From Predictive Mapping of Mineral ... - Wiley Online Library

doi: 10.1111/j.1751-3928.2010.00146.x

Original Article

rge_146

Resource Geology Vol. 61, No. 1: 30–51

30..51

From Predictive Mapping of Mineral Prospectivity to Quantitative Estimation of Number of Undiscovered Prospects Emmanuel J. M. Carranza Department of Earth Systems Analysis, Faculty of Geo-Information Science and Earth Observation (ITC), University of Twente, Enschede, the Netherlands

Abstract This paper proposes that the spatial pattern of known prospects of the deposit-type sought is the key to link predictive mapping of mineral prospectivity (PMMP) and quantitative mineral resource assessment (QMRA). This proposition is demonstrated by PMMP for hydrothermal Au-Cu deposits (HACD) and by estimating the number of undiscovered prospects for HACD in Catanduanes Island (Philippines). The results of analyses of the spatial pattern of known prospects of HACD and their spatial associations with geological features are consistent with existing knowledge of geological controls on hydrothermal Au-Cu mineralization in the island and elsewhere, and are used to define spatial recognition criteria of regional-scale prospectivity for HACD. Integration of layers of evidence representing the spatial recognition criteria of prospectivity via application of data-driven evidential belief functions results in a map of prospective areas occupying 20% of the island with fitting- and prediction-rates of 76% and 70%, respectively. The predictive map of prospective areas and a proxy measure for degrees of exploration based on the spatial pattern of known prospects of HACD were used in one-level prediction of undiscovered mineral endowment, which yielded estimates of 79 to 112 undiscovered prospects of HACD. Application of radial-density fractal analysis of the spatial pattern of known prospects of HACD results in an estimate of 113 undiscovered prospects of HACD. Thus, the results of the study support the proposition that PMMP can be a part of QMRA if the spatial pattern of discovered prospects of the deposit-type sought is considered in both PMMP and QMRA. Keywords: evidential belief functions, fractal analysis, Fry analysis, GIS, hydrothermal Au-Cu, mineralization controls, spatial association analysis.

1. Introduction Predictive mapping of mineral prospectivity (PMMP) and quantitative mineral resource assessment (QMRA) are two distinct predictive modeling processes with a common aim of deriving information that is essential for strategic planning in mineral exploration and development. Despite this common goal,

PMMP has not been a necessary part of QMRA. Many workers have suggested or demonstrated that PMMP could be a part of QMRA. Drew and Menzie (1993) introduced conceptual metrics for estimating indices of likelihood of mineral deposit occurrence in geologically-permissive tracts. Raines and Mihalasky (2002) showed that weights-of-evidence (WofE) analysis and weighted logistic regression are useful for

Received 5 May 2010. Accepted for publication 6 July 2010. Corresponding author: E. J. M. CARRANZA, Department of Earth Systems Analysis, Faculty of Geo-Information Science and Earth Observation (ITC), University of Twente, 7500AA Enschede, the Netherlands. Email: [email protected]

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© 2010 The Author Resource Geology © 2010 The Society of Resource Geology

Prospectivity for undiscovered prospects

delineation of geologically-permissive terranes for assessment of pluton-related deposits. Raines et al. (2007) showed that WofE analysis is useful for delineation of geologically-permissive terranes for assessment of porphyry-Cu deposits. Scott and Dimitrakopoulos (2001) showed that, in a case study for porphyry copper deposits, WofE analysis of mineral prospectivity complements the U.S. Geological Survey three-part QMRA (Singer, 1993) by providing additional valuable information for estimation of the number of undiscovered deposits. Fallon et al. (2010) used Zipf’s Law to estimate undiscovered gold endowment in the Plutonic Marymia Greenstone Belt (Western Australia) and then used WofE and logistic regression to map prospective zones where undiscovered gold endowment could occur in the belt. Here, a strong link between PMMP and QMRA is discussed to show that PMMP could be a necessary part of QMRA. Unlike in Scott and Dimitrakopoulos (2001), Raines and Mihalasky (2002) Raines et al. (2007) and Fallon et al. (2010), data-driven evidential belief functions (Carranza, 2002, 2008; Carranza & Hale, 2003) were employed here for PMMP. Unlike in Scott and Dimitrakopoulos (2001) and Fallon et al. (2010), one-level prediction (McCammon & Kork, 1992; McCammon et al., 1994) and fractal analysis (cf. Raines, 2008; Zuo et al., 2009b) were employed here for estimation of the number of undiscovered prospects. It is proposed here that the spatial pattern of known pros-

pects of a deposit-type is the key to a strong link between PMMP and QMRA. This is demonstrated in regional-scale predictive mapping of prospectivity and estimation of the number of undiscovered prospects for hydrothermal Au-Cu deposits (HACD) in Catanduanes Island (Philippines).

