Carranza E. Geochemical anomaly and mineral prospectivity mapping in GIS

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Knowledge-Driven Modeling of Mineral Prospectivity 243

the value of

in equation (7.21). The fuzzified evidential scores of spatial evidence of

geochemical anomalies in the case study are illustrated in Fig. 7-23. The shape of the

fuzzy logic membership function of the multi-element geochemical anomaly scores is

similar to the shape of the fuzzy membership function of the same data set (Fig. 7-12B).

Of the two above-stated options for obtaining an integrated geochemical-geological

wildcat model of mineral prospectivity, option (a) does not result in a satisfactory model

of mineral prospectivity in the case when the spatial evidence of geochemical anomalies

does not represent in situ materials as do the pieces of spatial evidence of geologic

controls on mineralisation. For example in the case study area, PC1 reflects dissociation

between geological and geochemical evidence, PC2 and PC3 both reflect association

between geochemical evidence and some structural control evidence and PC4 and PC5

both reflect association between geochemical evidence, heat source control evidence and

some structural control evidence (Table 7-XII). Thus, PC4 and PC5 represent equivocal

integrated geochemical-geological evidence of mineral prospectivity. Between PC4 and

Fig. 7-23. Fuzzified evidential scores (fS

) of multi-element geochemical anomaly scores (see Fig.

5-12), Aroroy district (Philippines).

TABLE 7-XII

Principal components of fuzzified evidential scores (fS

) of classes of proximity to geological

features (see Table 7-X and Fig. 7-21B) and classes of multi-element geochemical anomaly scores

(Fig. 7-23) in the Aroroy district (Philippines).

NNW

ANOM

% of variance Cum. % of variance

PC1 -0.498 -0.580 -0.182 -0.591 0.181 35.47 35.47

PC2 -0.421 -0.218 0.678 0.199 -0.525 20.86 56.33

PC3 0.258 -0.087 0.685 -0.141 0.661 18.49 74.82

PC4 0.689 -0.335 0.073 -0.422 -0.479 12.92 87.74

PC5 0.181 -0.704 -0.179 0.643 0.159 12.26 100.00

NNW-trending faults/fractures.

NW-trending faults/fractures.

NE-trending faults/fractures.

Nabongsoran Andesite porphyry.

Integrated PC2 and PC3 scores obtained from the catchment

asin analysis of stream sediment geochemical data (see Chapte

3).

244 Chapter 7

PC5, the former is the more plausible integrated spatial evidence of hydrothermal

deposit prospectivity because the loadings on NW, NA and ANOM are more-or-less

similar whereas the latter reflects mainly evidence of heat-source control because the

loadings on NA are much higher than the loadings on NW and ANOM. However, the

map of PC4 scores (negated by multiplying with -1 because loadings on NW, NA and

ANOM are negative) is, just by visual inspection, a non-satisfactory model of

hydrothermal deposit prospectivity in the case study area (Fig. 7-24). Therefore, option

(b) is offer another method of obtaining an integrated geochemical-geological wildcat

model of mineral prospectivity.

An integrated geochemical-geological wildcat model of hydrothermal deposit

prospectivity in the case study area (Fig. 7-25A), obtained as a product of the fuzzified

evidential scores of multi-element geochemical anomaly scores (Fig. 7-23) and the PC1

scores of geological evidence (Table 7-XI; Fig. 7-22A), is like the earlier models except

the model based on EBFs because it does not have predictions in locations without

geochemical evidence. However, it shows a pattern of prospective areas that are similar

to those of the earlier models of epithermal Au prospectivity in the case study area and

therefore it is a much better model than the model shown in Fig. 7-24. If 20-50% of the

case study area is considered prospective, then the integrated geochemical-geological

wildcat model of hydrothermal deposit prospectivity delineates correctly seven (or about

