Spatial Modeling for Base-Metal Mineral Exploration

8/18/2019 Spatial Modeling for Base-Metal Mineral Exploration

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Natural Resources Research, Vol. 9, No. 1, 2000

Spatial Modeling for Base-Metal Mineral ExplorationThrough Integration of Geological Data Sets

G. Venkataraman,1 B. Babu Madhavan,2 D. S. Ratha,3 Joju P. Antony,1 R. S. Goyal,4

S. Banglani, and S. Sinha Roy4

Received 28 October 1999; accepted 27 November 1999

This study involves the integration of information interpreted from data sets such as LandsatTM, Airborne magnetic, geochemical, geological, and ground-based data of Rajpura– Dariba,Rajasthan, India through GIS with the help of (1) Bayesian statistics based on the weights of evidence method and (2) a fuzzy logic algorithm to derive spatial models to target potentialbase-metal mineralized areas for future exploration. Of the 24 layers considered, five layers(graphite mica schist (GMS), calc-silicate marble (CALC), NE-SW lineament 0–2000 m

corridor (L4-NESW), Cu 200–250 ppm, and Pb 200–250 ppm) have been identified from theBayesian approach on the basis of contrast. Thus, unique conditions were formed based onthe presence and absence of these five map patterns, which are converted to estimate posteriorprobabilities. The final map, based on the same data used to determine the relationships, showsfour classes of potential zones of sulfide mineralization on the basis of posterior probability.In the fuzzy set approach, membership functions of the layers such as CALC, GMS, NE-SWlineament corridor maps, Pb, and Cu geochemical maps have been integrated to obtain thefinal potential map showing four classes of favorability index.

KEY WORDS: Spatial modeling; mineral exploration; Bayesian statistics; fuzzy logic.

INTRODUCTION airborne magnetic, surface geochemistry and ground-based mineral occurrence information in the Rajpura–

Mineral exploration can be augmented efficiently Dariba belt in Rajasthan (Fig. 1) to delineate potentialthrough integration approaches involving GIS tech- areas of sulfide mineralization for further investigation.niques (Bonham-Carter, Agterberg, and Wright, 1989; The Rajpura–Dariba belt in Rajasthan has beenHarris, 1989; Moon, Chung, and An, 1991; Venkatara- explored for base-metal minerals by various organiza-man and others, 1997). In mineral exploration efforts, tions such as the Geological Survey of India (GSI) andan integrated view of lithology, structure, and geophys- Hindustan Zinc Ltd (HZL). The study area (Fig. 1)ical and geochemical characteristics is helpful to delin- covers an area of 550 km2 and contains a numbereate target areas more precisely with a high confidence of base-metal sulfide deposits (Fig. 2), including alevel. In this study an attempt has been made to inte- working lead– zinc mine (grade 7.26% zinc and 1.83%grate diverse data sets, such as lithology, structure, lead) at Dariba. The estimated reserves of all the depos-

its in the belt, according to GSI, are about 200 Mt.The Rajpura–Dariba tract contains a linear metasedi-

mentary belt occurring within the Older Metamorphites1 Centre of Studies in Resources Engineering, Indian Institute of of the Mangalwar Complex, trending N-S for 135 km,Technology, Bombay 400 076, India. e-mail: [email protected]

2 GIS Laboratory, Faculty of Environmental Information, Keio whichis thepossible equivalent of theBanded GneissicUniversity, 5322, Endo, Fujisawa, Kanagawa 252, Japan. Complex. There is a major doubly plunging synform

3 Pidilite Systems & Engineering Services, MIDC, Mahad,along the Rajpura– Dariba belt with closures at the

Maharashtra, India.northern and southern ends. Parallel to this, there is a4 Geological Survey of India, Western Region, Jaipur, Rajasthan,

India. synform trending north-south along the Akola-Jashma

27

1520-7439/00/0300-0027$18.00/0 2000 International Association for Mathematical Geology


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Spatial Modeling for Base-Metal Mineral Exploration 29

Figure 2. Base-metal deposits occurrence map.

