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Acknowledgments
First and foremost, the editors would like to thank their authors for contributing book chapter. This book would not have taken shape without the support of all the contributing authors belonging to geologically and geographically diverse places and institutions. We particularly acknowledge Chhavi Chaudhari, M. L. Sharma, Shusil Gupta, Parveen Kumar, Rinku Mahanta, Vipul Silwal, M.L. Sharma from IIT Roorkee, India; Sandeep, Monika, Amritansh Rai, Prashant Kumar Singh, Ankit Singh, Dipankan Srivastava, Pankhudi Thakur, Shatrughan Singh, Indrajit Das from BHU Varanasi, India; and Ranjit Das, Claudio Menesesa, Marcelo Saavedrab, Genesis Seranob, Franz Machacab, Roberto Mirandabc, BryanA, Urra-Calfuñirc from Chile for contributing book chapter. The editors from the bottom of their hearts are indebted to all of them for the time they took to pen down their findings and research so that it can be disseminated to a larger audience. One of the editors (Dr. S.P. Maurya) would like to thank the financial support from UGC, Govt. of India (grant no. M-14-585), and Institute of Eminence (IoE-BHU) with grant no. 6031B. The book would not have been completed without their support. Additionally, we would like to express our gratitude to Dr. Rohtash Kumar, who originally wrote the book’s proposal. Sadly, he passed away at a very young age, and we have just finished writing this book in his honor. His help in both our personal and professional lives will always be appreciated. We also like to thank a few of my colleagues who supported us in finishing this book after the tragic passing of Dr. Rohtash Kumar, the book’s original corresponding editor. This book would not have been a reality without the typesetting work and continuous support of Banaras Hindu University Varanasi research students Dr. Prabodh Kumar, Mr. Amritansh Rai, Mr. Ankit Singh, Mr. Ravi Kant, Mr. Nitin Verma, Ms. G. Hema, and Mr. Ajay Kumar. They have been the backbone of the entire process. From organizing the book chapters, figures, and tables, their effort has been
noteworthy. A big thank you to all. We also thank the Department of Geophysics, BHU Varanasi and Department of Earth and Planetary Science, Veer Bahadur Singh Purvanchal University, Jaunpur, UP, India for their support in completing this book. Last but not least, to the efforts of all those behind the scenes and whose names are not captured here, we would like to take a bow to show our gratitude towards you.
1 Earthquake Occurrence Models 1
Chhavi Chaudhari, M. L. Sharma, and Shusil Gupta
2 Estimation and Validation of Arias Intensity Relation Using the 1991 Uttarkashi and 1999 Chamoli Earthquakes Data ..
Parveen Kumar, Sandeep, and Monika
15
3 Exploring the Concept of Self-Similarity and High-Frequency Decay Kappa-Model and fmax-Model Using Strong-Motion Surface and Borehole Data of Japan: A Statistical Approach ... . . 25
Rohtash Kumar, Raghav Singh, Amritansh Rai, Sandeep, S. P. Singh, S. P. Maurya, and Prashant Kumar Singh
4 Body Waves– and Surface Waves–Derived Moment Tensor Catalog for Garhwal-Kumaon Himalayas ... ..... ..... . 47
Rinku Mahanta, Vipul Silwal, and M. L. Sharma
5 Exploring GRACE and GPS and Absolute Gravity Data on the Relationship Between Hydrological Changes and Vertical Crustal Deformation in South India 65
Ankit Singh, Rohtash Kumar, Amritansh Rai, Raghav Singh, and S. P. Singh
6 Moho Mapping of Northern Chile Region Using Receiver Function Analysis and HK Stacking . .. ..
Amritansh Rai, Rohtash Kumar, Dipankan Srivastava, Raghav Singh, Ankit Singh, and S. P. Maurya
7 Coulomb Stress Change of the 2012 Indian Ocean Doublet Earthquake
Pankhudi Thakur, Rohtash Kumar, Ranjit Das, Amritansh Rai, Raghav Singh, Ankit Singh, and S. P. Maurya
. 81
99
8
Earthquake Source Dynamics and High-Frequency Decal Characteristics of Japanese Arc Region ... ...... ....... . 109
Ankit Singh, Rohtash Kumar, and Amritansh Rai
9 Lapse-Time Dependence of Coda Quality Factor Within the Lithosphere of Northern Ecuador .......... ........... .. 121
Amritansh Rai, Rohtash Kumar, Ankit Singh, Raghav Singh, Indrajit Das, and S. P. Maurya
10 Coda Q Estimates of the Bilaspur Region of Himachal Lesser Himalaya ........... ................ ............ 133
Vandana, S. C. Gupta, Ashwani Kumar, and Himanshu Mittal
11 Data-Driven Spatiotemporal Assessment of Seismicity in the Philippine Region . .... ...
Amritansh Rai, Rohtash Kumar, Ankit Singh, Pankhudi Thakur, Raghav Singh, S. P. Maurya, and Ranjit Das
12 Determination and Identi fication of Focal Mechanism Solutions for the 2016 Kumamoto Earthquake from Waveform Inversion Using ISOLA Software 165