58%) to nine (or about 75%) of the cross-validation deposits (Fig. 7-25B). This means

that, based on 20-50% predicted prospective zones, the integrated geochemical-

Fig. 7-24. A non-satisfactory integrated geochemical-geological wildcat model of hydrothermal

deposit prospectivity, Aroroy district (Philippines). This wildcat predictive model is derived as a

principal components (in this case PC4; Table 7-XII) of fuzzified evidential scores of proximity to

geological features (Table 7-X) and multi-element geochemical anomaly scores (Fig. 7-23). The

PC4 scores are negated (i.e., multiplied by -1) in order to represent mineral prospectivity as high

scores. Triangles represent locations of known epithermal Au deposit occurrences.

Knowledge-Driven Modeling of Mineral Prospectivity 245

geological wildcat model performs equally as well as the fuzzy logic model (Fig. 7-17B)

and the evidential belief model (Fig. 7-19C). However, if more 50% of the case study

area is considered prospective, then the integrated geochemical-geological wildcat model

is inferior to the fuzzy logic model and evidential belief model. These results,

nonetheless, indicate that wildcat modeling of mineral prospectivity is a potentially

useful tool for guiding further exploration in greenfields frontier areas.

The wildcat methodology bears out the usefulness of reconnaissance (or small-scale)

geological maps in first-pass assessment of mineral prospectivity of greenfields

geologically permissive areas. The methodology, which is a knowledge-guided data-

driven technique for modeling of mineral prospectivity, is sensitive to the widths of

classes of proximity to geological features and to the types of geological features used in

the analysis. As demonstrated by Carranza and Hale (2002d), narrower classes of

proximity to geological features results in predictive models of mineral prospectivity

with higher prediction-rates. In the case study, classes of proximity narrower than the 5-

percentile intervals of map distances are likely to result in higher prediction-rates

although proving this hypothesis is not an objective here. The choice of which type of

geological features to include in modeling mineral prospectivity depends on the general

knowledge of which general types of mineral deposits are likely to occur in certain

greenfields geologically permissive areas. A good knowledge of general characteristics

Fig. 7-25. (A) An integrated geochemical-geological wildcat model of hydrothermal deposit

rospectivity, Aroroy district (Philippines), derived as product of fuzzified evidential scores o

multi-element geochemical anomaly scores (Fig. 7-23) and the PC1 scores (Table 7-XI; Fig. 7-

22A) of fuzzified evidential scores of proximity to geological features (Table 7-X). Triangles

represent locations of known epithermal Au deposit occurrences. (B) Prediction-rate curve o

roportion of deposits demarcated by the predictions versus proportion of study area predicted as

prospective. The dots along the prediction-rate curve represent classes of prospectivity values that

correspond spatially with a number of cross-validation deposits (indicated in parentheses).

246 Chapter 7

of mineral deposits (e.g., Cox and Singer, 1986; Roberts et al., 1988; Berger and Drew,

2002) and their tectonic environments (e.g., Mitchell and Garson, 1981; Sawkins, 1989;

Pirajno, 1992; Robb, 2004) is therefore essential in the wildcat methodology of modeling

mineral prospectivity as well as in the other techniques for knowledge-driven modeling

of mineral prospectivity.

CONCLUSIONS

Several techniques for knowledge-driven modeling of mineral prospectivity exist. All

the techniques demonstrated here are aided by a GIS in terms of creating and integrating

evidential maps and evaluating the performance of mineral prospectivity maps. It is

better to use multi-class evidential maps than binary evidential maps in modeling of

mineral prospectivity. Representation and incorporation of evidential uncertainty, as in

evidential belief modeling, result in better predictive models of mineral prospectivity, at

least in the case study area. The performance of knowledge-driven mineral prospectivity

maps depends chiefly on the subjective nature of expert judgments that are applied in

creating evidential maps and/or in integrating evidential maps. Therefore, depending on

the technique applied, deriving an optimum knowledge-driven predictive model of

mineral prospectivity entails trial-and-error or comparative analysis by (a) adjustment of

evidential scores of classes in evidential maps, (b) adjustment of evidential map weights

and/or (c) adjustment of inference networks for combining evidential maps.

