International Journal of Applied Earth Observation and Geoinformation 10 (2008) 374–387
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International Journal of Applied Earth Observation and Geoinformation
Knowledge-guided data-driven evidential belief modeling of mineral prospectivity in Cabo de Gata, SE Spain E.J.M. Carranza *, F.J.A. van Ruitenbeek, C. Hecker, M. van der Meijde, F.D. van der Meer International Institute for Geo-Information Science and Earth Observation, Hengelosestraat 99, P.O. Box 6, 7500 AA Enschede, The Netherlands
A R T I C L E I N F O
Article history: Received 2 July 2007 Accepted 27 February 2008 Keywords: Evidential belief functions Dempster’s rule of combination ASTER band ratios GIS Epithermal deposits
A B S T R A C T
Spurious evidence and spurious spatial associations between target mineral deposits and certain classes of spatial data undermine GIS-based data-driven modeling of mineral prospectivity. In a case study application of data-driven evidential belief functions, such problems were recognized and then, based on sound geological judgment, were addressed accordingly. By invoking knowledge of genetic associations between mineral deposits of the type sought and spatial geological attributes (lithology, fault/fracture density, hydrothermal alteration intensity), spurious spatial associations depicted in ‘original’ evidence maps were addressed by treatment of input spatial data via applications of certain basic GIS functionalities in order to derive ‘treated’ evidence maps. By invoking knowledge of geological processes involved in the formation of mineral deposits of the type sought and knowledge of how operations to combine evidence maps function, the integration of evidence maps was guided such that the inter-play of geological processes involved in the formation of mineral deposits of the type sought is represented in the modeling procedure and such that spurious evidence is filtered and not transmitted into the output map representing likelihood of mineral deposit occurrence in every location within a study area. The results show that: (a) using ‘treated’ evidence maps, instead of ‘original’ evidence maps, results in better mineral prospectivity maps and, thus, (b) knowledge-guided data-driven modeling of mineral prospectivity is better than a ‘purely’ data-driven modeling of mineral prospectivity. ß 2008 Elsevier B.V. All rights reserved.
1. Introduction To support decision-making in traditional or field-based methods of mineral exploration, GIS-based mineral prospectivity modeling can be performed to estimate likelihood for mineral deposit occurrence in every location within a study area. It involves creation and integration of evidence maps representing individual recognition criteria for the deposit-type sought. Evidence maps are derived from either ground-collected or remotely sensed data. Individual classes of spatial data in every input map are weighted, with respect to target deposits, by application of either
* Corresponding author. Fax: +31 53 4874336. E-mail address:
[email protected] (E.J.M. Carranza). 0303-2434/$ – see front matter ß 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jag.2008.02.008
bivariate or multivariate methods. The weights are degrees of spatial association between individual classes of spatial data and target deposits. Bivariate methods of creating evidence maps involve pairwise estimation of spatial association between a map of target deposits and a map of spatial data. Bivariate methods of creating evidence maps are either ‘knowledge-driven’ or ‘data-driven’. The former means that evidential weights are estimated subjectively based on one’s expert opinion about spatial association of target deposits with certain geological features, whereas the latter means that evidential weights are quantified objectively with respect to locations of known target deposits (Bonham-Carter, 1994). Examples of knowledge-driven bivariate methods of creating evidence maps include applications of fuzzy sets (Bonham-Carter, 1994; Carranza and Hale, 2001) and evidential belief functions (Moon, 1990;
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An et al., 1994a). Examples of data-driven bivariate methods of creating evidence maps include applications of Bayesian probability (Agterberg et al., 1990; Bonham-Carter, 1994) and evidential belief functions (Chung and Fabbri, 1993; An et al., 1994b). Multivariate methods of creating evidence maps are invariably data-driven and involve simultaneous quantifications of spatial associations between target deposits and all input maps of evidence. Examples of multivariate methods for creation of evidence maps are logistic regression (Chung and Agterberg, 1980; Reddy et al., 1991) and neural networks (Brown et al., 2000; Porwal et al., 2003). In mineral prospectivity modeling, data-driven methods are more popular than knowledge-driven methods because the former provide objective rather than subjective weighting of evidence. Data-driven methods could, however, result in spurious (i.e., geologically meaningless) evidential weights. This happens when certain classes of data in some maps show spatial association with target deposits even if they are genetically not associated with the target deposits. This issue is usually not resolved in many (although not necessarily published) case studies of ‘purely’ (or black-box) data-driven methods, whereby the quantified spatial associations between the target deposits and every class of spatial data in every map are ‘respected’. This issue usually happens in applications of multivariate methods because of automatic creation and integration of evidence maps. Hence, in applications of multivariate methods there is usually less opportunity for intuitive assessment of geological meaning of evidential weights compared to applications of bivariate methods. There is, however, no specific way of assessing geological meaning of evidential weights (as opposed to assessing statistical significance of evidential weights) because every case of mineral prospectivity modeling is unique in terms of geographic location, type of mineral deposits of interest, quality and quantity of input ground-collected and/or remotely sensed data. For example, in a case application of data-driven evidential belief functions (hereafter denoted as EBFs) to model epithermal deposit prospectivity in the Cabo de Gata area (SE Spain; Fig. 1), we recognized spurious spatial associations of epithermal deposits with mapped units of sediment cover and with some high values of ASTER band 4/band 6 ratios. The spatial association between epithermal deposits and mapped units of sediment cover is spurious because it is known that epithermal deposits in the area are hosted by certain volcanic rocks. The spatial association between epithermal deposits and some high values of ASTER band 4/band 6 ratios is partly spurious because they coincide either with certain volcanic rocks hosting epithermal deposits or with greenhouses for which the study area is (in) famous. Spurious evidence and spurious spatial associations between target deposits and certain classes of spatial data, if not addressed properly during the modeling process (i.e., in the creation and then integration of evidence maps), will undermine the quality of a mineral prospectivity model. There are applications of bivariate methods in datadriven modeling of mineral prospectivity, particularly in cases of small number of target deposits (e.g., Agterberg and Cheng, 2002; Carranza, 2004), in which the statistical
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Fig. 1. Location of the case study area (upper panel) and the distribution/ variation of Neogene volcanic rocks, locations of epithermal deposits (adapted from IGME, 1981) and caldera margins (adopted from Cunningham et al., 1990, Rytuba et al., 1990). See Table 1 for explanation of legend of lithologic units. Map coordinates are in meters (UTM project, zone 30N, International 1924 ellipsoid, European 1950 datum).
