MINERAL PROSPECTIVITY MAPPING Alok Porwal Centre of Studies in Resources Engineering,

1. MINERAL PROSPECTIVITY MAPPING Alok Porwal Centre of Studies in Resources Engineering, Indian Institute of Technology (Bombay) India

2. Introduction • GIS-based mineral prospectivity mapping • Generalized methodology • Weights of evidence model • Fuzzy model • Other models (if time)

3. Geology Geology Geophysics Geophysics Remote Sensing Remote Sensing Geochemistry Geochemistry GIS Analyse / Combine Mineral potential maps Good Data In, Good Resource Appraisal Out Garbage In, Garbage Out GIS Analyse / Combine Mineral potential maps

4. Systematic GIS-based prospectivity mapping Knowledge-base database Conceptual models Processing Mineralization processes Predictor maps Mappable exploration criteria Overlay CONCEPTUAL Spatial proxies GIS MODEL Continuous-scale favorability map Binary favorability map Validation MINERAL POTENTIAL MAP

5. Systematic GIS-based prospectivity mapping Knowledge-base Conceptual models Mineralization processes Mappable exploration criteria Spatial proxies database Processing Predictor maps Overlay GIS MODEL Continuous-scale favorability map Binary favorability map Validation MINERAL POTENTIAL MAP

6. Mineral systems approach (Wyborn et al. 1995) 2. Ligand 3. Source 4. Transport 1. Energy 5. Trap 6. Outflow Mineral System Deposit Halo (≤ 500 km) (≤ 10 km) Deposit (≤ 5 km) Model I Metal source Model II Ligand source Energy(Driving Force) Model III Transporting fluid Fluid Discharge Trap Region No Deposits • Deposits focal points of much larger mass flux and energy systems • Focus on critical processes that must occur to form a deposit • Allows identification of mineralization processes at all scales • Not restricted to particular geologic settings/deposit type • Amenable to probabilistic analysis

7. Mineral systems approach : Processes to Proxies 3. Source 4. Transport 5. Trap 2. Ligand 1. Energy 6. Outflow Mineral System Deposit Halo (≤ 500 km) (≤ 10 km) Transporting fluid Deposit (≤ 5 km) Model I Ligand/brine source Model II Metal source Energy(Driving Force) Fluid Discharge Model III Trap Region Deformation MetamorphismMagmatism Connate brinesMagmatic fluidsMeteoric fluids Enriched source rocksMagmatic fluids Structures Permeable zones Structures Chemical traps Structures aquifers MAPPABLE CRITERIA Fault/shear zones, folds geophysical/ geochemical anomalies, alteration Dilational traps, reactive rocks, geophyiscal/ geochemical anomalies, alteration magnetic/ radiometric/ geochemical anomalies, alteration, structures Radiometric anomalies, geochemical anomalies, whole-rock geochemistry Metamorphic grade, igneous intrusions, sedimentary thickness Evaporites, Organics, isotopes SPATIAL PROXIES

8. Scale dependence of exploration criteria (e.g. orogenic gold system - McCuaig and Beresford, 2009) Broad Regional 2-D GIS-based prospectivity mapping ‘Camp’ Prospect

9. Model-based mineral potential mapping database Knowledge-base Processing Conceptual models Mineralization processes Predictor maps Mappable exploration criteria Spatial proxies Overlay MODEL Continuous-scale favorability map Binary favorability map Validation MINERAL POTENTIAL MAP

10. Creation of candidate layers in GIS: Feature extraction What are the exploration criteria for the mineralisation? solid geology structural geology airborne magnetic gravity Primary data distance to faults Empirical strike of nearest fault rheological contrast reactivity (Fe2+/(Fetot+ Mg + Ca) contrast fav. host rock lithology Conceptual fav. litho. contact type fav. tectonic environment

11. 11 Proxies to Predictor Maps: Systematic Analysis of Exploration Data Geochemistry Geophysics Remote Sensing Geology • Create candidate layers (Feature extraction based on mineral systems model) GIS • Hypothesis testing • Select input layers Test/Analyse • Input layers Derivative predictor maps

12. 12 For each exploration criteria, define a hypothesis in terms of GIS layer(s) - Define an experimental plan - Generate all appropriate layers - Examine each layer’s spatial relationship to the targeted mineral deposits Redefine hypothesis - Quantify results Hypothesis incorrect Hypothesis correct Discard layer Factor identified, keep GIS layer for prospectivity mapping

13. Example: Rheology as an exploration criteria for gold trap BIF 5 Granophyric dolerite GRANITE-GREENSTONE BELTS Tholeiitic basalt 4 Dolerite Dolomite-Qtz rock Felsic Volcanics Ultramafic 3 Reactivity (Fe x [Fe/Fe+Mg+Ca]) Tonalite High-Mg basalts Andesitic Porphyry 2 Granodiorite Volcaniclastic/ clastic sedimentary rocks 1 Monzogranite Gneiss Foliated monzogranite 4 0 1 2 3 4 5 Rheological strength Basalt 5 Granite 1 Komatiite (Provided by David Groves)