belt (Samaddar, 1987). The folds are tight oppressed layers, series of lenses, irregular bodies, and, occasion-ally, brecciated. Structural controls such as fold hingesisoclinal folds (F1), which have been refolded by

north-south trending upright folds (F2) (Samaddar and and limbs, axial plane, cleavage/fractures, and shear

zones are important loci for mineralization.Das Gupta 1990a, 1990b). The rock formations of this belt belong to early to mid-Proterozic succession The conspicuous absence of quartz vein zones,the absence of wall rock alteration, the absence of named the Bhilwara Supergroup or Pre Aravallis. The

rocks are represented by carbonaceous schists, calcsu- open-space fillings, the absence of prominent cross-cutting relationship of the ore bands vis-á-vis theite of rocks, quartz-amphibole-magnetite rock, amphi-

bole schist, quartzite, mica schist, etc., with intrusion enclosing rocks, and the presence of stromatolite withPb– Zn ores in this area suggest syngenetic mineraliza-of pegmatite and quartz veins.

This belt has been studied by several workers and tion (Samaddar and Das Gupta, 1990a, 1990b; Deb,Banerjee, and Bhattacharya, 1978). According to Deb,the overview of the geologic setting and mineralization

aspects have been well documented by Deb and Sarkar Banerjee, and Bhattacharya (1978), the stratiform oreswere deposited in a nearshore shallow marine environ-(1990). Both lithological and structural controls of

mineralization are noticed conspicuously in this belt. ment, developed on basement highs, and later meta-morphosed up to amphibolite stage deformation of The important host lithounits for base–metal mineral-

ization include: carbonaceous schist, calc silicate-bear- their enclosing rocks. In general, the genesis of thisdeposit, although considered to be syngenetic, theing dolomite (CALC), graphite mica schists (GMS),

and banded magnetite rocks with carbonate bands in occurrence of fluorite, barites, and apatite (Jayaramand Mathur, 1975) do not rule out at least locallyan envelope of mica chert sequences. The main sulfide

minerals are sphalerite, galena, chalcopyrite, pyrite, epigenetic origin. In this area, a numberof significantlylarge occurrences of supergene enrichments showingand pyrrhotite and accessory amounts of magnetite and

silver-bearing minerals. Sulfides occur as thin bands to the presence of hydrated iron oxides including limonite


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30 Venkataraman and others

Table 1. Data Sets Used and Information Extracted

Field Data Date Information

Remote sensing Landsat-TM F.C.C. 234 & 257- 20/1/1990 Lithology, lineaments structure

1:50000 digital data interpreted.Geophysical Airborne magnetic & electromagnetic 1968 Magnetic axes; magnetic breaks

contour map-1:30000Ground resistivity map 1:5000 Field season 1979 Electrical property of rock formations

Geo chemical Surface so il sample an alysis data Field season 1 985 Pb an d Cu concentration values(point data)

Mineral occurrence Known mineral occurrences Before this study Location of existing base-metal deposits

in the form of grid cellsOthers GSI geological map 1:250000 and 1981 Used as base map, and ground–truth

1:50000 information

and other oxides, such as hematite and jarosite in some A composite map made from PC-1, PC-2, andNE-directional filtered Landsat-TM image data hasplaces, old workings associated with the presence of

oxide and carbonate minerals also were noticed. enhanced the structural features. The lineaments inter-preted from the Landsat-TM data were integrated withThe statistical model of base–metal mineraliza-

tion accomplished through the characteristic, cluster, lithological map (Fig. 1). It was observed that thetrend of some of the lineaments represented diverseand regression analysis of geological, geophysical, and

geochemical data established that the magnetite quartz- lithological contacts. Many of the fault lineaments inGSI’s geological maps were extended and it wasite and carbon phyllite form the important host rocks,

and the limb of folds are the important structure associ- observed that the lineaments and Landsat-TM linea-ments correspond to each other, for example, interpre-ated with the mineralization (GSI communication).