Despite the subjectivity of ‘expert’ knowledge applied in knowledge-driven

modeling of mineral prospectivity, the techniques demonstrated here are useful in first-

pass assessments of mineral prospectivity of greenfields geologically permissive areas

where no or very few mineral deposits of interest are known to occur. This is further

demonstrated by the results of the application of the knowledge-guided data-driven

wildcat technique of mineral prospectivity, which is based on generic knowledge of

geological environments of mineral deposits rather than on knowledge of empirical

spatial associations between mineral deposits of the type sought and indicative

geological features. However, because of the subjective nature of ‘expert’ knowledge

applied in knowledge-driven or knowledge-guided data-driven modeling of mineral

prospectivity, it is obligatory to evaluate performance of derived mineral prospectivity

maps. It is possible to do so in cases where a few occurrences of mineral deposits of

interest are known, but it is difficult, if not impossible, to do so in cases where there are

no known occurrences of mineral deposits of interest. In any case, the quality and

quantity of exploration data that are available in greenfields geologically permissive

areas also influence the quality of a knowledge-driven model of mineral prospectivity.

Presumably, more and better data allow better expert judgments in creating and

integrating evidential maps of mineral prospectivity.

Knowledge-driven modeling of mineral prospectivity is also applicable in relatively

well-explored areas where the objective is to find new exploration targets for mineral

deposits of the type sought in the presence of several discovered mineral deposits of the

Knowledge-Driven Modeling of Mineral Prospectivity 247

type sought. However, in order to achieve objectivity in creating evidential maps, it is

then preferable to apply data-driven modeling of mineral prospectivity.

249

Chapter 8

DATA-DRIVEN MODELING OF MINERAL PROSPECTIVITY

INTRODUCTION

Data-driven mineral prospectivity mapping is appropriate in areas representing

moderately- to well-sampled (or so-called ‘brownfields’) mineralised landscapes, where

the objective is to demarcate new targets for further exploration of undiscovered deposit-

type locations based on the following suppositions. Known deposit-type locations are a

sample set of locations with high likelihood of mineral deposit occurrence in a

mineralised landscape. This sample set embodies or provides a collection of geological

knowledge that there are certain combinations of spatial evidential features (e.g.,

proximity to faults/fractures, geochemical anomalies, etc.) associated with every deposit-

type location in a mineralised landscape. This collection of geological knowledge, which

constitutes a conceptual model of prospectivity recognition criteria for undiscovered

deposit-type locations, indicates that mineral deposit occurrence is a function of the

degrees of presence and relative importance of individual pieces of spatial evidential

features (see Fig. 1-2). Thus, if more important evidential features are present in one

location than in another location in a mineralised landscape, then the former location has

higher mineral prospectivity than the latter location. The conceptual model of mineral

prospectivity recognition criteria provides the framework for establishing or quantifying

empirical spatial associations between a set of known deposit-type locations and

individual sets of spatial evidential data in most, if not all, locations in a mineralised

landscape under investigation (see Fig. 1-3). The quantified empirical spatial

associations between known deposit-type locations and individual sets of spatial

evidential data depict relative indices of likelihood of deposit-type occurrence portrayed

in predictor maps. These predictor maps are then integrated in order to delineate, in a

mineralised landscape, new targets for further exploration of undiscovered deposit-type

locations. The quantified empirical spatial associations of known deposit-type locations

and individual sets of spatial evidential data could also be used in re-defining previously

established conceptual models of prospectivity recognition criteria for mineral deposits

of the type sought in moderately- to well-sampled mineralised landscapes.