14. 14 4 Basalt 5 Granite 1 Komatiite Experiment 1: Host Rock Rheology Hypothesis: More deposits in high rheological strength rocks Expected Results 1.00 0.80 0.60 Spatial association 0.40 0.20 0.00 1 2 3 4 5 Rheology Value

15. 15 1.00 0.80 Edjudina Kalgoorlie 0.60 Laverton Spatial association 0.40 Leonora Yandal 0.20 0.00 1 2 3 4 5 Rheology Value Experiment 1: Host Rock Rheology The Results Hypothesis rejected!

16. Experiment 2: Rheological Contrast 4 Hypothesis: More deposits adjacent to lithological contacts that have a higher rheological contrast Basalt 5 Granite 1 Komatiite Expected Results 1.00 0.80 0.60 Spatial association 0.40 0.20 0.00 1 2 3 4 5 Rheology contrast across geological contacts

17. 1.00 0.80 Edjudina Kalgoorlie 0.60 Laverton Spatial association 0.40 Leonora Yandal 0.20 0.00 0 1 2 3 4 Rheology Contrast at lithological contacts Experiment 2: Rheological Contrast The Results Hypothesis rejected!

18. 18 Change in Philosophy Frequent change in rheology Increased fluid flow Deposit localization Region of increased fluid flow

19. 19 Experiment 3: Rheological contrast density Hypothesis: Expect deposits to be more common in regions of greater density of rheological contrast. Expected Results 1.00 0.80 0.60 Spatial association 0.40 0.20 0.00 1 2 3 4 5 Geological contact density weighted by rheology contrast

20. 20 Experiment 3: Rheological contrast density Rheology contrast at lithological contacts Rheology contrast density Kalgoorlie Kalgoorlie HIGH LOW 0 1 2 3 4

21. 21 1.00 0.80 0.60 Spatial association 0.40 0.20 0.00 LOW HIGH Rheological Contrast Density Edjudina Kalgoorlie Laverton Leonora Yandal Experiment 3: Rheology Contrast Density Results • Deposits more common in regions of greater rheology contrast density • Select rheology contrast layer for inputting into mineral potential models

22. Model-based mineral potential mapping database Knowledge-base Processing Conceptual models Mineralization processes Predictor maps Overlay Mappable exploration criteria Spatial proxies MODEL Continuous-scale favorability map Binary favorability map Validation MINERAL POTENTIAL MAP

23. 23 Structure of a model for mineral resource potential mapping ∫ Integrating function • linear or non-linear • parameters Output mineral potential map • Grey-scale or binary Input predictor maps • Categoric or numeric • Binary or multi-class

24. 24 GIS-based mineral resource potential mapping - Modelling approaches • Exploration datasets with homogenous coverage– required for all models • Expert knowledge (a knowledge base) and/or • Mineral deposit data Expert knowledge Training data Knowledge-driven Hybrid Data-driven Model parameters estimated from both mineral deposits data and expert knowledge (Known deposits necessary) Semi-brownfields to brownfields exploration Examples – Neuro-fuzzy systems Model parameters estimated from mineral deposits data (Known deposits required) Brownfields exploration Examples - Weights of evidence, Bayesian classifiers, NN, Logistic Regression Model parameters estimated from expert knowledge (Known deposits not necessary) Greenfields exploration Examples – Fuzzy systems; Dempster-Shafer belief theory

25. 25 Which model is best? Theory Rich Symbolic Artificial Intelligence Any of the methods best: Hybrid Systems Neuro-fuzzy; fuzzy WofE Fuzzy Systems Bayesian Neural Networks/ GA Poor Data Rich Poor Brownfields Greenfields

26. GIS MODELS FOR MINERAL EXPLORATION • Probabilistic Model (Weights of Evidence): • used in the areas where there are already some known deposits • spatial associations of known deposits/oil well with the geological features are used to determine the probability of occurrence of a mineral deposit (or well) in each unit cell of the study area. • Fuzzy Model: • used in the areas where there are no known mineral deposits • each geological feature is assigned a weight based on the expert knowledge, these weights are subsequently combined to determine the probability of occurrence of mineral deposit in each unit cell of the study area.

27. Weights of Evidence Model for Mineral Prospectivity Mapping

28. Probabilistic model (Weights of Evidence) • What is needed for the WofE calculations? • A training point layer – i.e. known mineral deposits; • One or more predictor maps in raster format.