The major objective of this study was to integrate ted NE-SW trending lineament (RR) presence wasidentified near Bamnyan Kalan in a dug well. Somevarious geological, geochemical, and geophysical data

sets in an indigenously developed Geographic Infor- of the lineaments (Fig. 1) are identified as faults tothe south of Dariba. A good discrimination betweenmation System (GIS) involving algorithms based on

Bayesian statistics and fuzzy logic to derive spatial NE–SW and NW–SE lineaments was observed in thestudy area. The N–S and NNE–SSW trends are litho-models to get potential base-metal mineralized areas

for future exploration. logical and fold axial trends. It was reported by GSIthat the limbs of folds and the lineaments trendingNE– SW crossing Dariba possess workable base-metalmineral deposit. The NE–SW lineaments are parallelINFORMATION LAYERSto the reported mineralized zones (Venkataraman andothers, 1997) and, hence, considered as one of theDatabase for lithological, structural, geophysical,

and geochemical characteristics of the area was built important structural information layers in this study.The mineralogical composition of these sulfidethrough the analysis of the data sets summarized in

Table 1. GIS (internal programming) methods deposits makes the airborne magnetic data analysesuseful. The airborne magnetic data have been interpret-employed are analysis of various geological data,

building of raster database, and integration. ed with full reference to the geology map and theresultant observation reveals the economic importanceThe Bhilwara Supergroup was identified from the

analysis and interpretation of Landsat TM data along of faults and folds on a regional scale. The magnetic

axes and breaks have been interpreted from the air-with the geological map based on ground-based geo-physical (resistivity) survey. Other major groups iden- borne magnetic contour map (Fig. 3). Several magnetic

anomalies were observed in the central part of the area,tified include the Rajpura-Dariba, Pur-Banera, andMangalwar (Venkataraman and others, 1997). The lith- which can be related to the trend of Rajpura–Dariba

mineralized belts. Magnetic axis can be attributed toological map is shown in Figure 1. Based on the associ-ation, field evidence, and literature, CALC and GMS shear zones as reported by Sammadar and Das Gupta

(1990a, 1990b) and it is significant to note that thelithounits favor the base-metal mineralization.


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Figure 3. Airborne magnetic axes and breaks (after Venkataraman and others, 1997).

high magnetic axis falls on formations such as the formations and structural features, respectively, andare significant in the sulfide mineralization of theferruginous quartzites and graphitic schists, which are

marked as strong magnetic zones. study area.

More than 5000 surface soil samples have beenThe general trend of the magnetic breaks is inthe east–west direction that can be attributed to the collected in a grid pattern from the study area for the

analysis of trace element concentration, such as lead,offsetting of folds resulting from faults and plungesor closure of the folds. The magnetic break identified copper, zinc, nickel, and cobalt. The analysis has been

carried out using Atomic Absorption Spectrophotome-in the north of Bethumbi and south of Dariba representsthe closing of the plunging synform. Thus, magnetic try (AAS). However, for this study, only lead and

copper concentrations have been considered as zinc hasaxis and break are related closely to the lithological


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Figure 4. Binary map of calc-silicate/dolomite marble.

greater mobility and gives rise to spurious anomalies. tions, such as map index overlay, classification,corridor analysis, and mathematical analysis can beCobalt and nickel values were determined to be

irrelevant. implemented easily in a raster domain. The Cressmanalgorithm, available in the GRAM GIS system, wasOn the basis of detailed exploratory investigations

carried out by GSI, known mineral occurrence and used to generate Pb and Cu concentration surface mapsfrom the point data concentrations. Buffering algo-deposit locations have been marked for the entire study

area and the mineral occurrence map of the study area, rithms have been employed to generate corridors forlineaments, magnetic breaks, and magnetic axes. Forincluding known deposits and occurrence, have been

compiled and presented in Figure 2. the purpose of this study, the following binary mapshave been prepared.The maps thus prepared have been digitized,

transferred to a uniform scale (1:50,000), and inte-grated to understand the spatial relation between geo- (1) Graphitic mica schist (GMS).

