Predicting gold targets using cokriging in SURFER 17

Predicting gold targets using cokriging in SURFER 17 Valls Álvarez, R. A. (2019) DOI 10.17605/OSF.IO/XHJ8G

Abstract Golden Software Inc. included the method of cokriging in the newest version of SURFER 17. This has opened a new tool for interpreting geochemical data. We can use cokriging in SURFER 17 to improve the quality of maps and to predict similar targets in nearby areas. We use cokriging when we want to process data from different datasets. One dataset is always smaller than the other. Here, I first tasted the method with a hypothetical geochemical model combining a smaller dataset of FA gold results with a larger dataset of ICP-MS multi-elements. Later, I applied this method to real data from a soil sampling project in Mozambique. I tested a known mineralized target and also an extended area to predict gold targets. I also had the gold results for the extended area. They allowed me to confirm the effectiveness of cokriging in predicting the new targets. There are many opportunities where we can apply cokriging as a prediction tool. One situation is when an initial sampling returned a group of interesting but isolated gold results. We can then use a cheaper method, like ICP-MS, to better understand the gold distribution in the area. Keywords: Cokriging, SURFER 17, geochemistry, gold targets, prediction

Introduction Kriging is an essential part of the graphical representation of a dataset. Kriging or Gaussian process regression is a method of interpolation for which we interpolate the values by a Gaussian process governed by prior covariances. Under suitable assumptions on the priors, kriging gives the best linear unbiased prediction of the intermediate values. We use this method in the domain of spatial analysis and computer experiments. We also know the technique as Wiener–Kolmogorov prediction, after Norbert Wiener and Andrey Kolmogorov1. Kriging estimates the least squares of the data (Srivastava, 2009). It uses z-scores to generate an estimated surface model from the spatial description of a scattered set of data points. One advantage of this interpolation is that it not only generates an interpolated spatial model, it also generates an estimate of the uncertainty of each point in that model. Golden Software introduced the cokriging option in their SURFER 17 version. We can use cokriging methods to take advantage of the covariance between two or more related regionalized 1

https://www.wikiwand.com/en/Kriging

variables when the main attribute of interest is sparse, but related secondary information is abundant (Stein and Corsten, 2006). The main variable of interest is Z1, and both autocorrelation for Z1 and cross it uses to make better predictions. However, the specifics of the application of Surfer's 17 cokriging option for processing geological data are still unclear for the field geologist. This study tested a hypothetical model to explain step-by-step how to use cokriging to interpret geochemical data and then I applied it to a real case scenario processing soil samples from a project in Mozambique. Cokriging allowed the prediction of several new gold targets in the studied area. Since we had the gold results for the predicted area, we could confirm the effectiveness of cokriging in this case. Therefore, I recommend the use of this method as an exploration tool to identify new targets.

Materials & Methods Cokriging is an interpolation technique that allows a better estimation of map values when we know what is the distribution of a secondary variable(Myers, 1991). If the primary variable is difficult or expensive to measure, then cokriging can improve interpolation estimates without having to more intensely sample the primary variable (Stein and Corsten, 2006). Consider the following hypothetical example.

Figure 1. Model of the mineralization. We initially sampled this area with potential for gold mineralization with a wide grid of 400 x 400 m.

Figure 2. Initial sampling. Table 1 shows the results of this sampling. Table 1. Original results for Au and As. UTM E UTM N Elevation 0 0 5 0 400 6 0 800 5 400 0 6 400 400 135 400 800 110 800 0 6 800 400 80 800 800 30

Au 10 20 20 10 300 200 25 60 10

As 12 30 25 12 550 320 30 75 15

After modelling the data using compositional data analysis (Valls Alvarez, 2008) and SURFER’s variograms and kriging (Shapiro and Botha, 1991), we got the following map:

Figure 3. Gold distribution from the original sampling. Figure 4 shows that there is a great correlation between Au and As.

Figure 4. A strong correlation between Au and As from the original sampling. I continue to test the model using a 200 x 200 m grid. This time we included hypothetical data from an ICP multi-element analysis, which is cheaper than the FA for gold.

Table 2. Results from the additional sampling. UTM E UTM N Elevation 0 0 5 0 200 6 0 400 6 0 600 5 0 800 5 0 1000 5 200 0 6 200 200 50 200 400 75 200 600 80 200 800 50 200 1000 20 400 0 6 400 200 35 400 400 135 400 600 120 400 800 110 400 1000 50 600 0 5 600 200 55 600 400 85 600 600 50 600 800 45 600 1000 25 800 0 6 800 200 95 800 400 80 800 600 50 800 800 30 800 1000 10 1000 0 5 1000 200 6 1000 400 6 1000 600 5 1000 800 6 1000 1000 5

Figure 5 shows the new sampled area.

Au

As 1 2 2

1 300 200

25 60 1

7 8 10 12 10 15 10 50 120 200 100 50 7 250 550 425 320 100 20 180 210 50 40 30 30 100 75 25 8 10 5 8 10 4 12 5

Figure 5. New extended sampling. Figures 6 and 7 show the distribution of Au and As from the initial dataset.

Figure 6. Gold distribution.

Figure 7. Arsenium distribution. Figure 8 shows an overlie of both maps.

Figure 8. Overlay of both Au and As values.

Obtaining co-kriging maps Using SURFER 17, I completed the variogram analysis of both elements.

There will be cases where due to the small number of samples or the heterogeneity of the data, one element (usually gold), will not produce a variogram. In that case proceed as follow: 1. Do a normal kriging of both elements without concerning with their variograms and save the grid files. 2. Remember to take the gold from the smaller dataset corresponding to the original sampling and the other element (in our case As) from the larger file corresponding to the subsequent sampling. Make sure that both files will have the same number of rows and columns. 3. In SURFER open each grid file and export them as .dat. 4. You can check for the variograms now2.