13 Regression Relations for Magnitude Conversion of Northeast India and Northern Chile and Southern Peru ..
Ranjit Das, Claudio Meneses, Marcelo Saavedra, Genesis Serrano, Franz Machaca, Roberto Miranda-Yáñez, and Bryan A. Urra-Calfuñir Index
List of Figures
Fig. 1.1 The Himalayas and Characterization of three regions on the basis of tectonics and recorded seismicity of magnitude MW ⩾ 5.0 for the time period 1255–2017 .......................... 5
Fig. 1.2 Magnitude Frequency Distribution and magnitude of completeness in the subdivision of Himalaya using the EMR method ..................................................... . 6
Fig. 1.3 Variation of Cumulative rate of Nmin w.r.t. Mmax in North-West Himalaya using (a) Constant seismicity and (b) Constant Moment Release models ....................................................... . 7
Fig. 1.4 Variation of Cumulative rate of Nmin w.r.t. Mmax in Garhwal Himalaya using (a) Constant seismicity and (b) Constant Moment Release models ....................................................... . 8
Fig. 1.5 Variation of Cumulative rate of Nmin w.r.t. Mmax in Nepal Himalaya using (a) Constant seismicity and (b) Constant Moment Release models ....................................................... . 8
Fig. 1.6 Hazard assessment in North-West Himalaya: (a) annual occurrence rate of earthquake magnitude and (b) probability of earthquake occurrence in the speci fic time period .............. 9
Fig. 1.7 Hazard assessment Garhwal Himalaya: (a) annual occurrence rate of earthquake magnitude and (b) probability of earthquake occurrence in a speci fic time period ................................. 9
Fig. 1.8 Hazard assessment in Nepal Himalaya: (a) annual occurrence rate of earthquake magnitude and (b) probability of earthquake occurrence in a speci fic time period ................................. 10
Fig. 1.9 Hazard Maps of PGA having 10% probability of exceedance in 50 years using Boore and Atkinson (2008) for (a) Constant seismicity and (b) Constant Moment Release Models ............. 11
Fig. 1.10 Hazard Maps of PGA having 2% probability of exceedance in 50 years using Boore and Atkinson (2008) for (a) Constant seismicity and (b) Constant Moment Release Models ............. 11
Fig. 2.1 Seismicity during 1935–2021 of Uttarakhand Himalaya, India report by the bulletin of ISC (International Seismological Centre). The blue color star symbols represent the epicentre of the Uttarkashi and Chamoli earthquakes. (The figure is modi fied after Valdiya (1980) and Célérier et al. (2009)) ................... . 17
Fig. 2.2 The comparison of Arias intensity values obtained from empirical and observed data for the 1991 Uttarkashi and 1999 Chamoli earthquakes ... ........................................................ . 19
Fig. 2.3 (a) The blue color box shows the location of the study region for which Arias intensity maps are prepared. The Arias intensity map for (b) the Uttarkashi earthquake and (c) the Chamoli earthquake. The variation of Arias intensity values along the profile (d)ABand (e) CD. The symbol star denotes the location of the epicentres of the Uttarkashi and Chamoli earthquakes ..... 20
Fig. 2.4 The Arias intensity maps for future scenario earthquakes (Mw 8.5) correspond to the epicentre of the (a) Uttarkashi and (b) Chamoli earthquakes 21
Fig. 3.1 Map showing KIK-NET sites and the epicentres of earthquakes used in the study ...................................................... 27
Fig. 3.2 Average observed acceleration and displacement spectra along with the theoretical source model with fmax-model (solid line) and κ -model (dotted line) ............................................ . 30
Fig. 3.3 Plot showing the fmax-distance model on epicentral distance with an empirical model ............................................. . 31
Fig. 3.4 Plot showing the dependence of fmax-model on earthquake magnitude . ............................................................
Fig. 3.5 Dependency of power coefficient (s) on seismic magnitude .....
Fig. 3.7 Plot showing FAS of direct shear wave on the semi-log scale with fe and fx with a best-fit line to estimate the slop (λ) ......... . 34
Fig. 3.8 Dependency of κ -model on seismic magnitude (Mw) ............. . 35
Fig. 3.9 Observed and predicted value of surface data kappa κ (s) and borehole data kappa κ (w) along with their residuals estimated using multivariate regression analysis (MVLR) . 38
Fig. 3.10 Relationship between fmax-model and κ -model ..................... 38
Fig. 3.11 Stress drop variation with seismic moment (M0) and earthquake source radius (r). (Red and black dots are corresponding to surface and borehole values, respectively) ................. ..... . 40
Fig. 4.1 The seismicity map of the G-K region of the Himalayan arc covering a period of 2010 to 2021. The color contrast signifies the focal depth of each event, while the size of each circle corresponds to the magnitudes of the earthquakes. The thick black lines in the map represents the active faults in the region (Dasgupta et al., 2000) .............................................. .
Fig. 4.2 Illustrations of the locations of 18 broadband stations (depicted as blue inverted triangles) and 16 earthquake events (represented by circles) for which MT inversion is performed in this study. The variation in color signifies the focal depth of each event, while the size of the circles corresponds to the magnitudes of the earthquakes ... ................................................. .