(2) Calc-silicate/dolomitic marble/impure lime-logical variables and mineral occurrences using anindigenously developed PC-based raster GIS package stone (CALC) (Fig.4).

(3) Lineament corridors (0–500, 0–1000, 0–termed GRAM (Geo Referenced Area ManagementPackage; for details on the GIS system, see Venkata- 1500, and 0–2000 m) of NE–SW (Fig. 5)

and NW–SE directions.chalam and others, 1990). Many of the analytical func-


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Figure 5. NE–SW lineament corridors.

(4) Magnetic axis corridors (0–500, 0–1000, and Integration of these information layers isattempted here with the help of (1) Bayesian statis-0–1500 m).

(5) Magnetic break corridors (0–500, 0–1000, tics based on the weights of evidence modelingmethod and (2) a fuzzy logic algorithm to deriveand 0–1500 m).

(6) Lead assay values (100, 100–150, 150– spatial models to target potential base-metal miner-alized areas for future exploration. The integration200, and 200–250 ppm).

(7) Copper assay values (100, 100–150, 150– methodology involving Bayesian and fuzzy logicapproaches are described through an inference net-200, and 200–250 ppm).

(8) Mineral occurrence map. work in Figure 6.


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Figure 6. Inference network for predicting base-metal mineralization.

METHODOLOGY Carter, Agterberg, and Wright (1988), Watson, Rencz,and Bonham-Carter (1989), and a number of otherauthors have applied this method for mineral-potentialBayesian and fuzzy methods employed are

described briefly here. For a detailed explanation refer mapping. Reddy, Bonham-Carter, and Galley (1992)applied the same approach to the prediction of base-to Bonham-Carter (1994).

metal deposits in a greenstone belt.Let Pprior be the prior probability of a deposit

occurring within a small area of known size. Then,Bayesian Statistics Based on Weights of Evidence Modeling the prior odds (O) of the deposit can be defined as

O Pprior /(1 Pprior)Bayesian statistics can be used to combine severalmap patterns for evidence of mineralization. Agter- Using Bayes theorem, the posterior odds, denoted by

n can be expressed asberg, Bonham-Carter, and Wright (1990), Bonham-


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Table 2. Bayesian Method Calculation Resultsa

Map Totalpattern cells MO Corridor W+ sW W+ sW C s(C) C/s(C) Ppost

GMS 2499 994 2.8189 .409 .3166 .0202 3.1355 .0456 68.7444 .3978

CALC 6311 1775 2.2955 .280 .6540 .0243 2.9495 .0371 79.5692 .2813

L1-NE-SW 14460 1241 .5 km .8880 .0279 .2763 .0213 1.1433 .0366 31.299 .0858L2-NE-SW 28535 2455 1 km .8707 .0211 .8589 .0311 1.729 .0376 45.9814 .086

L3-NE-SW 39261 3190 1.5 km .8083 .0185 1.8919 .0566 2.7002 .0595 45.3518 .0813

L4-NE-SW 48310 3383 2 km .6475 .0178 2.6621 .0910 3.3095 .0928 35.6772 .07

L1-NW-SE 15738 682 .5 km .1392 .0391 .0309 .0192 .1702 .0436 3.9033 .0433

L2-NW-SE 31522 1397 1 km .1627 .0274 .0949 .0222 .2576 .0352 7.3133 .0443L3-NW-SE 45285 1940 1.5 km .1272 .0232 .1382 .0257 .2654 .0346 7.6628 .0428

L4-NW-SE 57145 2286 2 km .0558 .0213 .097 .0292 .1527 .0361 4.2266 .04MB1 9619 1032 9.5 km 1.1150 .0329 .2473 .0204 1.3623 .0388 35.1461 .1073

MB2 19490 1982 1 km 1.0552 .0237 .6146 .259 1.6698 .0351 47.5588 .1017MB3 28822 2577 1.5 km .9129 .0206 .9799 .0331 1.8928 .039 48.5353 .0894

