produced diverging results) during the modeling process, repeated divergence in the successive iterations occurred.

These results are based on the numbers pertaining to

the specific model used for the Ennis geothermal area. A third constraint is that individual blocks can be taken out of the inversion process.

This is done by assigning a large

Marquardt damping value ( A= 100) to specified blocks in the model.

In this way selected blocks may retain their initial

guess depth throughout the modeling process. Finally, in order to make the program more efficient, I did not allow another iteration to occur unless the new model


78

parameters reduced the error between the observed and calculated data by more than one percent (a meaningful improvement).

Gravity Models of the Ennis Geothermal Area

Topographic Model: Figure 22 shows the area to be modeled relative to the observed data area. The modeled area extends approximately 3 km beyond the boundary of the observed data set in north, south, and east directions and only 1 km to the west because of the shallowing of the bedrock to the west.

The extension of

the modeling area past the gridded observed data area serves the purpose of taking into account contributions to the gridded observed gravity values from sediments beyond the gridded observed gravity area.

It is an a priori assumption

that sediments outside the boundaries of the modeled area contribute negligibly to the gridded observed gravity values. Figure 23 shows selected elevation contours, at elevations of 1475, 1487, 1500, 1524, and 1585 m, taken from the Ennis 15 minute quadrangle in the modeled area.

The 1475, 1487, and

1500 meter (4840, 4880, 4920 feet) elevation contours were selected because they are the only contours drawn through the valley floor in the modeling area, while the 1524 and the 1585 meter (5000 and 5200 feet) elevation contours were selected because they were easily traceable.

Consequently, Figure 23 is

a representation of the topography in the modeled area where I


H 18

111.75

111.TJ

111.69

111.66

LONGITUDE (DEG.) Figure 22.

Modeling area (outer square) relative to the gridded observed gravity data area (inner square) as they would appear on the Ennis 15' quadrangle. â&#x20AC;˘~-i

to


80

1.72 111.69 LONGITUDE (DEG.) Figure 23.

111'. 66

Selected contour elevations (meters above sea level) taken from the Ennis 15' quadrangle map. These contours are assumed to give an adequate representation of the topography in the modeling area.


81

have assumed that this representation is adequate in defining the topography in the modeling area.

For the gravity modeling

program (using Talwani and Ewing's method) each of these contours was approximated by the horizontal polygons which are shown in plan view in Figure 24a and individually in Figure 24b.

The five polygons, at the elevations shown in Figure 24,

make up the model used to represent the topography.

In the

modeling program, the gravity contribution of each of these polygons is determined, and the total gravity anomaly is found by summing each of the contributions through the use of a quadrature formula described in Talwani and Ewing's (1960) paper.

Because the 120 gravity "stations" of the gridded

observed data set are located at different elevations, the model must be shifted relative to each station elevation so that the topography appears as it should from an observation point at the individual gridded station elevations. In effect what is being done is a local correction from which the gravity contribution of sediments from the highest to the lowest elevation in the modeled area is determined for each gridded gravity station.

Once these contributions are removed from the

gridded observed data set, it is as if all sediments in the modeled area to an elevation of 1475 meters have been stripped away as far as gravity contributions are concerned. Figure 25b shows the contours of the gravity contributions from the valley fill contained in the topographic model (ci = 0.2 mgals). values.

See Appendix E.3 for these calculated gravity

Note the correlation of the topographic correction


82

KILOMETERS

â&#x20AC;˘ EAST

1585 - : 1500 _- Z Z

lllli

{ M

Aw 1487 HJJ

<Hid 7 V

V V | V V V

V

V

V

V V

V

V \y

V V V V

V

"V V

N/

V V

V

^

v/

V

V

V

V

1475 V V N/

N/

V V

V

V

\/ V

s/

Figure 24. A) A plan view of the 5 polygons which comprise the topography model. These polygons are digitized representations of the 5 contours shown in Figure 23. B)

Schematic of the individual polygons.


83

:

soo

i

i-

1 1 000 a. ui

ul 1S00 2000 1 000

2000

3000

4000

METERS EAST - - >

200011000

2000

3000

4Q00

METERS E A S T - - - *

Figure 25. A) Contours (c.i. = 1 mgal) of the gridded gravity data with the gravity contributions of the gravity data included in topography model removed. B) Contours (c.i. = 0.2 mgals) of the gravity contributions from the valley fill included in the gravity model.


84

contours in Figure 25b with the elevation contours in Figure 2 3.

Figure 25a shows the contours of the gridded observed

gravity data (ci = 1 mgal) with the gravity contributions from the topographic model removed from the gridded observed gravity data set (shown in Figure 17). See Appendix E.4 for the actual gravity values.

Forward Model: Once the gravity contributions of the valley fill in the topographic model are removed, the sediments in the modeling area are assumed to start from a plane at an elevation of 1475 meters.

Consequently, for the forward modeling each of the

blocks are modeled with tops starting at an elevation of 1475 meters.

At each gridded gravity station, the entire model of

the sediments below 1475 meters is depth-shifted so that the model appears as it should from an observation point at the station's elevation.

Consequently, the forward model includes

a variably thick cushion of "air", the cushion thickness being determined by the difference between each station elevation and the 1475 meter elevation plane. In the forward model 80 blocks of earth, contained in the modeling area shown in Figure 22, were used.

These blocks

are shown in plan view in Figure 26 and the numbers on the blocks correspond to how they were numbered in the actual modeling of the Ennis hot springs area.

Those blocks directly

below the observed data set, blocks 1-54, were given a smaller cross-sectional area (in the x-y plane) because it is these


C\J

-

1

^r „

70

71

73

72

i

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69

55

68

1

2

3

4

5

10 19 28 37 46

II 20 29 38 47

12 21 30 39 48

13 22 31 40 49

14 23 32 41

/tid" i CO

a5^>a>

E •2 co

*t\T

67

6

7

8

9

15 24 33 42 50 51

16 25 34 43 52

17 26 35 44 53

18 27 36 45 54

65

66

74

59

58

57

56

60 61 62 76

63

64

75

CO

ro" <D

79

80

I

i

1.0

0.0

78

1.0

77 1

2.0 3.0 4.0 5.0 Kilometers -> East

.....

6.0

.

.J

7.0

Figure 26. Plan view of the spatial locations of the blocks used in the gravity modeling, The blocks are numbered as they were in the actual modeling. CO

en


86

blocks that, by virtue of their closeness to the gravity stations, should exhibit the most control over the shape of the gravity anomalies in the gridded observed gravity data. The forward modeling process consisted of manually altering the depths of the blocks until a reasonable match with the "topographically corrected" gravity values was obtained. The final model resulting from this modeling process is shown in Figure 27 (see Appendix F.1.1).

The numbers on the blocks

in Figure 27 represent the depth in meters of each block below the 1475 meter level to the bedrock.

In Figure 28b the gravity

values calculated from the model shown in Figure 27 are shown in contoured form (ci = 1 mgal, see Appendicies F.1.2 and F.1.3).

The "goodness" of these model results are shown in

Figure 29 which is a contour plot (ci = .5 mgals) of the absolute value of the differences between the "topographically corrected" gridded observed gravity data (Figure 28a) and the model results.

The normalized average root mean square error

(equation 6) between the forward model results and the topographically corrected data is approximately 1.0 mgals. See Appendix D for input to and output of the forward modeling program.

Inverse Model: In the inverse modeling process the depths of the blocks are automatically adjusted so that with each iteration of the computer, the error (see equation 6) between the gridded observed "topographically corrected" gravity data and the


CM i

1500

600

600

200

<* _ i

350

di

is-

300 4 0 0

200

I

800

500 700

125

4 0 0 450

125

100

600

ieo 2 3 0

850

850

800

9 0 0 700

800

800

750

950 7 0 0

800

7 0 0 850

850

1100

950

955 1250

9 0 0 1000

1000

l

a. — Ui Ul

o «

5

550

425

10

100

140

300

400

700

9 0 0 1100 1200

2

80

230

500

525

700

9 0 0 1250 1300

5

100

300 4 0 0

500

700

9 0 0 1250 1400

1000 1400

N

2 00

600

4 00

1000

900

to _ to

300 u>

700

1

I 0

1350

1100 I

I

i

4 KIL0METERS- •> EAST

Figure 27. Plan view of the final model output from the forward modeling process. The numbers in the blocks represent the depth (in meters) below a 1475 meter elevation datum to the bedrock.

CO


88

OBSERVED GRAVITY - TOPO. REMOVED

®

2000 1000

2 000

3000

4000

METERS—»• EAST

CALCULATED GRAVITY - FORWARD MODEL

2000 0

1000

2000

3000

©

4000

METERS--* EAST

Figure 28.

A) Contours (c«i.=lmgal) of the "topography corrected' gridded observed gravity data, B) Contours (c.i.=lmgal) calculated using the forward modeling program with the model shown in Figure 27 input.


20001 000

2000

3000

4000

METERS-*EAST Figure 29. Contours of the absolute value of the differences between the gridded observed "topography corrected" gravity data (c.i. = 0.5 mgals) - Figure 28a and the calculated gravity data from the forward model - Figure 28b. The average root mean square misfit between the observed and calculated data is app. 1.0 mgal. CO


90

calculated gravity data is reduced.

The forward model shown in

Figure 27 is used as a starting model for the first iteration in the inversion process. After three iterations in the inversion program, the model shown in Figure 30 was output (see Appendicies F.2.1 and F.2.2).

The numbers in Figure 30 again

represent the depth to bedrock in meters below an elevation of 1475 meters. The "goodness" of the inverse model is displayed in Figures 31 and 32. Figure 31b shows the contours of gravity (ci = 1 mgal) calculated from the model shown in Figure 30 (see Appendix F.2.3).

Figure 32 shows contours (ci = .5 mgals)

of the differences between the "topographically corrected" gridded observed gravity data (Figure 31a) and the calculated gravity data from the inverse model (Figure 31b). The normalized average root mean square misfit (equation 6) between the inverse model results and the "topographically corrected" data is 0.49 mgals (within the assumed error of the gravity survey of 0.5 mgals). Approximately 20 minutes of CPU time on a VAX 8500 computer was necessary to complete the three iterations and obtain the inverse modeling results.

See Appendix D.2 for

input to and output of the inverse modeling program (program GINDEP).


cvj i

359

74

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467

510

i

513

348

293

O

913

847

534

1000

i

I

161

CC in

io-

368

302

870

721

1050

1170

980

629

891

240

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6IS

624

869

1060 931

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147

210

269

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860

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994 805

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w «>_ or —

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996 1320

1540

480

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1210

1610

1670

779

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1330 I860 1760

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61

358

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98

792

742

1100 1210

1530 1220

w

18

785

677

1250

1490

to _

15

1

<d-

-I

2

497

900

5

3

i

i

i

4

KILOMETERS--* EAST

Figure 30. Plan view of the model output after 3 iterations using the inverse gravity modeling program. The numbers in the blocks represent the depth (in meters) below the 1475 meter elevation datum to the bedrock.

to


92

500 cr o

•I 1000 CO

1500 ^ 2000 2000

3000

4000

M E T E R S — * EAST

CALCULATED GRAVITY- INVERSE MODEL)

0

1000

2000

3000

(g)

4000

METERS—> EAST

Figure 31. A) Contours (c.i. = 1 mgal) of the "topography corrected" gridded observed gravity data. B) Contours (c.i. = 1 mgal) calculated from the model shown in Figure 30 output after 3 iterations of the inverse modeling probram.


1 1 000 I

5 1500 2000 0

1000

2000

3000

4000

METERS â&#x20AC;&#x201D;>EAST Figure 32. Contours (c.i. = 0.5 mgals) of the absolute values of the differences between the gridded observed "topography corrected" gravity values - Figure 31a and the calculated gravity data using the model shown in Figure 30 - Figure 31b. The average root mean square misfit between the observed and calculated data is 0.49 mgals. CO


94

Reliability of the Inverse Model: The gravity calculated from the inverse model matches the gridded observed "topographically corrected" gravity data within the assumed error of the gravity survey; however, an infinite number of mass distributions can produce a given gravity distribution.

Therefore, because the gravity model

shown in Figure 30 is not unique (and incorporates a number of assumptions), a demonstration of how well this model matches other constraining data is necessary.

As shown in Figure 30,

80 blocks of earth were used in the model, however only the 54 blocks, located directly beneath the gridded observed gravity data, shall be used to check the reliability of the inverse modeling results.

It is assumed that the blocks located

directly beneath the gridded observed gravity data are the most highly constrained by the gridded observed gravity data.

Comparison with Seismic Refraction Two seismic refraction lines were shot in the area of the Ennis hot spring (see Figure 8).

The data from these surveys

was interpreted to determine the depth to bedrock in the area of the Ennis hot spring (see Figures 9 and 10). Comparisons of the depth to bedrock information from these seismic refraction lines and the inverse gravity model are shown in Figure 33. The dotted line in Figure 33 represents the seismic refraction results while the zones between the line segments indicate the depth to bedrock plus or minus the standard deviation of the


sW 0

NE

SH3

TX7

i

I

.........

TX2 -

1-

....

SHI V

SH5

1

rt=

^200 X l-

SCALE

ÂŁj400 Q

6

250

500 METERS

(NO VERT. EXAGG.)

N

TX6 0 1

-

SH4 1

.

TX2 i-

SE TX3

5 200 X t-

6 o 400

Figure 33. Comparison of the bedrock depths determined from the seismic refraction work and the inverse gravity modeling results. The dotted line shows the depth to bedrock interpreted (McRae, unpublished senior report) from the seismic refraction data, and the straight line segments represent the depth to bedrock +/- a standard deviation determined from the inverse gravity modeling.


96

calculated bedrock depth determined using the inverse gravity modeling program. The gravity and refraction interpretations match quite well considering that each of the blocks in the gravity modeling program received a bedrock depth based on gravity data that is averaged over the area of a block.

In the SW-NE

trending refraction line, the gravity modeling results indicate a significant bedrock drop not shown in the seismic refraction interpretation; however, this bedrock offset is located beyond the area where the seismic refraction data could have indicated this drop.

In the NW-SE trending refraction line, the gravity

modeling results indicate a drop in the bedrock located between wells TX-6 and SH-4 that is not included in McRae's (unpublished senior report) interpretation of the refraction data.

However, the data from the unreversed refraction profile

extending from SH-4 to TX-6 does indicate a drop in the bedrock in the area of offset implied by the gravity modeling (see Figure 10). Apparently McRae averaged the changes in slope of the time distance curve after the initial slope change (representing the refraction along the bedrock surface SE of the drop of the bedrock indicated in the gravity modeling) in his interpretation.

Comparison with Drilling Three of the test wells (Tx-9,ll,and 12) and one of the shot holes (SH-3) penetrated the bedrock.

Comparison of

bedrock depths determined from the gravity modeling and


97

drilling are shown in Table 8.

The middle depth to bedrock

column in the gravity modeling portion of Table 8 indicates the depth to bedrock below the 1475 meter datum plus or minus a standard deviation.

The matches between the depth to bedrock

determined from the drilling and the gravity modeling are reasonable (in my opinion) again considering the fact that the depth to the bedrock determined from the gravity modeling is based on averages of the gravity data over the area of the block.

Comparison with Seismic Reflection Susan Young (1984) in a masters thesis written for the University of Texas discusses eight seismic reflection lines located in the northern Madison valley.

From the processed

seismic data, Young picked and traced what she considered were "distinctive reflector horizons" on each line for interpretation purposes. A section of one of the seismic lines, line #2, (see Figure 11) crosses the gravity modeling area along a N-S line through the easternmost row of interpreted blocks. This seismic line was migrated and one velocity analysis was done along the line.

From this velocity analysis interval

velocities were computed by Young using the Dix equation. These interval velocities for line #2 are shown in Table 9. Figure 34 shows two pictures; the upper picture shows the picked and traced distinctive reflector horizons included by Young for line #2 while the lower picture in Figure 34 shows


datum: |768 (m.) SRg Shelhamer Ranch graben JCg

Jack Creek graben

gravity modeling results I Sec.

1

NMC 1 North Meadow Creek fault

.

I KM NMCf

I Sec.

Figure 34.

The upper picture shows "distinctive reflector horizons" picked and traced from seismic reflection line #2 by Young (1984). The lower picture shows Young's interpretation of the data shown in the upper picture. Superimposed on both of these pitcures are the depths to bedrock indicated from the inverse gravity modeling results.

W3 CO


99

Young's interpretation based on the reflector horizons shown in the uppermost picture. In both the upper and lower pictures of Figure 34, the depth to bedrock indicated from the gravity modeling in the appropriate section of line #2 is shown.

The depths to bedrock

indicated from the gravity modeling were converted to time using the velocity information contained in Table 9.

293

meters had to be added to the depth of each block because of the discrepancy between the 1768 m. datum elevation used in processing the seismic reflection data, and the 1475 m. datum used in the gravity modeling. Because only the picked and traced "distinctive" reflectors are shown, it is difficult to say whether the seismic reflection data supports the gravity modeling results.

Table 8. Comparison of bedrock depths determined from gravity modeling and drilling. 1) Drilling Well Surface Elevation(m.) TX-9 1502 TX-11 1489 TX-12 1499 SH-3 1503

Depth to bedrock (m. from surf.) 107 161 142 26

2) Gravity Modeling Well TX-9 TX-11 TX-12 SH-3

Depth to bedrock 51 +/- 26 210 +/- 56 129 + /- 46 0 +/- 19

Depth to bedrock (m. from surf.) 52 - 104 168 - 280 107 - 199 9-47


100

Table 9.

Interval velocities determined by Young, 1984 using the Dix equation for seismic reflection line #2. Time represents two way travel time. Two Way Time (sec.)

Interval Velocity (m/s)

0.0 2439 0.2 2530 0.4 2854 0.6 3259 0.8 3279 1.0 3257 1.2 3347 1.4

Nevertheless, the south dip of the picked reflector horizons (located immediately south, or to the left, of the bedrock high shown in the gravity modeling results) suggest the possibility of a bedrock high in the location the gravity modeling results indicate. As for Young's interpretation, I believe the gravity modeling results cast doubt on Young's inclusion of Paleozoic and Mesozoic rocks in the area south of the bedrock high shown in the gravity modeling.

If there was a thick sequence of

Paleozoic and Mesozoic rocks in this area, the gravity data should indicate a shallower depth of valley fill because of a density contrast between the valley fill and the Paleozoic and Mesozoic rocks.

Therefore, I believe that the reflectors Young


101

indicated as possibly being Paleozoic and Mesozoic rocks, in the area south of the modeled basement high, are probably reflectors contained in the Tertiary valley fill.


STRUCTURAL INTERPRETATION OF THE INVERSE 3-D GRAVITY MODELING RESULTS

Interpretation Considerations As shown in Figure 26, 80 blocks of earth were used in the model, 54 of which were located directly underneath the gridded observed gravity data, and it is these 54 blocks of valley fill that are interpreted.

Figure 36 shows the location

of the 54 blocks as they would appear on the Ennis 15 minute quadrangle map (see Figure 35 for an explanation of symbols). As

the numbers in the blocks represent the depth of valley

fill above bedrock (relative to a datum elevation of 1475 meters), it should be clear that Figure 36 represents a map of the bedrock topography in the area of the modeling. To structurally interpret this bedrock topography, I considered significant bedrock displacements (relative to the depth of the block), mappable along consistent trends, as faults.

As I did not believe the resolution in averaging the

gravity data over the area of the blocks justified the drawing of these interpreted faults as lines, I drew the faults as zones approximately 100 meters wide.

It should also be noted

that I considered all the faults to be associated with the tensional tectonics involved in the creation of the Madison Valley.

Consequently, I depict all the faults as normal faults

(except for a wrench fault); however, because gravity modeling can not detect whether high (or low) bedrock is the result of


103

LEGEND v T X 3 = test well 3 v-SH4 = shot hole 4 (for refraction survey) 2 0 = section number-Ennis quadrangle

= normal fault (assumed) down on bell side

= wrench fault (assumed)

= Madison River

'W = Ennis hot spring >BM

s

gravity benchmark

Figure 35. Explanation of symbols shown in Figures 36 and 37.


SECTION 20

T5S , RIW ENNIS 15' QUADRANGLE 500

1 0 0 0 METERS

Figure 36. Plan view of the 54 blocks of the inverse gravity model included for interpretation. These blocks are shown as they would appear on the Ennis 15' quadrangle, and the numbers in the blocks indicate the depth (in meters) below the 1475 meter elevation to the bedrock.


tensional or compressional forces, these interpreted fault motions represent at best an educated guess.

Further, high or

low bedrock may represent emplacement or erosional features or may be associated with tectonic activity resulting in something other than faulting (i.e. folding or flexure of the bedrock). These points should be remembered because in the writing to follow I concider the interpreted faults as such even though faulting may not have occurred.

Finally, these interpreted

faults are drawn as they would be located at the valley fill/bedrock interface.

Interpretation The interpretation of the bedrock topographic model shown in Figure 36 is illustrated in Figure 37. The major structural feature contained in this interpretation is an east-west trending feature depicted as the dotted zone located approximately 500 meters north of the Ennis hot spring on a north-south line.

If this dotted zone is to be call a fault,

it would have to be considered a wrench fault as displacement directions change along the strike of the dotted zone.

For

example, west of the Madison River the bedrock is dropped north of the dotted zone while the reverse is true east of the Madison River.

As the NW to NE trending faults appear to

terminate against this zone, I will assume that the east-west feature predates interpreted NW-NE trending faults.

If the

east-west feature does predate the primarily east-west extensional tectonics responsible for the creation of the


â&#x20AC;˘

SECTION 23

T5S, RIW ENNIS 15' QUADRANGLE

Figure 37. Interpretation of the inverse gravity modeling results shown in Figure 36 (see Figure 35 for an explanation of symbols).

o CM


107

Madison Valley, it is possible that shearing, during the period of extensional tectonics, occurred along the east-west trending feature.

At any rate, I will refer to the east-west trending

dotted zone shown in Figure 37 as a wrench fault (along which shearing has possibly taken place) for the discussion to follow. Structure in the gravity modeling area appears to have been controlled by this wrench fault because:

1) Many of the

interpreted Tertiary normal faults appear to terminate against the wrench fault; and

2) major changes in bedrock depths and

faulting relationships occur across this zone.

The changing

structural features of the bedrock across this zone is clearly demonstrated by comparing E-W cross sections located north and south of this wrench fault.

This comparison is shown in Figure

39 (see Figure 38 for the location of the cross section lines). Note that the vertial offsets of the bedrock shown in Figure 39 represent the drops across the individual blocks in the model; therefore, these vertical offsets need not represent locations of the interpreted faults shown in Figures 37 and 38. Remember I only interpreted a bedrock drop as a fault if I concidered that: 1) the offset was signifigant relative to the depth of the block; and 2) the offset could be traced along a consistent trend.

And as these consistent trends of signifigant offset

generally did not follow the edge of the blocks (N-S or E-W trends), I have interpreted faults which cut across the modeled blocks or, in other words, I have not interpreted only E-W and N-S trending faults. Therefore, even signifigant bedrock


SECTION 20

SECTION 23

CROSS SECTIONS

N

T5S, RIW ENNIS IS' QUADRANGLE

SCALE 0

Figure 38.

500

1000 METERS

Location of the cross section lines placed north and south of the wrench fault. o CO


c -5 rt>

ELEVATION (M.)

ELEVATION (M.)

S / N / N / V

/

/ V S '

N /

^

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N

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W

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y

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CD

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§

N / N S

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s

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w

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F

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/

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<

m x

W v. / '

/ * N

>

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/

N '

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>

X

<

sy \ / L,

S

x

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v / \ f

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110

displacements shown in Figure 39 need not correlate with the fault locations shown in Figures 37 and 38. North of the wrench fault, the gravity modeling indicates the bedrock drops off rapidly to the east reaching a maximum depth of over a kilometer underneath the Madison River (see Figure 39). East of the Madison River, however, the bedrock shallows forming an eastern wall to a northwest trending bedrock valley, a profile of which is shown in Figure 39. South of the wrench fault the basement remains relatively shallow west of the Madison River in contrast to the bedrock depths observed in the gravity modeling north of the cross fault (see figure 39).

East of the Madison River, the

shallowing of the bedrock, defining the eastern wall of the bedrock valley north of the wrench fault, is not indicated south of the wrench fault.

Interpretation Implications The purpose of the 3-D gravity modeling in the area of the Ennis hot spring was to determine the location of faults which have offset the bedrock and which might possibly control the ascending thermal waters of the Ennis geothermal system. Figure 37 represents my attempt to satisfy this purpose; however, the surface location of the Ennis hot spring can not definitely be explained by the gravity modeling results. This is because aquifers in the valley fill control the flow of the thermal waters above the bedrock.

Nevertheless, there are NW

and NE trending faults interpreted in the area of the surface


Ill

location of the springs.

If these fault planes are permeable,

they may act as conduits for geothermal water flowing in the bedrock and may therefore bring geothermal water into the vicinity of the surface location of the Ennis hot spring. To determine a promising place to drill in the Ennis geothermal area, the following question must be asked:

What

path(s) does the water follow from the reservoir to the hot spring on the ascending limb of the Ennis geothermal system? As the location of the reservoir relative to the hot spring is unknown, perhaps the best way to answer this question is to try and track the water path from the spring to the reservoir. Sonderegger and Zaluski (1983) discuss the north dipping fracture zone that is hydraulically connected between wells TX-12, TX-11, and MAC-1. Because the flow rate in the fracture 3 zone (.0242 m /s - from the Pump Test of MacMillan Well - MBMG in house publication) is approximately 20 times greater than 3 the flow rate of the Ennis hot spring (.0012 m /s - Leonard, written communication), the following is indicated:

1) The

surface flow of the Ennis hot spring is only a minor portion of the Ennis geothermal system; and 2) the fracture zone is an important near surface aquifer in the Ennis geothermal system and probably supplies hot water to the Ennis hot spring.

Based

on the inferred north dip of the fracture zone, I assume the hot water comes to the spring from a general northerly direction, however, because only two wells definitely intercepted the fracture zone, the 3-D orientation of the fracture zone is unknown.


112

If the fracture zone results from an overthrust effect, as Sonderegger and Zaluski (1983) suggest, then perhaps the fracture zone is a continuous feature that can be found in the deeper bedrock north of the wrench fault.

At any rate, I

recommend that a well be drilled in the area of the wrench fault because if the zone is transmissive, thermal water ascending from a reservoir east or west of the hot spring could be controlled by this feature.

The point along the wrench

fault that I recommend for drilling is at shot hole SH-5 because my interpretation of the modeling indicates that two faults to south of the wrench fault intersect the wrench fault in this area.

Also, SH-5 is reasonably close to well MAC-1

which intercepted the fracture zone.

The modeled depth to

bedrock north of the wrench fault in the area of SH-5 is 600 meters while south of the wrench fault the modeled depth to bedrock is approximately 200 meters (see Figures 36 and 37). To make a rough estimate of the water temperature that a well could intercept if drilled to the modeled bedrock depth in the area of SH-5, I will assume that the 90 C temperature encountered at approximately 150 meters in well TX-12 represents the temperature of the water below any cold water mixing zone.

This 90 C temperature is 70 C below the estimated

160 C reservoir temperature, and this reservoir is assumed to be located 3.3-5 kilometers below the land surface. These numbers indicate that the ascending geothermal waters lose 60 C in approximately 4 kilometers.

Based on this 60 C per 4

kilometer gradient, geothermal water circulating in the


wrench fault approximately 600 meters below the land surface will have attained a temperature of 99 C (9 degrees above the 90 C "unmixed" surface temperature). 99 C is a crude estimate.

I emphasize that this

If one is an optimist, the

wrench fault may represent a highly permeable aquifer by which the ascending geothermal water may travel with very little loss in temperature.

On the other hand, a pessimist would point out

that wrench fault may be impermeable and no water whatsoever would be intercepted by drilling the wrench fault.


SUMMARY

The following is a list of significant results gathered from the previous work in the Ennis geothermal area and discussed in this paper: 1) A north dipping (at approximately 30

assuming the

fracture zone is linear between wells TX-12 and MAC-1) fracture zone, approximately 30 meters wide, was intersected during the drilling of wells TX-12 and MAC-1.

The fracture zone is located in the Archean

metamorphic bedrock 157 meters below the surface in well TX-12 and 335 meters below the surface in well MAC-1. Hydraulic connection between the two wells (and also well TX-11) was confirmed during a pump test of the MAC-1 well.

The pumped flow rate in the fracture

zone is approximately 20 times greater than the measured surface flow rate of the Ennis hot spring and is possibly an important local supplier of water to the Ennis hot spring;

2) A heat flow study, which accounts for conductive and convective heat flow, indicates a heat flow range in the area of drilling from 0.42 to 10.5 MW assuming end value flow rates (the measured surface versus the assumed "safe yield" flow rate) for the Ennis geothermal system;


3) A reservoir temperature of approximately 160 degrees Celcius is assumed by Leonard (written communication) and Juncal (Project Milestone Report) based on geothermometry of the Ennis geothermal system. Assuming temperature gradients of 30 C/Km for the bedrock and 60 C/Km for the valley fill, a reservoir depth between 3.3 and 5 kilometers is indicated;

4) No presently mapped fault(s), observable at the surface in the area of the Ennis hot spring, obviously controls the present surface location of the spring. Major mapped faults, apparently important in the structural development of the upper Madison Valley (located a few to tens of kilometers north and east of the Ennis hot spring), include:

a) the Spanish Peaks

reverse fault; b) the Jack Creek thrust fault; c) the North Meadow Creek fault; and d) the Madison Range front normal fault;

5) Audio magneto-telluric survey results show a definite broadening of low resistivity values In 300 m skin depth results relative to 100 m results, in every direction but west of the hot spring.

Also, a

north-south low resistivity trend surrounding the hot spring is shown in the data indicating a possible N-S oriented structure; and


116

6) Young's (1984) interpretation of seismic reflection data indicates the Jack Creek thrust fault possibly extends west of the Madison Range front fault and a complex intra-valley bedrock topography including two grabens and numerous normal faults.

These previous work results provide a foundation on which my 3-D gravity modeling work is built. The 3-D forward gravity modeling involves a two-step process which includes modeling with vertically-stacked, horizontal, n-verticied polygons (based on Talwani and Ewing's 1960 method) and with blocks (based on an algorithm derived from integration of the gravity formula).

This two-step forward

modeling process is used to find a bedrock topography model from which calculated gravity data approximately matches the observed. Next, an inverse gravity modeling program is used to create an adjusted bedrock topography model that yields a normalized average root mean square error (see Equation 6), between the observed and calculated gravity data, which matches the observed gravity data within the error of the survey.

Although these

gravity modeling techniques were applied to finding offsets in the bedrock caused (presumably) by faulting which might control water of the ascending limb of a geothermal system, these gravity modeling techniques could also be used to solve geological and hydrogeological problems wherever a valley fill over bedrock geologic setting exists.


117

This two-step forward modeling process, used sequentially with the inverse modeling program, was applied to the gravity data collected in the area of the Ennis hot spring.

The bedrock

topography model (output using these modeling techniques) produced a normalized average root mean square error (see Equation 6) within the 0.5 mgal assumed error for the gravity data collected in the modeling area.

This bedrock topography

model also matched reasonably with seismic refraction data and depth to bedrock information from wells drilled in the area of the Ennis hot spring.

My interpretation of this bedrock

topography model indicates the following (see Figure 37): 1) An intersection of northwest and northeast faults in the bedrock which possibly control flow of thermal water in the bedrock in the area of the Ennis hot spring; 2) An east-west trending wrench fault upon which north-south, presumably Tertiary, normal faults terminate and across which structural relationships change; and 3) A northwest trending bedrock valley (graben?) having an eastern wall north of the wrench fault but not south of the wrench fault in the modeling area. This interpreted complex bedrock topography, in general, is not surprising concidering Young's (1984) interpretation of seismic reflection data shot to the east of my modeling area in the Madison Valley.


If further drilling is done in the area of the Ennis hot spring, I suggest drilling along the interpreted wrench fault because, if the wrench fault is transmissive, it could control recharge water from east or west of the hot spring.

A possibly

promising drilling site along the wrench fault in the area of shot hole SH-5 is suggested because: 1) SH-5 is reasonably close to well MAC-1 which intercepted an apparently important near surface fracture zone of the Ennis geothermal system; and 2) I interpret two faults to intersect the wrench fault in this area. A crude estimate indicates a 99 C temperature for the geothermal water in the bedrock beneath this drill site.