Fig. 4.3 The difference between raw waveform data (Upper set of three waveforms) and processed data (Lower set of three waveforms) after removal of instrument response and applying rotation. The processed data is used for the CAP method ...................
Fig. 4.4 MT solutions and waveform comparisons for the event 2021091100282800. Columns represent P wave components (vertical and radial), Rayleigh wave components (vertical, radial, and transverse Love wave) respectively. Stations are ordered by increasing epicentral distance, with observed and synthetic waveforms in black and red, respectively. Body waves are filtered at 3–10 s and surface waves are filtered at 16–40 s. Numbers below each station indicate epicentral distance and azimuth. Three values beneath each waveform pair include cross-correlation time shift, percentage of misfit, and amplitude ratio. Header lines are as per Silwal (2015) ..............................................
Fig. 4.5 The depth and magnitude search to find out the minimum misfit over grid points. In this case, the optimum depth was found at 6 km and magnitude, Mw 4.1 .................................... .
49
51
52
57
58
Fig. 4.6 The beachball diagram representing MT catalog of 16 earthquakes is shown in this figure. The results shows as distribution of thrust, normal and strike-slip oriented mechanisms rather than a preferred thrust solution ......................................................... 58
Fig. 5.1 GPS stations at Lucknow, Hyderabad and Bangalore. (Courtesy NEVADA GEODETIC LABORATORY) ......... 71
Fig. 5.2 The plot showing vertical crustal deformation obtained from GRACE in Lucknow region ...... 73
Fig. 5.3 Vertical crustal deformation obtained from GPS stationed at Lucknow .. ......................................................... . 73
Fig. 5.4 Vertical crustal deformation obtained from GRACE data for Hyderabad region .................. .............................. . 73
Fig. 5.5
Vertical crustal deformation obtained from GPS stationed at Hyderabad .......................................................... 74
Fig. 5.6 Vertical crustal deformation obtained from GRACE data for Bangalore region ................................................. . 74
Fig. 5.7 Vertical crustal deformation obtained from GPS stationed at Bangalore . ......................................................... . 75
Fig. 5.8 GRACE TWS analysis for Lucknow region ....................... . 76
Fig. 5.9 GRACE TWS analysis for Hyderabad region ..................... . 76
Fig. 5.10 GRACE TWS analysis for Bangalore .............................. . 77
Fig. 6.1 Seismotectonic of Northern Chile region .... ...................... . 84
Fig. 6.2 Teleseismic Events for stations (a) AC05, (b) AC06, (c) AF01, (d) CO10. The seismic stations are located by triangles, while events are shown with dots on the map ............................. 85
Fig. 6.3 Typical “flow” chart of a receiver-function analysis. First, the seismogram is rotated to a suitable coordinate system and deconvolved to remove the source and path effect. The deconvolved output is the receiver function, which can be inverted to obtain velocity structure beneath the seismic station ....... 87
Fig. 6.5 Rotation of the original three-component seismogram to new RTZ coordinate system . 89
Fig. 6.6 Illustration of the water-level deconvolution from (Ligorrfa & Ammon, 1999) .......................................... 90
Fig. 6.7 Receiver functions for station AC04 shown over 30 s. The (left) radial and (right) transverse components, sorted by back azimuth of incoming wave field within 10° bins. Slowness information is averaged out. The top traces show the receiver functions further averaged over all back azimuth and slowness values. Negative polarity arrivals are dominant at early record. Faint positive peak can be seen around 6 s which is coming from Moho discontinuity .......................................................... . 93
Fig. 6.8 Receiver functions for station AC05 shown over 30 s. Here positive peak is dominant at 7 s which is consistent with Ps conversions at Moho .. ............................................... . 93
Fig. 6.9 Receiver Functions over Station AC07 for 30 s. Figure format is same as earlier. Strong peak is observed at 5 s which is identified as Moho Ps phase. PpPs phase is observed at 15 s and PsPs phase is observed around 20 s 94
Fig. 6.10
Receiver Function over Station CO10 for 30 s. Figure format is same as before. The seismogram is dominated by negative phase arrivals. Faint positive peak is observed around 5 s. Strong positive peak is observed at 12 s .. ......................... . 95
Fig. 6.11 H-k stacking results for Vp/Vs (k) and crustal thickness (H) of all stations used in the study (a) AC04, (b) AC07, (c) AC05, (d) CO1 ................................................... . 95
Fig. 7.1 The Sumatran fault, subduction zone, and minor faults in the Indian Ocean Earthquake .................................... . 101
Fig. 7.2 The Coulomb stress changes (bar) in the transverse and lateral directions of the fault ................................................. 103
Fig. 7.3 Horizontal displacement vectors due to the main Sumatran fault .................................................................... 104
Fig. 7.4 Vertical displacement (colors and contours) due to the main Sumatran fault ........................................................ . 105
Fig. 8.1 Acceleration time history of the SH component of the seismogram ........................................................... . 110
Fig. 8.2 Displacement spectrum of the seismogram ........................ . 111
Fig. 8.3 The topographic map of Japan showing the major fault lines, plate boundaries and coastlines ...................................... 113
Fig. 8.4 Variation of M0 with fc for EW, NS and UD channels of seismometers. Left side of the panel represents data from surface seismometers. Right side of panel represents data from well seismometers .......................................................... 115
Fig. 8.5 Variation of fmax with Mw for EW, NS and UD channels of seismometers. Left side of the panel represents data from surface seismometers. Right side of panel represents data from well seismometers ..... ............................................... . 115
Fig. 8.6 The plot of fmax against epicentre for the surface data . ........... . 116
Fig. 8.7 The plot of fmax against epicentre for the well data ................ 116
Fig. 9.1 Tectonic setup of the study area showing all the important fault systems along with station (blue triangle) and events (white circles) used in this study (NPDB: North Panama Deforming Belt; ECT: Ecuador-Colombia Trench; LFS: Llanos Fault System; RFS: Romeral Fault System; SMBF: Santa Marta-Bucaramanga Fault; BF: Boconó Fault) 123
Fig. 9.2 An example of the seismogram recorded at OTAV (a) marked P, S and coda arrivals. A time window of 10.24 sec is shown in green shades (b) and (c) Seismogram with coda windows filtered at central frequencies of 1 Hz–2Hz and 4Hz–8 Hz along with estimated Qc
127
Fig. 9.3 Seismogram with coda windows filtered at central frequencies of 4 Hz–8 Hz ......................................................... . 128
Fig. 9.4 Seismogram with coda windows filtered at central frequencies of 8 Hz–16 Hz .........................................................