29. PROBABILISTIC MODELS (Weights of Evidence or WofE) • Four steps: • Convert multiclass maps to binary maps • Calculation of prior probability • Calculate weights of evidence (conditional probability) for each predictor map • Combine weights

30. The probability of the occurrence of the targeted mineral deposit type when no other geological information about the area is available or considered. Calculation of Prior Probability 1k Study area (S) 1k Target deposits D • Assuming- • Unit cell size = 1 sq km • Each deposit occupies 1 unit cell 10k Total study area = Area (S) = 10 km x 10 km = 100 sq km = 100 unit cells Area where deposits are present = Area (D) = 10 unit cells Prior Probability of occurrence of deposits = P {D} = Area(D)/Area(S)= 10/100 = 0.1 Prior odds of occurrence of deposits = P{D}/(1-P{D}) = 0.1/0.9 = 0.11 10k

31. Convert multiclass maps into binary maps • Define a threshold value, use the threshold for reclassification Multiclass map Binary map

32. Convert multiclass maps into binary maps • How do we define the threshold? Use the distance at which there is maximum spatial association as the threshold !

33. Convert multiclass maps into binary maps • Spatial association – spatial correlation of deposit locations with geological feature. A A 10km D D C C B B 1km 10km 1km Study area (S) Gold Deposit (D)

34. Convert multiclass maps into binary maps Which polygon has the highest spatial association with D? More importantly, does any polygon has a positive spatial association with D ??? A Positive spatial association – more deposits in a polygon than you would expect if the deposits were randomly distributed. D C B What is the expecteddistribution of deposits in each polygon, assuming that they were randomly distributed? What is the observed distribution of deposits in each polygon? If observed >> expected; positive association If observed = expected; no association If observed << expected; negative association

35. Convert multiclass maps into binary maps OBSERVED DISTRIBUTION Area (A) = n(A) = 25; n(D|A) = 2 Area (B) = n(A) = 21; n(D|B) = 2 Area(C) = n(C) = 7; n(D|C) = 2 Area(D) = n(D) = 47; n(D|D) = 4 Area (S) = n(S) = 100; n(D) = 10 A D C B

36. Convert multiclass maps into binary maps EXPECTED DISTRIBUTION A Area (A) = n(A) = 25; n(D|A) = 2.5 Area (B) = n(A) = 21; n(D|B) = 2.1 Area(C) = n(C) = 7; n(D|C) = 0.7 Area(D) = n(D) = 47; n(D|D) = 4.7 (Area (S) = n(S) = 100; n(D) = 10) D C B Expected number of deposits in A = (Area (A)/Area(S))*Total number of deposits

37. Convert multiclass maps into binary maps EXPECTED DISTRIBUTION OBSERVED DISTRIBUTION Area (A) = n(A) = 25; n(D|A) = 2 Area (B) = n(A) = 21; n(D|B) = 2 Area(C) = n(C) = 7; n(D|C) = 2 Area(D) = n(D) = 47; n(D|D) = 4 Area (S) = n(S) = 100; n(D) = 10 Area (A) = n(A) = 25; n(D|A) = 2.5 Area (B) = n(A) = 21; n(D|B) = 2.1 Area(C) = n(C) = 7; n(D|C) = 0.7 Area(D) = n(D) = 47; n(D|D) = 4.7 (Area (S) = n(S) = 100; n(D) = 10) A Only C has positive association! So, A, B and D are classified as 0; C is classified as 1. D • Another way of calculating the spatial association : • = Observed proportion of deposits/ Expected proportion of deposits • = Proportion of deposits in the polygon/Proportion of the area of the polygon • = [n(D|A)/n(D)]/[n(A)/n(S)] • Positive if this ratio >1 • Nil if this ratio = 1 • Negative if this ratio is < 1 C B

38. Convert multiclass maps into binary maps – Line features A L 10km D C B 1km 10km 1km Study area (S) Gold Deposit (D)

39. Convert multiclass maps into binary maps – Line features 1 1 2 3 4 5 6 7 8 9 1 0 2 3 4 5 6 7 8 1 1 1 0 2 3 4 5 6 7 8 2 1 2 3 4 5 6 7 0 1 0 3 2 1 2 3 4 5 6 1 3 2 1 1 0 2 3 4 5 6 4 3 2 1 1 0 2 3 4 5 4 3 2 1 1 1 2 3 4 0 5 4 3 2 0 1 1 2 3 4 1km 1 0 5 4 3 2 1 2 3 4 1km Gold Deposit (D)