REFERENCES CITED Arnorsson, Stefan, 1975, Application of the silica geothermometer in low temperature hydrothermal areas in Iceland: American Journal of Science, V. 275, p. 763-784. Blackwell, D. D., and Chapman, D. W., 1977, Interpretation of geothermal gradient and heat flow data for Basin and Range geothermal systems: Geothermal Resources Council Transactions, V. 1_, p. 19-20. Brook, C. A., Mariner, R. H., Mabey, D. R., Swanson, J. R., Guffanti, Marianne, and Muffler, L. J. P., 1979, Hydrothermal convection systems with reservoir temperatures >^ 90 C, in Mullfer, L. J. P., ed., Assessment of geothermal resources of the United States â&#x20AC;&#x201D; 1978: U. S. Geological Survey Circular 790, p. 18-85. Burfiend, W. J., 1967, A gravity investigation of the Tobacco Root Mountain, Jefferson Basin, Boulder Batholith and adjacent areas of southwestern Montana: Bloomington, Indiana University, Ph.D. thesis, 90 p. Carl, J. D. , 1970, Block faulting and development of drainage, northern Madison Mountains, Montana: Geol. Soc. America, Bull., V. 81_, p. 2287-2298. Chadwick, R. A., 1978, Geochronology of post-Eocene ryolitic and basaltic volcanism in southwestern Montana: Isochron/West, no. 22, Aug., p. 25-28. Chadwick, R. A., and Leonard, R. B., 1979, Structural controls of hot spring systems in southwestern Montana: U. S. Geological Survey Open-File Report 70-1333. Chapman, D. S., Kilty, K. T., Mase, C. W., 1978, Temperatures and their dependence on groundwater flow in shallow geothermal systems: Geothermal Resources Council Transactions, V. 2_, p. 79-82. Fournier, R. 0., 1981, Application of water geochemistry to geothermal exploration and reservoir engineering, in Rybach, L., and Muffler, L. J. P., eds., Geothermal Systems - - Principals and case histories: New York, John Wiley and Sons, p. 109-143. Fournier, R. 0., and Potter, R. W. II, 1978, A magnesium correction to the Na-K-Ca chemical geothermometer: Geochimica et Comochimica Acta, V. 4_3, no. 10, p. 1543-1550.


Fournier, R. 0., and Truesdell, A. H., 1973, An empirical Na-K-Ca geothermometer for natural waters: Geochimica et Cosraochimica Acta, V. 27_, p. 1255-1275. Fournier, R. 0., and Truesdell, A. H. , 1974, Geochemical indicators of subsurface temperature, Part 2, Estimation of temperature and fraction of hot water mixed with cold water: U. S. Geological Survey Journal of Research, V. 2^, no. 3, p. 263-270. Fournier, R. 0., White, E. D., Geochemical indicators of Basic Assumptions: U. S. Research, V. 2, no. 3, p.

and Truesdell, A. H. , 1974, subsurface temperature, Part 1, Geological Survey Journal of 259-262.

Garihan, J. M., Schmidt, C. J., Young, S. W., and Williams, M. A., 1983, Geology and recurrent movement history of the Bismark-Spanish Peaks - Gardiner fault system, southwest Montana: Rocky Mountain Association of Geologists Guidebook, p. 295-313. IMSL, 1982, IMSL Reference Manual: IMSL Inc., 7500 Bellaire Boulevard, Houston, Texas, 7 7036-5085, USA. Last, B. J., and Kubik, K., 1983, Compact gravity inversion: Geophysics, V. 48_, no. 6, p. 713-721. Lloyd, R. M., 1968, Oxygen isotope behavior in the sulfate-water system: Journal of Geophysical Research, V. 7_3, no. 18, p. 6099-6109. Long, C. L., and Senterfit, R. M. , 1979, Audio-magnetotelluric data log and station-location map for the Ennis hot springs area, Montana: U. S. Geological Survey Open-File report 7 9-1308, 7 p. Marquardt, D. W., 1963, An algorithm for least-squares estimation of nonlinear parameters: J. Soc. Indust. Appl. Math, Vol. 1_1_, no. 2, p. 431-441. Marquardt, D. W., 1970, Generalized inverses, ridge regression, biased linear estimation, and nonlinear estimation: Technometrics, V. 1_2, no. 3, p. 591-611. McKenzie, W. F., and Truesdell, A. H., 1977, Geothermal reservoir temperatures estimates from the oxygen isotope compositions of dissolved sulfate and water from hot springs and shallow drill holes: Geothermics, V. 5_, p. 51-61. McRae, M., 1978, unpublished senior report: physics/geophysics department, Montana College of Mineral Science and Technology, Butte, Mt.


121

Menke, W., 1984, Geophysical Data Analysis: Discrete inverse theory, Harcourt Brace Jovanovich, Academic Press, Inc. 260 p. Montagne, John, 1960, Geomorphic problems in the Madison Valley, Madison County: Billings Geol. Soc. 11th Annual Field Conference Guidebook, p. 165-169. Muffler, L. P. J., ed., 1979, Assessment of geothermal resources of the United States — 1978: U. S. Geological Survey Circular 790, 163 p. Nathenson, Manuel, Guffanti, Marianne, Sass, J. H., and Monroe, R. J., 1983, Regional heat flow and temperature gradients, in Reed, M. J., Assessment of low-temperature geothermal resources of the United States — 1982: U. S. Geological Survey Circular 892, p. 9-16. Pardee, J. T., 1950, Late Cenozoic block faulting in western Montana: Geological Society of America Bulletin, V. 6J^, p. 359-406. Paul, H. P., and L. A. Lyons, 1960, Quaternary surfaces along the Madison valley floor from Ennis Lake to English George Creek, Montana: Billings Geol. Soc. 11th Annual Field Conference Guidebook, p. 170-173. Payne, R. A., 1986, A gravity investigation of the Boulder Baldy quadrangle, Big Belt Mountains, central Montana: Montana College of Mineral Science and Technology, Butte, Montana, M.S. thesis, 74 p. Rybach, L., 1981, Heat flow in geothermal systems, in Rybach, L., and Muffler, L. J. P., eds., Geothermal Systems — Principals and case histories: New York, John Wiley and Sons., 280 p. Sampson, R.J., 1978, Surface II Graphics System: Computer Services Section, Kansas Geological Survey, Lawrence, Kansas. Schmidt, C. J., and Garihan, J. M., 1983, Laramide tectonic development of the Rocky Mountain foreland of southwest Montana: Rocky Mountain Association of Geologists Guidebook, p. 271-294. Senterfit, R. M. , 1980, Principal facts for a gravity survey of the Ennis, Montana geothermal area: U. S. Geological Survey Open-File Report 80-09, 8 p. Shelden, A. W., 1960, Cenozoic faults and related geomorphic features in the Madison Valley, Montana: Billings, Geo. Soc. 11th Annual Field Conference Guidebook, p. 178-184.


'- Shofield, J. D., 1981, Structure of the Centennial and Madison Valleys based on gravitational interpretation: Montana Geol. Soc. Field Conf. Guidebook, p. 275-283. Sonderegger, J. L., Pump test of MacMillan Well: Montana Bureau of Mines and Geology, in house publication. j Sonderegger, J. L., and Zaluski, Marek, 1983, Ennis geothermal system fracture porosity â&#x20AC;&#x201D; An overthrust effect [abs., AAPG Rocky Mountain Section meeting, Billings, Montana, September 18-21, 19831: American Association of Petroleum Geologists Bulletin, V. 6_7, no. 8, p. 1356. Swanson, R. W., 1950, Geology of a part of the Virginia City and Eldrige quadrangles, Montana: U. S. Geological Survey Open-File report 51-4, 12 p. Talwani, M., and Ewing, M., 1960, Rapid computation of gravitational attraction of 3-D bodies of arbitrary shape: Geophysics, V. J25, no. 1, p. 203-225. Truesdell, A. H., and Fournier, R. 0., 1977, Procedure for estimating the temperature of a hot water component in a mixed water by using a plot of dissolved silica versus enthalpy: Journal of Research of U. S. Geol. Survey, V. _5, no. 1, p. 49-52. v Vitaliano, C. J., and Cordua, W. S. , 1979, Geologic map of the southern Tobacco Root Mountains, Madison County, Montana: Geol. Soc. of America Map and Chart Series MC-31, Scale 1:62,500. Williams, T. R., 1975, Geothermal potential in the Bearmouth area, Montana: Missoula, University of Montana, M.S. thesis, 80 p. ; Young, S. W., 1984, Structural history of the Jordan Creek area, northern Madison Range, Madison County, Montana: University of Texas at Austin, M.S. thesis, 110 p.


APPENDIX A

GRAVITY DATA AND CORRECTIONS All corrections are referenced to U.S. Coast and Geodetic Survey benchmark Y145 labeled as BM in the data.

Three surveys

were completed at separate dates, and these surveys are referred to as the VALLEY FLOOR, the JEFFERS, and the JACK CREEK RANCH surveys.

The VALLEY FLOOR survey includes stations collected on

two east-west lines located west of the Madison River, the JEFFERS survey includes staions located on the southernmost loop of stations, and the JACK CREEK RANCH survey includes stations located on the northernmost loop of stations.

See Figure 15 in

text.

See the next four pages for the survey data.


124

VALLEY FLOOR SURVEY

(LOCATIONS, ELEVATIONS, OBSERVED AND REDUCED GRAVITY)

STA BM 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

LAT (DEG) 45.3782 45.3782 45.3782 45.3782 45.3782 45.3782 45.3782 45.3782 45.3782 45.3782 45.3782 45.3782 45.3782 45.3782 45.3782 45.3782 45.3782 45.3763 45.3763 45.3763 45.3763 45.3763 45.3763 45.3763 45.3763 45.3763 45.3763 45.3763 45.3763 45.3763 45.3763 45.3763 45.3763

LONG (DEG) 1 11.7315 1 11.7301 1 11.7288 1 11.7274 1 11.7261 1 11.7247 1 11.7234 1 11.7220 1 11.7206 1 11.7193 1 11.7179 1 11.7166 1 11.7153 1 11.7139 1 11.7126 1 11.7112 1 11.7099 1 11.7099 1 11.7122 1 11.7126 1 11.7139 1 11.7153 1 11.7166 1 11.7179 1 11.7193 1 11.7206 1 11.7220 1 11.7234 1 11.7247 1 11.7261 1 11.7274 1 11.7288 1 11.7301

OBS. GRV. (MGALS) 196.558 195.980 196.039 195.796 195.914 196.215 195.892 195.409 195.132 194.704 194.365 193.999 193.487 193.150 192.768 192.375 192.053 191.962 192.337 192.745 193.074 193.537 193.867 193.990 194.759 195.053 195.473 195.742 196.149 195.194 195.396 195.822 196.305

ELEV. (M. ) 1492.2 1491.9 1492.0 1492.0 1484.9 1484.9 1484.8 1484.4 1484.3 1484.6 1484.5 1484.5 1484.5 1484.1 1484.0 1483.6 1483.2 1484.5 1484.8 1485.2 1485.3 1485.4 1485.8 1485.3 1485.4 1485.8 1486.1 1486.1 1486.1 1492.1 1491.6 1491.6 1492.2

RED. GRV. 0.00 -0.56 -0.51 -0.74 -2.04 -1.77 -2.14 -2.72 -3.04 -3.44 -3.80 -4.19 -4.71 -5.14 -5.56 -6.04 -6.46 -6.18 -5.76 -5.29 -4.94 -4.48 -4.07 -4.04 -3.26 -2.90 -2.43 -2.15 -1.75 -1.53 -1.48 -1.06 -1.06

-186.65 -187.21 -187.16 -187.39 -188.69 -188.42 -188.79 -189.37 -189.69 -190.09 -190.45 -190.84 -191.36 -191.79 -192.21 -192.69 -193.11 -192.83 -192.41 -191.94 -191.59 -191.13 -190.72 -190.69 -189.91 -189.55 -189.08 -188.80 -188.40 -188.18 -188.13 -187.71 -187.71


VALLEY FLOOR SURVEY (CORRECTIONS-MGALS)

STA

ELEV

TERRAIN

LAT.

CURV.

DRIFT

BM 1 2 BM

0.00 -0.09 -0.07 0.00

1.48 1.48 1.47 1.48

-2.60 -2.60 -2.60 -2.60

-1.40 -1.40 -1.40 -1.40

-0.13 -0.02 -0.04 0.00

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 BM

-0.08 -1.48 -1.48 -1.49 -1.56 -1.58 -1.54 -1.55 -1.55 -1.55 -1.62 -1.64 -1.72 -1.80 -1.55 -1.50 -1.42 -1.39 -1.38 -1.30 -1.39 -1.37 -1.30 -1.24 -1.24 -1.24 -0.06 0.00

1.47 1.47 1.46 1.46 1.45 1.45 1.44 1.44 1.43 1.43 1.42 1.42 1.41 1.41 1.40 1.40 1.40 1.40 1.40 1.41 1.42 1.42 1.43 1.43 1.43 1.44 1.45 1.48

-2.60 -2.60 -2.60 -2.60 -2.60 -2.60 -2.60 -2.60 -2.60 -2.60 -2.60 -2.60 -2.60 -2.60 -2.43 -2.43 -2.43 -2.43 -2.43 -2.43 -2.43 -2.43 -2.43 -2.43 -2.43 -2.43 -2.43 -2.60

-1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40

-0.02 -0.04 -0.06 -0.09 -0.11 -0.13 -0.14 -0.15 -0.16 -0.17 -0.18 -0.20 -0.20 -0.21 -0.25 -0.26 -0.28 -0.29 -0.30 -0.31 -0.32 -0.33 -0.34 -0.35 -0.35 -0.36 -0.38 -0.40

30 31 32 BM

-0.15 -0.15 -0.03 0.00

1.45 1.46 1.47 1.48

-2.43 -2.43 -2.43 -2.60

-1.40 -1.40 -1.40 -1.40

-0.44 -0.45 -0.48 -0.52


JEFFERS LOOP SURVEY (LOCATIONS, ELEVATIONS, OBSERVED AND REDUCED GRAVITY) STA

LAT (DEG)

BM 45.3782 33 45.3792 34 45.3808 35 45.3825 36 45.3826 37 45.3826 38 45.3827 39 45.3824 40 45.3807 41 45.3790 42 45.3772 43 45.3754 44 45.3750 45 45.3749 46 45.3766 47 45.3784

LONG (DEG)

OBS. GRV. (MGALS)

LI 1.7315 ]111.6832 ][11.6832 1L11.6831 ]L11.6857 ]LI 1.6882 L11.6908 ]111.6935 ]111.6943 ]L11.6944 ]L11.6943 ]L11.6943 ]L11.6922 ]L11.6897 1L11.6863 ]LI 1.6863

196.804 187.208 187.607 187.971 188.464 188.862 189.420 189.704 189.209 189.031 188.660 188.251 188.131 187.857 187.718 187.856

ELEV. (M.) 1492.2 1493.3 1494.0 1496.3 1498.0 1499.8 1500.5 1500.0 1499.1 1498.6 1497.7 1497.1 1495.6 1494.9 1494.7 1494.4

RED. GRV. 0.00 -9.57 -9.15 -8.79 -7.87 -7.17 -6.30 -5.89 -6.36 -6.54 -6.86 -7.30 -7.49 -8.00 -8.41 -8.51

-186.65 -196.22 -195.80 -195.44 -194.52 -193.82 -192.95 -192.54 -193.01 -193.19 -193.51 -193.95 -194.14 -194.65 -195.06 -195.16

JACK CREEK RANCH SURVEY (LOCATIONS, ELEVATIONS, OBSERVED AND REDUCED GRAVITY) STA

LAT (DEG)

BM 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63

45.3782 45.3676 45.3676 45.3676 45.3641 45.3606 45.3569 45.3533 45.3494 45.3493 45.3494 45.3491 45.3532 45.3568 45.3604 45.3639 45.3644

LONG (DEG) 1 11.7315 1 11.6942 1 11.6979 1 11.7013 1 11.7027 1 11.7033 1 11.7038 1 11.7046 1 11.7046 1 11.6992 1 11.6944 1 11.6887 1 11.6887 1 11.6884 1 11.6888 1 11.6890 1 11.6936

OBS. GRV. (MGALS) 185.201 174.550 175.125 176.017 175.417 174.461 173.286 171.949 170.914 168.263 166.673 165.324 167.121 169.483 170.975 172.653 173.525

ELEV. (M.) 1492.2 1491.9 1492.4 1491.6 1494.5 1497.2 1499.4 1501.5 1503.3 1505.0 1505.6 1505.0 1501.6 1498.1 1495.7 1493.9 1493.7

RED. GRV.

0.00 -9.90 -9.25 -8.57 -8.30 -8.47 -8.86 -9.41 -9.71 -12.01 -13.41 -15.15 -14.33 -12.35 -11.69 -11.00 -10.28

-186.65 -196.55 -195.90 -195.22 -194.95 -195.12 -195.51 -196.06 -196.36 -198.66 -200.06 -201.80 -200.98 -199.00 -198.34 -197.65 -196.93


JEFFERS LOOP SURVEY (CORRECTIONS-MGALS) STA

ELEV

TERRAIN

LAT.

CURV.

DRIFT

BM 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

0.00 0.04 0.19 0.32 0.78 1.10 1.45 1.60 1.49 1.33 1.22 1.04 0.92 0.64 0.46 0.39

1.48 1.57 1.58 1.59 1.57 1.55 1.51 1.47 1.46 1.46 1.45 1.44 1.46 1.50 1.55 1.55

-2.60 -2.70 -2.84 -2.99 -3.00 -3.00 -3.00 -2.98 -2.83 -2.68 -2.51 -2.35 -2.32 -2.31 -2.46 -2.62

-1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40

0.00 D R I F T

BM

0.00

1.48

-2.60

-1.40

N E G L I G A B L E 0.02

LAT.

CURV.

DRIFT

JACK CREEK RANCH SURVEY (CORRECTIONS-MGALS)

STA

ELEV

TERRAIN

BM 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63

0.00 -0.10 0.01 -0.16 0.43 0.94 1.38 1.80 2.16 2.47 2.59 2.48 1.82 1.12 0.65 0.30 0.25

1.48 1.38 1.35 1.30 1.27 1.24 1.26 1.30 1.33 1.37 1.44 1.50 1.50 1.50 1.46 1.46 1.40

-2.60 -1.65 -1.65 -1.65 -1.34 -1.03 -0.70 -0.38 -0.03 -0.03 -0.03 -0.37 -0.69 -0.37 -0.69 -1.33 -1.37

-1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40 -1.40

0.00 D R I F T

BM

0.00

1.48

-2.60

-1.40

0.08

N E G L I G A B L E


APPENDIX B

FORTRAN CODE OF PROGRAMS GRAVBL, GINDEP, AND 3D

B.l

CODE FOR PROGRAM GRAVBL

B.2

CODE FOR PROGRAM GINDEP

B.3

CODE FOR PROGRAM 3D


129

B.l

FORTRAN CODE OF PROGRAM GRAVBL:

A 3-D FORWARD GRAVITY MODELING PROGRAM USING BLOCKS (MAX.=100) OF EARTH


c c C... GRAVBL IS A FORWARD GRAVITY PROGRAM C... THAT MODELS THE EARTH BY USING BLOCKS C (UP TO 500) OF VARIABLE DENSITY. C C

c C. . VARIABLE I.T ST C C C. .(JKOMKTUY VARI ABLKS C ** ALL DISTANCE UNITS IN METERS ** c

C C . NBLKS = NUMBER OF BLOCKS IN MODEL J-L.NBL.KS C . XL(J) = LEFT (OR MIN. X) EDGE OF BLOCK J C XR(J) = RIGHT (OR MAX. X) EDGE OF BLOCK J C . ZU(J) = TOP (OR MIN. Z, Z POS. DOWN) C... EDGE OF BLOCK J C . ZD(J) = BOTTOM (OR MAX. Z, Z POS. DOWN) C EDGE OF BLOCK J C -WHERE ZU AND ZD ARE THE POSITIVE DISTANCE C DOWN FROM THE DATUM ELEVATION CONSIDERING C THE DATUM ELEVATION ZERO C C . LAMNUM(J) = NUMBER OF LAMINAE USED TO FORM C BLOCK J C . Y(I,J) = Y POSITION OF LAMINAE I ON BLOCK J C. . 1=1 ,LAMNUM(J) C . DEN(J) = DENSITY OF BLOCK J C C C..GRID VARIABLES C (PREDICTED GRAVITY AS OBSERVED FROM GRID) c

C C. C. C. C. C. C C. C. C C C C.

XSIZE = SIZE OF GRID IN X-DIRECTION YSIZE = SIZE OF GRID IN Y-DIRECTION COLS - NUMBER OF COLUMNS IN GRID ROWS - NUMBER OP ROWS IN GRID ELEV(I) - ELEVATTON OF GRID POINT I -- READ IN FROM SURFII SAVED FILE DATELV = DATUM ELEVATION XPOS.YPOS - CURRENT X,Y POS. OF OBSKRVAT I ON ON GRID CALCULATION VARIABLES

c

C C . ANOM(l.J) - ANOMALY CALCULATED FOR C LAMINAE I OF BLOCK J


131

. V ( J ) = ANOMALY OF BLOCK J R E S U L T I N G FROM A Q U A D R I T U R E F O R M U L A SUMMATION OF THE C O N T R I B U T I O N S OF EACH L A M I N A E IN BLOCK J . T A N O M ( J ) - V A R I A B L E USED FOR THE S U M M A T I O N OF THE C O N T R I B U T I O N S OF EACH BLOCK IN THE MODEL AT O B E R S E R V ATION POINT X P O S . Y P O S ON THE G R I D . T A N O M ( N B L K S ) IS T H E R E F O R E THE TOTAL A N O M A L Y OF THE PRESENT M O D E L AT O B S E R V A T I O N POINT X I'OS , Y I'd «i ON Till" C P I D .

MISCELLANEOUS

VARIABLES

. MP » VALUE THAT C O N T R O L S HOW MANY BE USED TO DEFINE A BLOCK.

LAMINAE

WILL

COMMON /GRAV/MP,XSIZE,YSIZE,COLS.ROWS,XL(500) , XR(500),ZD(500),ZU(500),DEN(50O),Y(500,500), ELEV(500),LAMNUM(500),V(500),ANOM(5O0,500), NBLKS.XPOS,YPOS,TANOM(500),M1,YMAX(500) CHARACTER*20 MODEL

FILENAME

INPUT

OPEN(22,FILE='GRAVBL.DAT',STATUS='OLD') OPEN( 23 , FILE=»'GBL. DAT' , S T A T U S " ' NEW ' ) OPEN ( 24 ,FILE<= 'GEOM. DAT ', S T A T U S - ' NEW' ) W R 1 T E ( 2 4 , '( ' ' BLOCK YMIN YMAX WRITE(24,'(''

XL XR DEN * ' ) * )

ZU

ZD

. )- )

READ(22,*)NBLKS DO J=l,NBLKS READ(22,*)XL(J),XR(J),ZU(J),ZD(J),Y(1,J),Y(2,J), &DEN(J) YMAX(J)-Y(2,J) WR1TE( 24 , ' ( 14 , 7 F 1 0 . 1 ) * ) J , XL( J ) , XR ( .J ) , ZU( J ) , Z D( J ) &,Y( 1 ,J) , Y ( 2 , J ) , D E N ( J ) END DO READ(22,*)XSIZE,YSIZE,COLS,ROWS READ(22,*)MP . . INPUT

FOR T O P O G R A P H Y :

READ(22,*)LL IF(LL.EQ.1)TH

EN

IF WANT T O P O G R A P H Y ELSE SET LL .NE. 1

SET

LL=1


132

C C... READ DATUM ELEVATION C READ(22,*)DATELV C C... ENTER FILENAME OF SAVED SURFII DATA FILE C... CONTAINING GRID LOCATIONS AND GRID POINT C... ELEVATIONS C C READ(22 , '(A2 0)' )FILENAME C OPEN(27,FILE=FILENAME,STATUS='OLD',FORM='UNFORMATTED', &ACCESS='SEQUENTIAL* ) C C C... READ IN FIRST RECORD C

READ(27)NCOLS,NROWS,IZRRO C C C... READ IN SECOND RECORD C READ(2 7)IROWS,JCOLS,DIFY,DIFX,XMN,XMX,YMN, &YMX,DUMMY C C... READ IN ELELVATIONS (METERS) C DO I=NROWS,l,-1 IBEG=(I-1)*NCOLS+l IEND-IBEG+NCOLS-1 READ(27)(ELEV(J),J=IBEG,IEND) END DO C DO 1=1,NROWS*NCOLS ELEV(I)=ELEV(I)-DATELV END DO C C DO J=l ,NBLKS ZU(J)=ZU(J)+ELEV(1) ZD(J)-ZD(J) + ELEV( 1) END DO C END IF C DO 1-1,NBLKS CALL REORDER(I) C C... MAKE SURE LAMNUM(l) IS AN ODD NUMBER SO C... THAT QUADR1TIJRE FORMULA WILL WORK C L]=LAMNUM(I)/2 Tl-(LAMNUM(I)/2.)-Ll


133

IF(LAMNUM(I).GT.2)THEN XF(T1.EQ.O.O)THEN Y(LAMNUM(I)+1,I)=Y(LAMNUM(I),I) Y(LAMNUM(I),I)=Y(LAMNUM(I),I)-1

CALL FORWARD(LAMNUM(I),1) LAMNUM(I)=LAMNUM(I)+1 END IF END IF PRINT *,I,' LAMNUM=',LAMNUM(I) END DO M1=0 M-l CHECK-0.0 XDELTA=XSIZE/(COLS-l ) YDELTA=YSIZE/(ROWS-l) PRINT * PRINT *,'GRID INFORMATION (UNITS = METERS) ' PRINT * PRINT XSIZE=',XSIZE,'YSIZE=*,YSIZE COLS,'COLUMNS',',',ROWS,'ROWS' PRINT DIST. BETWN. COLS.=*,XDELTA PRINT DIST. BETWN. ROWS =',YDELTA PRINT * PRINT *

c 10

IF(M. XPOS-O.O YPOS-0.0 TANOM( 1 )-0.0

C DO J"2 .NBLKSH C CALL QUAD(J-1 ) TANOM( J)=»TANOM( J-1 )+V( ( (LAMNUM( J-1 )-l )/2)+l ) END DO WRITE(23, *(3F12.4) ' )XPOS,YPOS,TANOM(NBLKS+1) M-M+l GO TO 10 ELSE DO 1=1,C0LS*R0WS-1 CALL GRID(I.CHECK,XDELTA,YDELTA) DO J=2,NBLKS+1 C C C

, IF CHOSE TOPOGRAPHY LL=1 IF(LL.EQ.l)THEN ZU(J-1)=ZU(J-1)+ELEV(I+l)-ELEV(I) ZD(J-1) = ZD(J-1 ) + ELEV(I+l )-ELEV(I) END IF CALL FORWARD(1,J-1) DO K-2,LAMNUM(J-1 ) CALL FORWARD(K,J-1 ) END DO


CALL QUAD(J-1) TANOM(J)=TANOM(J-1)+V(((LAMNUM(J-1)-l)/2)+l) END DO WRITE(23,'(3F]2.4)')XPOS,YPOS f, ,TANOM( NBLKS+1 ) END DO END IF C CLOSR(22) CLOSE(23) C PRINT *,* PRINT *,* OUTPUT IN FILE GBL.DAT!' PRINT *,' ' CALL EXIT END C C Q* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

C C... SUBROUTINES C C C . SUBROUTINE REORDER DETERMINES HOW EACH C . BLOCK WILL BE CUT UP IN THE Y-DIRECTION. C . ENOUGH LAMINAE WILL BE INSERTED SO THAT C . THE GRAVITATION ATTRACTION BETWEEN C . ADJACENT LAMINAE DOES NOT VARY BY MORE C . THEN AN INPUT PERCENTAGE (DEF. BY VAR. MP). C SUBROUTINE REORDER(I) C COMMON /GRAV/MP,XSIZE,YSIZE,COLS,ROWS,XL(500) &,XR(500),ZD(500),ZU(500),DEN(50 0),Y(500,5 00), &ELEV(5 00),LAMNUM(5 00),V(500),AN0M(500,500),NBLKS ft ,XPOS,YPOS,TANOM(5 00) , Ml , YMAX( 5 00 ) G C C . CUT UP EACH BLOCK LAMNUM(I) TIMES C K1-ABS(Y(2,I)-Y( l . D ) R2-AB9(XR(1)-XL(I)) LAMNUM(I)=(K1*MP*(JMAX0(K1,K2)/JMIN0 &(K1,K2)))/100 IF(LAMNUM(I).LT.10)LAMNUM( I)= 1 0 C IF(LAMNUM(I).GE.500)LAMNUM(I)=49 7. C YDIST=K1/FLOAT(LAMNUM(I)) CALL F0RWARD(1,1) LAMNUM(I)=LAMNUM(I)+l DO K=2,LAMNUM(I) Y(K,I)-Y(K-1 . D + YDIST CALL FORWARD(K.I)


135

END DO C RETURN END C C C... SUBROUTINE FORWARD CALCULATES THE GRAVITY C... ANOMALY/UNIT WIDTH FOR EACH LAMINAE I IN BLOCK J C SUBROUTINE FORWARD(I.J) C COMMON /GRAV/MP,XSIZE,YSIZE,COLS,ROWS,XL(500), &XR(500),ZD(500),ZU(500),DEN(500),Y(500,500), &ELEV(500),LAMNUM(500),V(5 00),ANOM(500,500) , &NBLKS ,XPOS,YPOS,TANOM(5 00),M1 ,YMAX(5 00) C C GO-6.6 7E-8 C C START CALCULAT1N' C C... PREVENT DIVIDE BY ZERO C IF(XR(J).EQ.O.O)XR(J)=lE-20 IF(XL(J).EQ.0.0)XL(J)=lE-20 IF(Y(I,J).EQ.0.0)Y(I,J)=lE-20 C AO=(ZD(J)*ZD(J))+(Y(I,J)*Y(I,J)) B«(ZU(J)*ZU(J))+(Y(I,J)*Y(I,J)) A1=XL(J)+SQRT((XL(J)*XL(J))+B) A2=XR(J)+SQRT((XR(J)*XR(J))+B) B1=XR(J)+SQRT((XR(J)*XR(J))+AO) B2=*XL( J) + SQRT((XL(J)*XL(J))+A0) C 1F((A1.EQ.O.O).OR.(A2.EQ.O.O).OR.(B1.EQ.O.O) &.OR.(B2.EQ.O.O))M1=M1+1 C C... PREVENT TAKING LOG OF 0.0 OR NEGATIVE NUMBER C IF(A1.LE.0.0)A1-.001 IF(A2.LE.0.0)A2«.001 IF(B1.LE.0.0)B1«.001 IF(B2,LE.0.0)B2».00l IF((Al.EQ.0.001).OR.(A2.EQ.0.001).OR.(Bl.EQ.0.001) &.OR.(B2.EQ.0.001))THEN PRINT *,*HAVE HIT A ZERO OR NEGATIVE NUMBER; &THIS NUMBER HAS BEEN CHANGED TO .00 1 SO THAT &TAKING ITS LOG IS POSSIBLE.* PRINT *,'YOU MAY WANT TO CHANGE THE GEOMETRY &0F BLOCK : » ,J END IF C C... THE 100000 IS TO GET THE ANOMALY IN UNITS OF MGALS C


ANOM(I ,J ) = -l00000.*G0*DEN(J)*(L0G(A1 ) &+LOG(Bl)-LOG(A2)-LOG(B2)) C RETURN END C C C... C C

SUBROUTINE GRID GIVES X,Y GRID POSITIONS SUBROUTINE GRID(KOUNT,CHECK,XDELTA,YDELTA)

C COMMON /GRAV/MP,XSIZE,YSIZE,COLS,ROWS,XL(500), &XR(50O),ZD(5OO),ZU(50O),DEN(500),Y(500,500), &ELEV(5 00),LAMNUM(5 00),V(500),ANOM(5 00,500), &NBLKS,XPOS,YPOS,TAN0M(500),M1,YMAX(500) C NI=KOUNT/COLS XPOS=KOUNT*XDELTA-(NI*XSIZE+XDELTA*NI) IF(ABS(XPOS).LE.1 .OE-0 1 )XPOS = 0.OOE + 00 YPOS-NI*YDELTA I F ( X S IZ E . G T . C H E C K ) T H E N

CHECK-CHECK+XDELTA DO J«I,NBLKS XL(J)»XL(J)~XDELTA XR(J)=XR(J)-XDELTA END DO ELSE CHECK="0.0 DO J-1,NBLKS C XL(J)=XL(J) + XDELTA*(C0LS-1 ) XR(J)=XR(J)+XDELTA*(C0LS-1) C DO 1=1,LAMNUM(J) Y(I, J) = Y(I,J)-YDELTA END DO END DO END IF RETURN END C C C... C... C... C... C C

SUBROUTINE QUAD CALCULATES THE ANOMALY ASSOCIATED WITH EACH BLOCK K BY DOING THE INTEGRATION IN THE Y-DIRECTION USING THE QUADRATURE FORMULA TALWANI USED. SUBROUTINE QUAD(K)

C COMMON /GRAV/MP,XSIZE.YSIZE,COLS,ROWS,XL(500), &XR(500) ,ZD(500),ZU(500),DEN(500),Y(500,500), &ELEVC500) ,LAMNUM(500) ,V(5()0) , ANOM( 500 , 500 ) ,


& NBLKS, XPOS , YPOS,TANOM(50(.l) , Ml , YMAX(5O0) C DIMENSION TEMP(500) C C. . . FIND THE ANOMALY C IF(LAMNUM(K)-1.GT.1)THEN 1=1 V(1 )=0.0 DO J=2,((LAMNUM(K)-l)/2)+l C A0=ANOM(I,K)*((Y(I,K)-Y(I+2,K))/(Y(I,K)&Y(I+1,K)))*(3.0*Y(1+1,K)-Y(I+2,K)-2.0*Y(I,K)) C B=AN0M(I+1,K)*((Y(I,K)-Y(I+2,K))**3)/(( &Y(I+1,K)-Y(I+2,K))*(Y(I+1,K)-Y(I,K))) C C=AN0M(I+2,K)*((Y(I,K)-Y(I+2,K))/(Y(I+2,K) &-Y(I+l,K)))*(3.0*Y(I+l,K)-Y(I,K)-2.*Y(I+2,K)) C TEMP(J-1)=(A0+B+C)/6.0 C V(J)-V(J-1)+TEMP(J-1) 1=1+2

END DO C ELSE C C... C

TRAPEZOIDAL RULE FOR ONE AREA

V(((LAMNUM(R)-l)/2)+l)»(Y(2,K)-Y(l,K))*.5 &*(ANOM(I,K)+ANOM(2,K)) END IF C RETURN END


B.2

FORTRAN CODE OF PROGRAM GINDEP:

A 3-D GRAVITY MODELING PROGRAM THAT INVERTS ON MAXIMUM DEPTHS OF BLOCKS OUTPUT FROM PROGRAM GRAVBL


139

C C... PROGRAM GINDEP IS AN INVERSE GRAVITY C... MODELING PROGRAM THAT PREDICTS LOWER C... BLOCK DEPTHS THAT WILL GIVE A BEST FIT C... TO OBSERVED GRAVITY DATA BASED ON FORWARD C... MODELING THAT USES UP TO 100 RECTANGULAR C... BLOCKS OF EARTH. RIDGE REGRESSION, C... WEIGHTING AND SCALING ARE USED C £********************************************** C C. VARIABLE LIST C C C . GEOMETRY VARIABLES C ** ALL DISTANCE UNITS IN METERS ** c

C C. C. C. C. C C.. C C C C C C C. C. C. C G C. C

NBLKS XL(J) XR(J) ZU(J)

= =

NUMBER OF BLOCKS IN MODEL J-1,NBLKS LEFT (OR MIN. X) EDGE OF BLOCK J RIGHT (OR MAX. X) EDGE OF BLOCK J TOP (OR MIN. Z, Z POS. DOWN) EDGE OF BLOCK J ZD(J) - BOTTOM (OR MAX. Z, Z POS. DOWN) EDGE OF BLOCK J -WHERE ZU AND ZD ARE THE POSITIVE DISTANCE DOWN FROM THE DATUM ELEVATION CONSIDERING THE DATUM ELEVATION ZERO LAMNUM(J) = NUMBER OF LAMINAE USED TO FORM BLOCK J Y(I,J) - Y POSITION OF LAMINAE I ON BLOCK J 1=1 ,LAMNUM( J) DEN(J) - DENSITY OF BLOCK J GRID VARIABLES (PREDICTED GRAVITY AS OBSERVED FROM GRID)

c

C C.. C. C. C. C. C C. C. C C C C.