128
Fig. 9.5 Seismogram with coda windows filtered at central frequencies of 12 Hz–24 Hz ...................................................... 129
Fig. 9.6 Seismogram with coda windows filtered at central frequencies of 16 Hz–32 Hz ....................................................... 129
Fig. 9.7 Plots of frequency-dependent Qc at lapse time of 10 s, 20 s, 30 s, 40 s, 50 s and 60 s ..............................................
130
Fig. 9.8 Plot showing variation in Qavg for all lapse times versus frequency .............................................................. 131
Fig. 10.1 Map shows the tectonic features along with instrumental stations located in the study region ........................................... 135
Fig. 10.2 Plot of the event recorded at SKND station on July 5, 2009. (a)Unfiltered data-trace with coda window, (b)to(e) bandpass filtered displacement amplitudes of coda window at 1–2 Hz, 4–8 Hz, 8–16 Hz, and 16–32 Hz, respectively, and the RMS amplitude values multiplied with lapse time along with the best square fits of selected coda window at central frequencies of 1.5, 6, 12 and 24 Hz, respectively. The Qc is determined from the slope of the best square line. Abbreviations are P: P-wave arrival time; S: S-wave arrival time ............................................................ 139
Fig. 10.3 Map showing the spatial distribution reference to a single station .. 142
Fig. 10.4 Plots of quality factors and central frequencies for all distance ranges with linear regression frequency-dependent relationship
Fig. 10.5 Comparison of Qc values for the Bilaspur region of Himachal Lesser Himalaya, India with the existing Q studies in India . .... . 143
Fig. 11.1 The topographic map of Philippines Island showing the distribution of earthquake events of magnitude M > 7.8 (Yellow stars) along with plate boundaries ........................ . 148
Fig. 11.2 Histogram of temporal distribution of the earthquake events from 1940 to 2022 in the Philippines island ...... ................. . 153
Fig. 11.3 Distribution of event’s depth throughout the period of 1940 to 2022 in Philippines Island ........................................ . 154
Fig. 11.4 Zmap generated map showing the distribution of magnitude of completion (Mc) for the study region. Mc can be seen to be varied from 4.0 to 5.1 with majority of the study region having the Mc = 4.8 ......................................................... 155
Fig. 11.5 Plot of the cumulative number of earthquakes for the study region against magnitude 156
Fig. 11.6 Spatial distribution of b-values in the study region during the period of 1973–2022 .... ........................................ . 157
Fig. 11.7 Spatial distribution of Z-values in the study region during the period of 1973–2022 .... ........................................ . 158
Fig. 11.8 Plot showing the (a) annual probability of occurrence of earthquake of certain magnitude, (b) the period after which the earthquake of certain magnitude will occur again (recurrence period) ................................................... .
Fig. 11.9 Plots showing the variation of b-values in 5 different time windows of 10 Years for the time periods (a) 1973–1982, (b) 1983–1992, (c) 1993–2002, (d) 2003–2012 and (e) 2013–2022, respectively, starting from the top left and moving clockwise .. ............................................. .
Fig. 12.1 Topographic map of Japan showing the major fault lines, plate boundaries, and coastlines generated by Zmap ............. .
Fig. 12.2 Correlation between observed and synthetic waveforms and focal mechanism of solutions is plotted against the depth of the source. The DC% value scale has been shown on the right side
Fig. 12.3 Plot of correlation v/s time shift. Source position and DC%
Fig. 12.4 Plot of an observed and synthetic waveform. Black represents the observed waveform and red represents the synthetic waveforms. The blue color number represents the VR between the waveforms .
Fig. 12.5 Plot of SNR v/s frequency
Fig. 12.6 Plot of power spectrum v/s frequency
Fig. 12.7 Amplitude response of the PZ files of the instrument .............
