1. Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" by K. Modis, National Technical University of Athens and K. Komnitsas, Technical University of Crete

2. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 2 Summary The objective of this work is to apply recently established theoretical results (Modis and Papaodysseus, 2006) in order to estimate the optimum sampling grid for AMD prediction in an Underground Sulphide Mine in northern Greece. The objective of this work is to apply recently established theoretical results (Modis and Papaodysseus, 2006) in order to estimate the optimum sampling grid for AMD prediction in an Underground Sulphide Mine in northern Greece.

3. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 3 Introduction The theoretical results are based on the sampling theorem of information which states that a band limited random waveform can be reconstructed by its samples if the sampling rate is greater than a critical value depending on the waveform characteristics The theoretical results are based on the sampling theorem of information which states that a band limited random waveform can be reconstructed by its samples if the sampling rate is greater than a critical value depending on the waveform characteristics

4. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 4 Introduction In simple words, the methodology followed is an extension of information theory applied to the mineral exploration practice. In simple words, the methodology followed is an extension of information theory applied to the mineral exploration practice. But, is it reasonable that there is a limit in sampling density, and more samples will add little to the quality of the approximation? But, is it reasonable that there is a limit in sampling density, and more samples will add little to the quality of the approximation?

5. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 5 Introduction The answer in fact is YES!, under the condition that the frequency content of the study variable is limited. Band limitedness ensures slow variation. And it is easier to sample a slow varying phenomenon than a rapidly one. The answer in fact is YES!, under the condition that the frequency content of the study variable is limited. Band limitedness ensures slow variation. And it is easier to sample a slow varying phenomenon than a rapidly one. There are two important facts about our approach … There are two important facts about our approach …

6. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 6 Introduction Fact 1: It is the first method to estimate a theoretical limit to the sampling density, above which there is no significant improvement to the accuracy of estimation. Fact 1: It is the first method to estimate a theoretical limit to the sampling density, above which there is no significant improvement to the accuracy of estimation.

7. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 7 Introduction Fact 2: In the case of an existing sampling grid, if the drill hole density is close to the ideal one, it is proved that the results of all interpolation algorithms converge to reality. Fact 2: In the case of an existing sampling grid, if the drill hole density is close to the ideal one, it is proved that the results of all interpolation algorithms converge to reality.

8. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 8 About the theory According to the aforementioned sampling theorem, only bandlimited waveforms can be reconstructed by their samples. According to the aforementioned sampling theorem, only bandlimited waveforms can be reconstructed by their samples. Modis and Papaodysseus (2006) have pointed out that earth phenomena represented by a variogram model with a sill (e.g. Spherical scheme) are approximately bandlimited. Modis and Papaodysseus (2006) have pointed out that earth phenomena represented by a variogram model with a sill (e.g. Spherical scheme) are approximately bandlimited.

9. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 9 About the theory For example, the fourier transform of a linear variogram/ covariance model with a sill, For example, the fourier transform of a linear variogram/ covariance model with a sill, (b) 1 h γ(h) a-a 0 1 h R(h) a -a (a) 0 is approximately bandlimited

10. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 10 About the theory Or, the fourier transform of the spherical variogram/ covariance model with a sill, Or, the fourier transform of the spherical variogram/ covariance model with a sill, is also approximately bandlimited

11. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 11 About the theory In that case, it is also shown that the critical sampling interval equals half the range of influence of the underlying variogram model. In that case, it is also shown that the critical sampling interval equals half the range of influence of the underlying variogram model. According to the above, the estimation of the critical sampling rate of a spatial phenomenon is done in two steps: According to the above, the estimation of the critical sampling rate of a spatial phenomenon is done in two steps:

12. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 12 About the theory Step 1.At the structural analysis stage, the variogram/ covariance model is estimated. If it is a model without a sill, the process stops here. Step 1.At the structural analysis stage, the variogram/ covariance model is estimated. If it is a model without a sill, the process stops here.

13. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 13 About the theory Step 2.At the estimation stage, the critical sampling interval is estimated by halving the range of influence of the underlying variogram model. Step 2.At the estimation stage, the critical sampling interval is estimated by halving the range of influence of the underlying variogram model.

14. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 14 The Stratoni sulphide deposit The Stratoni mining area, situated in the north-eastern part of Macedonia, Greece, is the largest mixed sulphide mining operation in Greece and will be examined as a case study. The Stratoni mining area, situated in the north-eastern part of Macedonia, Greece, is the largest mixed sulphide mining operation in Greece and will be examined as a case study.

15. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 15 The Stratoni sulphide deposit The ore is mined with cut-and –fill but in the past, sub-level caving was employed, and resulted in extensive cracks in the overlying strata inducive to water infiltration and acid generation. The ore is mined with cut-and –fill but in the past, sub-level caving was employed, and resulted in extensive cracks in the overlying strata inducive to water infiltration and acid generation.

16. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 16 The Stratoni sulphide deposit What is aimed is to predict the AMD potential in various parts of the mine, for use especially after mine closure. What is aimed is to predict the AMD potential in various parts of the mine, for use especially after mine closure. For this purpose, we need to develop a spatial NNP model based on available drill hole samples. For this purpose, we need to develop a spatial NNP model based on available drill hole samples.

17. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 17 Sampling The Stratoni deposit has been surveyed by a drilling campaign, which includes 171 drill holes. The Stratoni deposit has been surveyed by a drilling campaign, which includes 171 drill holes. Average distance between drill holes was 150 m Average distance between drill holes was 150 m 25000 -24000 2550026000265002700027500280002850029000 -24500 -25000 -25500 -26000 -24000 -24500 -25000 -25500 -26000 250002550026000265002700027500280002850029000 600 500 400 300 200 100 200 300 400 500 600

18. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 18 Sampling Drill hole loggings included chemical analyses of the mineralization. NNP values of these samples were calculated based on their sulfur content from a curve fitted to experimental data. Drill hole loggings included chemical analyses of the mineralization. NNP values of these samples were calculated based on their sulfur content from a curve fitted to experimental data. S(%) NNP -1400 -1200 -1000 -800 -600 -400 -200 0 0204060 NNP Model

19. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 19 Sampling The NNP values for non- mineralized samples were calculated by assigning them to a set of predefined rock classes which were chemically processed to determine their NNP. The NNP values for non- mineralized samples were calculated by assigning them to a set of predefined rock classes which were chemically processed to determine their NNP. 2336 - 11,6 2039 - 29,7 2576 - 20,7 1776 - 34,4 1998 - 26,8 1530 - 45,5 717 - 70,4 2290 - 15,7 2250 - 13,2 2395 - 19,9 2478 - 12,8 1885 - 35,8 2182 - 17,8 2463 - 16,8 2411 - 22,1 2417 - 17,6 2502 - 11,3 2238 - 28,3 1477 - 51,2 0,00 23,20 24,20 37,30 37,60 38,50 39,70 40,30 40,90 41,50 42,80 43,00 89,30 89,80 90,80 92,30 94,00 94,50 94,90 95,50 95,70 98,40 98,80 100,10

20. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 20 Application of the theory As previously stated, the estimation of the critical sampling rate of a spatial phenomenon is done in two steps: As previously stated, the estimation of the critical sampling rate of a spatial phenomenon is done in two steps:

21. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 21 Step 1. Structural analysis Using the data derived from the drilling campaign concerning overall assigned NNP of each sample, the variogram function of this variable was calculated. Using the data derived from the drilling campaign concerning overall assigned NNP of each sample, the variogram function of this variable was calculated.

22. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 22 Step 2. Sampling rate estimation It is clear from the previous figure that there is a range of influence up to 90 m in NNP variogram model (Spherical). It is clear from the previous figure that there is a range of influence up to 90 m in NNP variogram model (Spherical). Using the above mentioned Modis and Papaodysseus (2006) formula to estimate the optimal sampling grid we get a value of 45 m. Using the above mentioned Modis and Papaodysseus (2006) formula to estimate the optimal sampling grid we get a value of 45 m.

23. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 23 Results From the above analysis it is seen that some (small) parts of the wider mining area are over- sampled since drillhole distances can be as short as 20 m which is shorter than the recommended distance of 45 m. The rest of the area is under- sampled since no drill holes are as close as the optimum distance. From the above analysis it is seen that some (small) parts of the wider mining area are over- sampled since drillhole distances can be as short as 20 m which is shorter than the recommended distance of 45 m. The rest of the area is under- sampled since no drill holes are as close as the optimum distance. Thus, the drill holes are distributed unevenly indicating over-sampling in some parts and under-sampling in others. Thus, the drill holes are distributed unevenly indicating over-sampling in some parts and under-sampling in others.

24. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 24 Conclusions The variogram model generated by structural analysis of NNP spatial distribution in the mining area under study enables the establishment of a critical sampling grid; The variogram model generated by structural analysis of NNP spatial distribution in the mining area under study enables the establishment of a critical sampling grid; in some parts of the ore body the sampling grid is denser than required.

25. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 25 Conclusions  If the density of the sampling grid is close to the critical value, the calculation of the NNP numerical model can be implemented by using simpler interpolation algorithms, such as inverse distance square having equal accuracy to geostatistics.

26. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 26 Conclusions  In general, the design of the drilling campaign can be considered as an optimization problem. The selection of the appropriate grid size can maximize the information regarding the distribution of NNP values;  it can also contribute to considerable savings in money and time.

27. K. Modis- K. Komnitsas "Optimum Sampling Density for the Prediction of AMD in an Underground Sulphide Mine" 27 Thank You!