MA1 8140 559 .5 km .6265 0.438 .0847 .0188 .7112 .0477 14.9178 .0687MA2 16268 1075 1 km .5852 .0316 .1790 .0206 .7643 .0377 20.2722 .0661MA3 24656 1585 1.5 km .5557 .0260 .3017 .0232 .8574 .0384 24.6442 .0643

Cu 100 ppm 7510 1135 100 1.5080 .0322 .317 .0208 1.8250 .0757 47.5656 .1511Cu 150 ppm 761 316 100–150 2.8914 .0736 .0895 .018 2.9809 .1351 39.3564 .4152

Cu 200 ppm 223 113 150–200 3.2606 .1339 .0315 .0175 3.2922 .2693 24.3722 .5067

Cu 250 ppm 65 45 200–250 4.0447 .2687 .0127 .173 4.0574 .0387 15.0664 .6923

Pb 100 ppm 6631 1129 100 1.6500 .0327 .325 .0208 1.9750 .0705 50.9850 .1703Pb 150 1158 285 100–150 2.1143 .0682 .075 .0179 2.1893 .0798 31.0346 .2461Pb 200 ppm 776 239 150–200 2.4242 .0778 .0646 .0178 2.4888 .039 31.1981 .3080

Pb 250 ppm 536 216 200–250 2.8407 .0881 .06 .0178 2.9007 .0898 32.29 .4030

a MO, number of cells containing mineral deposits; W+, W+, weights; sW and sW, standard deviation of weights; C, contrast; s(C),

standard deviation of C; C/s(C), studentized C; Ppost posterior probability; GMS, graphitic mica schist; CALC, calc-silicate marble/ dolomite marble; L1–L4, lineament corridors; MB1–MB3, magnetic break corridors; MA1–MA3, magnetic axis corridors; Cu, copperconcentration; Pb, lead concentration; total number of cells, 92416; number of cells containing a deposit 3504; prior probability, 0.0379155;

prior odd, 0.0394098; log of prior odds, 3.233742; standard deviation of prior probability, 0.000632; standard deviation of log of priorodds, 0.0168934. Patterns in bold letters are significant for predicting base-metal deposits.

(1991), An, Moon, and Bonham-Carter (1992), andn exp (ln O

m

j1

W k j ) Moon and An (1991). The fuzzy logic approach canbe effective when the proposition itself is vague and

where the superscript k represents the presence or when it is applied to single-node problems (Moon,absence of the variable, that is W k j is W

j if the variable 1993). Fuzzy logic uses membership functions ()is present, W j if it is absent, and “0” if it is missing. and different combination operators. Mathematically,Then, the posterior probability of an ore deposit a fuzzy set A is a set of ordered pairs,occurring is

A {( x, A ( x)) x ε X }Ppost n /(1 n)

where, X collection of objects, also known as theuniversal set and A( x) membership function orThe conditional probability terms and the weight for

the jth feature can be computed as described by Bon- degree of compatibility of x in A.The range of A( x) normally used is [0,1], whereham-Carter, Agterberg, and Wright (1988).

0 represents nonmembership and 1 represents fullmembership. By using the fuzzy OR (max operator),the combined membership values are limited by theFuzzy Logic Algorithmmost suitable of the evidence map patterns. The ORoperator can be used where two map patterns representA fuzzy logic approach has been applied for min-

eral exploration program by An, Moon, and Rencz same level of evidence, and the combinations suggest


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Figure 7. Binary map of Pb 200–250 ppm.

evidence at higher probability. A gamma operator, by approximately 75 m. In order to have an uniformlysized grid cells based on the actual total area of the siteusing fuzzy algebraic product and algebraic sum, can

be employed by using suitable values for . For a (covering 304 rows 304 columns), it was decided tobuild the raster database with cells of 77 77 m sizereview on the fuzzy operators for combining geological

data sets, refer to Bonham-Carter (1994). (0.0059 km2). It was observed that with a grid size of 77 m, the smallest lithological units of the study areaGIS (internal programming) methods employed

are analysis of various geological data and the building were represented by a minimum of 10 pixels.of a raster database and integration. The resolution of the raster maps composed by using GRAM GIS hasbeen determined by the size of the important spatial RESULTS AND DISCUSSIONobjects, such as impure limestone (Dariba) and smallpockets of GMS (Jashma). For example, the minimum Integration by Bayesian Approach

area that the impure limestone of Dariba (Fig. 1) occu-pied was approximately less than 0.01 km2. A conve- The upper part of the Figure 6 illustrates the