In a study area, the relative index of prospectivity (

) for mineral deposits (D, the

target variable) of the type sought, based on known

D deposit-type locations, can be

defined as a function (

f) of combinations of a number of X

(i=1,2,…,n) spatial evidential

features (i.e., explanatory/predictor variables), thus:

Geochemical Anomaly and Mineral Prospectivity Mapping in GIS

by E.J.M. Carranza

Handbook of Exploration and Environmental Geochemistry, Vol. 11 (M. Hale, Editor)

250 Chapter 8

),,(

niD

XXfP != . (8.1)

For a study area, the map of

D (i.e., the target variable) and each of the individual maps

of explanatory/predictor variables are usually partitioned into equal-sized unit cells,

which are usually squares. That is, relative indices of prospectivity (

) are expressed as

degrees of likelihood of deposit-type occurrence per unit cell. Each of the individual

maps of

spatial evidential features are discretised further into a number of C

(

j=1,2,…,m) classes of evidence. For each unit cell in the study area, P

can be defined

further as:

),,(

mnjiD

wCwCfP "= , (8.2)

where

represents evidential weights (i.e., degree of spatial associations) of C

classes of individual

spatial evidential features with respect to D. The evidential

weights relate to the degree of spatial coincidence or association between

D and every

in X

maps. Unit cells characterised by high values of wC

in most, if not all, maps of

, therefore, have spatial geological attributes that are similar to (in terms of spatial

association with) the unit cells containing the known locations of

D. Equations (8.1) and

(8.2), thus, simultaneously involve interpolative and extrapolative analyses of unit cells

that likely contain unknown (or undiscovered) locations of

D based on the spatial

associations of

in X

maps with unit cells containing the known locations of D.

In Chapter 6, the methods for quantifying spatial associations between a map of

deposit-type locations and individual maps of relevant geoscience spatial data do not

lead directly to the derivation of values of

for C

classes in X

maps of spatial

evidential features. However, there are different data-driven techniques for deriving

directly values of

for C

classes in X

maps of spatial evidential features with respect

D (i.e., creating predictor maps) and then combining these predictor maps, via an

integration function

f (equation (8.2)), in order to obtain a predictive model of

prospectivity (i.e., a map of

) for mineral deposits of the type sought. Chung and

Fabbri (1993) proposed a unified mathematical framework for spatial predictive

modeling of geo-objects (e.g., geohazard-prone areas, prospective areas, etc.).

There are two types of mathematical techniques for GIS-based data-driven predictive

modeling of mineral prospectivity: bivariate and multivariate. Bivariate techniques

(Table 8-I) involve pairwise analysis of spatial association between a map of

D and a

map of

with C

classes. In the applications of bivariate techniques, predictor maps are

explicitly created and then integrated after the pairwise analyses of spatial associations.

Weights-of-evidence modeling is the most commonly used bivariate technique.

Multivariate techniques (Table 8-II) involve simultaneous analysis of spatial associations

between a map of

D and maps of X

with C

classes. In the applications of multivariate

techniques, predictor maps are usually created automatically and then integrated ‘on-the-

fly’ or dynamically whilst the spatial associations between a map of

D and maps of X

Data-Driven Modeling of Mineral Prospectivity 251

with C

classes are being quantified. It seems that logistic regression and artificial neural

networks are the most commonly used multivariate techniques for data-driven predictive

modeling of mineral prospectivity. The multivariate techniques outnumber the bivariate

techniques for creating and then integrating predictor maps in mineral prospectivity

modeling. This indicates that, because of the highly complex nature of spatial

associations between mineral deposits and geological features, it is in most cases more

desirable to develop and/or apply multivariate rather than bivariate techniques for data-

driven modeling of mineral prospectivity. In some cases it is even more desirable to

develop and/or apply hybrid methods for data-driven modeling of mineral prospectivity,

like fuzzy weights-of-evidence modeling (Cheng and Agterberg, 1999; Porwal, 2006;

Porwal et al., 2006a), data-driven fuzzy modeling (Luo and Dimitrakopoulos, 2003;

Porwal et al., 2003b) and neuro-fuzzy modeling (Porwal et al., 2004; Porwal, 2006).