XSIZE - SIZE OF GRID IN X-DIRECTION YSIZE = SIZE OF GRID IN Y-DIRECTION COLS = NUMBER OF COLUMNS IN GRID ROWS « NUMBER OF ROWS IN GRID ELEV(I) = ELEVATION OF GRID POINT I — READ IN FROM SURFII SAVED FILE DATELV - DATUM ELEVATION XPOS.YPOS - CURRENT X,Y POSITION OF OBSERVATION ON GRID CALCULATION VARIABLES

c

C C . ANOM(I.J) = ANOMALY CALCULATED FOR LAMINAE I


140

C

OF

BLOCK J

C . V(J) = ANOMALY OF BLOCK J RESULTING FROM A C QUADRITURE FORMULA SUMMATION OF THE C CONTRIBUTIONS OF EACH LAMINAE IN BLOCK J C C . TANOM(J) = VARIABLE USED FOR THE SUMMATION OF C THE CONTRIBUTIONS OF EACH BLOCK IN C THE MODEL AT OBERSERVATION POINT XPOS, C YPOS ON THE GRID. TANOM(NBLKS) IS C THEREFORE THE TOTAL ANOMALY OF THE C PRESENT MODEL AT OBSERVATION C POINT XPOS,YPOS ON THE GRID. C C C . MISCELLANEOUS VARIABLES c

C C». C C

MAXPER »

VALUE THAT CONTROLS HOW MANY LAMINAE WILL BE USED TO DEFINE A BLOCK.

COMMON /GRAV/XL(L0O),XR(lO0),ZDd00,10O),ZU(lOO), &I)EN(100),Y(500,500),NBLKS, XSIZE.YSIZE.NCOLS, &NROWS,YMAX(5OO),YMIN(50O),MAXPER,LAMNUM( 5 00), &XP0S,YPOS,AN0M(500,500),V(500),ELEV( 500) C COMMON /CBGINV/NDAT.NPARMS,KEPTRK,IA,IB,IC,LL,KVAR C CHARACTER CHARM C DIMENSION A(500,500),DPRED(500,500),DAMP(100), &NF(50) C DIMENSION WDEP(250,250),DELT(400,1),DOBS(400), &SQE(20,1),WS(250,250),WKAREA(10500),C(250,250), &GINV(250,250),DELTM(2 50,1),DELTN(250,1),SQEN(20,1), &ERR(2 0,1),COVM(2 5 0,2 50),SIGMAM(250),CA(250,250), &D(250,2 50),WSS(250,250),WERR(250,250) C CHARACTER*20 FILENAME,FILNAM £**AAAA*********************AAA AAA*AA A****************

C C C C

INPUT MODEL DATA FOR FORWARD PROGRAM DATA IN COMAND FILE G.DAT

OPEN(26,FILE='G.DAT' ,STATUS=* OLD' ) C C... READ FILENAME OF SAVED SURFII GRIDF1LE C READ(26,'(A20)')FILENAME READ(26,*)TDEPL READ(26,*)TDEPH C C... READ NUMBER OF BLOCK(S) TO FIX AT DEPTH GIVEN C... IN THE FOWARD MODEL


141

C READ(26,*)NUMFIX IF(NUMFIX.GT.0)READ(2 6,*)(NF(I),1=1.NUMFIX) C READ(26,*)NBLKS DO J=l,NBLKS READ(26,*)XL(J),XR(J),ZU(J),ZD(J,1),Y(1,J), &Y(2,J),DEN(J) YMIN(J)=Y(1,J) YMAX(J)=Y(2,J) END DO READ(26,*)MAXPER C C C

INPUT DATA FOR INVERSION READ(26,*)RATIO READ(26,*)STDDEV READ(26,*)ITMAX

C C... IF WANT TOPOGRAPHY SET LL=1, ELSE SET LL .NE. 1 C READ(26,*)LL IF(LL.EQ.1)THEN C C C***A**AA***ft**A*AAA**********AA****A*******AA**AAA

C C INPUT FOR TOPOGRAPHY C C... INPUT DATAUM ELEVATION FOR SURVEY C READ(26,*)DATELV C CAA****AAAAAAA***AAAA*****AAA***********************

C C C INPUT - ELEVATION OF OBSERVATION POINTS (GRAVITY C STATIONS) FROM SAVED SURFII GRIDFILE C C... ENTER FILENAME OF SAVED SURFII GRIDFILE C READ(26,'(A2 0)')FILNAM C OPEN(28 ,FILE = FILNAM,STATUS='OLD* ,FORM='UNFORMATTED' &,ACCESS='SEQUENTIAL') C C C... READ IN FIRST RECORD C READ(28)NCOLS,NROWS,IZERO C C... READ IN SECOND RECORD C READ(28)IROWS.JCOLS,DIFY,DIFX,XMN,XMX,YMN,YMX,DUMMY


c C... READ IN ELEVATIONS C DO I-NROWSJ ,-1 IBEG=(1-1 )*NCOLS+l IEND=IBEG+NCOLS-l READ(28)(ELEV(J),J=I BEG,IEND) END DO C DO 1=1 ,NCOLS*NROWS ELEV(I)=ELEV(I)-DATELV END DO C END IF C C C**AA**AAAAAAAA*ft**********AA***AA*AAAAAAAAAA*

C C INPUT-OBSERVED GRAVITY DATA C FROM SAVED SURFII GRIDFILE C C C... ENTER FILENAME OF SAVED SURFII DATA FILE C. . . IN FILE G.DAT C OPEN(27,FILE=FILENAME,STATUS='OLD*,FORM= &'UNFORMATTED' ,ACCESS*'SEQUENTIAL * ) C C C... READ IN FIRST RECORD G

READ(27)NCOLS,NROWS,IZERO C C... READ IN SECOND RECORD C READ(2 7 )IROWS,JCOLS,DIFY,DIFX,XMN,XMX,YMN,YMX, &DUMMY C C... READ IN OBS DATA C DO I=NROWS,l,-l IBEG»(I-1 )*NCOLS+l IEND=IBEG+NCOLS-l READ(2 7)(DOBS(J),J=IBEG,I END) END DO C XSIZE=ABS(XMX-XMN) YSIZE-ABS(YMX-YMN) C CLOSE(27) NDAT=NCOLS*NROWS C NPARMS=NBLKS


OPEN(16 ,FILE='GINDEP.OUT* ,STATUS='NEW' ) WRITE(16,'(*' *')') WRITE(16 ' ( ' * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * &************AAAAAAA********AAAft***AA'•)•)

WRITE(16,'(* * WRITE(16,'(*' WRITE(16, *( ' ' WRITE ( 16, '( ' '

'')') GRID INFO'')') ' ' )* ) . . ). )

&

WRITE(16,'(''$GRID SIZE IN X DIRECTION &(METERS)='',E12.4)')XSIZE WRITE(16,'(''$GRID SIZE IN Y DIRECTION &(METERS)='*,E12.4)')YSIZE WRITE(16,'( ' *$NUMBER OF COLUMNS''',I 3)*)NCOLS WRITE(16, '( * '$NUMBER OF ROWS=' ' ,13 ) ' )NROWS WRITB( 16 , '( ' ' &

..).

)

WRITE(16,'( * ' WRITE(16,'(''

' ' )' )

WRITE( 16, '( ' ' WRITE(16,*('' WRITE(16, '( ' ' WRITE(16,'(*'

' ' ) ' ) INPUT MODEL'')') ' ' )')

&

' ' )' )

. . ). )

&

WRITE(16,*(*' BLOCK # XMIN XMAX &YMIN YMAX ZMIN ZMAX DENSITY'*)') DO J = l ,NPARMS WRITE(16,'(3X,I3,2X,F7.1,2X,F7.1,2X,F7.1,2X,F7. &2X.F7.1 ,2X,F7.1 ,2X,F7.2) ' ) &J,XL(J),XR(J),Y(1,J),Y(2,J),ZU(J),ZD(J,1),DEN(J) END DO WRITE(16 '(''A********************************* &AAAA************AAAAAAAAAA********'')')

WRITE(16,'(''

'')')

WRITE(16,'( * ' ' ' )* ) WRITE(16 ' ( ' * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * $,************************************ ' ' ) ' )

WRITEd6,'('* '')') WRITE(16,'('' TABLE OF CONVERGENCE*')') WRITE(16,'('' '')') WRITE(16 , '( ' ' . • )- )

&

CLOSE(28) IF(LL.EQ.1)THEN DO J=»l , NBLKS ZU(J)=ZU(J)+ELEV(1) ZD(J,1 )-ZD(J,l) + ELEV( 1 ) END DO END IF


c c IA=250 IB=250 IC-250 CDAMP=.001 C KEPTRK=1 KOUNT-O KVAR=0 C CALL FWRD(A.DPRED) C 5

KOUNT-KOUNT+l IF(KOUNT.GT.ITMAX)THEN PRINT *,'MAXIMUM NUMBER OF ITERATIONS EXCEEDED & CONVERGENCE NOT OBTAINED' GO TO 20 END IF

C C. . . FIND A MATRIX C CALL DERIV(A) C C... FIND DEPTH WEIGHTING MATRTX C IF(RAT T 0.EQ.0.0)RAT 10=1 E-04 DO 1=1.NPARMS DO J=l , NPARMS 1F(t.EQ.J)THEN WDEP(I ,J)«( I./(ABS(ZD(J.KEPTRK))+10E-12) )+l. IF(ZD(J,KEPTRK).LT.TDEPL)THEN ZD(J,KEPTRK)=TDEPL DAMP( D-15E+1 ELSE IF(ZD(J,KEPTRK).GT.TDEPH)THEN ZD(J,KEPTRK)=TDEPH DAMP(I)=15E+1 END IF ELSE WDEP(I,J)=0.0 END IF END DO END DO C C... FIND A*WDEP*A(TRANSPOSE) MATRIX FOR NOISE C... WEIGHTING C CALL VMULFF(A,WDEP.NDAT,NPARMS,NPARMS,500, &IB,C,IC,IER) CALL VMULFP(C,A,NDAT,NPARMS,NDAT,IA,50 0, &WERR,IC.IER) C DO I-l.NDAT DO J=l,NDAT


IF(1.NE.J)WERR(I.,J) = 0.0 END DO END DO C CALL

VMULFM(A,WERR,NDAT,NPARMS,NDAT.500,

& 1B . C, I C , I ER )

CALL VMULFF(C,A,NPARMS,NDAT,NPARMS,[A, 15.500,WS, IC, IER) C C... SCALE THE A(TRANSPOSE)WA MATRIX FOR ONES C... ON THE DIAGONAL C DO 1=1.NPARMS DO J-1,NPARMS IF(I.EQ.J)THEN D(I,J)=1./(SQRT(WS(I,I))) ELSE D(I,J)=0.0 END IF END DO END DO C CALL VMULFF(D,WS,NPARMS.NPARMS.NPARMS,IA,IB, &CA,IC,IER) CALL VMULFF(CA,D,NPARMS,NPARMS,NPARMS,IA,IB, &WSS,IC,IER) C C... ADD THE "NOISE/SIGNAL" RATIO C DO 1=1.NPARMS WSS(I,I)=WSS(I,I)+RAT10*RATIO END DO C DO 1=1,NDAT DELT(I,1) = DOBS(I)-DPRED( I,KEPTRK) END DO C C. . . FIND ERROR C CALL VMULFM(DELT,DELT,NDAT,I,1,400,4 00, &SQE.20,IER) WRITE ( 16, * ( ' '$ ITERATION //' * , I 3 ) ' )KOUNT WRITE(16,'( ' '$STARTING DATA ERROR-' ' ,EI 2.4)' ) &SQRT(SQE( 1 , 1 )/(NDAT-NPARMS)) C C**A******** MARQUARDT LOOP ********************* C 10 IF(CDAMP.GE.100000)THEN WRITE(16,'(''DAMPING FACTOR HAS REACHED 100000 & - WILL NOT CONVERGE TO PRESENT INPUT DATA STD. &DEV. ' ' )' ) CALL EXIT END IF


146

LL=1 DO 1=1.NPARMS C IF(DAMP(I).NE.15E+1)DAMP(I)=CDAMP C IF(1.EQ.NF(LL))THEN DAMP(I)=1000. LL=LL+1 END IF C WSS(I,I)=WSS(I,I)+DAMP(I) C IF(ZD(I.KEPTRK).LT.TDEPL)THEN ZD(I,KEPTRK)=TDEPL DAMP(I)=15E+1 ELSE IF(ZD(J,KEPTRK).GT.TDEPH)THEN ZD(I,KEPTRK)=TDEPH DAMP(I)«15E+1 END IF END DO C C... FIND INVERSE OF WS C CALL LINV2F(WSS,NPARMS,IA,C,1,WKAREA,IER) C C... FIND GENERALIZED INVERSE GINV C CALL VMULFF(D,C,NPARMS,NPARMS,NPARMS,IA,IB, &CA,IC,IER) CALL VMULFF(CA,D,NPARMS,NPARMS,NPARMS,IA,IB, &C,IC.IER) CALL VMULFP(C,A,NPARMS,NPARMS,NDAT,I A,500, &CA.IC,IER) CALL VMULFF(CA,WERR,NPARMS,NDAT,NDAT,IA,IB, &GINV,IC,IER) C C... DELTM IS THE JUMP HOPEFULLY TOWARD A SOLUTION C CALL VMULFF(GINV.DELT,NPARMS,NDAT,1,IA,400, &DELTM,250,IER) C WRITE(16 , '( ' ' ' * )' ) WRITE(16,'('' BLOCK PARM. JUMP. NEW PARMS.'1)') C DO 1=1 .NPARMS 4 5 ZD(I.KEPTRK+1)=DELTM(I,1)+ZD(I,KEPTRK) C C... PRVENT FLAKY MODELS C C IF(ZD(I,KEPTRK+1).LE.ZU(I) )THEN DELTM(I , 1 ) = DELTM(I,1)/10 GO TO 45 END IF


147

c IF(ZD(I,KEPTRK).EQ.TDEPL.AND.DAMP(I) &.EQ.15E+1)THEN IF(DELTM(I,1).GT.O.O)DAMP(I)=CDAMP C ELSE IF(ZD(I,KEPTRK).EQ.TDEPH.AND.DAMP(I) &.EQ.15E+1)THEN IF(DELTM(I,1).LT.O.O)DAMP(I)=CDAMP END IF C WRITE(16,'(1X,I3,3X,E12.4,IX,E12.4)*)I, &DELTM(I,1),ZD(I,KEPTRK+1) END DO C WRITE( 16 , '( ' '$DAMPING (MARQUARDT) VALUE=* ' , E12.4 ) ' ) &CDAMP C C... NOW HAVE NEW PARAMS. C KEPTRK-KEPTRK+1 CALL FWRD(A.DPRED) C DO 1=1,NDAT DELTN(I , 1 )»DOBS( I)-DPRED(1 .KEPTRK) END DO C C... DO NEW PARAMS REDUCE ERROR? C CALL VMULFM(DELTN,DELTN,NDAT,1 ,1 ,IA, &IB.SQEN,20 , IER) WRITE( 16, '( ' '$NEW DATA ERROR=' ' , E 1 2 . 4 ) ' ) &SQRT(SQEN(l,l)/(NDAT-NPARMS)) C IF(SQEN(1,1 ).GE.SQE(I ,1))THEN C DO 1=1,NPARMS ZD(I,KEPTRK) = ZD(I,KEPTRK-1 ) END DO CDAMP-10.*CDAMP GO TO 1 0

ELSE 12 PERCENT=((SQRT(SQE(1,1)/(NDAT-NPARMS)) &-SQRT(SQEN(I,1)/(NDAT-NPARMS) ))/SQRT(SQE(1,1) &/(NDAT-NPARMS)))*100. C C... ERROR MUST BE IMPROVED BY AT LEAST ONE PERCENT FOR C... NEW ITERATION C IF(PERCENT.LT.1. )THEN CDAMP=10.*CDAMP

GO TO 10 END IF C SQE( 1 , 1) = SQEN(1,1)


CDAMP-CDAMP/10. DO 1=1, NDAT DELT( I , 1 ) = DELTN(I , I ) END DO END IF C C... CHECK TO SEE IF SOLN. IS WITHIN STD. DEV. C... OF DATA C CALL VMULFM(DELT,DELT,NDAT,1,1,400,400,ERR, &20,IER) CHIERR=( 1 ./(NDAT-NPARMS) )*ERR( 1 ,1 ) C C C IF(SQRT(CHIERR).LE.STDDEV)GO TO 20 WRITE(16,'('' '*)') GO TO 5 (]AA*AAA**** OUTPUT C 20 WRITE(16,'(''

******************************** . . ). )

WRITE(16, WRITE(16,

* ' )') •*************AAA*******AAAAAAAAAAAA

&**********'

WRITE(16, WRITE(16,

&*AA*A***A*'

)

" )*) *******************AAAAAAA*****AA***

' ')') WRITE(16, OUTPUT-PROGRAM GINDEP'')') WRITE( 16, " ) ' ) WRITE(16 , CALL VMULFP(GINV,GINV,NPARMS,NDAT,NPARMS,IA.IB, &C,IC.IER) DO 1=1 .NPARMS DO J=l,NPARMS COVM(I,J)=CHIERR*C(I,J) END DO END DO

DO 1=1, NPARMS SIGMAM(I)=SQRT(COVM(I,I)) END DO WRITE(16,'('* ")')

WRITE(16,'('' &

' ')' )

WRITE(16,'(''I WRITE(16,'('' &

ZD(I) +/- STD.DEV.'*)')

" )')

DO 1=1.NPARMS WRITE(16,'(1X,I2,3X,E10.3,2X,E10.3)') &I,ZD(I.KEPTRK).SIGMAM(I)


END DO WR1TE(16,'(*' &

")')

C WRITE(16 , '( ' * &

' * )' )

WRITE(16, '( ' 'SINPUT STD. DEV. = ' ' ,E12 . 4 ) ' )STDDEV WRITE(16,*(*'$CALC. DATA STD. DEV. = '*,E12.4)') &SQRT(CHIERR) WRITE(16,'(''SNUMBER OF ITERATIONS FOR SOLUTION = & ' ' ,13) ' )KOUNT WRITE( 16 , ' ( * ' &

• ')•)

C WRITE(16,'('* &

. .).)

WRITE(16,*(*' MODEL RESOLUTION MATRIX'')') CALL VMULFF(GINV,A,NPARMS,NDAT,NPARMS,IA,500,C, &IC.IER) WRITE(16 , '( * * * ' )' ) C IF(NPARMS.GT.15)THEN WRITE ( le.'dX.Al.llX.AlO^X.AS^X.AlO)')'!', &'...(1,1-2).. .','(1,1) * , '(1,1 + 2 ) . . . ' WRITE(16,'(1X,I3,1X,A1,22X,3F6.2,10X,A1)*) &1,' | ' ,(C(1 ,J),J=1 , 3 ) , ' | ' WRITE(16,'(1X,I3,1X,A1,16X,4F6.2,10X,A1)') &2,' | ' ,(C(2,J),J=1 , 4 ) , ' | ' DO 1=3,NPARMS WRITE(16,'(1X,I3,1X,A1,10X,5F6.2,10X,A1)')I,* | ' , &(C(I,J),J=I-2,I+2),' | ' IF(1+2.EQ.NPARMS)THEN WRITE(16,'(1X,I3,1X,A1,10X,4F6.2,16X,A1)*) &NPARMS-1 , ' | ' ,(C(NPARMS-1 ,J),J-NPARMS-3,NPARMS) , ' | ' WRITE(16,'(1X,I3,1X,A1,10X,3F6.2,22X,A1)') &NPARMS, ' | " ,(C(NPARMS,J),J=NPARMS-2,NPARMS), ' | ' GO TO 21 END IF END DO C ELSE C DO 1=1 .NPARMS WRITE(I6,'(1X,A1,<NPARMS>F6.2,2X,A1)')' |' ,(C(I,J) & , J-1 ,NPARMS), * | ' END DO C END IF C 21 &

WRITE(16, '( ' ' * ' )')

WRITE(16 , ' ( * ' &

_

' • )•)

WRITE( 16 , '( ' ' DATA RESOLUTION MATRIX'*)')


WRITE(16 , '( ' * ' ' )' ) CALL VMULFF(A,GINV,NDAT,NPARMS,NDAT,500,IB, &C,IC.IER) C IF(NDAT.GT.15)THEN WRITE(16,'(1X,A1,11X,A10,7X,A5,7X,A10)') & I , ...(1,1—2)... , &*(I,I)' , '(1,1 + 2 ) . . . ' WRITE(16,'(1X,I3,1X,A1,22X,3F6.2,10X,A1)*) &1 ,' | ' ,(C(1,J),J=1,3),' | ' WRITE(16,'(1X,I3,1X,A1,16X,4F6.2,10X,A1)*) &2,* | * ,(C(2,J),J=1 ,4),' | ' DO 1=3,NDAT WRITE( 16 , '(1X.I3,1X,A1 ,10X.5F6.2,10X,A1)' )I, ' | ' , &(C(I , J ) , J-l-2,1 + 2) , ' | ' IF(1+2.EQ.NDAT)THEN WRITE(16,'(1X,I3,]X,A1,10X,4F6.2,16X,A1)') &NDAT-J , * | * .(C(NDAT-) ,J),J=NDAT-3,NDAT), ' | * WRI.TE( 16 , ' ( 1X,I3,1X,A1 , i OX , 3 F6 . 2 , 22 X , A 1 ) ' ) &NDAT,' | ' ,(C(NDAT,J),J = NDAT-2 ,NDAT) , * | ' GO TO 2? END IF END DO C ELSE C DO 1 = 1 ,NDAT WRITE(16 , '(1X.A1,<NDAT>F6.2,2X,A1)')'|',(C(I,J) &,J=1 ,NDAT) , * j ' END DO C END IF C 2 2 W R I T E ( 1 6 , '( ' ' &

' ')' )

C WRITE(16, ' ( ' ' &

* ')')

WRITE( 16 , '( ' ' COVARIANCE MATRIX'')') WRITE( 16, '( ' ' ' * )* ) IF(NPARMS.GT.15)THEN WRITE(16,'(1X,A1,12X,A10,13X,A5,19X,A10)') &*I',*...(I,I-2)...','(I,I)*,'(I,I+2)...' WRITE(16, '(1X,I3,1X,A1,30X,3E10.2,10X,A1)') &1,* |',(COVM(l,J),J=l,3),'|' WRITE(16,'(1X,I3,1X,A1,20X,4E10.2,IOX,A1)') &2,'|',(C0VM(2,J),J=1,4),'|* DO 1=3,NPARMS WRITE(16,*(1X,I3,1X,A1,10X,5E10.2,10X,A1)')I,'|', &(COVM(I,J),J=I-2,I + 2) , ' | ' IF(1 + 2.EQ. NPARMS)THEN WRITE(16,'(1X,I3,1X,A1,10X,4E10.2,20X,A1)') &NPARMS-I,*|',(COVM(NPARMS-1,J),J-NPARMS-3.NPARMS),' WRITE(16,'(1X,I3,1X,A1,10X,3E10.2,30X,A1)')


f, N P A R M S , ' I ' ,(COVM( N P A R M S , J ) , J = NP A R M S - 2 , N P ARMS ) , ' | * GO TO 2 3 END IF END DO ELSE C DO 1 = 1 , N P A R M S WRITE(16,'(1X,A1,<NPARMS>E10.2,2X,A1)')'|', &(COVM(I,J),J=l.NPARMS),'|' END DO C END IF C 23 &

WRITE(16,'(*' ' ' )*)

C WRITE(16,*(*' ")•) WRITE(16,*('' CORRELATION MATRIX'1)') W R I T E ( 16 , *( ' ' ' ' )' ) DO 1=1.NPARMS DO J=l,NPARMS C(I,J)=COVM(I,J)/(SQRT(COVM(I,I)) &*SQRT(COVM(J,J))) END DO END DO C IF(NPARMS.GT.15)THEN WRITE(16,'(1X,A1,11X,A10,7X,A5,7X,A10)') & ' I' , ' . ..( 1,1-2). .. ' , ' (1,1)* , '( I ,1 + 2 ) . . . ' WR1TE(16,'(1X,I3,1X,A1,22X,3F6.2,10X,A1)') 61, ' | * ,(C(1,J),J=1 , 3 ) , ' | ' WRITE(16,'(1X,I3,1X,A1,16X,4F6.2,10X,A1)') 62, ' | ' ,(C(2,J),J=1 , 4 ) , ' | ' DO 1 = 3,NPARMS WRITE( 16,'(1X,I3,1X,A1,10X,5F6.2,10X,A1)')I,'|', &(C(I,J),J=I-2,I + 2 ) , ' | ' IF(1+2.EQ.NPARMS)THEN WRITE( 16,'(1X,I3,1X,A1,10X,4F6.2,16X,A1)') &NPARMS-1,'|',(C(NPARMS-1,J),J=NPARMS-3,NPARMS),'|' WRITE(16,'(1X,I3,1X,A1,10X,3F6.2,22X,A1)') &NPARMS, ' | ' ,(C(NPARMS,J),J = NPARMS-2.NPARMS), ' | ' GO TO 24 END IF END DO C ELSE C DO 1=1.NPARMS WRITE(16,'(1X.A1,<NPARMS>F6.2,2X,A1)')'|',(C(I,J) & ,J=1 .NPARMS), ' | ' END DO C END IF &


152

24

WRITE(16,'(' ************************************

&***************! I) I )

50

CLOSE(16) PRINT *,' OUTPUT IN FILE GINDEP.OUT.' CALL EXIT END

C C**AA*A****AAA*A********ft******AAA*AA**A*AAAAAA*AAAA

C

SUBROUTINES

c C... SUBROUTINE FWRD IS A FORWARD GRAVITY PROGRAM C... THAT MODELS THE EARTH BY USING BLOCKS (UP C... TO 100) OF VARIABLE DENSITY. C SUBROUTINE FWRD(A,DPRED) C COMMON /GRAV/XL(100),XR(100),ZD(100,100),ZU(100), &DEN(100),Y(500,5 00),NBLKS,XSIZE,YSIZE,NCOLS, &NR0WS,YMAX(500),YMIN(5 00),MAXPER,LAMNUM(500), &XPOS,YPOS,ANOM(5 00,500),V(500),ELEV(500) C COMMON /CBGINV/NDAT.NPARMS,KEPTRK,IA,IB,IC,LL,KVAR DIMENSION A(500,500),DPRED(500,500),B(250,1), &G(500,500) C M1=0 M=l CHECK-0.0 XDELTA-XSIZE/(NC0LS-1) YDELTA=YSIZE/(NR0WS-1) C IF(KEPTRK.EQ.1.AND.KVAR.NE.20)THEN DO 1=1,NBLKS CALL REORDER(I) C C... MAKE SURE LAMNUM(I) IS AN ODD NUMBER SO THAT C... QUADRATURE FORMULA WILL WORK C Ll=LAMNUM(I)/2 Tl=(LAMNUM(I)/2.)-Ll IF(LAMNUM(I).GT.2)THEN IF(T1.EQ.O.O)THEN Y(LAMNUM(I)+1,I)=Y(LAMNUM(I),1) Y(LAMNUM(I),I)=Y(LAMNUM(I),I)-1. CALL FORWARD(LAMNUM(I),1) LAMNUM(I)=LAMNUM(I)+1 END IF END IF END DO C 10 IF(M.EQ.1)THEN XPOS=0.0 YPOS=0.0


153

30

DO J=2,NBLKS+1 CALL QUAD(J-1) G( 1 , J-1) = V(((LAMNUM(J-1)-l)/2)+l) END DO M=2 GO TO 10 ELSE DO 1=1,NC0LS*NR0WS-1 CALL GRID(I,CHECK,XDELTA,YDELTA) DO J = 2 , NBLKS+1

C IF(LL.EQ.1)THEN ZU(J-]) = ZU(J-1) + ELF.V(I+1)-ELEV(I) ZD(J-l,KEPTRK)=ZD(J-l,KEPTRK)+ELEV(I+l)-ELEV(I) END IF C CALL FORWARD(I,J-1) DO K=2,LAMNUM(J-1) CALL

FORWARD(K,J-1)

END DO CALL QUAD(J-1) G(l + 1 ,J-1) = V(((LAMNUM(J-1)-1 )/2)+J ) END DO END DO C C. C

FIND THE A MATRIX IK KVAR-20 IF(KVAR.EQ.20)THEN DO 1=1,NDAT DO J=l,NPARMS A(I , J) = G(I,J)*DEN(J) IF(A(I,J).EQ.0.0)A(I,J)=1E-10 END DO END DO GO TO 7 END IF

C DO 1=1.NPARMS B(I,I )«=DEN(I) END DO C CALL VMULFF(G,B,NDAT,NPARMS,1,500,IB,DPRED, &500.IER) C DO 1=1,NDAT DPRED(I,KEPTRK) = DPRED(I , 1 ) END DO C 7 C