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List of Tables
Table 2.1 The geographical location of the stations used in the present work ................................................................. 18
Table 3.1 The fmax-models available in Japan region ........................ 33
Table 3.2 Statistics of fmax-model with multivariate regression analysis (MVLR) ............................................................. . 33
Table 3.3 Statistics of κ -model with multivariate regression analysis (MVLR) ............................................................. . 36
Table 3.4 Comparison of observed kappa values with other worldwide values estimated by various researchers .. ........................ . 37
Table 4.1 Event information of 16 earthquakes provided by ISC .......... 50
Table 4.2 Detail information of the location of 18 seismic stations used in this study . .................................................. . 53
Table 4.3 Velocity and resolution variation with depth after Mahesh et al. (2013). Vp and Vs are velocities of P and S waves, respectively. Qp and Qs denote the quality factors employed to quantify the attenuation of seismic waves ... 53
Table 4.4 Summary of all 16 fault-plane solutions obtained after performing MT estimation, as well as, depth and magnitude search ................................................................ 59
Table 6.1 Moho Depth and Possion’s ratio for all the stations ............. 97
Table 8.1 Obtained kappa value for all stations of surface as well as for wells .......................................................... . 117
Table 9.1 Average quality factor at different lapse times and frequencies for OTAV station .... .............................................. . 130
Table 10.1 Site characteristics and epicentral locations of the recording stations . ............................................................. . 136
Table 10.2 Various central frequencies with low-cut and high-cut frequency bands are used for filtering ......................................... 137
Table 10.3 Q values calculated in different distance ranges, where N is the number of data points and SD is the standard deviation ... ......................................................... . 140
Table 10.4 shows the maximum depth of ellipsoid volume formulation given by Pulli (1984) at Sknd station at different distance ranges ...................................................... 141
Table 12.1 The obtained focal plane solutions ............................... . 173
Table 13.1 Error estimations of different types of magnitudes (Wason et al., 2018) ............................................... . 180
Chapter 1 Earthquake Occurrence Models
Chhavi Chaudhari, M. L. Sharma, and Shusil Gupta
1.1 Introduction
The Seismic Hazard Assessment (SHA) is generally based on two approaches, namely probabilistic and deterministic. A popular technique for SHA is called probabilistic seismic hazard analysis (PSHA), which forecasts a correlation between the maximum ground motions or response spectra and the annual rate of exceedance and return period. Through the use of a mathematical model, PSHA incorporates the occurrence frequencies and ground motions for all earthquakes in an area. PSHA often involves several logic trees, recurrence times, seismic sources, and ground motion attenuation relationships. The rate of occurrence of earthquake events for identified seismogenic source zone is the necessary part of PSHA. The earthquake frequency-size distribution has attracted the attention of numerous researchers. It was initiated by Ishimoto and Iida (1939) and continued by Gutenberg and Richter (1944), and it became one of the frequently used magnitude-frequency relationships in seismology. There are various statistical distributions that have been described which may better reflect seismic gap regions as compared with classical method G-R relationship. In this chapter, two models, namely Constant moment release (CMR) model and Constant seismicity (CS) model, have been described. The Himalayan area has been used as a case study to see the results of these two models.
C. Chaudhari · M. L. Sharma (✉) · S. Gupta
Department of Earthquake Engineering, Indian Institute of Technology Roorkee, Roorkee, India e-mail: m.sharma@eq.iitr.ac.in
The Gutenberg-Richter ’s(1954) relationship, which calculates the yearly occurrence exceedance rates in a designated seismogenic source zone, is the most often used relationship to assess the seismicity of seismogenic sources. According to Cornell and Vanmarcke (1969), a lower threshold magnitude Mmin and an upper bound magnitude Mmax are used to construct the recurrence relation. A temporal sequence of earthquake numbers and an earthquake size distribution exist if the catalogue completion threshold is constant across time. The truncated density function, n(M ), outlining the happening rate of earthquakes per unit magnitude at magnitude i can thus be defined as:
Here, the Heaviside step function is denoted by H ( ) and β = b*ln 10 (b is known as seismicity constant in GR relationship).
The corresponding cumulative distribution function is obtained as:
According to the relationship shown in Eq. 1.2, the occurrence rate of earthquakes N(M ) with magnitudes larger than or identical to the threshold magnitude Mmin does not change but the N(M ) diminishes exponentially to zero as M approaches Mmax. So, the term “constant seismicity exponential recurrence model” is used to describe this model. The stages of completeness for various magnitude varieties are a crucial step for modified G-R.