Bayesian (external and internal to GIS) procedures.nient rule of thumb, based on statistical samplingtheory, is to use a raster cell half the length (or one- Parameters to select binary patterns based on weights

of evidence modeling were obtained by external pro-fourth the area) of the smallest feature decided torecord (Star and Estes, 1990). Thus, a more conserva- gramming. The procedures followed and results are

described in the following section.tive suggestion followed was to use a raster cell of


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Table 3. Unique Conditions and Estimated Posterior variable. A pair of weights W+ and W and standardProbabilities Calculated by Weights of Evidence Model for deviations (sW+ and sW) was estimated for each

Graphitic Mica Schist (GMS), Calc-Silicate Dolomite Marblevariable. Contrast, C, was calculated as the difference(CALC), 0–2000 m Corridor of NE–SW Lineaments (L4-of weights, W+-W. C and its standard deviation s(C)NESW), 200–250 ppm Pb, and 200–250 ppm Cu Binary

Map Patterns were used to estimate the uncertainty of the posteriorprobability resulting from uncertainty in the weights.

L4- Cu 200– Pb 200– Posterior Studentized contrast [C/s(C)] also was calculated.No. GMS CALC NESW 250 ppm 250 ppm probability

Based on the geological interpretability (spatialrelationship of host rock, corridors containing more1 P P P P P .9999

2 P P P P A .9985 deposits, and relationship of concentration of geo-3 P P P A P .9953 chemical elements with mineral deposits) of the results,4 P P A P P .9977 a higher contrast (C) of 2.9 was considered as a cut-5 P A P P P .9984

off value to select significant patterns. From Table 26 P P P A A .9209it was noted that the five patterns GMS, CALC (Fig. 5),7 P P A A P .8855

8 P A A P P .9590 L4-NESW, Pb 200–250 ppm (Fig. 7), and Cu 200–2509 P P A A A .2985 ppm showed higher C values. These five patterns were

10 P A A A P .2884 selected for prediction and combined by a weighted11 P A A A A .0218

index overlay model suggested by Bonham-Carter12 P A P A P .9173(1994). Although three patterns of copper concentra-13 A A A A P .0173

14 A A A P A .0530 tion show contrast value higher than 2.9, the Cu 200–15 A A P A A .0258 250 ppm pattern has the highest contrast value. Further,16 A P A A A .0181 because this is basically a lead zinc sulfide deposit,17 A A A P P .5047

the higher copper concentration value has more18 A A P P A .6053significance.19 A P P A A .3362

20 A A P P P .9653 Combination rules using the Bayesian theorem21 A P P P A .9669 assumes conditional independence. A general test for22 A P P P P .9981 overall conditional independence was performed by23 A P A P A .5169

comparing the predictedvs. observed number of depos-24 A P P A P .9020its, as discussed by Bonham-Carter (1994). The expec-25 A P A P P .9511

26 P A P A A .3789 ted number of deposit was estimated to be 3548,27 A A P A P .3254 whereas the observed number of deposits (occur-28 A A A A A .0009

rences) was 3504. The five binary patterns were evalu-ated with respect to the mineral occurrence map(Fig.2). If a cell contains a mineral occurrence it isdesignated as (P), then the weight is (W+); if the cellThe prior probability of occurrence of base metal

for the study area is 0.037, based on the 3504 cells of does not contain an occurrence, it is (A) and (W)was assigned. The posterior probability for each uniqueevidence. Multiclass maps were converted to binary

patterns. Thus, 24 binary patterns were composed. condition then was computed. For example, in a uniquecondition APAPP, the calculation of posterior probabil-Relationship of base-metal mineral occurrences with

binary data sets, such as lithology (GMS and CALC), ity followed the procedure given as:lineament corridors (500, 1000, 1500, and 2000 m),