IF(KEPTRK.EQ.1)THEN GO TO 40 END IF IF(KK.EQ.2)G0 TO 40 END IF


1

ELSE C 20

KK=1 IF(KK.EQ.1)THEN XP0S=0.0 YPOS=0.0 DO J=2,NBLKS+1

C IF(LL.EQ.1)THEN ZU(J-1)=ZU(J-1)+ELEV(1) ZD(J-1,KEPTRK)=ZD(J-1,KEPTRK)+ELEV(1) END IF C CALL FORWARD(1,J-1) DO K=2,LAMNUM(J-1) CALL FORWARD(K,J-1) END DO CALL QUAD(J-l) G(1,J-1 ) = V(((LAMNUM(J-1 )-l )/2)+l ) END DO KK=2 GO TO 20 ELSE GO TO 30 END IF END IF C 40

DO J=l,NBLKS XL(J)=XL(J)+XSIZE XR(J)=XR(J)+XSIZE IF(LL.EQ.l)THEN ZU(J)=ZU(J)-ELEV(NROWS*NCOLS) ZD(J,KEPTRK)=ZD(J,KEPTRK)-ELEV(NROWS*NCOLS) END IF DO K=l,LAMNUM(J) Y(K,J)=Y(K,J)+YSIZE END DO END DO

C RETURN END C C C... C C

SUBROUTINES SUBROUTINE REORDER(I)

C COMMON /GRAV/XL(100),XR(100),ZD(100,100),ZU(100), &DEN(100),Y(500,500),NBLKS,XSIZE,YSIZE,NCOLS, &NROWS,YMAX(500),YMIN(5 00),MAXPER,LAMNUM(5 0 0 ) , &XPOS,YPOS,ANOM(5 00,5 00),V(5 00),ELEV(5 00)


COMMON &KVAR

/CBGINV/NDAT,NPARMS,KF.PTRK,IA,IB,IC,LL,

C K1=ABS(Y(2,I)-Y( 1,1)) K2 = ABS(XR(I)-XL( I)) LAMNUM(I) = (K1*MAXPER*( JMAX0(K1 ,K2)/ &JMINO(Kl,K2)))/100 C IF(LAMNUM(I).LT.10)LAMNUM(I)=10 C IF(LAMNUM(I).GE.5 00)LAMNUM(I)=49 7. C YDIST-K1/FLOAT(LAMNUM(I ) ) CALL FORWARD(1,1) LAMNUM(I)=LAMNUM(I)+1 DO K=2,LAMNUM(I)+1 Y(K,I)=Y(K-1,I)+YDIST CALL FORWARD(K.I) END DO C RETURN END C C C... SUBROUTINE FORWARD CALCULATES THE GRAVITY C... ANOMALY/UNIT WIDTH FOR EACH LAMINAE C SUBROUTINE FORWARD(I.J) C COMMON /GRAV/XL(100),XR(100),ZD(100,100),ZU(100), &DEN( 100),Y(500,500),NBLKS,XSIZE,YSIZE,NCOLS, &NROWS,YMAX(5 00),YMIN(5 00),MAXPER,LAMNUM(500 ) , &XPOS,YPOS,ANOM(5 00,500),V(500),ELEV(500) C COMMON /CBGINV/NDAT,NPARMS,KEPTRK,I A,IB,IC,LL & , KVAR C GO-O.0000000667 C C. . . START CALCULATIN' C C... PREVENT INSTABILITIES C IF(XR(J).EQ.0.0)XR(J)=1E-10 IF(XL(J).EQ.0.0)XL(J)=1E-10 IF(Y(I,J).EQ.0.0)Y(I,J)=1E-10 C C . FIND DERIVATIVE OF GRAVITY WRT ZD IF KVAR=20 C IF(KVAR.EQ.20)THEN C C1 = SQRT(XL(J)*XL(J) + ZD(J,KEPTRK)*ZD( J,KEPTRK) &+Y(I,J)*Y(I,J)) C2=SQRT(XR(J)*XR(J)+ZD(J,KEPTRK)*ZD(J,KEPTRK)


156

&+Y(I,J)*Y(I,J)) C AN0M(I,J)=((1./((XL(J)*C1)+(C1*C1)))-(l./((XR(J) &*C2)+(C2*C2))))*ZD(J,KEPTRK)*100000.*G0 C RETURN END IF C C AO=ZD(J,KEPTRK)*ZD(J,KEPTRK)+Y(I,J)*Y(I,J) B=ZU(J)*ZU(J)+Y(I,J)*Y(I,J) A1=XL(J)+SQRT(XL(J)*XL(J)+B) A2=XR(J)+SQRT(XR(J)*XR(J)+B) B1=XR(J)+SQRT(XR(J)*XR(J)+A0) B2 = XL(J )+SQRT(XL(J)*XL(J)+AO) IF((A1.EQ.O.O).OR.(A2.EQ.O.O).OR.(B1.EQ.O.O) &.0R.(B2.EQ.0.0))M1=M1+1 C C... PREVENT TAKING LOG OF 0.0 C IF(Al .EQ.0.0 )A1 = .001 IF(A2.EQ.0.0)A2=.001 IF(B1.EQ.0.0)B1=.001 IF(B2.EQ.0.0)B2=.001 C IF(Al.EQ.0.001.OR.A2.EQ.0.001.OR.Bl.EQ.0.001.OR &.B2.EQ.0.001 )THEN PRINT *,' HAVE HIT A ZERO OR NEGATIVE NUMBER; &THIS NUMBER HAS BEEN CHANGED TO .001 SO THAT STAKING ITS LOG IS POSSIBLE.' PRINT *,' YOU MAY WANT TO CHANGE THE GEOMETRY &OF BLOCK :',J END IF C C... THE 100000 IS TO GET THE ANOMALY IN UNITS OF MGALS C ANOM(I,J)=-10 0O0O.*G0*(AL0G(A1) &+ALOG(Bl )-ALOG(A2)-ALOG(B2) ) C RETURN END C C C... SUBROUTINE GRID GIVES X,Y GRID POSITIONS C C SUBROUTINE GRID(KNT,CHECK,XDELTA,YDELTA) C COMMON /GRAV/XL(100),XR(100),ZD(100,100),ZU(100), &DEN(100),Y(500,500),NBLKS,XSIZE,YSIZE,NCOLS, &NROWS,YMAX(500),YMIN(5 00),MAXPER,LAMNUM(5 00 ) , &XPOS,YPOS,ANOM(5 00,5 00),V(500 ) , ELEV(500 ) C COMMON /CBGINV/NDAT.NPARMS.KEPTRK,IA,IB,IC , LL,


157

&KVAR C NI-KNT/NCOLS XPOS=KNT*XDELTA-(NI*XSIZE+XDELTA*NI) IF(ABS(XPOS).LE.I.OE-01)XPOS=0.OOE+OO YPOS=NI*YDELTA IF(XSIZE.GT.CHECK)THEN CHECK=CHECK+XDELTA DO J=l,NBLKS XL(J)=XL(J)-XDELTA XR(J)=XR(J)-XDELTA END DO ELSE CHECK=0.0 DO J=l,NBLKS C XL(J) = XL(J) + XDELTA*(NCOLS-l ) XR(J)=XR(J)+XDELTA*(NCOLS-l) C DO 1=1,LAMNUM(J) Y(I,J)=Y(I,J)-YDELTA END DO END DO END IF RETURN END C C C... SUBROUTINE QUAD CALCULATES THE ANOMALY C... ASSOCIATED WITH EACH BLOCK BY DOING THE C... INTEGRATION IN THE Y-DIRECTION USING TALWNI'S C... QUADRITURE FORMULA C C SUBROUTINE QUAD(K) C COMMON /GRAV/XL(100),XR(100),ZD(100,100),ZU(100), &DEN(100),Y(500,500),NBLKS,XSIZE,YSIZE,NCOLS , &NROWS,YMAX(500),YMIN(500),MAXPER,LAMNUM(5 00), &XPOS,YPOS,ANOM(500,5 00),V(500),ELEV(500) C COMMON /CBGINV/NDAT,NPARMS,KEPTRK,IA,IB,IC,LL, &KVAR C DIMENSION TEMP(500) C C. . . FIND THE ANOMALY C IF(LAMNUM(K)-1.GT.1)THEN 1=1 V(1)=0.0 DO J=2,((LAMNUM(K)-l )/2) + l C A1=AN0M(I,K)*((Y(I,K)-Y(I+2,K))/(Y(I,K)-


158

&Y(I+1,K)))*(3.0*Y(I+1,K)-Y(I+2,K)-2.0*Y(1,K)) B=ANOM(I+1,K)*((Y(I,K)-Y(I+2,K))**3)/ &((Y(I+1,K)-Y(I+2,K))*(Y(I+1,K)-Y(I,K))) <

C=ANOM(I+2,K)*((Y(I,K)-Y(I+2,K))/(Y(I+2,K) «.-Y(l + l,K)))*(3.0*Y(I+l,K)-Y(I,K)-2.*Y(I + 2,K)) C TEMP(J-l)=(Al+B+C)/6.0 C V(J)=V(J-1)+TEMP(J-1) 1=1 + 2 END DO ELSE C C... C

TRAPEZOIDAL RULE FOR ONE AREA

V(((LAMNUM(K)-l)/2)+l)=(Y(2,K)-Y(l,K))*.5 &*(ANOM(1,K)+ANOM(2,K)) END IF C RETURN END C C C. C... C... C. C... C... C

SUBROUTINE DERIV IS USED TO SET KVAR TO 20 SO THAT DERIVITIVES OF GRAVITY WRT ZD WILL BE CONTAINED IN THE A MATRIX. THE A MATRIX IS USED TO LINEARIZE THIS NONLINEAR PROBLEM SO THAT INCREMENTAL PARAMETER JUMPS TOWARD THE SOLUTION CAN BE FOUND. SUBROUTINE

DERIV(A)

C COMMON /GRAV/XL(100),XR(100),ZD(100,100),ZU(100), &DEN(100),Y(50 0,500),NBLKS,XSIZE,YSIZE,NCOLS, &NROWS,YMAX(500),YMIN(500),MAXPER,LAMNUM(5 0 0 ) , &XPOS,YPOS,ANOM(5 0 0,5 00) ,V(500) ,ELEV(5 00) C COMMON &KVAR

/CBGINV/NDAT,NPARMS,KEPTRK.IA,IB,IC.LL,

C DIMENSION A(500,500),DPRED(500,500) KVAR=20 CALL FWRD(A,DPRED) KVAR-0 RETURN END


159

B.3

FORTRAN CODE OF PROGRAM 3D:

A 3-D GRAVITY MODELING PROGRAM BASED ON TALWANI AND EWING'S (1960) ALGORITHM


160

COMMON NUMPTS(150),DENLAM(150),DEPTH(150), «.LAMNUM,X( 150,1 50),Y( 150,1 50) DIMENSION STAELV(500) ,ELEV(500) INTEGER COLS,ROWS CHARACTER*20 FILENAME C 0PEN(1,FILE='3DGRV.DAT'.STATUS-'OLD') C C*****************A************************ft****AA****

C MODEL INPUT C C... FILENAME OF SAVED SURFII FILE CONTAINING C... STATION ELEVATIONS UNITS-METERS C C... IF NUMB=1 THEN INPUT STATION ELEVATIONS FROM SAVED C... SURFII FILE READ(1,*)NUMB IF(NUMB.EQ.1)READ(1,'(A20)*)FILENAME C IF(NUMB.EQ.1)OPEN(10,FILE=FILENAME,STATUS&'OLD'.FORM-'UNFORMATTED*,ACCESS='SEQUENTIAL') C READ(1,*),LAMNUM Ll-LAMNUM/2 Tl=(LAMNUM/2.)-Ll C IF(T1.EQ.0.0.AND.LAMNUM.NE.2)THEN PRINT *,'MUST HAVE ODD NUMBER OF LAMINAE &FOR PROGRAM TO WORK - START OVER SLAMEEL!1 CALL EXIT END IF C READ( 1 ,*) ,(NUMPTS(J),J=l ,LAMNUM) READ( 1,*) ,(DENLAM(J),J=1 .LAMNUM) IF(NUMB.EQ.l)THEN READ(1,*),(ELEV(J),J=1,LAMNUM) ELSE READ( 1 ,*) ,(DEPTH(J),J=1 .LAMNUM) END IF READ( 1 ,*),XSIZE,YSIZE,COLS,ROWS DO 1=1,LAMNUM READ(1,*),(X(J,I),Y(J,I),J=1,NUMPTS(I)+1) END DO C C... IF NUMB=1 READ IN ELEVATIONS C IF(NUMB.EQ.1)THEN £*AAAAA***********AA****A****AAAA*****A*AAAAAAA

C C... STATION ELEVATION INPUT C C... READ IN FIRST RECORD C READ(10)NCOLS,NROWS,IZERO


161

c C... READ IN SECOND RECORD C READ( 10)I ROWS,JCOLS,DIFY,DIFX,XMN,XMX, &YMN,YMX,DUMMY C C... READ IN ELEVATIONS (METERS) C DO I-NROWS.1,-1 IBEG-(1-1 )*NCOLS+l IEND-IBEG+NCOLS-1 READ( 10)(STAELV(J) ,J-I BEG , IEND) END DO C C**************AAAAA*A******A******************AA***A

C END IF

c XDELTA=XSIZE/(COLS-l) YDELTA=YSIZE/(ROWS-l) CHECK-O.O XPOS=0.0000E+0O YPOS-O.OOOOE+OO C IF(NUMB.EQ.1)THEN DO J=l,LAMNUM DEPTH(J)=STAELV(1)-ELEV(J) END DO END IF C CALL TDCALC(XPOS.YPOS) DO 1=1,C0LS*R0WS-1 C IF(NUMB.EQ.l)THEN DO J-1 .LAMNUM DEPTH(J)=STAELV(I+1)-ELEV(J) IF(ABS(DEPTH(J)).LT.2.)DEPTH(J)=2. END DO END IF C NI-I/COLS XPOS=I*XDELTA-(NI*XSIZE+XDELTA*NI) IF ( ABS(XPOS).LE.1.0000E-01)XPOS-0.0000E+00 YPOS=NI*YDELTA IF (XSIZE.GT.CHECK)THEN CHECK-CHECK+XDELTA DO J-1.LAMNUM DO K-l,NUMPTS(J)+l X(K,J)=X(K,J)-XDELTA END DO END DO ELSE CHECK-O.O DO J=l,LAMNUM


162

DO K=l,NUMPTS(J)+1 Y(K,J)=Y(K,J)-YDELTA X(K,J)=X(K,J)+XDELTA*(COLS-l) END DO END DO END IF CALL TDCALC(XPOS,YPOS) END DO PRINT *,'OUTPUT IN FILE 3DGRVT.DAT!' CALL EXIT END C C... C... C... C... C... C... C... C... C C... C

SUBROUTINE TDCALC(GRIDX,GRIDY) SUBROUTINE 3DCALC CALCULATES THE GRAVITY ANOMALY PER UNIT THICKNESS OF HORIZONTAL LAMINAE OF UNIT THICKNESS(=V). TO GET THE TOTAL ANOMALY OF THE 3D BODY, THE AREA UNDERNEATH THE RESULTING V-Z CURVE IS CALCULATED. THIS PROGRAM IS BASED ON THE I960 TALWANI AND EWING PAPER FOUND IN GEOPHYSICS, VOLUME 25, 1960. SET UP MEMORY

COMMON NUMPTS(150),DENLAM(150),DEPTH(150), &LAMNUM,X(150,150),Y(150,150) REAL*8 R( 100, 100) ,R1(100,100),R2( 100, 100) , &XM(100,100),P(100,100),Q(10 0,100),F(100,10 0 ) , «,GANOM( 100),TEMP (100) ,TEMP1( 100, 1 00 ) , &TEMP2(100 , 100),V( 100) REAL*8 A,B,C,C1,C2,C3,C4,C5,C6,C7,C8,C9,C10 C C... C... C... C... C

OPEN FILE TO WRITE GRAVITY ANOMALY AND SURFACE OBSERVATION POINTS INTO - IN FORMAT USABLE FOR SURFACEII AND DISSPLA GRAPHICS. FILE CALLED 3DGRVT.DAT.

OPEN( 10 , FILE-'3DGRVT.DAT' ,STATUS-* NEW' ) C C... UNIVERSAL GRAVITY CONSTANT IN CGS UNITS C G0=0.0000000667 C C... CALCULATE THE GRAVITY ANOMALY/UNIT THICKNESS FOR C. . . EACH LAMINAE C DO J=l,LAMNUM TEMP2( 1 , J)=0.0 IF(NUMPTS(J).EQ.1)G0 TO 10 M=2 DO 1=1,NUMPTS(J) C C... R.R1.R2 CANNOT EQUAL 0.0 (COMPUTER WILL NOT LIKE C. . . IT)


R(I,J)-(X(I,J)**2. + Y(I, J)**2. )**0.5 IF(R(I,J).EQ.O.O)R(I,J)=0.00000000005 Rl(I,J) = (X(I+1 ,J)**2. + Y(I+l ,J)**2. )**0.5 IF( Rl(I,J).EQ.0.O)Rl(I,J)=0.00000000005 R2(I,J)=((X(I,J)-X(I+1,J))**2+(Y(I,J) Y(1+1 ,J) )**2)**0.5 IF(R2(I,J).EQ.0.0)R2(I,J)=0.000 00 00 0005 C1=X(I,J)/R(I,J) C2=Y(I,J)/R(I,J) C3=X(1+1,J)/Rl(I,J) C4 = Y(I+1 ,J)/R1(I,J) C5=(X(I,J)-X(I+1 ,J))/R2( I, J) C6=(Y(I , J)-Y(I+1 ,J) )/R2(I,J) XM(I,J)=C2*C3-C4*C1 P(I,J)=(C6*X(I,J))-(C5*Y(I,J)) IF(P(I,J).GE.0.0)THEN S=l .0 ELSE S = -l .0 END IF IF(XM(I,J).GE.0.0)THEN W=l .0 ELSE W=-l.0 END IF C7=(P(I,J)*P(I,J)+DEPTH(J)*DEPTH(J))**0.5 Q(I,J)-C5*C1+C6*C2 F(I,J)=C5*C3+C6*C4 C8=C1*C3+C2*C4 C9=(DEPTH(J)*Q(I,J)*S)/C7 C10=(DEPTH(J)*F(I,J)*S)/C7 . . . .

PREVENT ROUNDOFF ERROR IN COMPUTER FROM GIVING NUMBER G.T. 1.0 OR L.T.-l - COMPUTER WILL NOT LIKE THIS NUMBER (DEALING WITH SINES AND COSINES)

IF(C8-1.0.GT.0.0)C8=1.0 IF(C9-1.0.GT.0.0)C9=1.0 IF(C10-1.0.GT.0.0)C10=1.0 IF(C8.LT.-1 .0)C8 = -l.0 IF(C9.LT.-1 .0)C9=-1.0 IF(C10.LT.-1.0)C10=-1.0 TEMP1(I,J)=W*AC0S(C8)-ASIN(C9)+ASIN(C10) TEMP2(M,J)=TEMP2(M-1,J)+TEMP1(I,J) M-M+l


END DO C C... THE 100000 IS TO PUT V IN UNITS OF MGALS/METER C V(J)=GO*DENLAM(J)*TEMP2(NUMPTS(J)+1,J)*100000.0 C GO TO 20 10 V(J)-0.0 20 END DO C C... FIND THE ANOMALY (AREA UNDER V-Z CURVE) C IF(LAMNUM-1.GT.I)THEN 1=1 GANOM(1)=0.0 DO J-2,((LAMNUM-1)/2)+l C A = V(I)*((DEPTH(I)-DEPTH(1 + 2) )/ &(DEPTH(I)-DEPTH(I+l)))*(3.0*DEPTH(1+1) &-DEPTH(I+2)-2.0*DEPTH(I)) C B = V(I+l)*((DEPTH(I)-DEPTH(I. + 2))**3)/ &((DEPTH(I+1)-DEPTH(1+2))*(DEPTH(I+1)&DEPTH(1) ) ) C C=V(I+2)*((DEPTH(I)-DEPTH(I+2))/ &(DEPTH(I+2)-DEPTH(I+l))) &*(3.0*DEPTH(I+1)-DEPTH(I)-2.0*DEPTH(I + 2) ) C TEMP(J-I)=(A+B+C)/6.0 TEMP(J-1 ) = TEMP(J-1 ) C GANOM(J)=GANOM(J-1 ) + TEMP(J-1 ) 1 = 1+2 END DO C ELSE C C... TRAPEZOIDAL RULE FOR ONE AREA C GANOM(((LAMNUM-1)/2)+l)=(DEPTH(2)&DEPTH(1))*0.5*(V(1)+V(2)) END IF C C... PRINT THE 3D ANOMALY TO FILE 3DGRVT.DAT C WRITE(10,'(E12.4,2X,E12.4,2X,E12.4)*)GRIDX, &GRIDY,GANOM(((LAMNUM-1)/2)+l ) RETURN END


APPENDIX C

PREPARING OBSERVED GRAVITY DATA FOR USE WITH PROGRAMS GRAVBL AND GINDEP


166

Preparing Observed Gravity Data 1)

Saving gridded data on a file: Once an observed data set has been gridded using SURFACE II,

grid information may be stored in a file of the form FORO_.dat (where

represents a number from 11 to 99) using the SAVE command

of the SURFACE II contouring package.

The following is an example of

a SURFACE II program used to grid and save the observed gravity data for my modeling area in file F0R015.DAT: TITLE SAVING GRID INFORMATION IN FILE F0R015.DAT DEVICE 5,'CJWIDEMAN' ROUTLINE 39,1,'(2F12.7)' EXTREMES -111.74222,-111.687 78,45.36077,45.37962 IDXY 158,11,3,2,1,3,0,0,0,9999,'(3F12.4)' BOX .01,2,.005,1,3,-111.74222,45.36077,1,.2 GRID 0,15,8,0,0,1,0 SAVE 15 PERFORM STOP File F0R015.DAT will have a specific format (see SAVE command in the SURFACE II manual) and GRAVBL and GINDEP were written to read in a data grid based on the format of a saved SURFII file.

2)

Changing units from latitude, longitude to meters north, east: If the saved SURFACE II file has grid point locations based on

units of latitude and longitude, the units must be converted to meters east and meters north before GINIDEP and GRAVBL can be used. Also, the first point in the grid [(0,0) in units of meters] must be located in the upper left hand corner of the grid because of the way GRAVBL and GINDEP expect to receive the data.

I have written a

program (program RSURFILE) to read the saved SURFACE II file, output


pertinent grid information, and convert latitude and longitude t meters east and meters north based on the scale of the Ennis 15 minute quadrangle map. The program will write the data to a fil called GRID.DAT in the following order: xpos on grid, ypos on grid, data value in 3F12.4 format.

GRID.DAT will contain the number of columns

(NCOLS) times the number of rows (NROWS) lines of data.

Code fo

program RSURFILE is as follows:

DIMENSION A(10000), DUMMY(12), VAR(4) CHARACTER TOPOFILE*20,BL0CKFILE*20,OUTPUTFILE*20,CHARM C WRITE(*,'(''$TYPE IN SAVED SURFII FILE>*')') READ(*,'(A20)')T0P0FILE OPEN(21,FILE=T0P0FILE,ACCESS-'SEQUENTIAL',STATUS='OLD', &F0RM-'UNFORMATTED') C C C

READ IN FIRST RECORD OF THE SAVED SURFII FILE READ(21)NC0LS,NR0WS,IZER0 PRINT *,' '

C C C

READ IN SECOND RECORD READ(21)IROWS,JCOLS,DIFX,DIFY,XMIN,XMAX,YMIN,YMAX,DUMMY

C C C

CONVERT TO METERS, SCALE OF ENNIS 15' TOPO WRITE(*,'( "$C0NVERT TO METERS(Y/N)> " ) ' ) READ(*,'(A1)')CHAR

C IF(CHAR.EQ.'Y'.OR.CHAR.EQ.'y')THEN DIFY=DIFY*111840. DIFX=DIFX*79040. XSIZE=ABS((XMAX-XMIN)*7 9040) YSIZE=ABS((YMAX-YMIN)*111840) XDELTA=DIFX YDELTA=DIFY ELSE XSIZE=ABS(XMAX-XMIN) YSIZE-ABS(YMAX-YMIN) IF(DIFY.LT.0.0)THEN YDELTA—DIFY ELSE YDELTA=DIFY


168

END IF END IF

c PRINT PRINT PRINT PRINT PRINT

*,' *,' ' *,* MATRIX INFO' *,' ' *,* NCOLS,NROWS',NCOLS,NROWS

C PRINT *,' ' PRINT *,'DIFY(METERS)=',DIFY, &'DIFY(METERS)=',DIFX PRINT *,'XMIN=',XMIN,' XMAX=',XMAX PRINT *,* YMIN-',YMIN,' YMAX=',YMAX C PRINT *,'XSIZE(M)=',XSIZE, &' YSIZE(M)=',YSIZE PRINT *,' C C C C

NOW READ IN THE GRID MATRIX VALUES DO I=NROWS,l,-l IBEG=(I-l)*NCOLS+l IEND=IBEG+NCOLS-l READ(21)(A(J),J=IBEG,IEND) END DO DO I=l,NROWS*NCOLS IF(A(I).LE.-9.9999E+33)A(I)=0.0 END DO

C C C

PRINT GRID VALUES TO FILE GRID.DAT WRITE(*,'('$PRINT GRID VALUES IN FILE &GRID.DAT(Y/N)>'')') READ(*,'(A1)")CHAR IF(CHAR.EQ.*N')CALL EXIT OPEN(10,FILE-'GRID.DAT',STATUS-'NEW') XPOS-O.O YP0S=0.0 WRITE(10,'(3F12.4)')XPOS,YPOS,A(1) DO 1=1,NCOLS*NROWS-l NI=I/NC0LS XPOS=I*DELTA-(NI*XSIZE+XDELTA*NI) IF(ABS(XPOS).LE..1)XPOS=0.0 YPOS=NI*YDELTA WRITE(10,'(3F12.4)')XPOS,YPOS,A(I+1) END DO CLOSE(IO) CLOSE(21) CALL EXIT END


Example of using program RSURFILE Say you have used SURFACE II to create a grid of four columns and three rows where the distance between columns is 25 meters and the distance between rows is 30 meters (the data was collected in units of meters east and north), and this grid information is saved in file F0R019.dat.

IF RSURFILE is used to read F0R019.dat and

output the grid values in file GRID.DAT, these are the input steps and output displayed when RSURFILE is run: RUN RSURFILE TYPE IN SAVED SURFII FILE>F0R019.DAT CONVERT TO METERS(Y/N)>N MATRIX INFO NCOLS, NROWS

4,3

DIFY(METERS)=30 XMIN-0.0 YMIN=0.0

DIFX(METERS)=25 XMAX-75.0 YMAX=60.0

XSIZE-75.0

YSIZE=60.0

PRINT GRID VALUES IN FILE GRID.DAT(Y/N)>Y

Now file GRID.DAT has been created where the grid points are numbered as follows:

'I

*2

*3

'4

*5

*6

'7

*8

*9

*10

*11

'12

And the output contained in GRID.DAT will be:


170

0.0000 25.0000 50.0000 75.0000 0.0000 25.0000 50.0000 75.0000 0.0000 25.0000 50.0000 75.0000 4)

0.0000 0.0000 0.0000 0.0000 30.0000 30.0000 30.0000 30.0000 60.0000 60.0000 60.0000 60.0000

GRID VALUE 1 (mgals) top left of grid GRID VALUE 2

GRID VALUE 12 bottom right of grid

Removal of Topography Program 3D (coding is in Appendix B) is bsed on Talwani and

Ewing's (1960) method of describing 3-D bodies with horizontal, n-sided polygons.

Because n-sided polygons accurately describe

elevation contours, program 3D was used to model the topography in the survey area (see text).

In general, topography from the highest

elevation in the modeled area to the lowest station elevation should be included in the topography model.

A model may be created by

digitizing points of contours taken from a topographic map in the survey area.

Enough points on each contour and enough contours

should be chosen so that the topography is described reasonably. Input to program 3D is read from a data file called 3DGRV.DAT, and the input must be ordered as follows:

Line

Input 1 if the station elevations are to be read from a saved SURFII grid file any other integer if the stations are assumed to be collected on a plane. Saved SURFII file of elevations (i.e. FOR032.DAT). Number of laminae (horizontal polygons) used in the model. For example, if five elevation contours are digitized, then 5 would be input on this line.


171 Number of verticies in each laminae of the model separated by a comma. For example, if three laminae were used in the model where: top laminae: 5 verticies, middle laminae: 16 verticies, and bottom laminae: 8 verticies, then input here would be: 5,16,8 3 Density of each laminae (gm/cm ) separated by a comma. Elevation (meters above sea level) of each laminae separated by a comma. X-size of grid(m), Y-size of grid(m), number of columns in grid, number of rows in grid. These numbers should match the grid parameters used for programs GINDEP and GRAVBL. X,Y location in meters of each point on each laminae entered in clockwise order. The starting point must be repeated as the final point so that the laminae is closed. For example, consider a model with three laminae: top laminae - 5 verticies: (0 ,0) ,(100,200), (200,300),(100,20), and (-50,20) middle laminae - 3 verticies: and (50,-20)

(-100,20),(100,20),

bottom laminae - 3 verticies: and (-10,-10).

(-40,60),(50 ,10),

Then input would be ordered as follows: Line 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Input 0.0,0.0 100.0,200.0 200.0,300.0 100.0,20.0 -50.0,20.0 0.0,0.0 -100.0,20.0 100.0,20.0 50.,-20. -100.0,20.0 -40.0,60.0 50.0,10.0 -10.0,-10.0 -40.,60.


172

Note: Those repeat points used to close the laminae are not counted as extra points for the input of line #4. For the model above the input for line #4 would be 5,3,3. Output of program 3D is written to a file named 3DGRVT.DAT which will contain (NCOLS x NROWS) lines of data (NCOLS = number of columns in the grid, NROWS = number of rows in the grid), and each line will contain the X-position on the grid, the Y-position on the grid, and the gravity value of the grid point (in mgals).

This information is

written in 3F12.4 format, and the first data point output is the one located in the upper left hand corner of the grid.

The data con-

tained in file 3DGRVT.DAT can best be explained using an exmaple. Say you create a grid of data with 4 columns and 3 rows with the distance between columns = 30 meters and the distance between rows = 25 meters.

Assume the values of the 12 grid points in this grid are as

follows:

Grid point

Grid value (mgals)

1 2 3 4 5 6 7 8 9 10 11 12

12 15 16 20 7 9 12 17 5 7 10 15

The output in file 3DGRVT.DAT for this example would be: 0.0000 30.0000 60.0000 90.0000 0.0000 30.0000

0.0000 0.0000 0.0000 0.0000 25.0000 25.0000

12.0000 (upper left corner of grid) 15.0000 16.0000 20.0000 7.0000 9.0000


173

60.0000 90.0000 0.0000 30.0000 60.0000 90.0000

25.0000 25.0000 50.0000 50.0000 50.0000 50.0000

12.0000 17.0000 5.0000 7.0000 10.0000 15.0000 (bottom right corner of grid)

The gravity contributions of the topography to each grid point should be removed from the gridded observed gravity set contained in file GRID.DAT output from program RSURFILE.

To do this the grid

parameters and locations of the grid used for the topography model must identically match that of the grid determined for the observed gravity data.

4)

Removing a DC (constant gravity value from the data If the observed gravity data is tied into a gravity "net" con-

sisting of base stations where actual gravity values are known, a constant must be removed from each gridded gravity value so that the gravity values generated by the modeling program will match the observed gravity values.

For example, the gravity data that I

collected is tied to base stations at Helena and Three Forks at which actual values of gravity are known.

Therefore, the gravity values in

my data set represent actual gravity values which range from -(980)178 mgals to -(980)198 mgals (the 980 mgals is constant for all the stations and is not recorded in my data set). However, the gravity modeling program duplicates the relative changes in the gravity data (a maximum of 20 milligals in my data area) not the actual gravity values.

Consequently, I removed a constant value of


174 -178 mgals from each of the gridded observed data values before using the modeling programs because these programs should generate numbers in a range from 0-20 milligals to match my data set.

Summary

In summary, the following four steps should be used to prepare the data used in the gravity modeling programs: 1)

Grid the gravity and elevation data with SURFII and save the gridded data using the SAVE command of SURFII;

2)

Run RSURFILE for both the gridded gravity and elevation data.