The different methods of GIS-based data-driven modeling of mineral prospectivity

are well-documented in the literature and are now mostly well-established. In Tables 8-I

and 8-II, the researches described in the references cited for each method range from

seminal studies in developing a method, to innovative or adaptive studies providing

improvements of a method, to instructive studies in various cases demonstrating or

addressing further certain aspects that are vital in the application of a method. Moreover,

some of the references cited in Tables 8-I and 8-II compare and contrast some of the

techniques for data-driven modeling of mineral prospectivity. Therefore, this chapter

does not attempt to explain and demonstrate each of the different methods of GIS-based

data-driven techniques for modeling mineral prospectivity. However, one bivariate

technique (evidential belief modeling) and one multivariate technique (discriminant

analysis) are explained and demonstrated here in a case study of mapping epithermal Au

prospectivity in the Aroroy district (Philippines).

TABLE 8-I

Bivariate mathematical models/methods used for data-driven mapping of mineral prospectivity.

Model/method References to examples

Weights-of-evidence modeling Bonham-Carter et al. (1988, 1989), Agterberg et al. (1990, 1993a),

Bonham-Carter and Agterberg (1990), Agterberg (1992), Bonham-

Carter (1991, 1994), Cheng and Agterberg (1999), Mihalasky

(1999), Raines (1999), Singer and Kouda (1999), Pan and Harris

(2000), Mihalasky and Bonham-Carter (2001), Harris et al.

(2001b), Agterberg and Cheng (2002), Harris et al. (2003),

Carranza (2004b), Porwal et al. (2001, 2006a), Coolbaugh and

Bedell (2006), Harris and Sanborn-Barrie (2006), Porwal (2006)

Evidential belief modeling Chung and Fabbri (1993), An et al. (1994b), Carranza (2002),

Carranza and Hale (2003), Carranza et al. (2005, 2008a, 2008b;

2008c), this volume

252 Chapter 8

In the case study area (covering roughly 130 km

; see Fig. 3-9), there are 13 known

locations of epithermal Au deposits and the epithermal Au prospectivity recognition

criteria (defined in Chapter 6) are as follows.

 Proximity to NNW-trending faults/fractures (representing structural controls).

 Proximity to NW-trending faults/fractures (representing structural controls).

 Proximity to intersections of NNW- and NW-trending faults/fractures (representing

structural controls as well as proxies for heat source controls).

 Presence of multi-element stream sediment geochemical anomalies (representing

surficial evidence).

The spatial data sets used in the case study are: (a) distance to NNW-trending

faults/fractures; (b) distance to NW-trending faults/fractures; (c) distance to intersections

of NNW- and NW-trending faults/fractures; and (d) integrated PC2 and PC3 scores

obtained from the catchment basin analysis of stream sediment geochemical data (see

Chapter 5 and Fig. 5-12).

Before explaining and demonstrating evidential belief modeling and discriminant

analysis of mineral prospectivity, this chapter first discusses techniques or strategies

TABLE 8-II

Multivariate mathematical models/methods for data-driven mapping of mineral prospectivity.

Model/method References to examples

Discriminant analysis Chung (1977), Prelat (1977), Bonham-Carter and Chung (1983),

Harris and Pan (1999), Pan and Harris (2000), Harris et al. (2003),

this volume

Characteristic analysis Botbol et al. (1977, 1978), McCammon et al. (1983, 1984), Harris

(1984), Pan and Harris (1992a, 2000)

Logistic regression analysis Chung (1978, 1983), Chung and Agterberg (1980, 1988),

Bonham-Carter and Chung (1983), Agterberg (1988, 1992, 1993),

Agterberg et al. (1993a), Harris and Pan (1991, 1999), Sahoo and

Pandalai (1999), Pan and Harris (2000), Harris et al. (2001b, 2006),

Carranza and Hale (2001b), Carranza (2002), Harris et al. (2003)

Favourability analysis Pan (1989, 1993a, 1993b, 1993c),

Pan and Portefield (1995), Pan

and Harris (1992b, 2000)

Likelihood ratio analysis Chung and Fabbri (1993), Chung et al. (2002), Chung and Keating

(2002), Chung (2003), Harris and Sanborn-Barrie (2006)

Artificial neural networks Singer and Kouda (1996, 1997, 1999), Harris and Pan (1999), Pan

and Harris (2000),

Brown et al. (2000, 2003), Bougrain et al.