significance as well as the geological meaning of spatial associations between target deposits and input spatial data are explicitly and thoroughly assessed in order to create evidence maps. To the best of our knowledge, however, the explicit treatment of input spatial data to address (i.e., reduce or eliminate) spurious spatial associations between target deposits and certain classes of spatial data has not been reported in case applications of bivariate methods to data-driven modeling of mineral prospectivity. Thus, we make a novel contribution to this subject by showing here that a knowledge-guided data-driven mineral prospectivity model is better than a ‘purely’ data-driven mineral prospectivity model. We show that, by invoking knowledge of genetic relations between target deposits and
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geological attributes (lithology, fault/fracture density, hydrothermal alteration intensity), spurious weights in ‘original’ evidence maps can be addressed by treatment of input spatial data via applications of basic GIS functionalities in order to derive ‘treated’ evidence maps. We then show that using ‘treated’ evidence maps, instead of ‘original’ evidence maps, results in better mineral prospectivity maps. We further show that, by invoking knowledge of geological processes involved in mineral deposit formation and knowledge of how operations to combine EBFs functions, integration of evidence maps can be guided such that the inter-play of geological processes in mineral deposit formation is represented and such that spurious evidence is filtered and not transmitted into the output map of mineral prospectivity. To model mineral prospectivity, we applied data-driven EBFs because (a) they allow quantification and adept interpretation of spatial association between target deposits and every class of input spatial data, (b) they allow assignment of evidential weights to parts of a study area where spatial data are lacking and (c) the Dempster’s (1968) rule of combining EBFs offers ability to integrate maps of evidences in a geologically meaningful way and thus ability to filter geologically irrelevant or spurious evidence. We organized this paper as follows. First, we describe the geology and mineralization of the study area. Next, we explain EBFs, their estimation by data-driven techniques (after Carranza and Hale, 2003) and their integration by Dempster’s (1968) rule of combination. Then, we explain and discus the different aspects of data-driven modeling mineral prospectivity in the study area, especially the treatment input spatial data in order to address spurious spatial associations between target deposits and certain classes of spatial data in an input map of univariate spatial data. Finally, we discuss significance of results and give conclusions and recommendations. 2. Geology and epithermal gold mineralization in the Cabo de Gata area The Sierra del Cabo de Gata in the southeastern portion of the Betic Cordillera of the Iberian Peninsula (Fig. 1) consists of Neogene volcanic rocks, which are separated, by the SW–NE trending Carboneras fault zone and intervening Neogene sedimentary basins, from uplifted massifs of Paleozoic to Mesozoic metamorphic basement rocks. The volcanic rocks vary from andesitic and dacitic lavas to dacitic and rhyolitic pyroclastics (Fig. 1, Table 1) of Middle to Late Miocene age (Zeck et al., 2000). The volcanic rocks are, at places, overlain by Late Miocene to Pliocene calcareous sediments and quaternary alluvium/colluvium derived from such volcanic rocks. Calderas in the area (Fig. 1) were formed by relatively similar geologic processes that generated the volcanic rocks within a relatively short period during Middle Miocene (Cunningham et al., 1990; Rytuba et al., 1990). The Los Frailes caldera is older than the Rodalquilar caldera complex. The caldera-forming processes are older than and, thus, not genetically associated with known hydrothermal mineralizations in the area (Rytuba et al., 1990; Arribas et al., 1995). The caldera-related faults and faults/
Table 1 Description of mapped lithologic units in Fig. 1 (adopted from IGME, 1981) Map code in Fig. 1
Explanation
v01 v02
Amphibole andesite and dacite Dacitic–rhyolitic ignimbrites and tuffs Fine dacitic tuff Fine lapilli tuff of pyroxene andesite Polygenetic tuff Pyroclastic andesite breccia Pyroxene andesite Reddish dacite dyke Reddish-purple biotite-amphibole dacite Calcareous sediments; alluvium/colluvium
v03 v04 v05 v06 v07 v08 v09 v10
fractures due to other geologic processes probably have provided excellent plumbing systems for the hydrothermal mineralizations (Arribas et al., 1995). Hydrothermal mineralizations and alterations in the area have characteristics that are typical of epithermal type of mineral deposits (Demoustier et al., 1999). Mineralizations southwest of the Los Frailes caldera are associated with hydrothermally altered pyroxene andesites, are low-sulphidation epithermal deposits and contain mainly Pb, Zn and Ag with minor Au (Pineda, 1984). Mineralizations within the Rodalquilar caldera complex are either low-sulphidation or high-sulphidation sub-type of epithermal deposits (Arribas et al., 1995). The former consists of Pb–Zn–(Cu–Ag–Au) quartz veins, whereas the latter consists of alunite veins and, more importantly, Au– (Cu–Te–Sn) chalcedonic quartz veins and hydrothermal breccias. The precious-metal epithermal deposits are associated with intensely hydrothermally altered rocks characterized by a silicic (vuggy silica) central zone, which grades outwards to an advanced argillic (mainly quartz + alunite kaolinite) zone and then to an argillic (mainly quartz, kaolinite, illite) zone. The base-metal epithermal deposits occur in propylitic (mainly quartz, chlorite, illite) zones peripheral to the intensely hydrothermally altered zones. The precise temporal relationship between the basemetal epithermal deposits and the precious-metal epithermal deposits, however, is not clearly known (Arribas et al., 1995). 3. Evidential belief functions The framework for estimation of EBFs is provided by the Dempster–Shafer theory of evidence (Dempster, 1967; Shafer, 1976). The theoretical formalization of EBFs is very involved, so the following discussion for its application here is simplified and informal. Estimation of EBFs for spatial data is always in relation to a proposition, which in this case study is: ‘‘This location is prospective for epithermal deposits based on given evidence’’. The EBFs are Bel (degree of belief), Dis (degree of disbelief), Unc (degree of uncertainty) and Pls (degree of plausibility). The Bel and Pls are, respectively, lower (or ‘pessimistic’) and upper (or ‘optimistic’) degrees of belief that the proposition is true based on given evidence. Thus, Pls is often greater than or