1.1.2 Constant Moment Release (CMR) Model
In CS model, the overall frequency of earthquakes with magnitudes larger than the minimum is unrelated to the maximum magnitude Mmax. Conversely, a lower value of Mmax indicates that there is a lesser moment release in the seismogenic source region that does not correspond to the physical significance of the source region according to the CS model. This may be remedied by limiting the moment release degree that is necessary in a particular location. As a result, the increase in the overall number of minors to moderate earthquakes compensates for the decrease in Mmax. As a result, it is feasible to alter the CMR models utilising the N(Mmin), which was calculated using the moment release rate M 0 M max ðÞ, which was found geologically for the given Mmax (Anderson, 1979; Molnar, 1979; Chatelain et al., 1980; Shedlock et al., 1980). The CMR model often makes the following presumptions: (1) If creep
is not specifically stated, the complete slide on a fault or within a seismic source is seismic. (2) The average value of the slip rate across large time intervals applies to the future time period of interest, while short-term changes in the slip rate are insigni ficant. (3) Surface slip rates are typical of slip rates at seismogenic depths and throughout the whole fault segment of interest. By balancing the seismic moment release rate (SMRR) caused by the regular great time period slip rate that can be obtained by geological or geodetic field study. The long-term mean yearly occurrence rate, denoted by the symbol N(Mmin) is calculated under these assumptions. First, the seismic moment rate can be calculated using the formula _ M 0 = μAS, where S is the slip rate in centimetres per year (Brune, 1968). “A” stands for the plane area of the fault rupture in cm2, and μ represents the crustal rock’s modulus of rigidity in dyne/cm2. Shaping the seismic moment linked through the sources is required for the CMR constraint method’s assessment of the overall occurrence rate. The seismic moment linked through any size, according to Kostrov (1974), is determined by the relations as:
where L stands for length, W denotes seismogenic source width, E stands for strain rate and M 0 is the total seismic moment rate that has been released as a result of strain rate (Kostrov, 1974; Chatelain et al., 1980; Savage & Simpson, 1997). To calculate the seismic moment, the rate of strain must be precisely measured. The seismic moment rate tensor _ M ij in the seismogenic source zone is directly related to the tensor of strain rate ɛij, which has been calculated using GSRM, and this relation is based on Kostrov (1974) _ M ij = 2μAD _ εij . A seismogenic zone volume’s SMRR has been translated from the estimated strain rate at the earth’s surface using this connection (Ward, 1998; Choudhary & Sharma, 2017; WGCEP, 1995). Due to the 2-D strain rate tensor, this relationship measurement is not particular and does not like the double-couple tool proposed by Savage and Simpson (1997). They then proposed a variant to get over this restriction by giving the best resemblance between the rate of scalar moment M 0 and the rate of crustal strain.
ð
where the two main parts of the strain rate tensor are _ ε1 and _ ε2 . The frequencymagnitude figures of earthquakes with a given slope (b) and seismogenic source zone maximum magnitude have been considered to be best modelled by the exponential distribution. So, hypothetically, the SMRR resulting from all earthquakes up to magnitude Mmax can be calculated as:
4C.Chaudharietal.
where M is seismic moment of magnitude, which can be calculated by log M0(M ) = 16 + 1.5 M in dyne-cm (Hanks & Kanamori, 1979). n(M), the exponential density function, is defined in terms of the upper bound magnitude Mmax and the occurrence rate N(Mmin). In order to express the estimated seismic moment rate during an earthquake, which is given by Eq. 1.5, in dyne-cm units, use the form _ M 0 . Equation 1.6 can be represented as follows following integration: _ M 0 M ðÞ = NM min ðÞ e - β M - M min ðÞ _ M 0 M max ðÞ b d - b ð1 6Þ
In these expressions, _ M 0 M max ðÞ denotes the moment released by the maximum possible magnitude of Mmax.
Because of the power-law nature of the earthquake magnitude dispersal and the shortage of historical and instrumental earthquake archives for relatively lesser seismic areas, the GR law provides estimates for tiny space-time volumes that are extremely uncertain and occasionally unsteady (McCaffrey, 1997; Arora & Sharma, 1998; Holt et al., 2000). The law is catalogue dependent and gives no indication of the greatest magnitude. It is crucial to apply statistical techniques that closely examine the distribution’s tail, or the variety of its extreme standards, in addition to the main distributions.
1.2 Seismic Hazard Parameter Estimation
The seismic hazard modelling depends on individual tectonic setup and the environment, which implies that model applicability varies with the region, which becomes more complex within the fact that even within the same geological environment, earthquake frequency varies greatly. Various studies have been carried out worldwide to recognize the seismicity processes for different regions, but with such scientific rise, we are quite incapable of modelling real situation. Thus, most of the studies conclude that no single methodology can capture the physical phenomena of earthquake occurrence in specific regions. To model and analyse an earthquake process, one must understand the entire tectonic environment, incorporating route impacts, the rupture mechanism, the source, and the focal mechanism, within the local site circumstances. The stress accumulates due to tectonic plate movement, which is released in the form of earthquakes of several extents ranging from micro seismic measures to macro seismic measures. The quality of the dataset also plays a domineering characteristic of modelling in a pragmatic view. For case study, the Himalayas region has been selected. The orogeny of the Himalaya is characterised by the creation of major earthquakes, making it one of the world’s most active zones. The following sections discuss these study areas by applying different models of earthquake occurrences.