Figure 9. Gold variogram. You can go now to the co-kriging option of SURFER 17. Table 3 shows all the possible combinations of co-kriging. I identified with an “X” those combinations that gave bad results.

2

According to Kari Dickenson from Golden Software Inc, another way to deal with the problem of not having pairs of data in the variogram is to increase the specified Max Lag Distance.

Table 3. Matrix of results. Au As Au dat As dat

Au X Fig. 12 X Fig. 16

As Fig. 10 X Fig. 14 X

Au dat X Fig. 13 X Fig. 17

As dat Fig. 11 X Fig. 15 X

Because in this model we were not able to obtain the variograms from the original data, we will analyse only the graphics of the “.dat” grid files. Figure 11 shows a better internal structure of the anomaly.

Figure 10. Au vs As.

Figure 11. Au vs As dat.

Figure 13 not only shows a better structure, but also covers a larger area.

Figure 12. As vs Au.

Figure 13. As vs Au dat.

Figure 14. Au dat vs As.

Figure 15. Au dat vs As dat.

Figure 17 shows the best results in comparison with the original model of mineralization (Fig. 1).

Figure 16. As dat vs Au.

Figure 17. As dat vs Au dat.

Results A Real Case Scenario African Lion Resources Inc. completed an irregular soil sampling in an area with potential for gold mineralization in one of their licenses in Mozambique (Fig. 18).

Figure 18. Location of the original samples. The results of this program showed a correlation of 0.71 between Au and Cu. Table 4 shows the original results.

Table 4. Results for Au and Cu from the original sampling program. X 522835 522890 522899 523226 523250 523274 523271 522989 522989 522930 523427 523427 524016 522696 522392 520975 522407 523042 522853 522853 522815

Y Sample 8436719 6 8436470 10 8436402 11 8435609 16 8435712 20 8435946 21 8435422 38 8435075 43 8435075 44 8434405 49 8434200 53 8434200 54 8434816 59 8435450 63 8435427 64 8435409 70 8435450 117 8435333 118 8436777 128 8436777 129 8435619 158

Au 1.535 2.020 2.040 3.070 1.580 0.110 407.455 23.550 4.745 5.030 630.020 27.020 7.520 1.520 4.020 3.020 226.520 0.470 11.020 11.020 6.520

Cu 105.000 59.000 113.000 97.000 93.000 103.000 30.000 32.000 27.000 50.000 469.000 45.000 36.000 4.000 17.000 31.000 42.000 29.000 23.000 57.000 50.000

Considering the good initial results, the company completed a second sampling program covering a larger area this time. We will be comparing the maps obtained by cokriging of the original gold results with the extended copper results (Cu1) and the reverse cokriging. The extended dataset included gold values determined by enzyme leach. While these results are not as exact as those from FA, we will use them to present on each case maps for tested and confirmed data.

Au vs Cu 1 When comparing the predicted with the original map, we can see a more detailed structure of the anomaly.

Figure 19. Original, predicted, tested, and confirmed gold distribution from the original sampling. Tested values show the Au results for these samples determined by Enzyme Leach (not FA). When we compare the areas of the predicted targets with the tested results, we can see that more than half of the predicted area were confirmed as potential gold targets.

Cu 1 vs Au When we make the cokriging map of Cu1 vs Au, first we obtain predicted targets for a much larger area (Fig. 20). This is because we have more Cu values from the extended sampling than the gold values from the original sampling.

Figure 20. Predicted, tested, and confirmed gold values in the extended area.

When we compare the predicted targets with the real ones, even when not using FA for the real gold values, we can see that the cokriging was very effective in determining these new gold targets.

Discussion This study has investigated how can we use cokriging to predict new exploration targets. Here, I explained step-by-step how to select the correct data for the cokriging analysis and how to interpret the results. I did this both with a hypothetical model and a real case dataset. The study revealed that cokriging is an effective tool to predict new targets by using less expensive laboratory methods. We can use the method to get a better understanding of the mineralization within a sampled area or to predict potential new targets over a larger target.

Conclusions This study has demonstrated the effectiveness of cokriging to predict new gold targets in nearby areas. The results show that using elements with significant correlations in the smaller dataset, we can predict target zones when we expand the sampling to nearby areas. It is important to note that cokriging allows predicting gold values (FA) with multi-elements got from an ICP method. This represents a significant reduction in the laboratory costs and, therefore, of the cost of the exploration program.

Acknowledgment Actlabs Group of Companies analyzed the enzyme leach data and African Lion Resources Inc. graciously provided the dataset for this study

References Myers, D.E., 1991. Pseudo-cross variograms, positive-definiteness, and cokriging. Math. Geol. 23, 805–816. https://doi.org/10.1007/BF02068776 Shapiro, A., Botha, J.D., 1991. Variogram Tutorial. Comput. Stat. Data Anal. 11, 87–96. https://doi.org/10.1016/0167-9473(91)90055-7 Srivastava, M., 2009. Nicolas Remy, Alexandre Boucher and Jianbing Wu: Applied Geostatistics with SGeMS: A User’s Guide. Math. Geosci. 41, 353–356. https://doi.org/10.1007/s11004009-9217-5 Stein, A., Corsten, L.C.A., 2006. Universal Kriging and Cokriging as a Regression Procedure. Biometrics 47, 575. https://doi.org/10.2307/2532147 Valls Alvarez, R.A., 2008. Why and How Should Geologists Use Compositional data Analysis, 1st ed. Wikibooks, Toronto.