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sometimes equal to Bel. The Unc is ignorance (or doubt) about the proposition based on given evidence; it is equal to Pls–Bel. If Unc = 0, then Bel = Pls. The Dis is belief that the proposition is false based on given evidence; it is equal to 1–Pls or 1–Unc–Bel. Thus, Bel + Unc + Dis = 1. However, if Bel = 0, then Dis = 0 because if there is no belief there can be no disbelief but there can only be uncertainty. Interestingly, if Unc = 0, then Bel + Dis = 1, as in probability approach. Note that Bel, Unc and Dis are the EBFs used to integrate evidences according to Dempster’s (1968) rule of combination. Mineral prospectivity modeling by application of EBFs is usually knowledge-driven or based on expert opinion (e.g., Moon, 1990; An et al., 1994a). Knowledge-driven estimation of EBFs is suitable usually in cases where spatial data pertaining to target deposits are lacking or insufficient. However, for cases where several target deposits are known, data-driven estimation of EBFs is applicable (Chung and Fabbri, 1993; Carranza and Hale, 2003). In this paper, application of data-driven EBFs is adopted to model prospectivity for epithermal deposits in the study area. 3.1. Data-driven estimation of EBFs Procedures for data-driven estimations of EBFs described by Chung and Fabbri (1993) and An et al. (1994b) are suitable where both mineralized and nonmineralized locations are sufficiently known. In situations where mineralized and non-mineralized locations are insufficiently known, Carranza and Hale (2003) proposed similar but different data-driven estimation procedures, which are adopted here. Suppose an exploration area T consists of N(T) total number of unit cells or pixels and mineral deposits D occur in N(D) number of pixels. Suppose further that Xi (i = 1, 2, . . ., n) evidence maps, with Cij (j = 1, 2, . . ., m) classes of evidence, have been created for certain deposit recognition criteria. An example of Xi is a map of lithologic units, in which each lithologic unit is Cij. Another example of Xi is a map of classified fault/fracture density, in which each class of fault/fracture density is Cij. Via overlay (or cross) operations between binary map of D and each multi-class evidential map, number of Cij pixels overlapping with D pixels [i.e., N(Cij \ D)] and number of Cij pixels not overlapping with D pixels [i.e., N(Cij) – N(Cij \ D)] are determined. Then, the values of BelCi j and DisCi j are derived. The equation for data-driven estimation of BelCi j is (Carranza and Hale, 2003): WC D BelC i j ¼ Pm i j j¼1 W C i j D
W Ci j D ¼
relative strength of W Ci j D for every jth Cij class of evidence in map Xi. The equation for data-driven estimation of DisCi j is (Carranza and Hale, 2003): W C D¯ DisC i j ¼ Pm i j j¼1 W C i j D¯
NðC i j \ DÞ=NðC i j Þ NðDÞ NðC i j \ DÞ=NðTÞ NðC i j Þ
The W Ci j D in Eq. (1) is ratio of the conditional probability that D exists given presence of Cij to the conditional probability that D exists given absence of Cij. The W Ci j D , thus, is the weight of Cij in terms of D being more present than absent as may be expected due to chance. Thus, the degree of belief for Cij, BelCi j , as defined in Eq. (1), is the
(2)
where W C i j D¯ ¼
NðC i j Þ NðC i j \ DÞ=NðC i j Þ NðTÞ NðDÞ ½NðC i j Þ NðC i j \ DÞ=NðTÞ NðC i j Þ
The W Ci j D¯ in Eq. (2) is ratio of the conditional probability that D does not exist given presence of Cij to the conditional probability that D does not exist given absence of Cij. The W Ci j D¯ , thus, is the weight of Cij in terms of D being more absent than present as may be expected due to chance. Thus, the degree of belief for Cij, DisCi j , as defined in Eq. (2), is the relative strength W Ci j D¯ for every jth Cij class of evidence in map Xi. If, for Cij, the estimated W Ci j D ¼ 0, which means that BelCi j ¼ 0, then the corresponding estimate of W Ci j D should be re-set or forced to zero, even if it is not, so that the corresponding DisCi j ¼ 0. The value of BelCi j is a ‘pessimistic’ measure of spatial association of D with every Cij in map Xi, whereas the value of DisCi j is a measure of spatial dissociation of D with every Cij in map Xi. Finally, values of UncCi j and PlsCi j are calculated according to the relationships of the EBFs explained above. The value of UncCi j is a measure of uncertainty of D being associated with every Cij in map Xi. The value of PlsCi j is an ‘optimistic’ measure of spatial association of D with every Cij in map Xi. 3.2. Combining of EBFs EBFs of evidence map X1 can be combined with EBFs of evidence map X2 according to Dempster’s (1968) rule of combination in order to create an integrated map of EBFs. The Dempster’s (1968) rule can be implemented using either AND or OR operation (An et al., 1994a). The formulas for combining EBFs of two evidence maps (X1, X2) according to an AND operation are given by (An et al., 1994a): BelX 1 X 2 ¼
BelX 1 BelX 2 b
(3)
DisX 1 X 2 ¼
DisX 1 DisX 2 b
(4)
UncX 1 UncX2 þ BelX 1 UncX 2
(1)
where
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UncX 1 X 2 ¼
þ BelX 2 UncX 1 þ DisX 1 UncX 2 þ DisX 2 UncX 1 b
(5)
where b ¼ 1 BelX 1 DisX2 DisX1 BelX2 is a normalizing factor to ensure that Bel + Unc + Dis = 1. Eqs. (3) and (4) are both multiplicative, so they result in a map of integrated Bel and integrated Dis, respectively, in which there is support and lack of disbelief, respectively, for the proposition being evaluated if pieces of evidence in two input maps coincide (or intersect) with each other. In contrast, Eq. (5) is both commutative and associative, so it results in a map of integrated Unc in which the output
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values are controlled by pieces of evidence with larger uncertainty in either of the two input maps. Thus, an AND operation is apt for combining two pieces of complementary evidence in order to support proposition of mineral prospectivity. In mineral exploration, for example, hydrothermal alteration and fault/fracture density can be two sets of complementary evidence of the presence of mineral deposits, because the formation of several types of mineral deposits is usually accompanied by chemical reactions between rocks and hydrothermal fluids and because several types of mineral deposits are formed in highly faulted/fractured rocks. In addition, Eqs. (3) and (4) function similar to an intersection operation in classical set theory, so they inhibit or minimize the transmission of effect of spurious evidence into a map of integrated Bel or Dis. That is because spurious evidence in one map of a univariate spatial data usually does not coincide with realistic evidence in another map of a univariate spatial data. The formulas for combining EBFs of two evidence maps (X1, X2) according to an OR operation are given by (An et al., 1994a): BelX 1 X 2 ¼
BelX 1 BelX 2 þ BelX 1 UncX 2 þ BelX 2 UncX 1 b
(6)
DisX 1 X 2 ¼
DisX 1 DisX 2 þ DisX 1 UncX 2 þ DisX 2 UncX 1 b
(7)
UncX 1 X 2 ¼
UncX 1 UncX2 b
(8)