The stress regime conditions along the Himalayan belt are highly heterogeneous due to different convergence rates in the various segments of the Himalaya. To accompany the heterogeneity in the Himalaya region, we selected three sub-regions
Fig. 1.1 The Himalayas and Characterization of three regions on the basis of tectonics and recorded seismicity of magnitude MW ⩾ 5.0 for the time period 1255–2017
in the Himalaya, viz. the North-West Himalaya, Garhwal Himalaya and Nepal region (Fig. 1.1). To incorporate the diversity of stress rates in SHA, we have considered Constant Seismicity and CMR models. Constant Seismicity model is derived from compiled earthquake catalogue, and for implication of CMR model, global strain rate data is utilized. The estimated seismicity for all three regions using both recurrence models have been compared.
The seismicity parameters gathered employing two separate approaches were employed to determine the likelihood of an earthquake occurrence of a certain magnitude during a given time period (Shanker & Sharma, 1997; Sharma and Dimri, 2003; Sharma, 2001, 2003; Lindholm et al., 2006; Mahajan et al., 2010; Kushwaha et al., 2021). These recurrence probabilities have been represented using the Poissonian distribution, which calculates the likelihood of the number of earthquakes occurring in a given location and time frame. One of the most important parameters in Probabilistic Seismic Hazard Assessment is the estimation of annual earthquake occurrence rates (Arora & Sharma, 1998; Sharma, 2001; Sharma et al., 2002; Sharma & Malik, 2006; Choudhary & Sharma, 2017, 2018a, b). The seismic hazard calculation of three unique locations spanning the Central Himalaya to the North-West Himalaya has been handled here employing the CS model and the CMR model. Three areas were chosen based on the strain rate build-up heterogeneity and successive release in the form of tectonics, seismic events and geomorphology (Fig. 1.1).
The recurrence rate in the Constant Seismicity model is determined by the lower bound magnitude Mmin Mmin was calculated for computational purposes using the Woessner and Wiemer (2005) technique, while Mmax may be found using the relationship described by Kijko (2004). Figure 1.2 depicts the magnitude frequency distribution and magnitude of completeness for the Himalaya subdivision using the EMR approach.
Fig. 1.2 Magnitude
Frequency Distribution and magnitude of completeness in the subdivision of Himalaya using the EMR method
North West Garhwal Himalaya
Fig. 1.3 Variation of Cumulative rate of Nmin w.r.t. Mmax in North-West Himalaya using (a) Constant seismicity and (b) Constant Moment Release models
The seismicity parametres values estimated employing the CS model for each section are mentioned in Fig. 1.2.
The cumulative numbers larger than or equivalent to threshold magnitude earthquakes in the Constant Seismicity model are not dependent on the maximum magnitude Mmax. Although, a lesser Mmax value results in a lower moment release rate, which is not taken into account by the CS model, it may be avoided by confining the moment release rate in a speci fied zone. As a result, the decrease in Mmax is compensated for by increasing the earthquakes’ overall number N(Mmin), as illustrated in Figs. 1.3, 1.4, 1.5. Thus, adopting the N(Mmin), it is feasible to change the CS recurrence models.
The seismically active region of the North-West Himalaya (fold and thrust belt) has resisted big to moderate earthquake occurrences. According to the findings of an inclusive seismological investigation of the North-West Himalaya, entire seismicity is associated with crucial thrust and undiscovered faults. The majority of the earthquakes happen at shallow depths. In 2005, an earthquake of magnitude 7.6 struck near latitude 34.493°N and longitude 73.629°E, with a focal depth of approximately 26 km. The outcomes show that the overall seismicity rate calculated employing CMR is 55.67% greater than those found using the CS model in the North-West area, indicating that gathered strain was not entirely released by previous earthquakes. This suggests that gathered strain is remunerated for by
1.4 Variation of Cumulative rate of Nmin w.r.t. Mmax in Garhwal Himalaya using (a) Constant seismicity and (b) Constant Moment Release models
Fig. 1.5 Variation of Cumulative rate of Nmin w.r.t. Mmax in Nepal Himalaya using (a) Constant seismicity and (b) Constant Moment Release models
supplementary tectonic activity, such as fault and locking mechanisms, or that the earthquake inventory is incomplete and insuf ficient. Using CS and CMR models, the predicted total seismicity N(Mmin) values are 70.56 and 109.83, respectively. The estimated yearly occurrence of earthquakes employing the CMR model rate is greater than that projected by the CS model rate for all magnitude ranges in the North-West area, as shown in Fig. 1.6. In the North-West area for CS and CMR, an earthquake of magnitude 7 Mw is predicted to occur in 60 years and 40 years, respectively, according to Fig. 1.6, which shows the likelihood of occurrences of magnitude 7 Mw and 7.5 Mw with duration of exposure (year). Using CS and CMR, an earthquake of magnitude 7.5 is expected to happen in 200 years and 300 years, respectively (Choudhary & Sharma, 2018a, b; Richa et al., 2022).
A similar pattern has been seen in the Garhwal Himalaya area, where the total seismicity N(Mmin) rate derived by CS and CMR is 4.6 and 16.3, respectively. The Garhwal Himalaya area is located in the centre seismic gap and has seen less seismicity than the North-West area. The gathered energy budget in the Garhwal Himalaya implies that an earthquake with a magnitude Mw ≥ 8 is about to strike in
Fig.