2. Study area Catanduanes Island, lying east of the southeastern leg of Luzon Island (Fig. 1a), is a part of the Late EoceneOligocene Northeast Luzon–Polillo–Catanduanes magmatic arc that is associated with subduction in the East Luzon–Philippine Trenches (Mitchell & Leach, 1991). It is not well-explored but it contains some small prospects of HACD (Fig. 1b, Table 1). The Catanduanes Formation (Fig. 1b), which forms the stratigraphic basement of the island, is inferred to be Jurassic and consists mostly of strongly folded indurated sandstones and, in places, phyllitic schists and conglomerates (Miranda & Vargas, 1967). Overlying the Catanduanes Formation unconformably is the Yop Formation. It is inferred to be Cretaceous and is composed mainly of spilitic basaltic lavas with intercalations of tuffaceous volcaniclastic rocks (Miranda & Vargas, 1967). The Yop Formation underlies conformably on and/or inter-tongues with the Bonagbonag Limestone, which is of Cretaceous age and is composed of stratified limestone with minor shale and

Fig. 1 (a) Regional geotectonic map of Philippines. (b) Simplified geologic map of Catanduanes Island and locations of known prospects of Au/Cu deposits (compiled/ adopted from Miranda & Vargas, [1967] and JICA-MMAJ [1994]). A, alluvium; BI, Batalay Intrusives; BL, Bonagbonag Limestone; CF, Catanduanes Formation; PF, Payo Formation; SDF, Santo Domingo Formation; VC, Viga Conglomerate; YF, Yop Formation. Curvi-linear features = faults; saw-teeth indicate up-thrusted block. Numbers are references of prospects’ descriptions in Table 1. Map coordinates are in meters (UTM projection, zone 51). © 2010 The Author Resource Geology © 2010 The Society of Resource Geology

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E. J. M. Carranza

Table 1 Known prospects of Au-Cu deposits in Catanduanes Island Prospect†

Style of deposit

Host rock(s)‡

Ore minerals§

Alteration¶

Remarks

1

Vein

CF, BI

Cp, Py, Mal

Sil

2

CF

Cp

3

Vein, disseminations Vein

YF, BI

Cp, Py, (Mo)

4

Vein

CF, BI

Py, Cp

5

Vein, skarn

PF, BI

P, Sph, Py, Hm

6

Vein

YF BI

Py

7

Vein

CF, BI

8

Vein, skarn

CF, BI

9

Veinlets

CF, PF, BI

10

Vein

CF, PF, YF, BI

Mag, Cp, Py, (Sph)

Sil, Py

11

Vein, disseminations Veinlets, disseminations

CF

Py

Sil

PF, BI

Py, (Cp)

Sil

Native Cu, Mal

Sil, Epi Arg

Py

Sil, Py

More than 10 veins 0.1–1.4 m wide; sample yield 0.06–1.445% Cu (JICA-MMAJ, 1994) Gossanous outcrop on vertical sea cliff (JICA-MMAJ, 1994) Angular floats of quartz veins in cultivated area; samples yield max 0.474% Cu, 0.25 g t-1 Au, 0.133% Mo (JICA-MMAJ, 1994) 3 samples: nil to 1 g t-1 Au, 0.28–8.96% Cu, 5.5–41.5 g t-1 Ag (Miranda & Vargas, 1967) 1 sample: 0.964 g t-1 Au, 22 g t-1 Ag, 1.35% Cu (JICA-MMAJ, 1994) 4 samples: nil to 0.03 g t-1 Au, 0.022–0.033% Cu (JICA-MMAJ, 1994) Gold in stream sediment panned concentrates (JICA-MMAJ, 1994) 5 samples: 0.63–5.93% Cu, nil to 2 g t-1 Au, 5–24 g t-1 Ag (Miranda & Vargas, 1967) Artisanal small-scale workings for Au (JICA-MMAJ, 1994) Artisanal small-scale workings for Au (JICA-MMAJ, 1994) 5 samples: nil to 21.5 g t-1 Au, 0.03–0.08% Cu (Miranda & Vargas, 1967) Samples yield 0.06–6.8% Cu (Miranda & Vargas, 1967); 2 samples: 0.062 and 0.156 g t-1 Au (JICA-MMAJ, 1994) 1 sample: 1.495% Cu (JICA-MMAJ, 1994) 2 samples: 22.706 and 28.024 g t-1 Au (JICA-MMAJ, 1994) Pre-WW II artisanal small-scale workings 2 samples: nil and 0.249 g t-1 Au, 0.007 and 0.026% Cu (JICA-MMAJ, 1994) 1 sample: 0.01% Cu (JICA-MMAJ, 1994)