where b is the same as in Eqs. (3)–(5). Eqs. (6) and (7) are both commutative and associative, so they result in a map of integrated Bel and integrated Dis, respectively, in which the output values are controlled by pieces of evidence with larger belief or larger disbelief in either of the two input maps. In contrast, Eq. (8) is multiplicative, so it results in a map of integrated Unc in which the output values is controlled by pieces of evidence with lower uncertainty in either of the two input maps. Thus, an OR operation is apt for combining two pieces of supplementary (as opposed to complementary) evidence in order to support proposition of mineral prospectivity. In mineral exploration, for example, hydrothermal alteration and fault/fracture density can be two sets of supplementary evidence of the presence of mineral deposits, because not all hydrothermally altered rocks necessarily mean the presence of certain types of mineral deposits and because not all highly faulted/fractured rocks necessarily mean the presence of certain types of mineral deposits. However, because Eqs. (6) and (7) function similar to a union operation in classical set theory, they do not inhibit nor minimize the transmission of effect of spurious evidence into a map of integrated Bel or Dis. That is because spurious evidence in one of the input maps, which may not coincide with realistic evidence in another map of a univariate spatial data, will be represented in the output map of integrated Bel or integrated Dis. A priori knowledge of how the AND or OR operation functions can thus be important in deciding which operation to apply in integrating maps of evidence representing different recognition criteria of mineral
prospectivity. After application of either Eqs. (3)–(5) or Eqs. (6)–(8), PlsX1 X2 is calculated according to the relationships of EBFs explained above. Note further that only EBFs of two evidence maps can be combined each time; EBFs of maps X3, . . ., Xn are combined one after another by repeated applications of either Eqs. (3)–(5) or Eqs. (6)–(8). The final integrated values of Bel are considered indices of mineral deposit prospectivity. Because Eq. (3) is multiplicative while Eq. (6) is associative and commutative, the output integrated values of Bel derived by Eq. (3) are always less than the corresponding output integrated values of Bel derived by Eq. (6). This means that values of EBFs should not be interpreted as probabilities in absolute terms but in relative terms (i.e., ordinal scale). Thus, in mineral prospectivity modeling integrated values of Bel are relative degrees of likelihood for deposit occurrence. 4. Evidential belief modeling of epithermal deposit prospectivity 4.1. Spatial recognition criteria for epithermal deposit occurrence Volcanism, flow of mineralizing fluids and fluid–rock reactions are among the geological processes that can be considered to have controlled the formation of epithermal deposits in the study area. Thus, in view of the geological characteristics of known epithermal deposits (Pineda, 1984; Arribas et al., 1995) and available datasets (geological maps, ASTER images) in the area, three spatial recognition criteria were considered in modeling prospectivity for epithermal deposits: (1) volcanic rocks; (2) fault/fracture density and (3) hydrothermal alteration intensity. 4.2. Preparation of training deposits and evidences for estimation of EBFs Evidence maps representing the first and second recognition criteria were derived from 1:50,000 scale geological map (IGME, 1981). Evidence representing the third recognition criterion was derived from ASTER imagery. The geological map and ASTER imagery were compiled in a GIS by georeferencing these spatial data sets to the UTM coordinate system projection (zone 30N, International 1924 ellipsoid, European 1950 datum). From the geological map, lithologic units were digitized as polygons, faults/fractures were digitized as line segments and locations of epithermal deposits were digitized as points. The digitized mapped geological features, in vector format, were stored in separate thematic maps. From the ASTER imagery, an image of band 4/band 6 (or b4/b6) ratios was created to represent hydrothermal alteration intensity. The reason for this is that, predominant minerals (e.g., alunite, kaolinite, illite) in intensely hydrothermally altered volcanic rocks associated with the epithermal deposits in the area have, according to published reference spectra (Clark et al., 1993), reflectance and absorption peaks in the wavelength regions covered by band 4 (1.600– 1.700 mm) and band 6 (2.185–2.225 mm), respectively. In preparing a map of training target deposits and a map of testing target deposits, one of two traditional methods
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may be followed. One method selects n 1 training deposits out of n deposits and the remaining one deposit is used for testing (Chung et al., 2002), which means that n models of mineral prospectivity are created from which to determine the best model. The other method random selects an arbitrary number, but representing a large proportion, of n deposits for training and the remainder is used for testing. This method of creating training and testing data subsets is usually applied in cases where the objective is to compare the performance of different methods of predictive modeling but not necessarily to obtain the best predictive model based on one method of predictive modeling (Agterberg and Bonham-Carter, 2005). We adopted the second method because the purpose here is to compare performance of knowledge-guided data-driven modeling versus ‘purely’ data-driven modeling, albeit both are based on application of EBFs. Of the 41 locations of epithermal deposits (Fig. 1), 31 (75%) were selected randomly and then rasterized to create a subset of training deposits for prospectivity modeling; thus, N(D) = 31. We pretend that the other 10 locations (25%) of known epithermal deposits are undiscovered in order to test prediction-rate of the prospectivity modeling (see further below). Certainly, there are other possible combinations of proportions of training and testing target deposit locations. In practice, however, locations of undiscovered deposits (i.e., testing deposits) are, of course, unknown. Thus, an ‘ideal’ proportion of testing and training deposits cannot be specified, although one usually prefers a proportion of testing deposits that is larger than the proportion of testing deposits with tacit assumption that the quantified spatial associations are robust and geologically explicable. To prepare the evidence maps, we first endeavored to find a suitable pixel size for raster representation of every point location of epithermal deposit as just one pixel. This is important because: (a) N(D) must be equal to actual number of training deposits used in modeling, and (b) EBFs must represent optimum spatial association (or dissociation) of individual classes of evidence with a set of training deposits. The suitable pixel size was determined via a point pattern analysis (Boots and Getis, 1988), which indicates for a set of points a distance from each point within which there is zero probability for occurrence of another point. The suitable pixel size was found to be 100 m 100 m. With this pixel size, N(T) for the study area is 49,871. The vector map of lithologic units (Fig. 1) and the vector map of faults/fractures were then rasterized using 100 m 100 m pixel size. A map of fault/fracture density [total length of faults/fractures per 100 m 100 m pixel] was then created. The image of ASTER b4/b6 ratios was re-sampled from 30 m 30 m to 100 m 100 m pixel resolution. Because the maps of fault/fracture density and b4/b6 ratios represent continuous variables, they must be discretized first into a number of classes so that datadriven EBFs can be estimated. For two reasons, both maps of continuous variables were discretized into classes of 5percentile intervals. One reason is application of uniform discretization to avoid introducing operational bias, due to different numbers of classes in individual maps, in the quantification of spatial associations by EBFs. The other reason, which is more important, is creation of, as much as