40. Convert multiclass maps into binary maps – Line features • Calculate observed vs expected distribution of deposits for cumulative distances 1 1 2 3 4 5 6 7 8 9 1 0 2 3 4 5 6 7 8 1 1 1 0 2 3 4 5 6 7 8 2 1 2 3 4 5 6 7 0 1 0 3 2 1 2 3 4 5 6 1 3 2 1 1 0 2 3 4 5 6 4 3 2 1 1 0 2 3 4 5 4 3 2 1 1 1 2 3 4 0 5 4 3 2 0 1 1 2 3 4 1 0 5 4 3 2 1 2 3 4 Gold Deposit (D) =< 1 – positive association (Reclassified into 1) > 1– negative association (Reclassified into 0)

41. 1k 1k Calculation of Weights of Evidence Weights of evidence ~ quantified spatial associations of the resource with predictor maps Study area (S) Unit cell Deposit locations 10k Predictor feature (B1) Predictor Feature (B2) 10k Objective: To estimate the probability of occurrence of D in each unit cell of the study area Approach: Use BAYES’ THEOREM for updating the prior probability of the occurrence of deposits to posterior probability based on the conditional probabilities (or weights of evidence) of the predictor features.

42. Observation Inference P{D& B} P{B|D} Posterior probability of D given the presence of B • P{D|B} = = P{D} P{B} P{B} P{D & B} P{B|D} • P{D|B} = Posterior probability of D given the absence of B = P{D} P{B} P{B} Calculation of Weights of Evidence Bayes’ theorem: D- Well B- Predictor Feature THE BAYES EQUATION ESTIMATES THE PROBABILTY OF A WELL GIVEN THE PREDICTOR FEATURE FROM THE PROBABILITY OF THE FEATURE GIVEN A WELL

43. +ive weight of evidence (W+) -ive weight of evidence (W-) Calculation of Weights of Evidence Using odds (P/(1-P)) formulation: P{B|D} • O{D|B} = Odds of D given the presence of B O{D} P{B|D} P{B|D} • O{D|B} = Odds of D given the absence of B O{D} P{B|D} Taking logs on both sides: P{B|D} • Loge (O{D|B}) = Log of odds of D given the presence of B Loge(O{D}) + loge P{B|D} P{B|D} • Loge (O{D|B}) = Log of odds of D given the absence of B Loge(O{D}) + loge P{B|D}

44. Contrast (C) measures the net strength of spatial association between the geological feature and mineral deposits Contrast = W+ – W- + ive Contrast – net positive spatial association -ive Contrast – net negative spatial association zero Contrast – no spatial association Can be used to test spatial associations Calculation of contrast

45. WEIGHTS OF EVIDENCE FOR MULTIPLE MAPS

46. WEIGHTS OF EVIDENCE FOR MULTIPLE MAPS

47. Feature B1 Well D n Loge(O{D}) + ∑W+/-Bi i=1 Feature B2 Log of odds of D given the presence of B1 and B2 • Loge (O{D|B1, B2}) = Loge(O{D}) + W+B1 + W+B2 Log of odds of D given the absence of B1 and presence B2 • Loge (O{D|B1, B2}) = Loge(O{D}) + W-B1 + W+B2 Log of odds of D given the presence of B1 and absence B2 • Loge (O{D|B1, B2}) = Loge(O{D}) + W+B1 + W-B2 Log of odds of D given the absence of B1 and B2 • Loge (O{D|B1, B2}) = Loge(O{D}) + W-B1 + W-B2 Or in general, for n predictor features, The sign of W is +ive or -ive, depending on whether the feature is absent or present • Loge (O{D|B1, B2, … Bn}) = The odds are converted back to posterior probability using the relation 0 = P/(1+P)

48. n • Loge (O{D|B1, B2}) = Loge(O{D}) + ∑W+/-Bi i=1 P{B|D} W+ = loge P{B|D} & P{B|D} W- = loge P{B|D} Implementation • Calculation of posterior probability (or odds) require: • Calculation of pr prob (or odds) of occurrence of wells in the study area • Calculation of weights of evidence of all predictor features, i.e,

49. Exercise-2 Layer – B1 (Fold Axes buffers 1.25k) ARAVALLI STUDY AREA Layer – B2 (Mafic volcanic rocks) There are 54 base-metal deposits in the study area. Out of these, 35 deposits occur within 1.25 km buffers of fold axes (B1), and 42 deposits are associated with maficvolcanic rocks (B2). The total area in the fold axes buffers is 7132 sq km, while the mafic volcanic rocks occupy 4374 sq km area. If the total study area is 55987 sq km, calculate the following (assuming 1 sq km unit area size): 1. Prior probability and odds of base-metal deposits in the study area; 2. W+B1, W-B1, W+B2, W-B2; 3. Contrast values for B1 and B2; and 4. Posterior Log(odds) and probability of base-metal deposits in the study area, where i. Both B1 and B2 are present; ii. B1 present but B2 absent; iii. B2 present but B1 absent; and iv. Both B1 and B2 are absent

50. Feature B1 Well D EXERCISE Feature B2 Calculate posterior probability for each cell.