(W (W+) (W) (W+) (W+)magnetic breaks and axes (500, 1000, and 1500 m),geochemical values (Cu and Pb:100, 100–150, 150– ln Pprior X 200, and 200–250 ppm) was evaluatedthrough weights

Opost

e

x

of evidence model.Results obtained are summarized in Table 2. Ppost Opost /1 Opost

According to Agterberg (1992), the posterior probabili-ties calculated by any fixed set of weights are propor- Thus the estimated posterior probability for each

unique condition was calculated (Table 3) and a finaltional to unit cell size. It can be observed in Table 2,that there is a general inverse relation between the predictor map was obtained (Fig.8). Becausefive maps

were identified for prediction of base-metal mineraltotal number of cells and posterior probability for each


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Figure 8. Posterior probability map of sulfide mineralized zones by Bayesian method.

deposits, 32 unique conditions were expected. How- Integration by Fuzzy Logic Methodsever, only 28 unique conditions were obtained.Because all the five patterns have a strong relationship In the fuzzy logic approach, evidence maps werewith base-metal occurrence, the highest probability is combined in a series of steps illustrated in the lowerfor the condition where all the patterns were present part of Figure 6. Multiclass maps such as Pb ppm, Cuand least where all the five were absent. The impor- ppm, lithology, and NE– SW lineament corridors weretance of the presence or absence of a particular map combined by fuzzy methods. Based on field data andpattern is evident from Table 3, on the basis of posterior the authors knowledge about the terrain, suitable fuzzyprobability score. Results of Bayesian predictor model membership functions () were assigned to each class

showed that impure limestone, calc-silicate marble, in the multiclass maps (Table 4). Because fuzzy mem-and dolomite marble of Dariba-Malikhera formations bership values must reflect the relative importance of should be considered for further exploration as they each map, as well as the relative importance of eachare associated with higher probabilities in the range class of a single map, values were selected based onof 0.6 to 0.9 and0.9. Graphitic mica schist covering subjective judgment about the relative importance of Rajpura-Bethumbi has a lower probability score rang- the maps and their various states. For example, mem-

berships assigned to lithological and corridor mapsing from 0.3 to 0.6.


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Table 4. Memberships () for Classes

Geochemical

Lithological formationsLead Copper

ppm ppm Lithology

19.1143 0.000 16.688 0.000 Aravalli Super Group 0.0155.429 0.021 48.063 0.000 Gar. Graphitic mica schist 0.9091.714 0.164 79.483 0.117 Quartzite 0.00

128.000 0.307 110.813 0.242 Impure L.st/Marble 0.95

164.286 0.449 142.188 0.367 Calc-silicate Marble 0.95200.571 0.592 173.563 0.492 Dolomite marble (Potla) 0.02

236.857 0.735 204.938 0.617 Dolomite marble 0.95236.313 0.742 Graphitic mica schist 0.90

Corridor (lineaments, axes, breaks) Quartzite 0.01m Calc-gneiss 0.000–500 0.95 Amphibolite schist 0.02

0–1000 0.85 Quartzite 0.020–1500 0.50 Migmatitic complex 0.03

0–2000 0.30 Amphibolite schist 0.04

do not increase or decrease monotonically with class classes0.9 and 0.6– 0.9 were associated with impurelimestone, calc-silicate, and dolomitic marble of Mal-number, but were assigned in the 0, 1 range. This

suggests the subjective importance of individual map likhera–Dariba formations. The graphitic mica schistof Sindersar–Bhinder formation seems to host the 0.3–units. Thus, higher membership values were assigned

to lithological formations that were reported to host 0.6 probability class. The lowest probability class0.3is ubiquitous and occupies large areas associated withthe base-metal deposits or were considered highly

favorable, based on mapping. For example, a 0.9 or a Mangalwar formations.In the Bayesian approach, the weights were deter-greater fuzzy membership (definitely anomalous) was