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possible, narrow ranges (or classes) of spatial attributes and thus low number of Cij pixels [denoted as N(Cij)] in Xi evidence map in order to optimize estimates of EBFs as they depend on N(Cij) (Carranza and Hale, 2003). Aside from the classification of the ASTER b4/b6 ratios, some undefined pixels in the image of ASTER b4/b6 ratios pertaining to the northwestern corner of the study area not covered by ASTER data were classified as ‘‘missing data’’. This is important (a) so that the value of N(T) in every map is the same and (b) because estimation of EBFs requires the same value of N(T) (Carranza and Hale, 2003). 4.3. Knowledge-guided treatment of spurious evidence The map of data-driven values of Bel of mapped volcanic rocks is the ‘original’ volcanic rock evidence (Fig. 2a). Of the 31 training deposits, 21 training deposits coincide with four (v01, v02, v07, v09) of the nine mapped volcanic rock units (Table 2), whereas 10 training deposits coincide with mapped non-volcanic rock units (v10). The latter spatial association is spurious. A perfunctory check of the lithologic map (Fig. 1) shows that each of the 10 training deposits in v10 are located close to certain volcanic rock units but in areas underlain by colluvial deposits derived from nearby volcanic rocks. Based on experience, it is plausible that either the boundaries of mapped units are inaccurate or the deposits are associated with volcanic rocks beneath colluvial deposits. It was decided to buffer a mapped volcanic rock unit if (see Table 2) it either (a) contains at least one training deposit or (b) is nearest to any one of the 10 training deposits in v10. Buffering of a geological object, which aims to represent its presence, is a common practice in mineral prospectivity modeling (Bonham-Carter, 1994, p.159). Via proximity analysis, it was found that (a) v01, v06, v07 and v09 are each nearest to any one of the 10 training deposits in v10 and (b) each of the 10 training deposits in v10 is situated within 200 m to a nearest volcanic rock unit. Thus, in areas covered by v10, buffer zones of 200 m were created separately around v01, v02, v06, v07 and v09. The five buffer zones were considered different classes of volcanic rock evidence instead of merging them with the corresponding mapped volcanic rock units. The reason for this is that the buffer zones should have different EBFs as the mapped volcanic rocks because they are induced evidences and thus uncertainties related with them should not be propagated to the mapped evidences. The information given in Tables 2 and 3 justifies consideration of the buffer zones as separate evidences. The new results show that buffered units of v01, v06, v07 and v09 have higher Bel and lower Unc than v10 but have lower Bel and higher Unc compared to the mapped units. The v02 buffer does not contain a training deposit and thus have the same EBFs as v10. More importantly, the relative degrees of EBFs of the mapped volcanic rock units are maintained (see Tables 2 and 3). The map of data-driven Bel of mapped and buffered volcanic rocks is now the ‘treated’ volcanic rock evidence (Fig. 2b). The map of data-driven values of Bel of percentile classes of fault/fracture density is the ‘original’ fault/ fracture density evidence (Fig. 3a). The two classes of highest fault/fracture density have highest values of Bel
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Fig. 2. Estimated Bel of (a) mapped volcanic rocks and (b) mapped/buffered volcanic rocks.
and lowest values of Unc than the other classes of fault/ fracture density (Table 4). However, the spatial distribution of EBFs for classes of fault/fracture density less than 131.15 m/pixel (Table 4) shows alternating bands of zero and very low values of Bel (Fig. 3a) or very high and maximum values of Unc. The fault/fracture density of less than 131.15 m/pixel at some locations, especially at and around four training deposits (Table 4), is plausibly due to bias in geological mapping or it plausibly suggests that epithermal deposits occur in fractured rocks beneath sediment cover. Either of these two reasons can be verified only via fieldwork, but the latter reason was followed to eliminate the spurious alternating patterns of low EBFs in the fault/fracture density evidence map. The alternating patterns were eliminated by re-grouping fault/fracture density classes less than 131.15 m/pixel and then recalculating the EBFs (Table 5). This resulted in slight increase of values of Bel and Unc for fault/fracture density classes greater than 131.15 m/pixel and slight decrease in
values of Bel and Unc for fault/fracture density classes less than 131.15 m/pixel. The map of data-driven Bel of regrouped percentile classes of fault/fracture density is now the ‘treated’ fault/fracture evidence (Fig. 3b). The map of data-driven values of Bel of percentile classes of ASTER b4/b6 ratios is the ‘original’ hydrothermal alteration evidence (Fig. 4). The two highest percentile classes of ASTER b4/b6 ratios contain 20 of the 31 training deposits (Table 6). These initial results suggest that (a) 11 deposits are associated with moderate to low hydrothermal alteration intensity (Table 6) and (b) intense hydrothermal alteration may be present in small and sporadic locations underlain by rock unit v10 in the western, northwestern and northern portions of the study area (Fig. 4). The former is realistic but the latter is spurious. The spots of very high ASTER b4/b6 ratios in the western, northwestern and northern portions are actually greenhouses and thus are spurious evidence of epithermal deposit prospectivity. It is proposed to address this
Table 2 EBFs of mapped lithologic units Mapped lithologic units (see Table 1 for descriptions)
N(Cij\D)
N(Cij)–N(Cij\D)
Bel
Dis
Unc
v01 v02 v03 v04 v05 v06 v07 v08 v09 v10
2 1 0 0 0 0 11 0 7 10
1,502 345 152 131 1,252 4,398 4,098 23 2,381 35,558
0.1161 0.2497 0.0000 0.0000 0.0000 0.0000 0.3206 0.0000 0.3036 0.0100
0.2001 0.1998 0.0000 0.0000 0.0000 0.0000 0.1998 0.0000 0.1998 0.2005
0.6838 0.5505 1.0000 1.0000 1.0000 1.0000 0.4796 1.0000 0.4966 0.7895
N(T) = 49,871. N(D) = 31. Rows in bold indicate mapped volcanic rock units that coincide with training epithermal deposits (D).