(2003), Harris et al. (2003), Porwal et al. (2003a, 2004), Rigol-

Sanchez et al. (2003), Harris and Sanborn-Barrie (2006), Porwal

(2006), Skabar (2005, 2007a, 2007b), Nykänen (2008)

Bayesian network classifiers Porwal (2006), Porwal et al. (2006b), Porwal and Carranza (2008)

Data-Driven Modeling of Mineral Prospectivity 253

addressing the issues of (a) objective selection of a suitable unit cell size for data-driven

modeling mineral prospectivity, (b) selection of coherent deposit-type locations for data-

driven modeling of mineral prospectivity and (c) cross-validation of data-driven mineral

prospectivity models. These three issues are vital to the application of any bivariate or

multivariate technique of GIS-based data-driven modeling of mineral prospectivity, so it

is of foremost importance that they are given prior considerations.

SELECTION OF SUITABLE UNIT CELL SIZE FOR MODELING

Because known deposit-type locations are

samples of a mineralised landscape under

investigation, it is essential to consider and determine a suitable

sampling density in

data-driven modeling of mineral prospectivity. By doing so makes data-driven modeling

of mineral prospectivity consistent with the general principles of the statistical theory,

sampling theory and information theory. Mineral prospectivity is one type of (spatial)

information, which is derived systematically via (statistical) analysis of multiple sets of

various geo-exploration data (i.e., explanatory/predictor variables) at known deposit-type

locations and at non-deposit locations. Prospective areas, as we recall from Chapter 2,

are not only

definition-limited but also sampling-limited geo-objects.

Sampling density in data-driven modeling of mineral prospectivity is defined by a

unit cell size that is used for representing known deposit-type locations and in

discretising spatial data of explanatory/predictor variables. A unit cell is equivalent to a

grid cell in sampling. It is also equivalent to a pixel in GIS (see Fig. 2-5). The size of a

unit cell is described by its length or width, if it is a rectangle, or by its diameter or

radius, if it is a circle. The size of a unit cell defines the

spatial resolution (grid or pixel

resolution) of models of spatial data (see Chapter 2). The size of a unit cell, therefore,

defines the spatial accuracy of the derived pieces of geo-information portrayed in maps

or images. Fine unit cells represent high sampling density and thus good spatial accuracy

of information, whereas coarse unit cells represent low sampling density and thus poor

spatial accuracy of information. This comparison of unit cell sizes and, thus, sampling

densities, in the context of mineral prospectivity mapping, is pertinent only to a

particular areas, because the spatial distributions of mineral deposits and their spatial

associations with geological features vary from one area to another. The size of a unit

cell also determines the scale of a cartographic map. The finer the unit cell, the larger the

map scale; the coarser the unit cell, the smaller the map scale. However, map scale does

not symbolise and, thus, should not be confused with size of a study area.

Most, if not all, studies of GIS-based data-driven modeling of mineral prospectivity

make use of equal-sized (usually square) unit cells. The choice of a suitable unit cell size

in GIS-based data-driven modeling of mineral prospectivity is based on (a) the

knowledge that every mineral deposit is unique, even if they are classified to certain

types of mineral deposits, and (b) the assumption that each unit cell must contain just

one of each of the known locations of mineral deposits of the type sought. However, the

choice of a suitable unit cell size in most studies of GIS-based data-driven modeling of