RSURFILE will convert station locations in units

of latitude and longitude to meters east and meters north (for the Ennis 15' quadrangle), display grid information, and write grid locations and values to file GRID.DAT in 3F12.4 format; 3)

Run 3D to remove the topography from the highest elevation in the modeled are to the lowest station elevation; and

4)

Remove a constant value from each of the gravity stations so that the gravity values represent the relative changes of gravity values across the survey area.


APPENDIX D

INPUT TO AND OUTPUT OF PROGRAMS GRAVBL AND GINDEP

D.l

INPUT TO AND OUTPUT OF PROGRAM GRAVBL

D.2

INPUT TO AND OUTPUT OF PROGRAM GINDEP


176

D.l

INPUT TO AND OUTPUT OF PROGRAM GRAVBL


177

1)

Input to program GRAVBL: Program GRAVBL is a 3-D forward gravity modeling program in

which up to 100 rectangular blocks of earth may be used.

GRAVBL

reads input out of a data file called GRAVBL.DAT, and the input in file GRAVBL.DAT must be ordered as follows:

LINE

INPUT

1

Number of blocks in the model (max=100)

2

XL(1),XR(1),ZU(1),ZD(1),YMIN(1),YMAX(1), DEN(1) where: XL(1) = Minimum X-edge of block 1 XR(1) = Maximum X-edge of block 1 ZU(1) = Upper edge of block 1 (Z pos. down) ZD(1) = Lower edge of block 1 YMIN(l) = Minimum Y-edge of block 1 YMAX(l) = Maximum Y-edge of block 1 DEN(l) = Density of block 1 distance units = meters density = gm/cc XL(2),XR(2),ZU(2),ZD(2),YMIN(2),YMAX(2), DEN(2) XL(3),XR(3),ZU(3),ZD(3),YMIN(3),YMAX(3), DEN(3)

NBLKS + 1

XL(NBLKS),XR(NBLKS),

NBLKS + 2

XSIZE,YSIZE,NCOLS,NROWS where: XSIZE YSIZE NCOLS NROWS

NBLKS + 3

= = = =

MAXPER

X-size Y-size number number

of of of of

grid (meters) grid (meters) columns in the grid rows in the grid.


178 whe re: MAXPER = Multiplier which directly effects the number of laminae used in the quadrature formula. For example if MAXPER-5, then 5 times as many laminae will be used for the quadrature formula then if MAXPER was equal to one. NBLKS + 4

NUMB: If NUMB = 1, then include topography in the model. If NUMB is not equal to one then asuume the data is collected on a plane.

Last two lines used only if NUMB = 1. NBLKS + 5

Datum elevation (meters above sea level) of the tops of the blocks after the removal of the gravity contributions of the valley fill included in the topography model.

NBLKS + 6

Saved SURFACE II file of elevations (see Appendix C ) .

2) Output The output of program GRAVBL is written to a data file called GBL.DAT. data.

GBL.DAT will contain NCOLS x NROWS lines of

Each of these lines of data will contain the following:

XPOS , YPOS , GRIDDED GRAVITY VALUE (mgals) Where: XPOS = X-position of the grid point (meters east of origin) YPOS = Y-position of the grid point (meters south of origin). The data is written in 3F12.4 format and the first and last grid point represent the upper left and lower right grid values, respectively.


179

D.2

INPUT TO AND OUTPUT OF PROGRAM GINDEP


1) Input Program GINDEP is an inverse 3-D gravity modeling program that uses the forward modeling results of program GRAVBL to determine depths of the bedrock which reduce the error between the gridded observed graivity data and the calculated gravity data.

Therefore, the model output using the forward program

GRAVBL is used as the input model for program GINDEP.

In order

for program GINDEP to work, the blocks used in the forward modeling process must extend from the elevation that was used as the base elevation for the removal of topography to the assumed bedrock depth (see text for an explanation).

The input to

program GINDEP is read from a command file called G.DAT, and the input in the file G.DAT must be ordered as follows:

Line

Input

1

Filename of saved SURFII data file containing the prepared (see Appendix C) gridded observided gravity data.

2

TDEPL,TDEPH where: TDEPL = minimum expected depth (meters below the surface, z positive down) of valley fill. The program will constrain the parameter jumps so that each block's minimum depth will not go below this value during the inversion process. TDEPH = maximum expected depth (meters below the surface, z positive down) of valley fill. The program will constrain the parameter jumps so that each block's maximum depth will not exceed this value in the inversion process.


3

NUMFIX where: NUMFIX = total number of blocks to be held fixed to the initial maximum depth throughout the inversion process.

If NUMFIX is not equal to zero: 4

Individual block numbers whose maximum depths are to be held fixed separated by a comma. For example, if blocks 2,6,12, and 24 are to have their initial maximum depths held fixed throughout the iterations toward a solution, the following would be entered on line #4: 2,6,12,24. For this example, NUMFIX = 4.

If NUMFIX is equal to zero, the following would still be input; however, the above line is not input. Therefore, the following line numbers have values as if NUMFIX = 0 . If NUMFIX is not equal to zero, add one to each of the following line numbers. 4

Number of blocks in the model (NBLKS).

5

XL(1),XR(1),ZU(1),ZD(1),YMIN(1),YMAX(1),DEN(1) whe re: XL(1) XR(1) ZU(1) ZD(1) YMIN(l) YMAX(1) DEN(l)

Minimum X edge of block 1 Maximum X edge of block 1 Upper edge of block 1 (Z positive down) Lower edge of block 1 Minimum Y edge of block 1 Maximum edge of block 1 Density of block 1 3 Distances in meters, Density in gm/cm

6

NBLKS + 4

= = = = = = =

XL(2),XR(2),ZU(2),ZD(2),YMIN(2),YMAX(2),DEN(2)

XL(NBLKS),XR(NBLKS),ZU(NBLKS),ZD(NBLKS), YMIN(NBLKS),YMAX(NBLKS),DEN(NBLKS)


NBLKS + 5

MAXPER whe re: MAXPER =

NBLKS + 6

Multiplier which directly effects the number of laminae used in the quadrature formula. For example, if MAXPER = 5, then five times as many laminae will be used for the quadrature formula then if MAXPER was equal to one.

RATIO where: RATIO =

NBLKS + 7

Number which weights the overdetermined part of the solution relative to the unerdetermined part. If RATIO = 0, then the standard overdetermined solution is used (see text for an explanation).

STDDEV whe re: STDDEV =

NBLKS + 8

An input error value (mgals). When the error between the gridded observed and calculated data is less than this value the program will output the depth to bedrock values.

Maximum number of iterations allowed (i.e. 10)

Last three lines: NBLKS + 9

NUMB where: If NUMB = 1, then topography is included in the model. If NUMB is not equal to 1, the data is assumed to be collected on a plane.

Last two lines included only if NUMB is not equal to one: DATELV where: DATELV = Datum elevation (meters above sea level) at which the tops of the blocks are located (elevation to which topography has been removed).


Filename of saved SURFII file of elevations

2) Output Output from program GINDEP will be written to a file called GINDEP.OUT.

GINDEP.OUT will contain the input model, a table of

convergence (showing the parameter jumps, the new parameters, the Marquardt damping factor, and the error between the gridded observed and calculated data for each iteration), and finally a listing of the block along with the maximum depth of each block (meters) if the error between the observed and calculated data is less than the value of STDDEV as input.


APPENDIX E

MODELED GRAVITY DATA AND ITS PREPARATION FOR USE WITH PROGRAMS GRAVBL AND GINDEP

E.l

LOCATIONS AND GRAVITY VALUES OF THE MODELED GRAVITY DATA

E.2

X-POSITION, Y-POSITION, GRIDDED GRAVITY VALUE OF THE GRIDDED OBSERVED GRAVITY DATA

E.3

GRAVITY CONTRIBUTIONS OF THE VALLEY FILL INCLUDED IN THE TOPOGRAPHY MODEL

E.4

GRIDDED OBSERVED "TOPOGRAPHY CORRECTED" GRAVITY DATA


185

E.l

GRAVITY DATA USED IN MODELING THE ENNIS GEOTHERMAL AREA. DATA IS ORDERED AS FOLLOWS:

COLUMN

VALUE

1

LATITUDE (DEG.)

2

LONGITUDE (DEG.)

3

GRAVITY DATA (MGALS.)

4

TERRAIN CORRECTION (MGALS)

5

ELEVATIONS (METERS)


45.36415863 45.36415863 45.36066055 45.36415863 45.36066055 45.36415863 45.36066055 45.36415863 45.36066055 45.36415863 45.36066055 45.36415863 45.36066055 45.36666107 45.36066055 45.36832809 45.36415863 45.36098862 45.36233139 45.36415863 45.36098862 45.36415863 45.36098862 45.36415863 45.36098862 45.36415863 45.36098862 45.36415863 45.36098862 45.36415863 45.36098862 45.36733 45.36726 45.36726 45.36729 45.36705 45.36699 45.36692 45.36692 45.36777 45.36870 45.36938 45.37007 45.3701 1 45.37011 45.37011 45.37014 45.37011 45.37014 45.37000 45.37000 45.37007 45.36932 45.36846

, , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,

-111.713661 19 -111.71582794 -111.71665955 -111.71798706 -111.71883392 -111.72016907 -111.72116852 -111.72249603 -111.72332764 -111.72466278 -111.72565460 -111.72698975 -111.72783661 -111.72783661 -111.72998047 -111.73065948 -111.73116302 -111.73149109 -111.73149109 -111.73332214 -111.73365784 -111.73548889 -111.73583221 -111.737831 12 -111.73816681 -111.73999023 -111.74032593 -111.74233246 -111.74265289 -111.74466705 -111.74498749 , -1 11 .7297 -111.7284 -1 11 .7271 -1 11 .7260 -111 .7234 -111 .7222 -111.7210 -111.7198 -11 1 .7199 -111.7199 -111 .7198 -111.7199 -111 .721 1 -1 1 1 .7223 -111.7236 -1 11 .7249 -111.7261 -111.7267 -111.7274 -111 .7287 -111 .7299 -111.7300 -111.7300

, , , , , , , , , , , , , , , , , , , , , , , , , , ,

-190.32000000 -189.55000000 -190.14000000 -188.60000000 -189.71000000 -187.22000000 -189.16000000 -186.31000000 -188.40000000 -185.41000000 -187.60000000 -185.02000000 -186.48000000 -184.32000000 -185.24000000 -183.64000000 -183.82000000 -182.81000000 -182.94000000 -182.17000000 -181.55000000 -180.53000000 -180.65000000 -179.32000000 -179.35000000 -178.58000000 -178.46000000 -178.20000000 -179.07000000 -177 .96000000 -179.72000000 -184.01 -184.37 -184.75 -183.95 -187.06 -186.90 -187.64 -187 .71 -188.32 -188.02 -188.29 -188.34 -187.67 -186.98 -186.40 -186. 10 -185.68 -185.73 -185.43 -184.99 -184.56 -183.98 -184.26

, , , , , , , , , , , , , , , , , . , , , , , , , , , ,

1.42 1.39 1.38 1.39 1.38 1.40 1-39 1.41 1.39 1.42 1.40 1.45 1.43 1.40 1.45 1.38 1.39 1.37 1.38 1.42 1.40 1.45 1.44 1.52 1.51 1-55 1-55 1.65 1.63 1.78 1 .69 1 .38 1 .38 I .36 1 .37 1 .51 1 .44 1 .44 1 .44 1 .44 1 .44 1 .44 ] .43 1 .46 1 .45 I .44 1 .45 1 .37 1 .39 1 .40 I .42 1 .42 1 .42 1 .42

, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,

1493. 1494. 1496. 1494. 1496. 1495. 1496. 1494. 1496. 1495. 1497. 1493. 1497 . 1501 . 1497 . 1501 . 1502. 1505. 1504. 1502. 1505. 1502. 1505. 1502. 1504. 1502. 1504. 1502. 1504. 1503. 1509.

, , , , , , ,

1 501 . 1500 1500 1498 I486 149 1 1491 149 1

, , , , , , , , , , , , , , ,

14 9 0 14 9 0 1489 1489 1489 1489 1489 1490 1498 1498 1498 1498 1498 1498 1498


187

45.36771 -1 1 1 .7301 45.36802 -111 .7257 45.36890 -111.7260 -111.7261 45.36963 45.36835 -1 11 .7275 45.36757 -1 11.7275 45.36747 -111.7311 45.36740 -111.7324 45.36740 -111.7336 45.36753 -111.7350 45.36747 -1 1 1 .7362 45.36747 -111.7374 45.36744 -111.7387 45.36747 -111.7400 45.36750 -111.7411 4 5.36747 -111.7425 45.36835 -1 11 .7323 45.36904 -111.7323 45.36990 -111.7323 45.37079 -111.7323 45.37168 -111.7323 45.37233 -1 11 .7323 45.37323 , -1 11 .7323 45.37425 -111.7332 45.37490 -111.7355 45.37484 -111.7361 45.37418 -1 11.7366 4 5.37343 -111.7372 45.37299 -111.7378 45.37244 -111.7388 45.37189 , -1 11 .7396 -1 11 .7381 45.37178 -111.7371 45.37175 45.37182 -111.7359 45.37178 -111.7345 45.37182 -1 11 .7332 45.37744 , -111.7308 45.37744 -111.7296 45.37744 , -111.7284 45.37744 -111.7271 45.377440000 , -111.73010000 45.377440000 , -111.72880000 45.377440000 , -111.72740000 45.37 7440000 , -111.72610000 45.377440000 , -1 1 1 .72470000 45.377440000 , -111.72340000 45.377440000 , -111.72200000 45.377440000 , -111.72060000 45.377440000 , -111.71930000 45.377440000 , -111.71790000 45.377440000 , -111.71660000 45.377440000 , -111.71530000 45.377440000 , -111.71390000 45.377440000 . -111.71260000

-183.88 -185.07 -185.09 -185.59 -184.76 -184.34 -183.55 -183. 15 -18 2.45 -181 .91 , -181 .71 -181.00 -180.24 -179.75 -179.55 -179.31 -183.31 -183.31 -183.47 -184.07 -184.85 -185.53 -186.17 -186.07 -185.43 -185.03 -185.15 -184.25 -184.09 -183.91 -182.76 -183.50 -183.51 -184.18 -184.06 -184.56 -186.65 -187.02 -187.46 -187.87 , -187.21 , -187.16 , -187.39 , -188.69 , -188.42 , -188.79 , -189.37 , -189.69 , -190.09 , -190.45 , -190.84 , -191 .36 , -191 .79 . -192.21

, 1 .40 , 1500. , 1 .36 , 1499. , 1 .37 , 1498. , 1 .37 , 1498. , 1 .39 , 1499. , 1 .37 , 1501. , 1 .39 , 1500. , 1 .45 , 1500. , 1 .46 , 1499. , 1499. , 1.52 , 1 .53 , 1500. , 1 .56 1500. , 1 .61 1499. , 1.71 1499. 1499. , 1 .69 , 1.77 1501 . , 1.45 1499. , 1.44 1499. , 1.45 1497. 1497. , 1 .46 , 1 .47 1497. , I .50 1495. , 1-52 , 1495. 14 94. , 1.52 , 1 .58 14 9 5. 1496. , 1 .59 14 9 5. , 1.63 , 1.63 1496. 1497. , 1 .63 1497 . , 1.65 , 1 .64 1498. , 1.62 1496. , 1.60 1497. ,1.57 1497. 1496. , 1 .53 1496. , 1.49 , 1.50 1493. 1491. , 1.50 , 1.46 1492. , 1.45 , 1492. 1.48 , 1 491 .92 1.48 , 1 492.02 1.47 , 1 491.97 , 1 .47 , 1 484.85 1.46 , 1 484.85 1.46 , 1 484.80 , 1.45 , 1 484.44 1.45 , 1 484.34 1.44 , 1 484.55 1.44 , 1 484.50 1.43 , 1 484 .50 1.43 , 1 484.50 1.42 , 1 484. 14 1.42 . 1 4 8 4.04


188

45.377440000 45.377440000 45.375540000 45.375540000 45.375540000 45.375540000 45.375540000 45.375540000 45.375540000 45.375540000 45.375540000 45.375540000 45.375540000 45.375540000 45.375540000 45.375540000 45.375540000 45.375540000 45.3782 45.3792 45.3808 45.3825 45.3826 45.3826 45.3827 45.3824 45.3807 45.3790 45.3772 45.3754 4 5.3750 45.3749 45.3766 4 5.3784 45.3676 45.3676 45.3676 45.3641 45.3606 45.3569 45.3533 45.3494 45.3493 45.3494 , 45.3491 45.3532 45.3568 45.3604 45.3639 45.3644 ,

,-111.71120000 , -192.69 , -111.70990000 , -193. 11 , -111.70990000 , -192.83 , -111.71120000 , -192.41 , -111.71260000 , -191.94 , -111.71390000 , -191.59 , -111.71530000 , -191 .13 , -111.71660000 , -190.72 , -111.71790000 , -190.69 , -111.71930000 , -189.91 , -111.72060000 , -189.55 , -111.72200000 , -189.08 , -111.72340000 , -188.80 , -111.72470000 , -188.40 , -111.72610000 , -188.18 , -111.72740000 , -187 . 13 , -111.72880000 , -187.71 , -111.73010000 , -187. 13 -111.7311 , -186.65 -196.22 -1 1 1 .6832 -111.6832 -195.80 -195.44 -111.6831 -111.6857 -194.52 -193.82 -111.6882 -111.6908 -192.95 -192.54 -111.6935 -111.6943 , -193.01 -111.6944 -193. 19 -193.51 -111.6943 -193.95 -111.6943 -194 .14 -111.6922 -111.6897 -194.65 -195.06 -111.6863 -195.16 -111.6863 -196.55 -111.6942 -111.6979 -195.90 -195.22 -111 .7013 -111.7027 -194.95 -195. 12 -111.7033 -195.51 -111.7038 -196.06 -111.7046 -196.36 -111.7046 -198.66 -111.6992 -200.06 -111.6944 -111.6887 , -201.80 -200.98 -111.6887 -199.00 -111.6884 -198.34 -111.6888 -197.65 -111.6890 -196.93 -111.6936

, , , , , , , , , , , , , , ,

,

,

1.41 , 1.41 , 1 .40 , 1 .40 , 1 .40 , 1 .40 , 1 .40 , 1 .41 , 1 .42 , 1.42 , 1 .43 , 1 .43 1 .44 1 .44 , 1.45 , 1.45 , 1.46 , 1 .47 1.48 1 .57 1 .58 , 1.59 1 .57 1 .55 1 .51 , 1 .47 , 1 .46 , 1 .46 , 1.45 , 1 .44 1 .46 , 1 .50 , 1.55 , 1.55 , 1 .38 , 1.35 , 1.30 , 1 .27 , 1.24 , 1 .26 , 1 .30 , 1 .33 , 1.37 , 1 .44 , 1 .50 , 1 .50 , 1 .50 , 1 .46 , 1 .46 , 1.40 ,

1483.63 14 8 3.22 1484.50 1484.75 1485.16 1485.31 1485.36 1485.77 1485.31 1485.41 1485.77 1486.07 1486.07 1486.07 1492.07 1491.62 1491.62 1492.22 1492.59 1493.32 1494.01 1496.33 1497.99 1499.76 1500.52 1499.97 1499.15 1498.57 1497.67 1497.06 1495.63 1494.86 1494.69 1494.37 1491.88 1492.41 1491 .57 1494.54 1497.16 1499.41 1501.54 1503.35 1504.95 1505.55 1505.00 1501.62 1498.06 1495.67 1493.89 1493.66


189

E.2

GRIDDED OBSERVED GRAVITY DATA DATA IS ORDERED AS FOLLOWS:

COLUMN

VALUE

1

METERS EAST

2

METERS SOUTH

3

GRIDDED GRAVITY VALUE (MGALS)

A CONSTANT OF -178 MGALS HAS BEEN REMOVED FROM EACH GRID VALUE


0.0000 306.2545 612.5089 918.7634 1225.0178 1531.2723 1837.5267 2143.7813 2450.0356 2756.2900 3062.5447 3368.7991 3675.0535 3981 .3079 4287.5625 0.0000 306.2544 612.5088 918.7632 1225.0176 1531.2725 1837.5269 2143.7813 2450.0356 2756.2900 3062 .5444 3368.7988 3675.0532 3981.3081 4287 .5620 0.0000 306.2539 612.5088 918.7637 1225.0176 1531 .2725 1837.5264 2143.7813 2450.0352 2756.2900 3062.5449 3368.7988 3675.0537 3981.3076 4287.5625 0.0000 306.2539 612.5078 918.7627 1225.0176 1531 .2715 1837.5264 2143.7803 2450.0352

0 .0000 0 .0000 0 .0000 0 .0000 0 .0000 0 .0000 0 .0000 0 .0000 0 .0000 0 .0000 0 .0000 0 .0000 0 .0000 0 .0000 0 .0000 301 .1504 301 . 1 50 4 301 .1504 301 .1504 .1504 301 , 301,. 1504 301 , . 1504 301 , .1504 301,.1504 301 , .1504 301,. 1504 301 , .1504 301 . .1504 301 . . 1504 301 . 1504 602..3008 602..3008 602.,3008 602.,3008 602.,3008 602.,3008 602.,3008 602.,3008 602.,3008 602.,3008 602. 3008 602.,3008 602.,3008 602.,3008 602.,3008 903.,4512 903.,4512 903. 4512 903. 4512 903. 4512 903. 4512 903. 4512 903. 4 512 903. 4512

-6 .0900 -6 .9950 -7 .7967 -8 .6975 -9 .9980 -10 .8983 -12 .0986 -13 . 1987 -1.4 . 1989 -14 .5990 -14 .8991 -15 .0992 -15 . 1992 -15 .5993 -16 .2993 -5 .6994 -6,.7994 -7,.7994 -8,.9995 -9,.9995 -10,.8995 -12,.1995 -13,.1996 -14,.5996 -15,. 1996 -15..2996 -15..4996 -15..6996 -15.,8997 -16.,7997 -4.,9997 -6.,2997 - 7 .,6997 -8.,7997 -9.,7997 -10..6997 -1 1 ,8997 . -12.,9997 -14.,1997 -15.,0998 -15. 6998 -15. 7998 -15. 9998 -16. 5998 -17. 1998 - 3 . 5998 - 5 . 0998 - 5 .,9998 - 7 . 1998 - 8 . 2998 -9. 5998 -10. 7998 -12. 1998 -13. 5998


2756.2891 3062.5430 3368.7988 3675.0527 3981.3066 4287.5625 0.0000 306.2539 612.5078 918.7637 1225.0176 1531 .2715 1837.5273 2143.7813 2450.0352 2756.2891 3062.5449 3368.7988 3675.0527 3981.3086 4287.5625 0.0000 306.2539 612.5098 918.7637 1225.0176 1531.2734 1837.5273 2143.7813 2450.0352 2756.2910 3062.5449 3368.7988 3675.0527 3981.3086 4287.5625 0.0000 306.2539 612.5078 918.7617 1225.0156 1531 .2715 1837.5254 2143.7793 2450.0352 2756.2891 3062.5430 3368.7969 3675.0527 3981.3066 4287.5605 0.0000 306.2539 612.5078

903.4512 90 3.4512 903.4512 903.4512 9 0 3.4512 903.4512 1204.6016 1204.6016 1204.6016 1204.6016 1204.6016 1204.6016 1204.6016 1204.6016 1204.6016 12 0 4.6016 1204.6016 1204.6016 1204.6016 1204.6016 1204.6016 1505.7520 1505.7520 1505.7520 1505.7520 1505.7520 1505.7520 1505.7520 1505.7520 1505.7520 1505.7520 1505.7520 1505.7520 1505.7520 1505.7520 1505.7520 1806.9023 1806.9023 1806.9023 1806.9023 1806.9023 1806.9023 1806.9023 1806.9023 1806.9023 1806.9023 1806.9023 1806.9023 1806.9023 1806.9023 1806.9023 2108.0527 2108.0527 2108.0527

-14 .9998 -15 .7998 -16 .4998 -16 .8998 -17 .3998 -18 .0998 -1 .8998 -3 .4998 -4 .9998 -5 .9998 -6 .9998 -9 .1998 -10 .3998 -1 1.8999 -13 .0999 -14,.7999 -16 .0999 -17 . , 1999 -17 .8999 -18,.4999 -19,.0999 -1,.0999 -2,.0999 -4,.1999 -5,.7999 -6..8999 -8,.4999 -9,.9999 -11..5999 -12,.9999 -14,.7999 -16,.2999 -17 .4999 , -18..2999 -19..1999 -19..3999 -0..0999 -1 .2999 . -2..9999 -5..7999 -7 .2999 . -8.,2999 -9.,9999 -1 1 .7999 . -13..0999 -14.,9999 -16.,4999 -17.,7999 -18.,4999 -19..1999 -19..5999 -0.,9999 ,4999 -1 . -3.,1999


918.7617 1225.0156 1531.2695 1837.5273 2143.7813 2450.0352 2756.2891 3062.5430 3368.7969 3675.0508 3981.3086 4287.5625

2108.0527 2108.0527 2108.0527 2108.0527 2108.0527 2108.0527 2108.0 527 2108.052 7 2108.0527 2108.0527 2108.0527 2108.0527

-6,. 5999 -8,.9999 -10,.2999 -11 .4999 , -12,.4999 -13,.8999 -15,.3999 -16,.9999 -18 .0999 , -18..7999 -19..5999 -20..2999


E.3

GRAVITY CONTRIBUTIONS OF THE VALLEY FILL INCLUDED IN THE TOPOGRAPHY MODEL DATA IS ORDERED AS FOLLOWS:

COLUMN

VALUE

1

METERS EAST

2

METERS SOUTH

3

CALCULATED GRAVITY VALUE (MGALS)

THESE VALUES WERE OUTPUT FROM PROGRAM 3D IN FILE 3DGRV.DAT

TOPOGRAPHY WAS REMOVED DOWN TO AN ELEVATION OF 1475 METERS ABOVE SEA LEVEL


0.0000 307.4000 614.7000 922.1000 1229.0000 1537.0000 1844.0000 2152.0000 2459.0000 2766.0000 3074.0000 3381.0000 3688.0000 3996.0000 4303.0000 0.0000 307.4000 614.7000 922.1000 1229.0000 1537.0000 1844.0000 2152.0000 2459.0000 2766.0000 3074.0000 3381.0000 3688.0000 3996.0000 614.7000 922.1000 1229.0000 1537.0000 1844.0000 2152.0000 2459.0000 2766.0000 3074.0000 3381.0000 3688.0000 3996.0000 4303.0000 0.0000 307.4000 614.7000 922. 1000 1229.0000 1537.0000 1844.0000 2152.0000 2459.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 301 .1000 301. 1000 301.1000 301 .1000 301.1000 301.1000 301.1000 301.1000 301.1000 301.1000 301.1000 301.1000 301.1000 301.1000 602.3000 602.3000 602.3000 602.3000 602.3000 602.3000 602.3000 602.3000 602.3000 602.3000 602.3000 602.3000 602.3000 903.4000 903.4000 903.4000 903.4000 903.4000 903.4000 903.4000 903.4000 903.4000

-0.3499 -0.3549 -0.3558 -0.4243 -0.0796 -0.0776 -0.0779 -0.0780 -0.0779 -0.0778 0.0103 -0.0903 -0.0904 -0.0951 -0.4204 -0.3544 -0.3567 -0.4269 -0.4243 -0.0823 -0.0137 0.0033 0.0047 -0.0779 -0.0776 -0.0775 -0.0805 -0.0808 -0.0838 -0.4265 -0.4258 -0.4230 -0.0313 -0.0161 -0.001 1 -0.0777 -0.0773 -0.0509 -0.0829 -0.0835 -0.0845 -0.4190 -0.3787 -0.4265 -0.4266 -0.3888 -0.4 2 52 -0.4170 -0.4232 -0.0562 -0.0769


2766.0000 3074.0000 3381.0000 3688.0000 3996.0000 4303.0000 0.0000 307,4000 614.7000 922. 1000 1229.0000 1537.0000 1844.0000 2152.0000 2459.0000 2766.0000 3074.0000 3381.0000 3688.0000 3996.0000 4303.0000 0.0000 307.4000 614.7000 922.1000 1229.0000 1537.0000 1844.0000 2152.0000 2459.0000 2766.0000 3074.0000 3381 .0000 3688.0000 3996.0000 4303.0000 0.0000 307.4000 614.7000 922.1000 1229.0000 1537.0000 1844.0000 2152.0000 2459 .0000 2766.0000 3074.0000 3381.0000 3688.0000 3996 .0000 4303.0000 0.0000 307.4000 614 .7000

903.4000 903.4000 903.4000 903.4000 903.4000 903.4000 1205.0000 1205.0000 1205.0000 1205.0000 1205.0000 1205.0000 1205.0000 1205.0000 1205.0000 1205.0000 1205.0000 1205.0000 1205.0000 1205.0000 1205.0000 1506.0000 1506.0000 1506.0000 1506.0000 1506.0000 1506.0000 1506.0000 1506.0000 1506.0000 1506.0000 1506.0000 1506.0000 1506.0000 1506.0000 1506.0000 1807.0000 1807.0000 1807.0000 1807.0000 1807.0000 1807.0000 1807.0000 1807.0000 1807.0000 1807.0000 1807.0000 1807.0000 1807.0000 1807.0000 1807.0000 2108.0000 2108.0000 2108.0000

0 .0059 -0 .4219 -0 .421 1 -0 .4189 -0 .4183 -0 .4215 -0 .3798 -0 .3788 -0 .3794 -0 .3749 -0 .4024 -0 .4276 -0 .4275 -0 .4268 -0 .2005 -0 . 1036 -o,.4253 -0,.4254 -0,.4249 -o,.4239 -0,.4223 -o,.3617 -0,.3615 -0,.3609 -0,.3675 -0,.3983 -0..4274 -0,.4270 -0,.4251 -0,.0875 -0..4163 -0..4256 -0..4258 -0..4250 -0..4238 -0..4218 -0.,3610 -0..3603 -0.,3602 -0..4262 -0..4281 -0.,4277 -0.,4272 -0.,4263 -0.,4235 -0.,4248 -0.,4259 -0.,4257 - 0 .,4249 -0.,4235 -0.,4212 - 0 .,3615 - 0 .,3603 - 0 .,4124


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197

E.4

GRIDDED OBSERVED "TOPOGRAPHY CORRECTED" GRAVITY DATA DATA IS ORDERED AS FOLLOWS:

COLUMN

VALUE

1

METERS EAST

2

METERS SOUTH

3

CALCULATED GRAVITY VALUE (MGALS)

THIS IS THE DATA SET THE FORWARD AND INVERSE GRAVITY MODELING PROGRAMS WILL ATTEMPT TO MATCH


0.0 000 306.2545 612.5089 918.7634 1225.0178 1531 .2723 1837.5267 2143.7813 2450.0356 2756.2900 3062.5447 3368.7991 3675.0535 3981.3079 4287.5625 0.0000 306.2544 612.5088 918.7632 1225.0176 1531.2725 1837.5269 2143.7813 2450.0356 2756.2900 3062.5444 3368.7988 3675.0532 3981.3081 4287.5620 0.0000 306.2539 612.5088 918.7637 1225.0176 1531.2725 1837.5264 2143.7813 2450.0352 2756.2900 3062.5449 3368.7988 3675.0537 3981.3076 4287.5625 0.0000 306.2539 612.5078 918.7627 12 2 5.0176 1531.2715 1837.5264 2143.7803 2450.035 2

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 301 . 1504 301.1504 301 . 1504 301.1504 301 . 1504 301. 1504 301.1504 301.1504 301 .1504 301.1504 301.1504 301 .1504 301.1504 301.1504 301.1504 602.3008 602.3008 602.3008 602.3008 602.3008 602.3008 602.3008 602.3008 602.3008 602.3008 602.3008 602.3008 602.3008 602.3008 602.3008 903.4512 903.4512 903.4512 903.4512 903.4512 903.4512 903.4512 903.4512 903.4512

-5 .7401 -6 .6401 -7 .4409 -8 .2732 -9 .9184 -10 .8207 -12 .0207 -13 . 1207 -14 . 1210 -14,.5212 -14,.9094 -15,.0089 -15 . 1088 -15,.5042 -15,.8789 -5,.3450 -6,.4427 -7,.3725 -8,.5752 -9..9172 -10..8858 -12,.2028 -13..2043 -14..5217 -15., 1220 -15.,2221 -15.,4191 -15.,6188 -15..8159 -16..3797 -4.,6431 -5.,9469 -7.,2732 -8.,3739 -9.,3767 -10,,6684 -11.,8836 -12.,9986 -14., 1220 -15.,0225 -15.,6489 -15.,7169 -15.,9163 -16. 5153 -16. 7808 -3.,2211 - 4 .,6733 - 5 . 5732 -6. 8110 - 7 . 8746 -9. 1828 -10. 3766 -12. 1436 -13. 5229