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Table 3 EBFs of mapped lithologic units and 200-m buffers around some mapped lithologic units Mapped and buffered lithologic units (see Table 1 for descriptions)
N(Cij\D)
N(Cij)–N(Cij\D)
Bel
Dis
Unc
v01 v02 v03 v04 v05 v06 v07 v08 v09 v10 v01 buffer v02 buffer v06 buffer v07 buffer v09 buffer
2 1 0 0 0 0 11 0 7 0 1 0 1 7 1
1,502 345 152 131 1,252 4,398 4,098 23 2,381 27,031 1,045 211 3,571 2,598 1,102
0.0802 0.1724 0.0000 0.0000 0.0000 0.0000 0.2214 0.0000 0.2096 0.0000 0.0562 0.0000 0.0156 0.1913 0.0533
0.1251 0.1249 0.0000 0.0000 0.0000 0.0000 0.1249 0.0000 0.1249 0.0000 0.1251 0.0000 0.1252 0.1249 0.1251
0.7947 0.7027 1.0000 1.0000 1.0000 1.0000 0.6537 1.0000 0.6655 1.0000 0.8187 1.0000 0.8592 0.6838 0.8216
N(T) = 49,871. N(D) = 31. Rows in bold indicate mapped volcanic rock units and buffers around mapped volcanic rocks units that coincide with training epithermal deposits (D).
spurious evidence not by similar treatment of the volcanic rock and fault/fracture density evidence maps but in the integration of EBFs of hydrothermal alteration intensity evidence with EBFs of the other two evidence maps. This is explained in the following section. 4.4. Integration of EBFs of evidences Like in fuzzy modeling of mineral prospectivity (e.g., Bonham-Carter, 1994; Carranza and Hale, 2001), an inference network is useful in combining logically EBFs of evidences of mineral prospectivity. An inference network is a series of steps or propositions to (a) represent inter-play of processes that control an outcome (e.g., formation of mineral deposits of the type sought) and (b)
filter out spurious evidence. An inference network is thus an instructive tool for simulating human knowledge in the process of logical decision-making (e.g., in modeling of mineral prospectivity). For the case study, in order to represent an intermediate evidence (or proposition) of structurally permeable volcanic rocks (Fig. 5), which may have facilitated flow of mineralizing fluids and thus aided fluid–rock reactions, the EBFs of volcanic rock evidence and EBFs of fault/ fracture density evidence are combined first using either the AND operation [Eqs. (3)–(5)] or the OR operation [Eqs. (6)–(8)]. On the one hand, the AND operation is used to represent proposition that certain locations are prospective for epithermal deposits if volcanic rocks are present and fault/fracture density is high. As epithermal
Fig. 3. Estimated Bel of (a) percentile classes of fault/fracture density and (b) re-grouped percentile classes of fault/fracture density.
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Table 4 EBFs of percentile classes of fault/fracture density Fault/fracture density (m/pixel)
N(Cij\D)
N(Cij)–N(Cij\D)
Bel
Dis
Unc
0.00 0.01–1.00 1.01–7.23 7.24–14.95 14.96–23.25 23.26–31.81 31.82–40.39 40.40–49.43 49.44–58.19 58.20–67.47 67.48–77.07 77.08–87.21 87.22–98.57 98.58–112.87 112.88–131.15 131.16–154.55 154.56–186.17 186.18–226.69 228.70–439.55
0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 4 5 9 9
6753 722 2493 2499 2493 2492 2493 2496 2495 2491 2495 2492 2493 2493 2495 2488 2489 2485 2483
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0258 0.0258 0.0000 0.0000 0.0258 0.0000 0.0258 0.1147 0.1488 0.3165 0.3168
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1251 0.1251 0.0000 0.0000 0.1251 0.0000 0.1251 0.1250 0.1249 0.1247 0.1247
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.8491 0.8491 1.0000 1.0000 0.8491 1.0000 0.8491 0.7603 0.7263 0.5588 0.5585
N(T) = 49,871. N(D) = 31.
deposits were formed initially at depths of up to 1 km below paleosurface, the integrated evidence map resulting from an AND operation suggests that locations prospective for epithermal deposits have been exhumed to similar erosion levels. On the other hand, the OR operation is used to represent proposition that certain locations are prospective for epithermal deposits either if volcanic rocks are present or if fault/fracture density is high. The integrated evidence map resulting from an OR operation suggests that there are locations prospective for epithermal deposits but they have been exhumed to different erosion levels. For example, prospectivity due to presence of volcanic rocks alone suggests that epithermal deposits associated with densely fractured rocks occur at depths. Then, the integrated EBFs of structurally permeable volcanic rocks and EBFs of hydrothermal alteration intensity are combined finally via AND operation (Fig. 5). The AND operation is used to (a) represent proposition that certain locations are prospective for epithermal deposits if densely fractured volcanic rocks are present and if they are intensely hydrothermally altered and (b) to filter out spurious evidence represented by high ASTER b4/b6 ratios related with greenhouses in the area. Integrating EBFs of evidences via the inference network (Fig. 5) results in two sets of prospectivity models: (1) model 1, using intermediate evidence of structurally permeable volcanic rocks derived via AND operation; (2)
model 2, using intermediate evidence of structurally permeable volcanic rocks derived via OR operation. For each of these models, four experiments were performed in order to verify whether remedial treatments of the volcanic rock evidence and the fault/fracture evidence were useful or not. Experiment A used EBFs of ‘original’ volcanic rock evidence (Table 2, Fig. 2a), ‘original’ fault/ fracture density evidence (Table 4, Fig. 3a) and hydrothermal alteration intensity evidence (Table 6, Fig. 4). Experiment B used EBFs of ‘treated’ volcanic rock evidence (Table 3, Fig. 2b), ‘original’ fault/fracture density evidence (Table 4, Fig. 3a) and hydrothermal alteration intensity evidence (Table 6, Fig. 4). Experiment C used EBFs of ‘original’ volcanic rock evidence (Table 2, Fig. 2a), ‘treated’ fault/fracture density evidence (Table 5, Fig. 2b) and hydrothermal alteration intensity evidence (Table 6, Fig. 4). Experiment D used EBFs of ‘treated’ volcanic rock evidence (Table 3, Fig. 2b), ‘treated’ fault/fracture density evidence (Table 5, Fig. 2b) and hydrothermal alteration intensity evidence (Table 6, Fig. 4). In addition, a third set of prospectivity model was derived by using only OR operation to integrate EBFs of evidences used in experiment A. This was necessary to verify which operation for combining EBFs allows filtration of spurious evidence. Thus, nine models of epithermal deposit prospectivity have been prepared—models 1A–1D, models 2A–2D and model 3.
Table 5 EBFs of re-grouped percentile classes of fault/fracture density Fault/fracture density (m/pixel)
N(Cij\D)
N(Cij)–N(Cij\D)
Bel
Dis
Unc
0.00–49.43 49.44–87.21 87.22–131.15 131.16–154.55 154.56–186.17 186.18–226.69 228.70–439.55
0 2 2 4 5 9 9
22,441 9,973 7,481 2,488 2,489 2,485 2,483
0.0000 0.0114 0.0161 0.1159 0.1504 0.3199 0.3201
0.0000 0.0910 0.0910 0.0909 0.0908 0.0907 0.0907
1.0000 0.8976 0.8929 0.7932 0.7588 0.5894 0.5892
N(T) = 49,871. N(D) = 31.
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Fig. 5. Inference network for combining evidences of epithermal deposit prospectivity.
Fig. 4. Estimated Bel of percentile classes of ASTER b4/b6 ratios.