Fig. 1.6 Hazard assessment in North-West Himalaya: (a) annual occurrence rate of earthquake magnitude and (b) probability of earthquake occurrence in the specific time period
Fig. 1.7 Hazard assessment Garhwal Himalaya: (a) annual occurrence rate of earthquake magnitude and (b) probability of earthquake occurrence in a specific time period
the seismic gap zone of Garhwal Himalaya (Bilham et al., 2001). Despite the fact that this region has seen the Uttarkashi earthquake (1991) with a magnitude Mw 6.5 and the Chamoli earthquake (1999) with a magnitude Mw 6.6. Preceding seismic hazard researches, however, have measured a greater likelihood of exceeding greater seismic activity in the Garhwal Himalaya area in the approaching year (Sharma, 2001), and this region has adequate prospective to generate an upcoming major earthquake (Choudhary & Sharma, 2017; Sharma, 2001). The estimated occurrence of yearly earthquakes employing the CMR rate model is 71% greater than that projected by the CS model for all magnitude ranges in the Garhwal Himalaya area, as shown in Fig. 1.7a. Using the CS and CMR models from Fig. 1.7b, this area has been characterised by an earthquake of magnitude Mw 6, which is projected to happen in 100 years and 50 years as reappearance periods of 5 years and 17 years, respectively (Choudhary & Sharma, 2017, 2018a; Maurya et al., 2023).
However, an intriguing pattern in calculated findings for the Nepal region may be detected. N(Mmin), the total seismicity projected employing the CS model is estimated to be 78% greater than that computed employing the CMR model. The outcome indicates that the majority of the collected energy has been unconfined as a result of the significant earthquake occurrence (Fig. 1.8a). According to historical records, Nepal has suffered four significant earthquakes of magnitude 8 and nine earthquakes of magnitude 7.0–7.9. The Gorkha earthquake with magnitude Mw 7.8 on 25 April 25 2015 partially cracked the Main Himalayan Thrust (MHT) fault, and it is worth noting that the shallower component of the MHT remained protected
Fig. 1.8 Hazard assessment in Nepal Himalaya: (a) annual occurrence rate of earthquake magnitude and (b) probability of earthquake occurrence in a specific time period
thereafter (Bilham et al., 2017). Using CS and CMR, a magnitude 8 earthquake will befall 700 years and 1100 years from now, respectively (Fig. 1.8b).
From the result estimated, seismicity using Constant Seismicity model is lower than seismicity obtained by Constant Moment release model for North-West. It implies that strain energy is constantly stored but not released in the form of earthquakes. However, the CMS model fails to capture realistic seismicity due to insufficient catalogue. Similar behaviour of seismicity has been identified in Garhwal Himalaya, but CS and CMR models depict low seismicity in comparison to the North West region. However, the Nepal region shows different pattern because maximum stress is released due to the recently large earthquake (Nepal Gorkha Earthquke 2015) that occurred in Nepal. Strain rate data play a vital role in estimating reliable SHA in the Himalaya.
To see the effect on PSHA of constant moment releasing constraint, a small segment of Himalaya as Uttarakhand has been selected. Uttarakhand lies in the central seismic gap of the Himalaya, a region where nonstop stress is gathering although not released with earthquakes, which is acknowledged as a seismic gap. To minimize the effect of earthquake and destruction of important structures, there is a need for seismic hazard examination of the Uttarakhand Himalaya. The PSHA is carried out based on parameter standards of the Gutenberg-Richter recurrence relationship. The estimation of parameters of the Gutenberg-Richter has been based on two models, Constant Seismicity using the past earthquake data seismicity and Moment release constraints method based on GSRM strain rate data. Further, these seismicity parameters have been used in PSHA at speci fic sites for an exposure time of 50 years using four New Generation Attenuation Relationships published in 2008 attenuation relationships. Uniform hazard contours for PGA have been obtained using constant seismicity and moment release constraint for a revelation time of 50 years for 90% and 98% confidence levels. For the estimation of PSHA, Uttarakhand is alienated into minor grids of size 0.2° × 0.2°. PGA has been estimated
Fig. 1.9 Hazard Maps of PGA having 10% probability of exceedance in 50 years using Boore and Atkinson (2008) for (a) Constant seismicity and (b) Constant Moment Release Models
Fig. 1.10 Hazard Maps of PGA having 2% probability of exceedance in 50 years using Boore and Atkinson (2008) for (a) Constant seismicity and (b) Constant Moment Release Models
at the centre point of each grid for 90% and 98% likelihood of occurrence in 50 years (return period of 475 years and 2475 years). The resulting PGA distribution Uttarakhand Himalaya is shown in contour Maps Fig. 1.9a, b, respectively, considering Constant Seismicity and using Moment Release constraint.
The comparison of PGA values at different sites, estimated by both models, indicates that PGA values based on Constant Moment release rate are higher than those based on Constant Seismicity model for return periods of 475 and 2475 years (Fig. 1.10a, b).
It has been observed that the values of PGA obtained from the Seismic Moment Release Constraint method are higher than the PGA from constant seismicity in those regions where the occurrence of large return period earthquake events is negligible, although enough potential to trigger a large event exists. In Constant Moment release rate, the accumulated energy may be compensated to increase the number of occurrences of small to moderate earthquakes.
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