2756 .2891 3062 .5430 3368 .7988 3675 .0527 3981 .3066 4287 .5625 0,.0000 306 .2539 612 .5078 918 .7637 .0176 1 225, 15 31,.2715 1837 .5273 2143,.7813 2450,.0352 2756,.2891 3062,.5449 3368,.7988 3675,.0527 3981,.3086 4287 .5625 , 0,.0000 306,.2539 612..5098 918,.7637 1225..0176 .1531 .2734 , 1837..5273 2143.. 7813 2450..0352 2756..2910 3062..5449 3368..7988 3675,.0527 .3086 3981 , 4287 , .5625 0..0000 306..2539 612..5078 918..7617 1225..0156 1531 . .2715 1837..5254 2143.,7793 2450.,0352 2756.,2891 3062 . ,5430 3368.,7969 3675.,0527 3981.,3066 4287.,5605 0.,0000 306.,2539 612.,5078

903 .451 2 903 .4512 903 .4512 903 .4512 903 .4512 903 .4512 1204 .6016 1204 .6016 1204 .6016 1204 .6016 1204 .6016 1204 .6016 1204 .6016 1204 .6016 1204 .6016 1204 .6016 1204 .6016 1204 .6016 1204 .6016 1204 .6016 1204 .6016 1505 .7520 1505 .7520 1505 .7520 1505 .7520 1505 .7520 1505 .7520 1505 .7520 1505 .7520 1505 .7520 1505 .7520 1505 .7520 1505 .7520 1505 .7520 1505 .7520 1505 .7520 1806 .9023 1806 .9023 1806 .9023 1806 .9023 1806 .9023 1806 .9023 1806 .9023 1806 .9023 1806 .9023 1806 .9023 1806 .9023 1806 .9023 1806 .9023 1806 .9023 1806 .9023 2108 .0527 2108 .0527 2108 .0527

-15 .0057 -15 .3779 -16 .0787 -16 .4809 -16 .9815 -17 .6783 -1 .5200 -3 .1210 -4,.6204 -5 .6249 -6 .5974 -8 .7722 -9 .9723 -11 .4731 , -12,.8994 -14,.6963 -15,.6746 -16,.7745 -17,.4750 -18,.0760 -18,.6776 -0,.7382 -1 .7384 , -3,.8390 -5,.4324 -6,.5016 -8,.0725 -9,.5729 -1 1 .1748 , -12,.9124 -14..3836 -15..8743 -17..0741 -17..8749 -18..7761 -18..9781 -0..2611 -0.,9396 -2..6397 -5.,3737 -6..8718 -7..8722 -9.,5727 -1 1 ,3736 . -12.,6764 -14.,5751 -16..0740 -17.,3742 -18.,0750 -18.,7764 -19.,1787 -0.,6384 -1 , . 1396 -2..7875


200

918 .7617 1225,.0156 1531 .2695 , 1837,.5273 2143,.7813 2450,.0352 2756,.2891 3062,.5430 3368,.7969 3675..0508 3981 , .3086 4287 . .5625

2108 2108 2108 2108 2108 2108 2108 2108 2108 2108 2108 2108

0527 0527 0527 0527 0527 0527 0527 0527 0 5 2.7

0527 0527 05 2 7

-6 .2025 -8 .5723 -9,.8723 -1 1 .0727 -12,.0730 -13,.4731 - 1 4 ,.9738 -16,.5740 - 1 7 ,.6745 -18..3752 -19,. 1768 -19..8795


APPENDIX F

FOWARD AND INVERSE 3-D GRAVITY MODELING RESULTS FOR THE ENNIS GEOTHERMAL AREA

F.l

F.2

FORWARD MODELING RESULTS F.1.1

FORWARD MODEL OF THE ENNIS GEOTHERMAL AREA

F.1.2

INPUT FILE (GRAVBL.DAT) FOR PROGRAM GRAVBL

F.1.3

CALCULATED GRAVITY OUTPUT FROM PROGRAM GRAVBL

INVERSE MODELING RESULTS F.2.1

INPUT FILE FOR PROGRAM GINDEP

F.2.2

OUTPUT OF PROGRAM GINDEP (FILE GINDEP.OUT)

F.2.3

GRAVITY VALUES CALCULATED USING THE RESULTS OF PROGRAM GINDEP


202

F.l

FORWARD MODELING (PROGRAM GRAVBL) RESULTS


203

F.1.1

FORWARD MODEL OF THE ENNIS GEOTHERMAL AREA

(SEE APPENDIX E

FOR A DESCRIPTION OF HEADINGS)


BLOCK 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

XL

0.0 500.0 1000.0 1500.0 2000.0 2500.0 3000.0 3500.0 4000.0 0.0 500.0 1000.0 1500.0 2000.0 2500.0 3000.0 3500.0 4000.0 0.0 500.0 1000.0 1500.0 2000.0 2500.0 3000.0 3500.0 4000.0 0.0 500.0 1000.0 1500.0 2000.0 2500.0 3000.0 3500.0 4000.0 0.0 500.0 1000.0 1500.0 2000.0 2500.0 3000.0 3500.0 4000.0 0.0 500.0 1000.0 1500.0 2000.0 2500.0 3000.0

XR

ZMIN

ZMAX

YMIN

500.0 1000.0 1500.0 2000.0 2500.0 3000.0 3500.0 4000.0 4500.0 500.0 1000.0 1500.0 2000.0 2500.0 3000.0 3500.0 4000.0 4500.0 500.0 1000.0 1500.0 2000.0 2500.0 3000.0 3500.0 4000.0 4500.0 500.0 1000.0 1500.0 2000.0 2500.0 3000.0 3500.0 4000.0 4500.0 500.0 1000.0 1500.0 2000.0 2500.0 3000.0 3500.0 4000.0 4500.0 500.0 1000.0 1500.0 2000.0 2500.0 3000.0 3500.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

300.0 400.0 500.0 700.0 850.0 800.0 900.0 700.0 800.0 125.0 400.0 450.0 600.0 800.0 750.0 950.0 700.0 800.0 125.0 100.0 180.0 230.0 700.0 850.0 850.0 900.0 1000.0 10.0 100.0 140.0 300.0 400.0 700.0 900.0 1100.0 1200.0 2.0 80.0 230.0 500.0 525.0 700.0 900.0 1250.0 1300.0 5.0 100.0 300.0 400.0 500.0 700.0 900.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 800.0 800.0 800.0 800.0 800.0 800.0 800.0 800.0 800.0 1200.0 1200.0 1200.0 1200.0 1200.0 1200.0 1200.0 1200.0 1200.0 1600.0 1600.0 1600.0 1600.0 1600.0 1600.0 1600.0 1600.0 1600.0 2000.0 2000.0 2000.0 2000.0 2000.0 2000.0 2000.0

YMAX 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 800.0 800.0 800.0 800.0 800.0 800.0 800.0 800.0 800.0 1200.0 1200.0 1200.0 1200.0 1200.0 1200.0 1200.0 1200.0 1200.0 1600.0 1600.0 1600.0 1600.0 1600.0 1600.0 1600.0 1600.0 1600.0 2000.0 2000.0 2000.0 2000.0 2000.0 2000.0 2000.0 2000.0 2000.0 2400.0 2400.0 2400.0 2400.0 2400.0 2400.0 2400.0

DEN -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5


O O s J s l M M N j M N j N j M M O O ^ O N O . O N O N O O ^ O N O ^ U l N / I U i y ' U I V J l U I O I C O O M O

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O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O W M r - u J * ' l N ) ' - i n O > o < M w l N ) l N ! * - o x * O O O v e v e C » C » U i 4 > * ' i N ; O O O u i O u i O O O O O u i O O O O O O O O U i U i U i O u i N J O u i O O O O O O O O O O O O O O O O O O O O U i O O O O U i O O

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206

F.1.2

INPUT FILE (GRAVBL.DAT) FOR PROGRAM GRAVBL


80

0 . , 5 0 0 . , 300 0 . • ,0. ,400. ,-.5 500. ,1000., o., 400. , 0. ,400. ,-.5 1000. , 1500.,0 .,500. ,0. ,400. ,-.5 1500. ,2000. ,0. ,700. ,0. ,400.,-.5 2000. ,2500. ,0. ,850. ,0. ,400. ,-.5 2500.,3000. ,0. ,800. ,0. ,400. ,-.5 3000. ,3500. ,0. ,900. ,0. ,400.,-.5 3500.,4000. ,0. ,700. ,0. ,400. ,-.5 4000. ,4500. ,0. ,800. ,0. ,400. ,-.5 0 . , 500. ,0. 125 , . ,400. ,800.,-.5 5 00. ,1000. ,0. ,400. , 400. ,800. ,-.5 1000. , 1500.,0. ,450. ,400. ,800. ,- 5 1500.,2000. .0. ,600. ,400.,800. ,-. 5 2000. ,2500. ,0. ,800. ,400. ,800. ,- .5 2500. ,3000. ,0. ,750. ,400. ,800 5 3000.,3500. ,0. ,950. ,400.,800.,-. 5 3500. ,4000. ,0. ,700. ,400.,800. ,-. 5 4000.,4500. ,0. ,800. ,400. ,800. ,-. 5 0. ,500. ,0. , 125 . ,800. ,1200. ,-.5 500. , 1000. ,o., 100. ,800.,1200.,-. 5 1000. , 1500.,0. , 180.,800. ,1200. ,--.5 1500.,2000. ,0. ,230. ,800. ,1200. ,--.5 2000.,2500. ,0. ,700. ,800. ,1200. ,--.5 2500. ,3000. ,0. ,850. ,800. ,1200. ,--.5 3000.,3500. ,0. ,850. ,800. , 1200. ,--.5 3500.,4000. ,o. ,900. ,800. ,1200. ,--.5 , 4000. ,4500. ,0. , 1000 . ,800 . , 1200 .-.5 0. ,500. ,0. , 10. ,1200 . , 1600 . ,-.5 500. , 1000. ,0. ,100. ,1 2 0 0 . , 1 6 0 0 . ,--.5 , 1000.,1500. ,0. ,140. ,1200. , 1 6 0 0 . -.5 1500. ,2000. ,0. ,300. , 1 2 0 0 . ,1600. ,-.5 2000. ,2500. ,0. ,400. ,1200. , 1 6 0 0 . , -.5 , 2500. ,3000. ,0. ,700. , 1 2 0 0 . , 1 6 0 0 . -.5 3000. ,3500. ,0. ,900. ,1200. , 1 6 0 0 . , -.5 . , 1 2 0 0 . , 1 6 0 0 . ,-.5 3500.,4000. ,0. , 1 100 4000.,4500. ,0. ,1200 . ,1200. ,1600. ,-•5 0. ,500. ,0. , 2., 1600. ,2000.,-.5 500. , 1000. ,0., 80. , 1600. ,2000. ,-.5 1000. ,1500. ,0. ,230. , 1 6 0 0 . , 2 0 0 0 . ,-.5 1500. ,2000. ,0. ,500. ,1600. , 2 0 0 0 . , -.5 2000. ,2500. ,0. ,525. ,1600. ,2000. , -.5 2500. ,3000. ,0. ,700. ,1600. , 2 0 0 0 . , -.5 3000. ,3500. ,0. ,900. , 1 6 0 0 . ,2000. , -.5 3500. ,4000. ,0. ,1250 . , 1 6 0 0 . , 2 0 0 0 . ,-•5 4000.,4500. ,0. ,1300 . , 1 6 0 0 . ,2000. ,-.5 0. ,500. ,0. , 5. ,2000. ,2400. ,-.5 500. ,1000., o., 100. ,2 0 0 0 . , 2 4 0 0 . ,- .5 1000. ,1500. ,0. ,300. ,2000. ,2400. , -.5 1500. ,2000. ,0. ,400. ,2000. , 2 4 0 0 . , -.5 2000. ,2500. ,0. ,500. ,2000. ,2400. , -.5 2500.,3000. ,0. ,700. ,2000. , 2 4 0 0 . , -.5 3000. ,3500. ,0. ,900. ,2000. , 2 4 0 0 . , -.5 3500. ,4000. ,0. ,1250 . ,2000. , 2 4 0 0 . ,-•5


4000.,4500. ,0. , 1400. ,2000.,2400. ,-.5 0. , 1000. ,0.,425. ,-800. ,0. ,-.5 1000. ,2000. ,0. ,550.,-800. ,0. ,-.5 2000. ,3000. ,0. ,800. ,-800.,0.,-.5 3000.,4000. ,0 . ,850. ,-800. ,0.,-.5 4000. ,5500. ,0. ,950. ,-800. ,0. ,-.5 4500. ,5500. ,0. ,955. ,0. ,800. ,-.5 4500. ,5500. ,0. , 1000. ,800. , 1600. ,.5 4500. ,5500. ,0. , 1000. ,1600. ,2400. ,-.5 4000. ,5500. ,0. ,1000. ,2400. ,3200. , -.5 3000. ,4000. ,0. ,900. ,2400. ,3200. ,- .5 2000. ,3000. ,0. ,600. ,2400. ,3200. ,- .5 1000. ,2000. ,0. ,400. ,2400. ,3200. ,- .5 0 . ,1000. ,0.,200. ,2400. ,3200. ,-.5 -1000. ,0. ,0 . ,200. ,0. ,800. ,-.5 -1000. ,0. ,0 . ,350. ,-800. ,0 . ,-.5 -1000. ,1000 . ,0. ,200. ,-2400. ,-800. ,-.5 1000. ,3000. ,0. ,600. ,-2400. ,-800. , -.5 3000.,5500. ,0. ,600. ,-2400. ,-800., -.5 5500.,7500. ,0. ,1500. ,-2400.,-800. ,-.5 5500. ,7500. ,0. , 1 100. ,-800. ,0. ,-.5 5500. ,7500. ,0.,1250. ,0. ,1600. ,-.5 5500.,7500. ,0. ,1400. , 1600. ,3200. ,-.5 5500.,7500. ,0. ,1350. ,3200.,4600. , -.5 3000.,5500. ,0. ,1100. ,3200.,4600. , -.5 1000. ,3000. ,0. ,700. ,3200. ,4600. ,- .5 -1000. ,1000 .,0.,300.,3200.,4600., -.5 4287 .5 ,2108 .1,15,8 5 1 1475. F0R012.DAT


209

F.1.3

CALCULATED GRAVITY VALUES OUTPUT FROM PROGRAM GRAVBL (FILE GBL.DAT)


0.0000 306.2500 612.5000 918.7500 1225.0000 1531 .2500 1837 .5000 2143.7500 2450.0000 2756.2500 3062.5000 3368.7500 3675.0000 3981.2500 4287.5000 0.0000 306.2500 612.5000 918.7500 1225.0000 1531.2500 1837.5000 2143.7500 2450.0000 2756.2500 3062.5000 3368.7500 3675.0000 3981.2500 4287.5000 0.0000 306.2500 612.5000 918.7500 1225.0000 1531.2500 1837.5000 2143.7500 2450.0000 2756.2500 3062.5000 3368.7500 3675.0000 3981.2500 4287.5000 0.0000 306.2500 612.5000 918.7500 1225.0000 1531.2500 1837.5000 2143.7500 2450.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 301 .1572 301 . 1572 301. 1572 301.1572 301.1572 301. 1572 301 .1572 301 . 1572 301 . 1572 301. 1572 301.1572 3 01.15 7 2 301.1572 301 . 1572 301 .1572 602.3143 602.3143 602.3143 602.3143 602.3143 602.3143 602.3)43 602.3143 602.3143 6 0 2.3143 602.3143 602.3143 602.3143 602.3143 602.3143 903.4715 903.4715 903.4715 903.4715 903.4715 903.4715 903.4715 90 3.47 15 903.4715

-6.5110 -7.3256 -8.1732 -9.0949 -10.0984 -11 .0935 -12.0770 -13.0059 -13.7758 -14.3777 -14.8602 -15.2375 -15.5726 -15.9787 -16.4592 -5.5927 -6.4180 -7.6150 -8.7 096 -9.7609 -10.8715 -11 .9795 -13.0126 -13.8786 -14.5690 -15.1205 -15.5284 -15.8803 -16.2981 -16.8049 -4.5250 -5.0262 -6.6296 -7.8447 -8.8944 -10.0456 -1 1 .3187 -12.6165 -13.6978 -14.5414 -15.2159 -15.7451 -16.1819 -16.6427 -17.1513 -2.9414 -4.1786 -4.916 1 -5.9172 -7.3018 -8.6134 -10.1731 -11.9788 -13.4020


2756.2500 3062.5000 3 368.7500 3675.0000 3981 .2500 4287 .5000 0.0000 306.2500 612.5000 918.7500 1225.0000 1531 .2500 1837 .5000 2143.7500 2450.0000 2756.2500 3062.5000 3368.7500 3675.0000 3981 .2500 4287.5000 0.0000 306.2500 612.5000 918.7500 1225.0000 1531.2500 1837.5000 2143.7500 2450.0000 2756.2500 3062.5000 3368.7500 3675.0000 3981.2500 4287.5000 0.0000 306.2500 612.5000 918.7500 1225.0000 1531.2500 1837.5000 2143.7500 2450.0000 2756.2500 3062.5000 3368.7500 3675.0000 3981.2500 4287.5000 0.0000 306.2500 612.5000

903.4715 903.4715 903.4715 903.4715 903.4715 903.4715 1204.6287 1204.6287 1204.6287 1204.6287 1204.6287 1204.6287 1204.6287 1204.6287 1204.6287 1204.6287 1204.6287 1204.6287 1204.6287 1204.6287 1204.6287 1505.7859 1505.7859 1505.7859 1505.7859 1505.7859 1505 .7859 1505.7859 1505.7859 1505.7859 1505.7859 1505.7859 1505.7859 1505.7859 1505.7859 1505.7859 1806.9430 1806.9430 1806.9430 1806.9430 1806.9430 1806.9430 1806.9430 1806.9430 1806.9430 1806.9430 1806.9430 1806.9430 1806.9430 1806.9430 1806.9430 2108.1001 2108.1001 2108.1001

-14 .4657 -1 5.3094 -15 .9802 -16 .5383 -17 .0566 -17 .5569 -1 .9494 -2 .85 20 -3 .9317 -4 .8452 -6 .2126 -7 .7570 -9 .5271 -11 .3777 -12 .9654 -14 .2734 -15 .3240 -16 .1708 -16 .8655 -17 .4452 -17,.9248 -1 .3618 , -1 .8776 -3,.5249 -4,.5664 -6,.0339 -7,.8185 -9,.6210 -J 1 .1996 , -12,.7222 -14..1441 -15,.3323 -16,.3195 -17., 1201 -17..7452 -18..2148 -1 .2369 . -1 .6729 . -3..3414 -4..6149 -6.,6528 -8.,3452 -9.,9494 -11 . ,3196 -12,,7031 -14.,0795 -15.,3155 -16.,3741 -17 . ,2353 -17 . ,8921 -18.,3640 -1 ,3644 . -1 . ,9025 -3.,7099


918.7500 1225.0000 1531.2500 1837.5000 2143.7500 2450.0000 2756.2500 3062.5000 3368.7500 3675.0000 3981.2500 4287.5000

2108.1001 2108.1001 2108.1001 2108.1001 2108.1001 2108.1001 2108.1001 2108.1001 2108.1001 2108.1001 2108.1001 2108.1001

-5.1071 -7.1975 -8.7005 -10.0999 -11.4072 -12.7231 -14.0392 -15.2694 -16.3492 -17.2309 -17.9008 -18.3832


213

F.2

INVERSE MODELING (PROGRAM GINDEP) RESULTS


214

F.2.1

INPUT FILE FOR PROGRAM GINDEP (FILE G.DAT)


FOROl8.DAT 5 2100 0 80 0. ,500. ,0. , 300 . ,0. ,400. ,-.5 500. ,1000. ,0 . ,<400. ,0 . ,400. ,-.5 1000. ,1500. ,0. ,500. ,0. ,400. ,-.5 1500.,2000. ,0. ,700. ,0.,400.,-.5 2000.,2500. ,0. ,850. ,0. ,400.,-.5 2500.,3000. ,0. ,800. ,0. ,400. ,-.5 3000.,3500. ,0. ,900. ,0. ,400. ,-.5 3500.,4000. ,0. ,700. ,0.,400.,-.5 4000. ,4500. ,0. ,800. ,0.,400.,-.5 0. ,500. ,0 . ,125 . ,400.,800.,-.5 1000. , 1500.,0. ,450. ,400. ,800. ,-. 5 1500. ,2000. ,0. ,600. ,400. ,800. ,-, 5 2000.,2500. ,0. ,800. ,400. ,800. ,-. 5 2500.,3000. ,0. ,750. ,400. ,800. ,-. 5 3000.,3500. ,0. ,950. ,400. ,800 5 3500. ,4000. ,0. 700. ,400.,800 5 4000. ,4500. ,0. ,800. ,400. ,800 . ,-.5 0. ,500. ,0. ,125 ,800 . , 1200. ,-.5 500. , 1000. 0. , ,]LOO. ,800. , 1200. ,-.5 1000.,1500. ,0. 180. ,800. , 1200. ,-.5 1500. ,2000. ,0. 230. ,800.,1200. ,--.5 2000.,2500. ,0. 700. ,800. ,1200. ,--.5 2500.,3000. ,0. ,850. ,800. , 1200 . ,-.5 3000. ,3500. ,0. ,850. ,800. , 1200. ,-.5 3500.,4000. ,0. ,900. ,800. , 1200. ,-.5 4000.,4500. ,0. 1000 . ,800. , 1200 .-.5 , 0. ,500. ,0. , 10. ,1200 . ,1600. ,-.5 500. ,1000. ,0. ,] 00. , 1200. ,1600. ,--.5 1000. ,1500. ,0. ,140. , 1200. , 1600.-.5 , 1500. ,2000. ,0. ,300. ,1200.,1600. ,-.5 2000.,2500. ,0. ,400. , 1200. , 1600.-.5 , , 2500.,3000. ,0. , 700. ,1200. , 1600. -.5 3000.,3500. ,0. ,900. , 1200. , 1600.-.5 , 3500.,4000. ,0. ,1100 . ,1200. ,1600. ,-*5 4000.,4500. ,0. , 1200 .,1200.,1600. ,-*5 0.,500.,0. ,2. ,1 600. ,2000.,-.5 500. ,1000. ,0. ,g10. , 1600. ,2000. ,-.5 1000.,1500. ,0. , 230. , 1600. ,2000. ,-.5 1500.,2000. ,0. , 500. ,1600. ,2000. ,-.5 2000. ,2500. ,0., 525. ,1600. ,2000. ,-.5 2500.,3000. ,0. , 700. , 1600. ,2000. ,-.5 3000. ,3500. ,0. , 900. ,1600.,2000. ,-.5 3500. ,4000. ,0. , 1250 .,1600.,2000. ,-*5 4000. ,4500. ,0. , 1300 . ,1600.,2000.,-•5 0.,500. ,0 . ,5. ,2 000. ,2400.,-.5 500.,1000. ,0. , 100. , 2000. ,2400. ,-.5 1000. ,1500. ,0. , 300. ,2000. ,2400. ,-.5 1500. ,2000. ,0. , 400. ,2000. ,2400. ,-.5


2 0 0 0 . ,2500. 2 5 0 0 . ,3000. 3 0 0 0 . ,3500. 3 5 0 0 . ,4000.

,0. ,500. ,2000. ,2400. ,-.5 , 0.,700. ,2000. ,2400. ,-.5 ,0. ,900. ,2000. ,2400. ,-.5 ,0. 1250 . ,2000. ,2400. ,-.5 4000. ,4500. 0. , 1400 . ,2000. ,2400. ,-.5 0. ,1000. ,0. ,425.,-8 00.,0.,-.5 1000. ,2000. ,0. ,550. ,-800. ,0. ,-.5 2000. ,3000. ,0. ,800. ,-800.,0.,-.5 3000. ,4000. 0. 850. ,-800 . ,0 . , -.5 4000. ,5500. 0. 950. ,-800.,0. ,-.5 4500. ,5500. 0. 955. ,0 . ,800. , -.5 4500. ,5500. 0. 1000 . ,800 . ,1600. ,- • 5 4500. ,5500. 0. 1000 . ,1600. ,2400. ,-.5 4000. ,5500. 0. 1000 .,2400.,3200•,-.5 3000. ,4000. 0. 900. ,2400. , 3200. ,-.5 2000. ,3000. 0. 600. ,2400.,3200.,-.5 1000. ,2000. 0. 400. ,2400.,3200. ,-.5 0. , 1000. , 0 . 200. ,24 00. ,3200. ,-.5 -1000 . ,0. ,0., 200. ,0.,800.,-.5 -1000 . ,0. ,0. ,350. ,- 800.,0.,-.5 -1000 .,1000. ,0. ,200 .,-2400. ,-800 . ,-.5 1000. ,3000. 0. 600. ,-2400.,-800. ,- . 5 3000. ,5500. , 0. 600. ,-2400.,-800. ,-.5 5500. ,7500. ,0. ,1500 . ,-2400. ,-800. ,-.5 5500. ,7500. ,0. ,1 100 .,-800.,0.,-.5 5500. ,7500., 0. ,1250 . ,0. , 1600. ,-.5 5500. ,7500., 0. ,1400 . , 1600. ,3200. ,-.5 5500. ,7500. ,0. 1350 .,3200.,4600.,-.5 3000. ,5500., 0. ,1100 . ,3200.,4600. ,-.5 1000. ,3000. , 0. ,700. ,3200.,4600.,-.5 -1000 . , 1000.,0. ,300 . ,3200.,4600. ,-.5 0 0.5 15 1 1475. F0R012.DAT


217

F.2.2

OUTPUT OF PROGRAM GINDEP (FILE GINDEP.OUT)


218

i V * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

GRID INFO GRID SIZE GRID SIZE NUMBER OF NUMBER OF

IN X DIRECTION (METERS)= IN Y DIRECTION (METERS)= COLUMNS= 15 ROWS= 8

0.4288E+04 0.2108E+04

INPUT MODEL BLOCK # XMIN XMAX 500.0 1 0.0 1000.0 500.0 2 1500.0 3 1000.0 2000.0 4 1500.0 2500.0 5 2000.0 3000.0 6 2500.0 3500.0 7 3000.0 8 3500.0 4000.0 9 4000.0 4500.0 500.0 0.0 10 1000.0 1 1 500.0 1500.0 12 1000.0 2000.0 13 1500.0 14 2000.0 2500.0 15 2500.0 3000.0 3500.0 16 3000.0 17 3500.0 4000.0 18 4000.0 4500.0 19 0.0 500.0 1000.0 500.0 20 1000.0 1500.0 21 1500.0 2000.0 22 2500.0 23 2000.0 24 2500.0 3000.0 25 3000.0 3500.0 26 3500.0 4000.0 27 4000.0 4500.0 28 0.0 500.0 29 500.0 1000.0 30 1000.0 1500.0 31 1500.0 2000.0 32 2000.0 2500.0 3000.0 33 2500.0 34 3000.0 3500.0 35 3500.0 4000.0 36 4000.0 4500.0

YMIN 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 800.0 800.0 800.0 800.0 800.0 800.0 800.0 800.0 800.0 1200.0 1200.0 1200.0 1200.0 1200.0 1200.0 1200.0 1200.0 1200.0

YMAX 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 400.0 800.0 800.0 800.0 800.0 800.0 800.0 800.0 800.0 800.0 1200.0 1200.0 1 200.0 1200.0 1200.0 1200.0 1200.0 1200.0 1200.0 1600.0 1600.0 1600.0 1600.0 1600.0 1600.0 1600.0 1600.0 1600.0

ZMIN ZMAX 0.0 300.0 0.0 400.0 0.0 500.0 0.0 700.0 0.0 850.0 0.0 800.0 900.0 0.0 0.0 700.0 0.0 800.0 125.0 0.0 400.0 0.0 450.0 0.0 0.0 600.0 0.0 800.0 0.0 750.0 0.0 950.0 0.0 700.0 0.0 800.0 0.0 125.0 0.0 100.0 0.0 180.0 0.0 230.0 0.0 700.0 0.0 850.0 0.0 850.0 0.0 900.0 0.0 1000.0 10.0 0.0 0.0 100.0 0.0 140.0 0.0 300.0 0.0 400.0 0.0 700.0 0.0 900.0 0.0 1 100.0 0.0 1200.0

DEN -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50


37 0.0 500.0 1600.0 2000.0 0.0 2.0 -0.50 1000.0 1600.0 38 500.0 0.0 2000.0 80.0 -0.50 1500.0 1600.0 2000.0 0.0 39 1000.0 230.0 -0.50 2000.0 1600.0 2000.0 40 1500.0 0.0 500.0 -0.50 41 2000.0 2500.0 1600.0 2000.0 0.0 525.0 -0.50 3000.0 1600.0 2000.0 42 2500.0 0.0 700.0 -0.50 3500.0 1600.0 2000.0 43 3000.0 0.0 900.0 -0.50 44 3500.0 4000.0 1600.0 2000.0 0.0 1250.0 -0.50 4500.0 1600.0 2000.0 0.0 1300.0 -0.50 45 40 00.0 500.0 2000.0 2400.0 0.0 46 0.0 5.0 -0.50 47 500.0 1000.0 2000.0 2400.0 0.0 100.0 -0.50 2400.0 300.0 48 1000.0 1500.0 2000.0 0.0 -0.50 2400.0 0.0 49 1500.0 2000.0 2000.0 400.0 -0.50 2500.0 2000.0 2400.0 0.0 500.0 -0.50 50 2000.0 3000.0 2000.0 2400.0 0.0 700.0 -0.50 51 2500.0 2400.0 0.0 900.0 -0.50 52 3000.0 3500.0 2000.0 4000.0 2000.0 2400.0 0.0 1250.0 -0.50 53 3 5 00.0 2400.0 0.0 1400.0 54 4000.0 4500.0 2000.0 -0.50 0.0 1000.0 -800.0 0.0 425.0 -0.50 55 0.0 0.0 0.0 550.0 -0.50 56 1000.0 2000.0 -800.0 0.0 0.0 800.0 -0.50 57 3000.0 -800.0 2000.0 850.0 0.0 0.0 58 3000.0 4000.0 -800.0 -0.50 0.0 0.0 950.0 59 40 00.0 5500.0 -800.0 -0.50 0.0 800.0 0.0 955.0 -0.50 60 4 5 00.0 5500.0 1600.0 0.0 1000.0 -0.50 61 4500.0 5500.0 800.0 5500.0 1600.0 2400.0 0.0 1000.0 -0.50 62 4500.0 0.0 1000.0 -0.50 5500.0 2400.0 3200.0 63 4000.0 64 3000.0 4000.0 2400.0 3200.0 0.0 900.0 -0.50 0.0 2000.0 600.0 -0.50 65 3000.0 2400.0 3200.0 2000.0 2400.0 3200.0 0.0 400.0 -0.50 66 1000.0 0.0 200.0 -0.50 67 0.0 1000.0 2400.0 3200.0 0.0 800.0 0.0 200.0 -0.50 68 -1000.0 0.0 -800.0 0.0 0.0 350.0 0.0 -0.50 69 -1000.0 0.0 200.0 -0.50 70 -1000.0 1000.0 -2400.0 -800.0 0.0 600.0 -0.50 3000.0 -2400.0 -800.0 71 1000.0 0.0 600.0 -0.50 5500.0 -2400.0 -800.0 72 3000.0 0.0 1500.0 -0.50 7500.0 -2400.0 -800.0 73 5500.0 0.0 0.0 1100.0 -0.50 7500.0 -800.0 74 5500.0 0.0 1600.0 0.0 1250.0 -0.50 7500.0 75 5500.0 0.0 1400.0 -0.50 1600.0 3200.0 5500.0 7500.0 76 3200.0 4600.0 0.0 1350.0 -0.50 77 5500.0 7500.0 0.0 1 100.0 -0.50 5500.0 3200.0 4600.0 78 3000.0 700.0 -0.50 0.0 79 1000.0 3000.0 3200.0 4600.0 -0.50 0.0 300.0 80 -1000.0 1000.0 3200.0 4600.0 ****************************************************** ******************************************************