5. Results and discussion 5.1. Evaluation of prospectivity models The performance of each prospectivity model represented by final integrated values of Bel was evaluated by (Agterberg and Bonham-Carter, 2005): (a) determining percentages of prospective zones defined by certain threshold values of integrated Bel; (b) determining success rate (or goodness-of-fit) of prospective zones against
training deposits and (c) determining prediction-rate of prospective zones against test deposits. The success and prediction rates are, respectively, percentage of training deposits and test deposits delineated correctly in prospective zones. Model performance curves are then created by plotting percentage of prospective zones versus success and prediction rates and the following discussions are based on prospective zones occupying 5–15% of the area (Fig. 6). Models 1A–1D and models 2A–2D all have better success rates (i.e., >5%) and prediction rates (>10%) than model 3 (Fig. 6). This means that spurious hydrothermal alteration intensity evidence is efficiently filtered by application of AND operation. Models 1B and 1D have slightly better success rates (i.e., >5%) and prediction rates
Table 6 EBFs of percentile classes of ASTER b4/b6 ratios Classes of ASTER b4/b6 ratios
N(Cij\D)
N(Cij)–N(Cij\D)
Bel
Dis
Unc
Missing data 0.6911–1.0271 1.0272–1.0401 1.0402–1.0486 1.0487–1.0556 1.0557–1.0617 1.0618–1.0674 1.0675–1.0726 1.0727–1.0780 1.0781–1.0831 1.0832–1.0844 1.0845–1.0938 1.0939–1.0993 1.0994–1.1052 1.1053–1.1114 1.1115–1.1182 1.1183–1.1265 1.1266–1.1370 1.1371–1.1512 1.1513–1.1781 1.1782–1.4787
0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 2 1 1 5 15
176 2483 2482 2468 2505 2443 2519 2460 2498 2469 2475 2517 2488 2488 2459 2487 2483 2488 2498 2485 2469
0.0000 0.0222 0.0000 0.0224 0.0000 0.0226 0.0000 0.0225 0.0221 0.0000 0.0223 0.0000 0.0000 0.0000 0.0225 0.0000 0.0460 0.0222 0.0221 0.1279 0.6253
0.0000 0.0834 0.0000 0.0834 0.0000 0.0834 0.0000 0.0834 0.0834 0.0000 0.0834 0.0000 0.0000 0.0000 0.0834 0.0000 0.0834 0.0834 0.0834 0.0832 0.0829
1.0000 0.8944 1.0000 0.8942 1.0000 0.8940 1.0000 0.8941 0.8945 1.0000 0.8943 1.0000 1.0000 1.0000 0.8941 1.0000 0.8706 0.8944 0.8945 0.7889 0.2918
N(T) = 49,871. N(D) = 31.
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Fig. 6. Mineral prospectivity success and prediction rates: (a) and (b) for models 1A–1D and model 3; (c) and (d) for models 2A–2D and model 3.
Fig. 7. Maps of two best epithermal deposit prospectivity models: (a) 1B; (b) 2D. RCC and LFC are Rodalquilar caldera complex and Los Frailes caldera, respectively (Fig. 1). A–D are localities discussed in the text.
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(i.e., mostly >5%) than models 1A and 1C (Fig. 6a and b). Likewise, models 2B and 2D have slightly better success rates (mostly >2%) and prediction rates (partly >5%) than models 2A and 2C (Fig. 6c and d). These results indicate that (a) treatment of the ‘original’ volcanic rock evidence by buffering of certain mapped volcanic rocks units is nontrivial and enhances performance of prospectivity modeling, but (b) treatment of the ‘original’ fault/fracture density evidence by re-classification is trivial and does not enhance performance of prospectivity modeling. Models 1A–1D have slightly better (i.e., mostly >5%) success rates than models 2A–2D (Fig. 6a and c). This means that combining the ‘treated’ volcanic rock evidence and the ‘treated’ fault/fracture density evidence by using the AND operation results in prospectivity models with better success rates than by using the OR operation. Models 1B and 1D have very similar prediction rates as models 2B and 2D, but models 1A and 1C have poor prediction rates than models 2A and 2C (Fig. 6b and d). This result reiterates the significance of buffering certain mapped volcanic rock units in order to treat spurious evidence and thus improve performance of prospectivity modeling. 5.2. Visualization and comparison of best prospectivity models The apparently best prospectivity models – 1B and 2D – were visualized (Fig. 7) and compared in order to discuss notable similarities and differences between them in terms of significance of the evidences and the operations used in modeling of epithermal deposit prospectivity. For this purpose, prospective zones occupying 10% of the area were considered because they have the same prediction rates for the best prospectivity models (Fig. 6). Both maps (Fig. 7) strongly reflect high values of Bel (or low values of Unc) related with the hydrothermal alteration intensity evidence (Fig. 4) in the Rodalquilar caldera complex and southwest of Los Frailes caldera (Fig. 1). Both maps do not reflect the spots of high values of Bel (or low value of Unc) related with spurious hydrothermal alteration intensity evidence in the western, northwestern and northern portions of the area (Fig. 6). These similarities show the importance of hydrothermal alteration intensity evidence in modeling of epithermal deposit prospectivity, so long as similarly appearing but spurious evidence is recognized and filtered out during the modeling process. Both maps also show low prospectivity near locality ‘‘A’’, although model 2D shows a small patch with high prospectivity (Fig. 7). The low prospectivity near locality ‘‘A’’ portrayed by both maps is due to the mapped/buffered volcanic rock evidence (Fig. 2b) and fault/fracture density evidence (Fig. 3b). The small patch with high prospectivity in model 2D is due mainly to the hydrothermal alteration intensity evidence (Fig. 4) and partly to the mapped/ buffered volcanic rock evidence (Fig. 2b). It seems that this small patch, as inspected in the ASTER images, is fresh excavation on hydrothermally altered bedrock as it coincides with buffer for v06 (Table 3). This interpretation and the proximity of locality ‘‘A’’ to known epithermal deposits north–northwest of the Rodalquilar suggest that the low to high prospectivity there warrants field investigation.