assigned to GMS and CALC lithological units. Litho- mined from the measured combination of individualmaps whereas the weights were subjective in the fuzzylogical units such as quartzite, amphibolite schist, calc-

gneiss, and the Aravalli Supergroup were assigned approach and were selected to reflect the degree of

membership of a set or category or map purely basedlower values () because they are not believed to besignificant for base-metal exploration. on an expert decision. In our view, the fuzzy approachwas not suitable because it yielded no insight into theAccording to Venkataraman and others (1997),

the 0–500 m corridors of the NE–SW lineaments have data when compared to the results in the Bayesianapproach. However, the possible mineralization loca-more base-metal mineral deposits. Therefore, a higher

membership value of 0.95 was assigned to the 0–500 tions predicted from both approaches use the samelithological formations.m structural lineament corridor. Because the Pb and

Cu geochemical maps both represent important evi-dence for the base-metal mineral deposits in the studyarea, it was decided to combine them to generate an CONCLUSIONSevidence map. Therefore, suitable fuzzy membershipvalues were assigned to Pb and Cu concentration and In this study, spatial modeling has been carried

out with locally developed software involving (1) aa fuzzy OR hypothesis was employed. Thus, an inter-

mediate geochemical evidence map showing member- Bayesian approach based on the weights of evidencemethod and (2) the fuzzy logic approach. The GRAMship values for possible mineral occurrence was

proposed (Fig. 9). Using 0.95, the geochemical GIS has facilitated the building of a spatial databasefrom diverse sources. In the Bayesian approach, of theintermediate map (Fig. 9), lithology, and the NE–SW

lineament corridor maps were combined and a final total 24 map patterns, five map patterns [GMS, CALC,NE–SW trending lineament (0– 2 km corridor), Cufuzzy membership map of favorable base-metal miner-

alization was obtained (Fig. 10). The probability 200–250ppm, and Pb 200–250ppm] have been identi-


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Figure 9. Map of fuzzy memberships for geochemical data. Pb and Cu data combined by fuzzyOR method.

fied for the base-metal occurrences in the area. The Given that this area of known occurrences was used todetermine the equations, perhaps this is not surprising.unique conditions were formed based on the presence

and absence of these five map patterns, which are Both positive and negative weights are intelligible tointerpret and variance of these weights permits theconverted to posterior probabilities for the same area

used to determine the weights. Finally, a map showing calculation of uncertainty. This method was well suitedfor modeling structural information, such as proximitypotential zones of base metal in the area was prepared

on the basis of the estimated posterior probabilities. to linear features, regional patterns of geochemical,and geophysical anomalies.The weights of evidence modeling method was

useful and unequivocal for predicting base-metal Results of Bayesian predictor model showed thatimpure limestone, calc-silicate marble, and dolomitepotential of Rajpura–Dariba region where a number

of representative base-metal occurrences are known. marble of the Dariba and Mallikhera formations should


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It is interesting to note that this exploration study coulddelineate a probability of 0.3 to 0.6 around Jashmain GMS.

The fuzzy logic approach has brought out thepresence of probabilities0.9 in the Mallikhera For-mation SW of Jashma, NW of Dariba, and also south

of Bethumbi. The sites SW of Jashma and at Bethumbiunder this category are seen only in the fuzzy approachmap where a probability of 0.6 to 0.9 is predicted inthe Dariba Formation west of Jashma and betweenDariba and Rajpura. In this category, the occurrenceat Jashma was not predicted by the Bayesian approach.GMS, west of Jashma and near Rajpura are character-ized by the probability range between 0.3 and 0.6 aspredicted by fuzzy method. Comparing the possiblemineral locations predicted by both methods, it hasbeen observed that the fuzzy method predicted morenew occurrences, although yet to be validated. How-ever, the locations predicted from both approachesused the same lithological formations.

ACKNOWLEDGMENTS

This research work was a part of ISRO SpaceTechnology Cell, Bombay, sponsored project under-taken by the Centre of Studies in Resources Engi-neering, Indian Institute of Technology, Bombay, India.

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Spatial Modeling for Base-Metal Mineral Exploration