TABLE OF CONVERGENCE $ITERATION // 1 $STARTING DATA ERROR=

0.1063E+01


JLOCK 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

PARM. JUMP. 0 . 1047E + 03 -0 . 1987E+03 0 .3554E+02 -0 .8374E+02 0 .6323E+03 0 .2014E+03 0 .3590E+03 0 .1582E+03 0 .5O70E+03 0 . 1078E + 03 0 .3168E+03 0 .2920E+03 0 .6470E+03 0 .3071E+03 0 .6297E+03 -0 .4196E+03 -0 .3855E+03 -0,.1095E+03 0 .6429E+02 0 .5369E+02 0 .3378E+02 0,.8988E+01 -0,.7681E+02 0,.4796E+03 -0,.6419E+03 0,.5044E+03 0,. 1630E+04 0,.2736E+02 0,.1102E+03 0,.8375E+02 0..4467E+03 0,.4179E+02 0..5776E+03 0..7077E+03 0..8904E+03 0., 1346E + 04 0..2308E+02 0..4745E+02 0., 1307E + 03 - 0 ,, 1482E + 03 0..4768E+03 -0., 1406E+03 0. 7510E+03 - 0 ., 1806E + 03 - 0 . 8592E+03 0. 1366E+03 0. 2746E+03 0. 8899E+03 0. 1095E+04 0. 4472E+03 0. 5935E+03 0. 2403EI-04

NEW PARMS 0 .4047E+03 0 .2013E+03 0 .5355E+03 0 .6163E+03 0 .1482E+04 0 . 1001E+04 0 .1259E+04 0 .8582E+03 0 .1307E+04 0 .2328E+03 0 .7168E+03 0 .7420E+03 0 .1247E+04 0 .1 107E+04 0 . 1380E+04 0 .5304E+03 0 .3145E+03 0 .6905E+03 0,. 1893E+03 0,. 1537E + 03 0,.2138E+03 0,.2390E+03 0,.6232E+03 0.. 1330E + 04 0,.2081E+03 0..1404E+04 0..2630E+04 0..3736E+02 0,.2102E+03 0..2237E+03 0..7467E+03 0..4418E+03 0.. 1278E+04 0.. 1608E + 04 0., 1990E + 04 0..2546E+04 0.•2508E+02 0. 1275E+03 0. 3607E+03 0. 3518E+03 0., 1002E + 04 0. 5594E+03 0. 1651E+04 0. 1069E+04 0. 4408E+03 0. 1416E+03 0. 3746E+03 0. 1190E+04 0. 1495E+04 0. 9472E+03 0. 1294E+04 0. 3303E+04


53 -0,.2462E+03 0,•1004E+04 -0 .9151E+03 54 0 .4849E+03 0 .2190E+03 0,.6440E+03 55 0,.3106E+03 56 0,.8606E+03 57 0,.3281E+03 0,.1 128E + 04 0,•6946E+02 58 0,.9195E+03 59 0,.6755E+03 0,. 1625E+04 0,.5635E+03 60 0,. 1518E+04 0,.6107E+03 0,.1611E+04 61 0,.8890E+03 62 0,.1889E+04 0,.2591E+04 63 0,.3591E+04 64 0,.8188E+03 0,. 1719E + 04 0,.7046E+03 65 0,. 1305E + 04 -0, 66 . 1667E+03 0,.2333E+03 67 -0.. 1696E + 03 0..3038E+02 0,.8858E+01 68 0..2089E+03 69 0.. 1581E + 03 0..5081E+03 70 -0..2600E+02 0..1740E+03 -0..5300E+03 71 0..7002E+02 72 -0.. 1251E + 03 0.•4749E+03 73 -0..3269E+03 0., 1 173E+04 74 -0.. 1036E + 04 0..6407E+02 75 -0..5869E+03 0..6631E+03 76 -0..9857E+03 0..4143E+03 77 -0..4518E+03 0..8982E+03 78 -0..7733E+03 0..3267E+03 79 -0.•2317E+03 0..4683E+03 80 0..1593E+04 0., 1893E+04 $DAMPING (MARQUARDT) VALUE0. $NEW DATA ERROR= 0. 5230E+01 iLOCK 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 17 18 19 20 21 22

PARM. JUMP. 0 .7300E+02 -0 .1534E+03 0 .3077E+02 -0 .1068E+03 0 .3212E+03 0 .4286E+03 -0 .9986E+02 0 .2035E+02 0 .7848E+02 0 .9340E+02 0 .2048E+03 0 .2285E+03 0,.1300E+03 0,.8238E+02 0,.4159E+03 -0..1677E+03 -0,.3259E+03 -0,.2154E+03 0,.4138E+02 0..4269E+02 0..2343E+02 0..3240E+02

1MEW PARMS. 0 .3730E+03 0 .2466E+03 0,.5308E+03 0 .5932E+03 0 .1171E+04 0,. 1229E+04 0,.8001E+03 0,.7203E+03 0,.8785E+03 0,.2184E+03 0,.6048E+03 0,.6785E+03 0..7300E+03 0..8824E+03 0., 1166E+04 0..7823E+03 0..3741E+03 0..5846E+03 0., 1664E+0 3 0.. 1427E+03 0..2034E+03 0..2624E+03


23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76

-0 .3366E+-03 0 .7025E+-02 -0 .5681E+•02 0 .9375E+•02 0 .4232E+-03 0 .8713E+•01 0 .7641E+-02 0 .4970E+ 02 0 .2525E+•03 0 .9755E+•01 0 .9009E+•01 0 .2049E+•03 0 .1601E+•03 0,.3276E+•03 -0 .5538E+•00 0 .7648E+•01 0 .6709E+-02 -0 .9227E+•02 0 .2640E+-02 -0 .3095E+ 03 0,.2809E+•03 - 0 ,.1474E+•03 0,.4634E+•02 0,.4717E+ 02 0,.7171E+•02 0,.5209E+•03 0,.2501E+ 03 0,.3244E+ 03 0,.4673E+ 02 0,.7588E+•03 - 0 ..4233E+ 02 0,.1794E+ 03 - 0 ,.2404E+ 02 0..1428E+ 02 0,. 5 461E +02 - 0 ..9558E+•01 0..9780E+ 02 0.,1027E+ 02 0.•2104E+ 03 0., 3839E +03 0.•5858E+ 03 0.,3375E+ 03 0. 2531 E +03 i I 0., 3561E +03 - 0 . 5125E + 0I 2 I - 0 . 2217E + 02 - 0 . 2228E + 02 I I - 0 . 7827E + 02 - 0 . 1774E+I03 - 0 . 5 6 0 5 E + 02 I - 0 . 8273E+I03 - 0 . 511 1E + 03 I - 0 . 141 6E + 03 I - 0 . 1 565E +03 C

0 .3634E+03 0 .9203E+03 0 .7932E+03 0,.9938E+03 0 . 1423E+04 0,.1871E+02 0 .1764E+03 0,.1897E+03 0,.5525E+03 0,.4098E+03 0,.7090E+03 0,. 1 105E+04 0,. 1260E + 04 0,.1528E+04 0 . 1446E+01 0,.8765E+02 0 .2971E+03 0,.4077E+03 0,.5514E+03 0,.3905E+03 0,. 1 181E + 04 0,.1103E+04 0,. 1346E+04 0,.5217E+02 0,.1717E+03 0..8209E+03 0..6501E+03 0..8244E+03 0..7467E+03 0..1659E+04 0..1208E+04 0.. 1579E + 04 0..4010E+03 0..5643E+03 0..8546E+03 0..8404E+03 0..1048E+04 0..9653E+03 0.•1210E+04 0., 1384E + 04 0., 1 586E + 04 0. 1237E+04 0. 853 1E + 03 0. 7561E+03 0. 1487E+03 0. 1 778E + 03 0. 3 2 7 7 E + 0 3 0. 1217E+03 0. 4 2 2 6 E + 0 3 0. 5 4 4 0 E + 0 3 0. 6 7 2 7 E + 0 3 0. 5 8 8 9 E + 0 3 0. 1 108E + 04 0. 1243E+04


223 77 -0.1009E+04 0.3414E+03 78 -0.1449E+03 0.9551E+03 79 -0.4719E+03 0.2281E+03 80 -0.1278E+03 0.1722E+03 $DAMPING (MARQUARDT) VALUE= 0.1000E-01 SNEW DATA ERROR* 0.1106E+01 JLOCK 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

1

PARM. JUMP. 0 •3570E+02 -0 .7553E+02 0 .1561E+01 0 .2226E+02 0 .1472E+03 0 .2414E+03 0 .6181E+01 -0 •1134E+03 -0 .1028E+03 0 .7730E+02 0 •1517E+03 0 .1341E+03 0 .6247E+02 0 .6477E+02 0 . 1779E+03 -0 .1537E+02 -0 .1577E+03 -0 .1 122E+03 0 .2940E+02 0 .3850E+02 0,.3133E+02 0,.4142E+02 -0,.4505E+02 0,.2878E+01 -0,.2004E+02 -0,.2625E+02 0,.6063E+02 -0,.4137E+01 0..529 IE+02 0..2850E+02 0..5596E+02 -0..5858E+02 -0..7249E+02 0..4113E+02 0.. 1230E + 03 0..2177E+03 -0..2517E+00 -0., 1047E+02 0..3643E+02 - 0 ..2858E+03 -0. 1273E+03 - 0 . 4066E+02 0. 1468E+03 0. 2 152E+0 3 0. 3425E+03 - 0 . 3205E+01

1 MEW PARMS 0 .3357E+03 0 .3245E+03 0 .5016E+03 0 •7223E+03 0 .9972E+03 0 .1041E+04 0 .9062E+03 0 .5866E+03 0 .6972E+03 0 .2023E+03 0 .5517E+03 0,.5841E+03 0 .6625E+03 0 .8648E+03 0,.9279E+03 0 .9346E+03 0 .5423E+03 0,.6878E+03 0,. 1544E+03 o,. 1385E+03 0,.2113E+03 0,.2714E+03 0,.6550E+03 0,.8529E+03 0..8300E+03 0,.8737E+03 0,. 1061E + 04 0..5863E+01 0.. 1529E + 03 0..1685E+03 0.•3560E+03 0..3414E+03 0..6275E+03 0.,941 1E+03 0., 1223E + 04 0., 1418E + 04 0., 1748E + 01 0.•6953E+02 0. 2664E+03 0. 2142E+03 0. 3977E+03 0. 6593E+03 0. 1047E+04 0. 1465E+04 0. 1642E+04 0. 1795E+01


47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

0.8160E+01 0.1082E+03 0.3671E+03 0.6671E+03 0.6595E+02 0.4660E+03 0. 1329E + 03 0.6329E+03 0. 1554E + 03 0.8554E+03 0.3268E+03 0.1227E+04 0.3497E+03 0. 1600E + 04 0.4617E+03 0.1862E+04 -0.7290E+02 0.3521E+03 -0.4379E+02 0.5062E+03 0.4531E+02 0.8453E+03 -0.1942E+02 0.8306E+03 -0.3393E+02 0.9161E+03 -0.3052E+02 0.9245E+03 0.7968E+02 0. 1080E+04 0.2095E+03 0.1210E+04 0, 2250E+03 0.1225E+04 0, 1773E+03 0.1077E+04 0. 1377E+03 0.7377E+03 0. 1936E+03 0.5936E+03 -0. 2 U 2 E + 0 2 0.1789E+03 - 0 . 1970E+02 0.1803E+03 -0.6541E+02 0.2846E+03 -0.4024E+02 0.1598E+03 -0.8369E+02 0.5163E+03 -0 5321E+02 0.5468E+03 -0, 3040E+03 0.1 196E + 04 0.8489E+03 -0. 251 1E + 03 0.1206E+04 -0. 4418E+02 0. 1385E+0 4 - 0 . 1516E+02 2681E+03 0. 1082E+04 -0. 2104E+02 0. 1079E + 04 -0. 1502E+03 0.5498E+03 -0. 0.2232E+03 - 0 . 7682E+02 $DAMPING (MAR1QUARDT) VALUE = 0.5 266E+00 $NEW DATA ERR0R= $ITERATION // 2 $STARTING DATA ERROR= BLOCK 1 2 3 4 5 6 7 8 9 10 11 12 13

PARM. JUMP, 0.4045E+02 -0.4400E+02 0.6452E+02 -0.1366E+03 0.1992E+03 0.3152E+03 -0.6450E+02 0.1062E+03 0.2458E+03 0.4421E+02 0.1895E+02 0.1522E+03 -0.4160E+02

0.5266E+00

NEW PARMS. 0.3762E+03 0 •2805E+03 0 -5661E+03 0 -5856E+03 0 , 1 196E + 04 0 1357E+04 0 8417E+03 0 6929E+03 0 9430E+03 0, 2465E+03 0. 5706E+03 0. 7364E+03 0. 6209E+O3


14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67

0 .8934E+-02 0 •3565E+-03 -0 . 1400E + •03 -0 .1007E+-03 -0 . 1024E+-03 0 .2517E+-01 0 .3520E+-01 -0 .1916E+•02 -0 .8721E+•01 -0 .3421E+•03 0 . 1098E +03 -0 . 1159E+•03 0 .8560E+•02 0 .4160E+•03 0 .2952E+-01 0 . 1290E + -02 -0 .2800E+•02 0 . 1217E +•03 0 .1486E+•02 0 .5378E+•02 0 . 1717E +•03 -0 .2841Ei u 1 0 . I431E +02 -0 .1748E+•01 -0 .1547E+•02 -0 .5941E+•02 -0 . 1220E +•0 3 0 .7218E+ 02 -0 .3818E+ 03 0 . 3399E +•03 -0 •3563E+ 03 -0 .4341E+ 03 0 .3465E+•02 0 .1619E+ 02 0 . 1026E +04 -0 •2341E+ 02 0 .1004E+ 03 0 . 1259E +03 0 .3401E+ 03 -0 .5854E+ 03 -0 .1232E+ 04 0 .5640E+ 02 0 .5504E+ 02 0 .97 29E+ 02 -0 .3891E- 01 0 . 1945E +03 0 .9113E+ 02 0 .2221E+ 03 0 .4552E+ 03 0 .5621E+ 03 0 .3958E+ 03 0,.1178E+ 03 0,.3200E+ 03 -0,.4774E+ 02

0. 9541E+03 0. 1284E+04 0. 7946E+03 0. 4416E+03 0. 5854E+03 0. 1569E+03 0. 1420E+03 0. 1922E+03 0. 2627E+03 0. 3129E+03 0. 9626E+03 0. 7141E+03 0. 9593E+03 0. 1477E+04 0. 8815E+01 0. 1658E+03 0. 1405E+03 0. 4777E+03 0. 3563E+03 0. 6813E+03 0. 1113E+04 0. 1195E+04 0. 1432E+04 0. 8941E-04 0. 5405E+02 0. 2070E+03 0. 9216E+02 0. 4699E+03 0. 2775E+03 0. 1387E+04 0. 1109E+04 0. 1208E+04 0. 3645E+02 0. 1243E+03 0. 1693E+04 0. 4425E+03 0. 7334E+03 0. 9813E+03 0. 1567E+04 0. 1014E+04 0. 6297E+03 0. 4085E+03 0. 5613E+03 0. 9426E+03 0. 8305E+03 0. 1111E+04 0. 1016E+04 0. 1302E+04 0. 1665E+04 0. 1787E+04 0. 1473E+04 0. 8555E+03 0. 9136E+03 0. 1311E+03


226 68 - 0 . 1125E + 02 0. 1690E + 03 0 .6808E + 02 0.3527E+03 69 -0.1096E+03 0.5014E+02 70 -0.2179E+0 3 0.2984E+03 71 -0.2993E+02 0.5169E+03 72 - 0 . 1029E+04 0.1673E+03 73 -0.3914E+03 0.4575E+03 74 0. 1047E + 04 - 0 . 1585E+03 75 -0.2241E+03 0. 1 161E + 04 76 - 0 . 1406E + 03 0.9413E+03 77 - 0 . 1662E + 03 0.9127E+03 78 -0.5619E+02 0.4936E+03 79 80 - 0 . 1655E+03 0.5772E+02 $DAMPING (MARQUARDT) VALUE= 0.1000E-01 0. 9319E+00 $NEW DATA ERROR= BLOCK 1 2 3 4 5 6 7 8 9 10 1 1 1 2 1 3 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

PARM. JUMP. 0. 1705E + 02 -0.2022E+O2 0.3533E+02 -0.6944E+01 0.3298E+02 0. 1030E + 03 0.2877E+02 0. 1827E + 02 0.8365E+02 0.2915E+02 - 0 . 1047E + 02 0.2525E+02 -0.2638E+02 -0.1256E+02 0.8233E+02 0. 1435E + 01 -0.5322E+02 -0.7506E+01 -0.4060E+01 0.5834E+01 -0.3653E+01 - 0 . 1383E + 01 -0.8467E+02 - 0 . 1285E+02 -0.1457E+02 -0.8245E+01 0.6899E+02 -0.3175E+01 0. 3480E + 01 -0.2387E+02 0.4742E+02 0.8801E+01 -0.4362E+02 0.2243E+02 0.6080E+02 0.9753E+02 -0.2722E+00

NEW PARMS. 0.3528E+03 0.3042E+03 0.5369E+03 0.7153E+03 0.1030E+04 0.1144E+04 0.9350E+03 0.6049E+03 0.7808E+03 0.2314E+03 0.5412E+03 0.6094E+03 0.6361E+03 0.8522E+03 0.1010E+04 0.9361E+03 0.4891E+03 0.6803E+03 0.1503E+03 0.1443E+03 0.2077E+03 0.2700E+03 0.5703E+03 0.8400E+03 0.8154E+03 0.8655E+03 0.1130E+04 0.2688E+01 0.1564E+03 0.1446E+03 0.4034E+03 0.3502E+03 0.5839E+03 0.9636E+03 0.1284E+04 0.1515E+04 0.1476E+01


38 - 0 . 1449E + 02 0.5504E+02 39 0.3584E+02 0.3023E+03 40 0. 1387E + 03 -0.7546E+02 41 0. 1492E + 02 0.4127E+03 42 0.5961E+03 -0.6326E+02 0. 1 135E+04 43 0.8828E+02 0. 1503E + 04 44 0.3732E+02 0. 1686E + 04 45 0.43 17E+02 -0.1471E+01 0.3236E+00 46 47 -0.4502E+01 0.1037E+03 48 0.2048E+03 0.8719E+03 0.6273E+03 49 0. 161 3E + 03 50 0.7024E+02 0.7032E+03 51 0.2983E+02 0.8853E+03 52 0. 1310E + 04 0.8345E+02 0. 1555E + 04 53 -0.4505E+02 54 0.1640E+04 -0.2217E+03 55 -0.7986E+01 0.3441E+03 56 - 0 . 1 193E + 01 0.5050E+03 57 0.3554E+02 0.8809E+03 O.7904E+O1 58 0.8385E+03 59 0.3788E+02 0.9540E+03 60 0.3109E+02 0.9556E+03 61 0.6699E+02 0. 1 147E + 04 62 0. 1380E + 04 0. 170OE + O3 63 0. 1537E + 03 0. 1379E + 04 64 0. 1 179E + 04 0.1013E+03 65 0.3630E+02 0.7740E+03 66 0.8518E+02 0.6788E+03 67 - 0 . 1999E+02 0.1589E+03 68 -0.1495E+02 0. 1653E + 03 69 0. 1088E + 01 0.2857E+03 70 -0.3717E+02 0. 1226E+03 71 -0.7569E+02 0.4406E+03 72 - 0 . 1845E+02 0.5283E+03 73 -0.3188E+03 0.8772E+03 74 - 0 . 1508E + 03 0.6981£+03 75 0. 1 158E + 04 -0.4771E+02 76 0. 1307E + 04 -0.7 7 87E+0 2 77 -0.5034E+03 0.5785E+03 78 -0.8314E+02 0.9958E+03 79 -0.2195E+03 0.3302E+03 80 -0.9685E+02 0.1263E+03 $DAMPING (MARQUARDT) VALUE= 0.10 $NEW DATA ERROR= 0. 5085E+00 $ITERATION # 3 $STARTING DATA ERROR = BLOCK 1 2 3 4

PARM. JUMP. 0.4183E+02 - 0 . 1496E + 02 0.8637E+02 - 0 . 1092E + 03

0.5085E+00

NEW PARMS. 0.3946E+03 0.2893E+03 0.6233E+03 0.6061E+03


5 6 7 8 9 10 1 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

0 . 1378E + 03 0 .1220E+03 -0 .5537E+02 0 .6047E+02 0 .3208E+03 0 .1867E+02 0 .5080E+01 0 .8006E+02 -0 .61 16E+02 0 .1680E+03 0 .2424E+03 -0 . 1379E+03 -0 .3778E+02 -0 . 1171E+03 0 .6642E+01 0 .2263E+00 -0,.3689E+01 0,.5191E+01 -0,.2249E+03 0,. 1644E + 03 -0,. 1303E + 03 0,.2898E+02 0,.2780E+03 0,.3046E+01 0,.7338E+01 -0,.2150E+02 0,.4960E+02 0,.1020E+01 0,.8155E+02 0.. 1652E + 03 -0,. 1452E+03 -0..2298E+03 -0..2424E+00 -0..5119E+01 0., 1 147E+02 -0., 1719E+02 0..9664E+02 -0..3322E+03 0..2675E+03 - 0 . 4299E+03 -0..5941E+03 0., 1505E + 02 0., 1611E + 01 0. 3416E+03 - 0 . 1752E+03 - 0 . 8465E+02 0. 1956E+03 0. 1 161E + 03 - 0 . 3651E+03 - 0 . 5839E+02 0. 8936E+02 0. 7392E+02 0. 1369E+03 0. 6864E+01

0 . 1 168E + 04 0 . 1266E + 04 0 .8796E+03 0 .6654E+03 0 .1 102E+04 0 .2501E+03 0 .5463E+03 0 .6894E+03 0 .5749E+03 0 . 1020E+04 0 .1253E+04 0 .7982E+03 0 .4513E+03 0 .5633E+03 0 . 1570E+03 0 . 1446E+03 0,.2040E+03 0,.2752E+03 0,.3454E+03 0,. 1004E+04 0,•6851E+03 0,.8945E+03 0,. 1408E + 04 0,.5734E+01 0,.1637E+03 0.. 1231E + 03 0,.4530E+03 0,.3512E+03 0,.6654E+03 0,.1129E+04 0..1139E+04 0,.1285E+04 0.. 1234E + 01 0..4992E+02 0., 3137E + 03 0., 1215E+03 0..5093E+03 0.•2639E+03 0., 140 3E + 0 4 0., 1073E + 04 0., 1092E + 04 0., 1538E + 02 0., 1053E + 03 0. 1214E+04 0. 4521E+03 0. 6185E+03 0. 1081E+04 0. 1426E+04 0. 1190E+04 0. 1582E+04 0. 4335E+03 0. 5789E+03 0. 1018E+04 0. 8453E+03


229 0.. 1197E+04 0 .2428E+03 0,. 1081E + 04 0 . 1252E + 03 0,. 1381E + 04 0 .2340E+03 0..1866E+04 0,.4862E+03 0.. 1868E+04 0,.4897E+03 0.. 1508E + 04 0,.3294E+03 0..8432E+03 0,.6920E+02 0.. 1032E + 04 0,.3528E+03 0.. 1282E + 03 -0,.3066E+02 0., 1687E + 03 0,.3384E+01 0..3820E+03 0,.9632E+02 0..1045E+03 -0,. 18 12E + 0 2 0.. 1680E+03 -0,.2727E+03 0..5012E+03 -0,.27 10E + 02 -0,.1435E+03 0..7337E+03 0..2843E+03 -0,.4138E+03 0..9605E+03 -0,.1976E+03 -0,.2201E+03 0., 1087E + 04 -0,.2052E+03 0..3734E+03 0..8549E+03 -0,.1409E+03 -0,.5427E+02 0..2760E+03 0..1071E+03 -0,.1926E+02 $ D A M P I N G (; MARQUARDT) VALUE0. $NEW DATA ERR0R= 0. 1026E+01 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

BLOCK 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

PARM. JUMP. 0 .1475E+02 -0 •2382E+01 0 .3352E+02 0 .5608E+01 0 . 1746E + 02 0 .2666E+02 0 . 1534E+02 0 .2433E+02 0 . 1105E + 03 0,.8875E+01 -0 .2335E+02 0,.6047E+01 -0,. 1247E + 02 0 . 1644E+02 0,.4908E+02 -0,.4957E+01 -0,.3962E+02 -0,.4170E+01 0,.4448E+00 0,.2667E+01 0,.2243E+01 -0,.6979E+00 -0..5402E+02 0..2000E+02 -0., 1081E+02 -0..2166E+02 0.• 4921E + 02 -0..3792E+00

NEW F A R M S . 1 0 .3675E+03 0 .3019E+03 0 .5704E+03 0 .7209E+03 0 .1048E+04 0 .1171E+04 0 .9503E+03 0 .6292E+03 0 .8913E+03 0 .2403E+03 0,.5179E+03 0 .6154E+03

o,.6236E+03 0 •8686E+03 0,.1059E+04 0,.9311E+03 0 .4495E+03 0,.6761E+03 0,. 1508E + 03 0., 1470E + 03 0..2099E+03 0..2693E+03 0..5163E+03 0..8600E+03 0..8046E+03 0..8438E+03 0., 1 179E + 04 0..2309E+01


0 .1582E+03 29 0.1842E+ 01 0 .1289E+03 30 -0.1577E+•02 0 .4237E+03 31 0.2035E+ 02 0,.3487E+03 32 -0.1543E+ 01 0 .5683E+03 33 -0.1557E+ 02 0 .9964E+03 34 0.3289E+ 02 0,.1319E+04 35 0.3568E+ 02 0 .1544E+04 36 0.2830E+ 02 37 -0.2789E+ 00 o,.1197E+01 0 .5123E+02 38 -0.3808E+ 01 0 .3554E+03 39 0.5317E+ 02 0 .1315E+03 40 -0.7208E+ 0 1 0 .4495E+03 41 0.3686E+ 02 42 -0.5946E+ 02 o,.5366E+03 0,.1211E+04 43 0.7611E+ 02 0,.1508E+04 44 0.5596E+ 01 0,.1666E+04 45 -0.2005E+ 02 0,.2840E+00 46 -0.3960E- 01 0,.9783E+02 47 -0.5833E+ 0 1 0,•7924E+03 48 -0.7950E+ 02 0, .7420E+03 49 0.1147E+ 03 0,.7794E+03 50 0.7621E+ 02 51 0.4034E+ 02 0,.9256E+03 0,.1326E+04 52 0.1593E+ 02 0,.1560E+04 53 0.5628E+ 01 0,.1761E+04 54 0.1206E+ 03 0,.3481E+03 55 0.3944E+ 01 56 0.8162E+ 01 0..5132E+03 0,.9129E+03 57 0.3201E+ 02 0,.8467E+03 58 0.8175E+ 01 0,.1002E+04 59 0.4827E+ 02 60 0.3798E+ 02 0,.9936E+03 61 0.6476E+ 02 0,.1211E+04 62 0.1499E+ 03 0..1529E+04 63 0.1106E+ 03 0..1489E+04 64 0.6740E+ 02 0..1246E+04 65 0.1151E+ 0 2 0.•7855E+03 66 -0.1675E+ 01 0.•6771E+03 67 -0.140 1E+ 03 0.. 1875E+02 68 -0.4748E+ 01 0.. 1606E + 03 69 0.7544E+ 01 0..2932E+03 0.•7438E+02 70 -0.4821E+ 02 71 -0.8144E+ 02 0..3592E+03 72 -0.1874E+ 02 0..5096E+03 73 -0.4098E+ 03 0.•4673E+03 0. 5341E+03 74 -0.1639E+ 03 0., 1099E + 04 75 -0.5923E+ 02 0. 1218E+04 76 -0.8867E+ 02 0. 4966E+03 77 -0.8190E+ 02 78 -0.9555E+ 02 0. 9003E+03 79 -0.3253E+ 03 0. 4964E+01 80 - 0 . U 1 2 E + 03 0. 1509E+02 $DAMPING (MARQUA RDT) VALUE0. $NEW DATA ERROR- 0. 4889E+00


231

******************************************************* ******************************************************* OUTPUT-PROGRAM GINDEP

ZD(I)

1 2 3 4 5 6 7 8 9 10 1 1 1 2

13 14 15 16 17 18 19 20 21 22 2.3 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

+/-

0 .368E+03 0 .302E+03 0,.570E+03 0 .721E+03 0 . 105E + 04 0,. 1 17E + 04 0 .950E+03 0,.629E+03 0,.891E+03 0,.240E+03 0,.518E+03 0,.615E+03 0,.624E+03 0 .869E+03 0,. 106E+04 0,.931E+03 0,.449E+03 0,.676E+03 0,.151E+03 0,. 147E + 03 0..210E+03 0..269E+03 0,.516E+03 0..860E+03 0..805E+03 0,.844E+03 0,. 1 18E+04 0..231E+01 0..158E+03 0..129E+03 0..424E+03 0..349E+03 0..568E+03 0.•996E+03 0., 132E+04 0. 154E+04 0. 120E+01 0. 5 1 2 E + 0 2 0. 3 5 5 E + 0 3 0. 131E+03 0. 4 5 0 E + 0 3 0. 5 3 7 E + 0 3

STD.DEV.

0 •975E+02 0 .755E+02 0 .1 13E+03 0 .124E+03 0 . 11 1E+03 0 . 1 13E+03 0,.155E+03 0,•140E+03 0 .137E+03 0 .663E+02 0,.809E+02 0,.888E+02 0 .949E+02 0,.928E+02 0,.975E+02 0,.1 17E + 03 0,. 113E + 03 0.. 160E + 03 0,.522E+02 0..392E+02 0..562E+02 0..668E+02 0..110E+03 0..967E+02 0.. 121E+03 0..130E+03 0.. 157E+03 0..22OE+02 0..421E+02 0..462E+02 0..985E+02 0. 8 1 5 E + 0 2 0., 1 19E + 03 0. 111E+03 0., 1 17E + 03 0. 131E+03 0, 230E+02 0. 258E+02 0. 913E+02 0. 427E+02 0. 974E+02 0. 119E+0 3


43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

0 . 121E + 04 0 .151E+04 0 . 167E + 04 0 .284E+00 0 .978E+02 0 .792E+03 0 .742E+03 0 .779E+03 0 .926E+03 0 133E+04 0.. 156E+04 0. 176E+04 0. 348E+03 0 .513E+03 0 .913E+03 0 .847E+03 0. 100E+04 0. 994E+03 0 .121E+04 0 153E+04 0. 149E+04 0. 125E+04 0. 785E+03 0 677E+03 0. 187E+02 0. 161E+03 0. 293E+03 0. 744E+02 0. 359E+03 0. 510E+03 0. 467E+03 0. 534E+03 0. 110E+04 0. 122E+04 0. 497E+03 0. 900E+03 0. 496E+01 0. 151E+02

0 .117E+03 0 . 107E+03 0 . 103E+03 0 . 189E+02 0 .400E+02 0 .101E+03 0 . 112E+03 0 .114E+03 0 . 130E+03 0 . 129E+03 0 . 126E+03 0 . 143E + 03 0 .502E+02 0 .552E+02 0 .651E+02 0 .650E+02 0 .688E+02 0 .717E+02 0 .860E+02 0 .979E+02 0 .816E+02 0 .690E+02 0. 566E+02 0 .517E+02 0. 729E+02 0. 501E+02 0. 128E+03 0. 229E+03 0. 614E+02 0. 699E+02 0. 198E+03 0. 262E+03 0. 486E+02 0. 691E+02 0. 405E+03 0. 544E+02 0. 111E+03 0. 614E+03

$INPUT STD. DEV. = 0.5000E+00 $CALC. DATA STD. DEV. = 0.4889E+00 $NUMBER OF ITERATIONS FOR SOLUTION = M ODEL RESOLUTION MATRIX I

...(1 ,1-2 ) 1 2 3 4 5 6

-0.10 -0.14 -0.06 0.02

0.04 0. 19 0. 14 0.21 0. 14

0.55 0.64 0.44 0.31 0. 18 0. 16

(1,1) 0.04 -0.02 0.05 -0.02 0.06 -0.01 0.08 0.00 0.09 0.01 0.15 -0.03

(1,1+2)..