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One notable difference between models 1B and 2D is prospectivity of areas southwest of Los Frailes caldera. Prospectivity in these areas according to model 1B (Fig. 7a) is related with fault/fracture density evidence (Fig. 3a) and hydrothermal alteration intensity evidence (Fig. 4), but according to model 2D (Fig. 7b) it is related mostly with hydrothermal alteration intensity evidence (Fig. 4). This difference invites the question: ‘‘Which model, 1B or 2D, portrays reliable prospectivity in areas southwest of Los Frailes caldera?’’ To answer this, we consider the knowledge that host rocks of epithermal deposits southwest of Los Frailes caldera and in the Rodalquilar area have similar degrees of fault/fracture density, but those in the former have less hydrothermal alteration intensity (Pineda, 1984; Arribas et al., 1995). Thus, in terms of prospectivity of areas southwest of Los Frailes caldera, model 1B is more reliable than 2D because the former is more consistent with ground conditions there. However, prospectivity information in model 2D that is somewhat inconsistent with ground conditions may warrant field investigation. For example, the area immediately west of ‘‘B’’ (Fig. 7b), with moderate prospectivity due to hydrothermal alteration intensity evidence (Fig. 4) and mapped/buffered volcanic rock evidence (Fig. 2b), warrants field investigation because the poor fault/fracture density evidence there (Fig. 3b) is unrealistic. Another notable difference between models 1B and 2D is at and near locality ‘‘C’’ southwest of Rodalquilar caldera complex (Fig. 7a). Model 1B shows low prospectivity at and near locality ‘‘C’’, whereas model 2D shows that this area is mostly non-prospective. The low prospectivity at and near locality ‘‘C’’ is due mainly to volcanic rock evidence and partly to fault/fracture density evidence. The lack of hydrothermal alteration intensity evidence is the key to the predicted low and non-prospectivity at and near locality ‘‘C’’. Thus, in this case either models 1B or 2D is reliable. A third notable difference between models 1B and 2D is near locality ‘‘D’’ northeast of Rodalquilar caldera complex (Fig. 7b). Model 1B shows low prospectivity in a small area east of ‘‘D’’, whereas model 2D shows low prospectivity in small areas east and west of ‘‘D’’. In model 1B, the low prospectivity in the small area east of ‘‘D’’ is due mainly to the mapped/buffered volcanic rock evidence (Fig. 2b) and partly to the fault/fracture density evidence (Fig. 3b) and hydrothermal alteration intensity. In model 2D, the low prospectivity in small areas west of ‘‘D’’ is due to mainly to the hydrothermal alteration intensity evidence (Fig. 4) and partly to the fault/fracture density evidence (Fig. 3b). The lithologic map (Fig. 1) shows that these small areas near ‘‘D’’ are covered by alluvial sediments. The rather weak hydrothermal alteration intensity evidence (Fig. 4), which mainly contributes to the predicted low prospectivity near locality ‘‘D’’, may be due to clays in the alluvial sediments. Thus, in this regard model 1B is more reliable than model 2D. A fourth notable difference between models 1B and 2D concerns the Carboneras fault zone (Fig. 1). Along this fault zone, model 1D shows almost no prospective locations except at locality ‘‘A’’ and at few isolated pixels further southwest (Fig. 7a), whereas model 2D shows several
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isolated pixels with low prospectivity (Fig. 7b). In model 1D, the few isolated pixels of low prospectivity southwest of locality ‘‘A’’ (Fig. 7a) are probably realistic as they are proximal to a known epithermal deposit (Figs. 2–4). In model 2D, the predicted low prospectivity at several isolated pixels along the fault zone is plausibly spurious because of two reasons. Firstly, they are mainly due to fault/fracture density evidence (Fig. 3b). Secondly, it is probably incorrect to use the faults/fractures along the fault zone in deriving the fault/fracture density evidence, because no studies have yet implicated the Carboneras fault system in the epithermal mineralizations in the area. Even so, due to poor volcanic rock evidence (Fig. 2b) and near absence of hydrothermal alteration evidence (Fig. 4) along the Carboneras fault zone, the influence of the fault/ fracture density evidence is almost completely degraded by the use of AND operation to combine EBFs of such evidences. Thus, the difference between the maps in terms of prospectivity along the Carboneras fault zone suggests that model 1B is more reliable than 2D. 6. Conclusions and recommendations The quality of mineral prospectivity models derived via bivariate data-driven methods, such as data-driven EBFs, is compromised if spurious evidence, arising from geologically meaningless spatial associations between target deposits and certain classes of data, is not recognized and thus allowed to propagate into the final model output. Sound geological judgment must guide remedial treatment of spurious evidence during the modeling process. We have shown here that, by invoking knowledge of genetic associations between target deposits and geological properties (e.g., lithology, fault/fracture density, hydrothermal alteration intensity, etc.), certain basic GIS functionalities can be aptly applied in treating classes of spatial data providing spurious spatial associations with target deposits. We have shown thus that using ‘treated’ evidence maps, instead of ‘original’ evidence maps, results in better mineral prospectivity maps. We have also show that, by invoking knowledge of geological processes involved in formation of mineral deposits and knowledge of how operations to combine EBFs functions, integration of evidence maps can be guided such that the inter-play of deposit-forming processes is represented and such that the effect of spurious evidence is filtered and thus not transmitted into the output mineral prospectivity model. For the case study area, the results show that, based on prospective zones occupying 5–15% of the area, the knowledge-guided data-driven epithermal deposit prospectivity models have better success rates (>5%) and better prediction rates (>10%) than those of a ‘purely’ data-driven epithermal deposits prospectivity model. The two best maps of epithermal deposit prospectivity derived in this case study show only two clusters of high exploration interest. Both of these two clusters already have had a long history of exploration and mining. Thus, the chance of finding undiscovered epithermal deposits in the study area is probably already very low. In the lessexplored northeast portions of the area, low epithermal
deposit prospectivity is related with small areas of exposed bedrock. Due to significant sediment cover there, further modeling of epithermal deposit prospectivity would require exploration datasets that allow imaging of subsurface evidences. If knowledge- or data-driven EBFs are applied, we speculate that integration of surface and subsurface evidences would require a geologically wellthought inference network in which the OR operation might be more useful than the AND operation; although this speculation remains to be verified given that the required data are available. Notwithstanding the positive results in this study, we advise treatment of recognized spurious evidence if, and only if, there is unavailability of other types of spatial data from which more accurate or more suitable evidence of mineral prospectivity can be derived. For example, if a bedrock map was available, we would have preferred it to the one used here. In addition, we advise treatment of recognized spurious evidence derived from optical remote sensing data only until such time that robust techniques are developed for mapping of indisputable spectral features related with target deposits. With multispectral remote sensing data, for example, there is still lack of robust techniques to discern accurately between clays due to weathering and clays associated with hydrothermal alteration. Robust techniques for mineral imaging from hyperspectral remote sensing data have become available in the last decade or so, but unlike multispectral remote sensing data the former data type is still wanting in many parts of the world where mineral resource development is important. Thus, although hyperspectral remote sensing data are available in the study area, ASTER data were used in this case study in order to show that, in mineral prospectivity modeling, spurious evidence derived from remotely sensed multispectral spatial data can and must be addressed accordingly.
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