7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0. 01 0.11 - 0 . 01 0.06 - 0 . 02 0.17 0. 00 0.00 0. 00 0.31 - 0 . 03 0.22 0. 00 0.18 0. 01 0.21 0. 02 0.16 0. 02 0.12 0. 00 0.05 - 0 . 01 0.21 0. 00 0.00 0. 00 0.01 - 0 . 03 0.02 - 0 . 04 0.05 - 0 . 11 0.26 - 0 . 08 0.25 - 0 . 03 0.15 0. 00 0.15 0. 03 0.20 0. 00 0.00 0. 00 0.12 - 0 . 05 0.03 - 0 . 03 0.26 - 0 . 08 0.13 - 0 . 08 0.23 - 0 . 06 0.22 0. 02 0.14 0. 07 0.11 0. 00 0.00 0. 00 -0.04 - 0 . 27 0.23 -0 .06 0.00 - 0 . 10 0.24 - 0 . 28 0.17 - 0 . 08 0.21 0. 04 0.12 0. 07 0.08 0. 00 0.00 0. 00 -0.58 1. 27 0.63 - 0 . 18 0.11 0. 01 0.22 - 0 . 02 0.19 0. 04 0.17 0. 08 0.11 0. 08 0.09 0. 00 0.00 0. 00 0.04 - 0 . 07 0.07 - 0 . 06 0.08 - 0 . 03 0.07 - 0 . 0 4 0.15

0.25 0.38 0.22 0.72 0.36 0.31 0.32 0.21 0.17 0.20 0.51 0.34 0.83 0.77 0.75 0.69 0.40 0.22 0.27 0.24 0.15 0.85 0.82 0.79 0.58 0.60 0.41 0.19 0.10 0.08 0.85 0.83 0.64 0.74 0.49 0.38 0.14 0.07 0.07 0.53 0.78 0.16 0.33 0.27 0.21 0.11 0.08 0.09 0.51 0.48 0.33 0.30 0.24 0.19

0.18 0.07 -0.02 0.06 0.13 0.11 0.08 0.08 0.12 0.21 0.08 -0.01 0.01 0.01 0.02 0.04 0.08 0.12 0.13 0.09 -0.28 0.01 0.03 0.03 0.09 0.05 0.06 0.07 0.05 -0.25 -0.01 0.01 0.01 0.02 0.04 0.04 0.05 0.04 -0.24 -0.02 0.02 0.09 0.10 0.07 0.06 0.06 0.06 0.00 0.02 0.02 0.07 0.05 0.0 8 0.08

-0.03 0.00 -0.02 0.00 0.00 0.00 0.00 0.01 -0.02 -0.01 0.01 0.00 -0.01 -0.01 -0.01 0.00 -0.01 0.00 0.01 -0.08 -0.04 0.00 0.00 -0.01 -0.01 0.00 0.00 0.02 -0.27 -0.05 0.00 -0.01 -0.02 0.00 0.00 0.00 0.02 -0.28 -0.02 0.00 0.00 0.00 0.00 0.01 0.01 0.03 0.00 0.00 -0.01 -0.02 -0.02 -0.01 -0.01 0.00


234 -0 .03 0.01 0.03 0.01 0.00 0.00 0.00 0.00 -0.01 0.55 0.00 0.00 0.08 0.41 0.03 0.01 0. 18 0.03 0.00 0.05

0. 1 1 0.15 0. 1 1 0.07 0.04 0.04 0.04 0.00 0.25 0.76 0.03 0.06 0.37 0. 16 0.03 0.08 0.37 0.01 0.04 0. 16

DATA RESOLUTION

MATRIX

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

0.19 0.17 0.18 0. 17 0.21 0. 19 0.27 0.75 0.67 0.21 0.20 0.23 0.10 0.15 0.10 0.11 0. 1 1 0.12 0. 12 0.33

.(1,1-2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

0.02 0.08 0.04 0.11 0.12 0. 13 0.12 0.12 0. 10 0.08 0.09 0. 10 0.08 0.00 0.00 0.05 0.01 0.02 0.06 0.04 0.05 0.05 0.05 0.04 0.04 0.02 0.04

0.17 0.24 0.29 0.20 0.24 0.25 0.20 0.17 0. 16 0.14 0.15 0. 18 0.18 0.23 0.00 0. 18 0.13 0.24 0.14 0.13 0.11 0. 10 0.08 0.07 0.07 0.08 0.10 0. 14

0.09 0.02 0. 16 0.03 0.11 -0.01 0.13 -0.01 0.13 -0.02 0. 12 0.00 -0.01 0.00 0.00 0.03 0.00 0.05 0. 18 0.01 0.01 0.05 0.02 0.03 0.08 0.13 0.07 0.26 0.06 0.01 0.09 0.03 0.55 0.16 0.03 0.05 0.11

(1,1+2)

(I.D 0.73 0.39 0.40 0.27 0.28 0.31 0.25 0.18 0.18 0. 17 0. 18 0.21 0.24 0.23 0.47 0.49 0.29 0.30 0.25 0. 17 0.14 0.13 0.09 0.09 0.09 0.10 0. 12 0.20 0. 17

0.15 0.26 0.22 0. 14 0.25 0.20 0.13 0. 14 0.15 0.15 0. 18 0.20 0. 19 0.24 0.00 0.08 0.12 0.20 0.09 0.11 0.09 0.08 0.07 0.07 0.08 0. 10 0.13 0. 14 0. 12

0.01 0.07 0.02 0.08 0. 10 0.07 0.07 0. 10 0.10 0.10 0.11 0. 11 0.08 0.00 0.00 0.02 0.01 0.01 0.03 0.03 0.04 0.03 0.04 0.04 0.05 0.04 0.05 0.01 0.00


30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83

0.01 0.00 0.00 0.03 0.02 0.04 0.04 0.04 0.05 0.05 0.04 0.04 0.03 0.02 0.04 0.01 0.00 0.00 0.00 -0.03 -0.08 0.04 -0.06 0.03 0.05 0.06 0.04 0.04 0.03 0.04 0.03 0.00 0.00 0.00 -0.01 -0.03 0.02 -0.04 0.01 0.03 0.03 0.06 0.05 0.05 0.04 0.03 0.00 0.00 -0.03 0.05 -0.04 0.02 -0.05 0.02

0. 12 0.0 0 0.2 1 0. 19 0.1 1 0.0 9 0.0 9 0.1 0 0.1 0 0.0 8 0.0 7 0.0 7 0.0 7 0. 10 0.1 7 0. 13 0.0 0 0.1 1 0.0 7 0.3 3 0.1 7 0.2 0 0.2 6 0.1 8 0. 14 0.0 9 0.0 8 0.0 8 0.0 8 0.0 9 0.0 9 0.0 0 0.0 7 0.0 9 0.1 9 0.0 9 0. 15 0.2 0 0. 12 0.1 8 0. 13 0. 11 0.0 8 0.0 7 0.0 7 0.0 8 0.0 0 0. 10 0.0 9 0.2 8 0.1 0 0.2 4 0.2 0 0.1 3

0.25 0.47 0.52 0.12 0.11 0.12 0.12 0.12 0.09 0.08 0.08 0.09 0.11 0.25 0.20 0.24 0.09 0.42 0.42 0.35 0.48 0.26 0.39 0.16 0.12 0.09 0.10 0.10 0.13 0.12 0.18 0.06 0.43 0.23 0.20 0.36 0.19 0.24 0.23 0.18 0.14 0.10 0.09 0.09 0.09 0.16 0.07 0.77 0.33 0.29 0.61 0.21 0.22 0.31

0.00 0.15 0.07 0.08 0.08 0.09 0.09 0.07 0.07 0.06 0.07 0.09 0.14 0.17 0.12 0.00 0.23 0.07 0.30 0.13 0.13 0.24 0.07 0.10 0.07 0.07 0.09 0.10 0.10 0.10 0.00 0.26 0.03 0.19 0.09 0.08 0.15 0.08 0.13 0.08 0.08 0.07 0.08 0.08 0.10 0.00 0.39 0.01 0.29 0.14 0.10 0.14 0.11 0.17

0.00 0.01 0.01 0.03 0.04 0.03 0.03 0.03 0.03 0.04 0.05 0.04 0.06 0.01 0.00 0.00 0.00 -0.03 -0.06 0.02 -0.04 0.01 0.01 0.03 0.03 0.04 0.05 0.05 0.03 0.00 0.00 0.00 0.00 -0.04 0.01 -0.02 0.00 0.02 0.01 0.03 0.03 0.04 0.04 0.04 -0.01 0.00 -0.01 0.01 -0.06 0.01 -0.01 0.01 0.02 0.00


84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 1 10 1 11 1 12 1 13 1 14 1 15 1 16 1 17 1 18 1 19 120

0.03 0.00 0.08 0.05 0.04 0.04 0.03 0.00 0.00 0.00 0.00 -0.29 0.17 -0.03 -0.08 0.08 0.03 0.08 0.05 0.05 0.04 0.03 0.00 0.00 -0.02 0.10 -0.06 0.15 0.07 0.09 0.12 0.10 0. 12 0. 10 0.10 0.09 0.10

0.22 0.16 0.13 0.08 0.06 0.06 0.07 0.00 0.11 0.03 0.38 0.44 0.12 0.23 0.22 0.22 0.15 0.13 0.08 0.07 0.06 0.08 0.00 0.12 0. 16 0.42 0.20 0. 10 0.16 0.20 0.18 0.18 0.17 0.13 0. 12 0.13 0.18

0.23 0.18 0.10 0.07 0.07 0.07 0.15 0.09 0.84 0.54 0.51 0.27 0.32 0.68 0.27 0.20 0.18 0.10 0.08 0.07 0.08 0.17 0.27 0.86 0.49 0.44 0. 10 0. 17 0.24 0.21 0.20 0.19 0.15 0.13 0. 14 0.17 0.32

0.09 0.09 0.06 0.06 0.06 0.09 0.01 0.43 0.01 0.35 0.07 0.26 0.38 0.05 0.16 0.10 0.09 0.06 0.06 0.07 0.10 0.04 0.47 0.01 0.38 0.03 0.12 0. 19 0.14 0.16 0.15 0.13 0.11 0. 12 0. 14 0.21

0.03 0.03 0.03 0.04 0.04 0.00 0.00 0.00 0.00 -0.04 0.06 -0.11 -0.03 0.01 0.01 0.04 0.03 0.03 0.04 0.05 0.02 -0.01 0.00 0.01 -0.01 0.03 0.10 0.07 0.07 0.07 0.08 0.07 0.08 0.09 0.12

COVABU A N C E MATRIX (VALUE PRINTED x 10E+04) I 1 2 3 4 5 6 7 8 9 10 1 1 12

. ..(1,1-2)

-0.07 -0.02 -0.49 -0.55 -0.80 -0.55 -0.72 0.01 -0.01 -0.06

(1,1+2)... (I,I) 0.95 -0.14 -0.01 - 0 . 14 0.57 - 0 . 13 -0.02 - 0 . 13 1 .30 -0.54 -0.49 -0.54 1 .50 0.39 -0.55 0.39 1 .20 0.35 -0.80 1 . 30 0.63 -0.55 0.35 2 .40 -0.14 -0.72 0.63 -0.14 2.00 0.28 0.05 0.28 1 .90 0.01 -0.01 0.44 -0.01 -0.06 0.01 0.66 -0.01 0. 16 -0.1 1 0.16 0.79 0. 15 -0.12


237 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

-0.11 -0.12 -0.17 -0.2 5 -0.11 -0.27 -0.00 0.00 0.02 0.02 0.03 -0.05 -0.24 -0.35 -0.53 -0.00 0.02 -0.00 0.01 0.01 -0.03 -0.04 -0.26 0.04 0.01 0.01 0.00 0.01 0.02 0.00 -0.04 -0.30 0.04 0.02 0.03 0.10 0.04 -0.36 -0.40 -0.44 -0.32 -0.11 0.01 0.02 -0.02 -0.01 -0.07 -0.13 -0.20 - 0 . 13 -0.21 -0.23 -0.07 -0.00

0.15 0.19 0.31 0.50 0.02 -0.01 0.00 -0.04 -0.05 -0.09 -0.10 0.16 0.27 0.36 0.97 0.00 0.00 -0.03 -0.09 -0.11 -0.12 0.03 0.70 1 .10 0.01 -0.00 -0.04 -0.09 0.02 -0.14 -0.00 0.87 0.68 0.01 -0.01 0.01 -0.03 0.28 0. 19 0.54 1 .20 1 .00 0.03 -0.04 - 0 . 10 -0.05 -0.13 0.02 0.10 0.36 0.46 0. 1 1 0.05 0.00

0.90 0.19 0.86 0.31 0.95 0.50 1.40 0.02 1.30 -0.01 2.60 0.00 0.27 -0.04 0.15 -0.05 0.32 -0.09 0.45 -0.10 1.20 0.16 0.93 0.27 1.50 0.36 1.70 0.97 2.50 0.00 0.04 0.00 0. 18 -0.03 0.21 -0.09 0.97 -0.11 0.66 -0.12 1 .40 0.03 1 .20 0.70 1.40 1 .10 1.70 0.01 0.05 -0.00 0.07 -0.04 0.83 -0.09 0. 18 0.02 0.95 -0.14 1.40 -0.01 1.40 0.87 1. 10 0.68 1 . 10 0.01 0.04 -0.01 0.16 0.01 1.00 -0.0 3 1.20 0.28 1 .30 0.19 1 .70 0.54 1 .70 1 .20 1.60 1.00 2.00 0.03 0.25 -0.04 0.30 -0.10 0.42 -0.05 0.42 - 0 . 13 0.47 0.02 0.51 0. 10 0.74 0.36 0.96 0.46 0.67 0. 1 1 0.48 0.05 0.32 0.00 0.27 0.08

-0.17 -0.25 -0.11 -0.27 -0.00 0.00 0.02 0.02 0.03 -0.05 -0.24 -0.35 -0.53 -0.00 0.02 -0.00 0.01 0.01 -0.03 -0.04 -0.26 0.04 0.01 0.00 0.00 0.01 0.02 0.00 -0.04 -0.30 0.00 0.04 0.03 0.10 0.04 -0.36 -0.40 -0.44 -0.32 -0.11 0.01 0.02 -0.02 -0.01 -0.06 -0.13 -0.20 -0.13 -0.21 -0.23 -0.07 -0.02 -0.03 -0.00


238 67 68 69 70 71 72 73 74 75 76 77 78 79 80

0.08 0.53 -0.00 0.00 -0.03 -0.00 -0.00 0.25 -0.22 -0.18 1 .60 0.22 - 0 . 12 0.00 -0.22 5.20 0.46 0.03 -0.18 0.22 0.24 0.46 0.38 0.02 -0.12 0.49 0.55 0.03 0.02 0.31 0.44 3.90 4.00 0.24 0.55 4.00 6.90 0.66 0.1 1 0.31 0.24 0.18 0.44 0.65 0.66 2.30 0.11 0.18 0.48 0.15 0.65 2.30 16.00 1 .80 2.80 1 .80 0.30 2.20 0.15 0.39 1.20 5.20 2.80 0.39 2.20 5.20 38.00

CORRELATION

MATRIX

I

. . .(1,1-2)

1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

-0.01 -0.02 -0.39 -0.39 -0.46 -0.35 -0.34 0.01 -0.01 -0.10 -0.14 -0.15 -0.18 -0.23 -0.10 - 0 . 14 -0.01 0.00 0.05 0.08 0.05 -0.07 - 0 . 18 -0.28 -0.28 0.00 0.02 -0.01 0.03 0.02 -0.03 -0.04 -0.19

-0.20 -0.15 -0.39 0.28 0.28 0.36 -0.07 0.15 0.01 -0.03 0.22 0.18 0.22 0.34 0.43 0.01 -0.01 0.01 - 0 . 17 -0.23 -0.25 -0.14 0.15 0.23 0.23 0.47 0.01 0.02 -0.14 -0.19 -0.14 -0.13 0.02 0.54

(1,1) 1 .00 -0.20 -0.01 1 .00 - 0 . 15 -0.02 1.00 -0.39 -0.39 1.00 0.28 -0.39 1.00 0.28 -0.46 0.36 -0.35 1.00 1 .00 -0.07 -0.34 1.00 0.15 0.01 1.00 0.01 -0.01 1 .00 -0.03 - 0 . 10 1.00 0.22 -0.14 1.00 0. 18 - 0 . 15 1 .00 0.22 -0.18 1 .00 0.34 -0.23 1.00 0.43 -0.10 1.00 0.01 -0.14 1.00 -0.01 -0.01 1 .00 0.01 0.00 1 .00 -0.17 0.05 1 .00 -0.2 3 0.08 1.00 -0.25 0.05 1.00 - 0 . 14 -0.07 1.00 0. 15 - 0 . 18 1 .00 0.23 -0.28 1 .00 0.23 -0.28 1.00 0.4 7 0.00 1.00 0.01 0.02 1 .00 0.02 -0.01 1 .00 - 0 . 14 0.03 0.02 1 .00 -0.19 1 .00 -0.14 -0.03 1 .00 -0.13 -0.04 1 .00 0.02 -0.19 1 .00 0.54 0.03 0.03 1 .00 0.71

(I,1 + 2 ) . . . |


36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

0.03 0.03 0.02 0.00 0.07 0.02 0.00 -0.03 -0.23 0.03 0.07 0.06 0.54 0.09 -0.31 -0.28 -0.30 -0.19 -0.06 0.01 0.03 -0.05 -0.04 -0.14 -0.28 -0.33 -0.18 -0.30 -0.34 -0.16 -0.04 -0.08 0.00 0.00 -0.16 -0.16 0.02 0.20 0. 17 0.45 0.06 0.33 0.41 0.62 0.66

0.71 0.03 -0.04 - 0 . 19 -0.24 0.04 -0.12 -0.01 0.70 0.62 0.06 - 0 . 12 0.02 -0.03 0.22 0.13 0.33 0.71 0.55 0.04 -0.16 -0.27 - 0 . 11 -0.29 0.04 0.16 0.43 0.58 0. 19 0.12 0.02 0.21 -0.01 -0.34 0.08 0.32 0.06 0.40 0.77 0.52 0.54 0.82 0.80 0.64 0.76

1.00 1.00 1.00 1.00 1 .00 1.00 1 .00 1.00 1.00 1 .00 1.00 1.00 1.00 1 .00 1 .00 1.00 1.00 1 .00 1.00 1 .00 1.00 1 .00 1.00 1 .00 1.00 1 .00 1 .00 1 .00 1.00 1 .00 1.00 1.00 1.00 1.00 1.00 1 .00 1.00 1.00 1.00 1.00 1 .00 1 .00 1 .00 1.00 1 .00

0.03 -0.04 -0.19 -0.24 0.04 -0.12 -0.01 0.70 0.62 0.06 -0.12 0.02 -0.03 0.22 0.13 0.33 0.71 0.55 0.04 -0.16 -0.27 -0.11 -0.29 0.04 0. 16 0.43 0.58 0.19 0. 12 0.02 0.21 -0.01 -0.34 0.08 0.32 0.06 0.40 0.77 0.52 0.54 0.82 0.80 0.64 0.76

0.02 0.00 0.07 0.02 0.00 -0.03 -0.23 0.03 0.07 0.06 0.54 0.09 -0.31 -0.28 -0.30 -0.19 -0.06 0.01 0.03 -0.05 -0.04 -0.14 -0.28 -0.33 -0.18 -0.30 -0.34 -0.16 -0.04 -0.08 0.00 0.00 -0.16 -0.16 0.02 0.20 0.17 0.45 0.06 0.33 0.41 0.62 0.66

* * * * * i* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *


240

F.2.3

GRAVITY VALUES CALCULATED USING THE RESULTS OF PROGRAM GINDEP


241

0,.0000 306,.2545 612,.5089 918,.7634 1225,.0178 1531 .2723 , 1837,.5267 2143,.7813 2450,.0356 2756,.2900 3062 .5447 , 3368,.7991 3675,.0535 3981 . .3079 4287 .5625 , 0..0000 306..2544 612,.5088 918..7632 1225,.0176 1531 .2725 , 1837,.5269 2143,.7813 2450,.0356 2756,.2900 3062..5444 3368..7988 3675..0532 3981 . .3081 4287 . .5620 0..0000 306..2539 612..5088 918,.7637 1225..0176 1531,.2725 1837,.5264 2143,.7813 2450,.0352 2756,.2900 3062 .5449 , 3368,.7988 3675..0537 .3076 3981 . .5625 4287 . 0..0000 306..2539 612..5078 918..7627 1225,.0176 1531..2715 1837 .5264 , 2143..7803 2450,.0352

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 301 301 301 301 301 301 301 301 301 301 301 301 301 301 301 602 602 602 602 602 602 602 602 602 602 602 602 602 602 602 903 903 903 903 903 903 903 903 903

0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 1504 1504 1504 1504 1504 1504 1 504 1504 1 504 1504 1504 1504 1504 1504 1504 3008 3008 3008 3008 3008 3008 3008 3008 3008 3008 3008 3008 3008 3008 3008 4512 4512 4512 4512 4512 4512 4512 4512 4512

-5 .9662 -6 .9124 -7 .6109 , -8 .6095 -9 .8940 -11 .0302 , -12,. 1 194 -13,.1976 -14,.0800 -14,.6725 -15,.0014 -15,. 1389 -15,.2551 -15,.5279 -15,.8873 -5,,4711 -6,.6817 -7,.6074 -8..7120 -10..0059 -1 1 ..1810 -12,.2954 -13,.4020 -14,.3557 -15..0418 -15,.4272 -15..5434 -15..6274 -15,.9523 -16..4417 -4,.8348 -6..0001 -7..2102 -8,.3581 -9..4742 -10..5861 -11,.7615 -13..0144 -14,.1416 -15,.0278 -15,.5916 -15,.8629 -16..0442 -16..4667 -17..0410 -3,.2114 -4..8745 -5..8054 -6..8351 -8,.0635 -9,.3307 -10,.7350 -12,.2893 -13,.6944


2756.2891 3062.5430 3368.7988 3675.0527 3981 .3066 4287.5625 0.0000 306.2539 612.5078 918.7637 1225.0176 1531 .2715 1837.5273 2143.7813 2450.0352 2756.2891 3062.5449 3368.7988 3675.0527 3981 .3086 4287.5625 0.0000 306.2539 612.5098 918.7637 1225.0176 1531.2734 1837 .5273 2143.7813 2450.0352 2756.2910 3062.5449 3368.7988 3675.0527 3981.3086 4287.5625 0.0000 306.2539 612.5078 918.7617 1225.0156 1531 .2715 1837.5254 2143.7793 2450.0352 2756.2891 3062.5430 3368.7969 3675.0527 3981.3066 4287.5605 0.0000 306.2539 612.5078

903.4512 9 0 3.4512 903.4512 90 3.45 12 903.4512 903.4512 1204.6016 1204.6016 1204.6016 1204.6016 1204.6016 1204.6016 1204.6016 1204.6016 1204.6016 1204.6016 1204.6016 1204.6016 1204.6016 1204.6016 1204.6016 1505.7520 15 0 5.7520 15 0 5.7520 1505.7520 1505.7520 1505.7520 1505.7520 1505.7520 J 505.7520 1505.7520 1505.7520 1505.7520 1505.7520 1505.7520 1505.7520 1806.9023 1806.9023 1806.9023 1806.9023 1806.9023 1806.9023 1806.9023 1806.9023 1806.9023 1806.9023 1806.9023 1806.9023 1806.9023 1806.9023 1806.9023 2108.0527 2108.0527 2108.0527

-14 .8655 -15 .7316 -16 .3083 -16 .7512 -17 .2702 -17 .8240 -2 .0467 -3 .1572 -4 .7922 -5,.7816 -6 .8518 -8 .4448 -10,. 1005 -1 1..6040 -13,.1340 -14,.6104 -15,.8296 -16,.7710 -17,.4966 -18,.10 6 3 -18,.5999 -1 .3245 . -1 .9272 . -4.. 1838 -5..4269 -6..7213 -8.,2383 -9.,7540 -11 . ,3338 -12.,9395 -14.,5597 -15.,9996 -17.,1906 -18..0926 -18..7568 -19..2190 -1 . 1931 -1 .7137 . -3.,3456 -5., 1333 - 7 . 8820 -8. 6233 -9. 5148 -11 . ,5823 -13.,2434 -14.,7712 -16.,2317 -17.,4917 -18.,4518 -19.,1357 -19.,5788 -1., 1344 -1.,6757 -3. 7892


243

918,.7617 1 225. .0156 1531..2695 1837,.5273 2143.,7813 2450..0352 2756..2891 3062..5430 3368..7969 3675.,0508 3981 . ,3086 4287.,5625

2108 2108 2108 2108 2108 2108 2108 2108 2108 2108 2108 2108

0527 0527 0527 0527 0527 0527 0527 0527 0527 0527 0527 0527

-6,.5183 -9,.0397 -9,.9535 -11 .6406 , -12,.2378 -14..5004 -16..9563 -16,.7855 -18..5421 -18..4231 -19..5371 -20..1332


APPENDIX G

TEST CASES FOR PROGRAMS GRAVBL, GINDEP


Test Cases for the Forward Modeling Program - Program GRAVBL 1) Horizontal Slab Comparison: Using potential theory, the gravity anomaly from an infinite horizontal slab is found to be: g

3 = 0.04191 x density of the slab (gm/cm ) x thickness of the slab (meters).

According to this formula, a 10 meter thick infinite horizontal slab of unit density produces an anomaly of .4191 mgals. To approximate this infinite slab and test program Gravbl, I modeled a 10 meter thick, 2000 meter long (in the x and y 3 directions) slab assigned a density of 1.0 gm/cm . The top surface of this slab is buried a depth of 20 meters below the x-y plane, and the slab is centered below the origin.

This slab

is described in data file GRAVBL.DAT as follows: $TYPE GRAVBL.DAT 1 -1000.0,1000.0,20.0,30.0,-1000.0,1000.0,1.0 100.0,100.0,2,2 20 0 (See Appendix D.l for an explanation of this data file.) Program Gravbl was then executed and the output stored in file GBL.DAT.

File GBL.DAT contained the following output:

$TYPE GBL.DAT 0.0000 0.0000 100.0000 0.0000 0.0000 100.0000 100.0000 100.0000

0.4097 0.4096 0.4096 0.4096

The first two columns of GBL.DAT contain the x,y position of the grid points in meters east and south of the 0,0 grid point, and


246

the third column contains the gravity data calculated at the individual grid points in units of mgals. The average RMS error between the theoretical and calculated gravity data for this case is approximately .001 mgals.

2) 2-D Gravity Model Results Comparison: I checked program GRAVBL against a 2-D gravity modeling program written by Dr. William Sill of the physics/geophysics department of Montana Tech.

With the 2-D gravity modeling

program, I modeled a rectangle of unit density having x,z coordinates of (0,25), (10,25), (10,100), and (0,100).

These

verticies describe a rectangle 10 meters wide (x-direction) and 75 meters thick (z-direction) where the top of the rectangle is buried a depth of 25 meters below the x-axis.

With this 2-D

gravity modeling program it is assumed that the body is infinite in the y-direction. The gravity values calculated using this 2-D modeling program for 5 evenly spaced stations located along the x-axis at distances of 0,2,4,6,8 and 10 meter distances from the origin are as follows: Sta

g

(mgals)

0 2 4 6 8 10

0.1817548 0.1832507 0.1840124 0.1840125 0.1832507 0.1817549

I approximated this 2-D rectangle (infinite in the y-direction) with a 3-D block 10 meters long in the x-direction,


6000 meters long in the y-direction (3000 meters either side of the x-axis), and 75 meters thick in the z-direction.

This block

was assigned a unit density and the upper edge of the block was buried a depth of 25 meters below the x-y plane. This block is described in data file GRAVBL.DAT as follows: $TYPE GRAVBL.DAT 1 0.0,10.0,25.0,100.0,-3000.0,3000.0,1. 10.0,10.0,6,6 1. 0 (See Appendix D.l for an explanation of this data file.) Program GRAVBL was then executed and the output stored in file GBL.DAT.

The fist row of this output which corresponds to the

2-D line of gravity stations is as follows: $TYPE GBL.DAT 0.0000 2.0000 4.0000 6.0000 8.0000 10.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.1817 0.1832 0.1839 0.1839 0.1832 0.1817

There are only round-off differences between the 2-D and 3-D gravity modeling results for this test case.


248

Test Case for the Inverse Gravity Modeling Program - GINDEP To test program GINDEP, I calculated gravity data from a forward model containing 3 blocks (see Figure 40a). Then, using the calculated gravity data from the known "correct model", I executed program GINDEP on a model identical to the "correct model" except I adjusted the maximum depths of the 3 blocks (see Figure 40b). If program GINDEP is working correctly, the depths output from program GINDEP (contained in file GINDEP.OUT) should have been adjusted to match the depths of the "correct model". The output of program GINDEP shows that in 4 iterations the "correct model" was obtained.

This output, contained in

file GINDEP.OUT, is as follows:

$TY GINDEP.OUT *********************************************************** GRID INFO

GRID SIZE GRID SIZE NUMBER OF NUMBER OF

IN X DIRECTION (METERS)- 0.1000E+03 IN Y DIRECTION (METERS)- 0.1000E+03 COLUMNS- 5 ROWS- 5

INPUT MODEL BL0CK# XMIN XMAX YMIN YMAX ZMIN ZMAX DENSITY 1 0.0 60.0 -60.0 0.0 50.0 140.0 2.00 2 60.0 100.0 -80.0 0.0 70.0 140.0 2.00 3 100.0 150.0 -60.0 0.0 130.0 140.0 2.00 *********************************************************** *********************************************************** TABLE OF CONVERGENCE


249

ZMAX 9 > 1901

ZMAX 1,2,9 â&#x20AC;˘ 140m Figure 40. A) B)

The "correct model". Input model for program GINDEP.


ITERATION # 1 STARTING DATA ERROR-

0.5536E-03

BLOCK PARM. JUMP NEW PARMS. 1 -0.9978E+01 0.1300E+03 2 -0.5912E+01 0.1341E+03 3 0.5251E+02 0.1925E+03 DAMPING (MARQUARDT) VALUE- 0.1000E-02 NEW DATA ERROR- 0.1246E-01 ITERATION # 2 STARTING DATA ERROR-

0.1246E-01

BLOCK PARM. JUMP NEW PARMS. 1 -0.8713E+01 0.1213E+03 2 0.1441E+02 0.1485E+03 3 0.9644E+01 0.2021E+03 DAMPING (MARQUARDT) VALUE- 0.1000E-03 NEW DATA ERROR- 0.2238E-02 ITERATION #3 STARTING DATA ERROR-

0.2238E-02

BLOCK PARM. JUMP NEW PARMS. 1 -0.7421E+00 0.1206E+03 2 0.8000E+01 0.1565E+03 3 -0.9044E+01 0.1931E+03 DAMPING (MARQUARDT) VALUE- 0.1000E-04 NEW DATA ERROR- 0.5536E-03 ITERATION #4 STARTING DATA ERROR-

0.5536E-03

BLOCK PARM. JUMP NEW PARMS. 1 -0.5210E+00 0.1200E+03 2 0.3100E+01 0.1596E+03 3 -0.2726E+01 0.1904E+03 DAMPING (MARQUARDT) VALUE- 0.1000E-05 NEW DATA ERROR- 0.7653E-04

*********************************************************** ***********************************************************

OUTPUT-PROGRAM GINDEP ZMAX(I) 1 2 3

0.120E+03 0.160E+03 0.190E+03

+/-

STD.DEV. 0.807E-01 0.393E+00 0.425E+00


INPUT STD. DEV. = 0.1000E-03 CALC. DATA STD. DEV. = 0.7653E-04 NUMBER OF ITERATIONS FOR SOLUTION =

4

MODEL RESOLUTION MATRIX 1.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 1.00 DATA RESOLUTION MATRIX I ...(1,1-2) (1,1+2)... (1,1) 1 0.29 0.27 0.11 2 0.23 0.26 0.19 0.06 3 0.09 0.19 0.27 0.23 0.10 4 0.07 0.27 0.34 0.24 -0.05 5 0.15 0.30 0.29 -0.09 -0.03 6 -0.07 -0.09 0.14 0.13 0.05 7 -0.03 0.11 0.11 0.07 0.02 8 0.05 0.07 0.08 0.07 0.04 0.02 0.07 0.11 0.10 0.00 9 10 0.05 0.12 0.16 0.01 0.02 11 0.00 0.01 0.06 0.06 0.04 12 0.03 0.05 0.05 0.04 0.03 13 0.03 0.04 0.04 0.05 0.05 0.04 0.05 0.07 0.09 0.02 14 15 0.07 0.11 0.14 0.04 0.05 0.04 0.05 0.03 0.04 0.04 16 17 0.07 0.03 0.04 0.04 0.05 18 0.03 0.04 0.05 0.06 0.07 19 0.05 0.06 0.08 0.09 0.03 20 0.08 0.11 0.13 0.04 0.05 21 0.05 0.06 0.02 0.03 0.03 22 0.07 0.02 0.03 0.04 0.04 23 0.03 0.03 0.04 0.05 0.06 24 0.04 0.05 0.07 0.08 25 0.07 0.08 0.10

COVARIANCE MATRIX 0.65E-02 -0.29E-01 0.29E-01 -0.29E-01 -0.15E+00 -0.16E+00 0.29E-01 -0.16E+00 0.18E+00

CORRELATION MATRIX 1.00 -0.92 0.83 -0.92 1.00 -0.98 0.83 -0.98 1.00 ***********************************************************


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