12

13 14

Vein Vein

YF CF

15 16

Vein Vein

YF YF

17

Vein

YF, CF

Py, Lim

Arg

Epi, Gar, skarn

†Number identifies mineral deposit in Figure 1b. ‡See Figure 1b caption for explanation of acronyms. §Cp, chalcopyrite; Hm, hematite; Mag, magnetite; Mal, malachite; Mo, molybdenite; Py, pyrite; Sph, sphalerite. Those in parentheses are present in minor amounts. ¶Arg, argillization; Epi, epidotization; Lim, limonitization; Py, pyritization; Sil, silicification. Those in parentheses are less intense alteration.

siltstone (BMG, 1982). Unconformably overlying the Catanduanes, Yop and Bonagbonag Formations is the Payo Formation, which is inferred be of Eocene age and is composed of the Cabugao sandstone, the HitomaPayo coal measures and Sipi Limestone members (Miranda & Vargas, 1967; BMG, 1982). Intruding the above volcano-sedimentary formations are the Batalay Intrusives, which consist of diorites, andesite porphyries, basalts and aplites that crop out mainly in the southern half of the island (Fig. 1b). K-Ar dating for the intrusive rocks yielded ages of 30.2 ⫾ 1.0 to 39.5 ⫾ 0.9 Ma or Eocene to Oligocene period (JICA-MMAJ,

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1994). Unconformably overlying the afore-mentioned lithologic units in the southern part of the island is the Santo Domingo Formation. Its basal portions consist of sandy to marly limestone with fossils of Late Miocene age, whereas its upper portions consist of tuffaceous to marly shale with fossils of Pliocene age (BMG, 1982). Overlying unconformably the Payo and Catanduanes Formations in the northeastern part of the island is the Pleistocene Viga Conglomerate, which consists mainly of conglomerates, with minor intercalations of sandstones and siltstones (BMG, 1982). Other lithologic units that do not appear at the scale of the map in © 2010 The Author Resource Geology © 2010 The Society of Resource Geology


Figure 1b are the Buti Hill Limestone and the San Vicente Formation, which occur in the southeastern parts of the island. The Buti Hill Limestone of Miocene age overlies unconformably the Bonagbonag Limestone, Yop Formation and Batalay Intrusives (BMG, 1982). The San Vicente Formation of Late Miocene age consists of conglomerates and sandstones that contain lithic fragments of pre-existing rocks in the island (BMG, 1982). Seventeen prospects of Au-Cu deposits have been identified in the island (Fig. 1b, Table 1). As observed in the field, most of the Au-Cu deposits are vein type although at least two of them are skarn type. There are no detailed genetic studies of the Au-Cu deposits although they are considered to be of hydrothermal origin and related to the Batalay Intrusives (Miranda & Vargas, 1967; JICA-MMAJ, 1994). The absence of pervasive hydrothermal alteration, except for silicification and pyritization, and the presence of calcite in most of the Au-Cu deposits (JICA-MMAJ, 1994) suggest that they are replacement vein-type deposits. The calcareous facies in the different host formations were likely replaced by silica (quartz) and/or re-crystallized to calcite accompanied by the deposition of precious and base metals. However, compared to the general geological/geochemical characteristics of epithermal deposits in the Philippines (UNDP, 1987; Mitchell & Balce, 1990; Mitchell & Leach, 1991), the Au-Cu prospects in the island are probably epithermal type of deposits.

3. Spatial analysis of geological controls on hydrothermal Au-Cu mineralization Analyses of the spatial pattern of known prospects of HACD and their spatial association with certain geological features afford the possibility to define relevant

geological controls on hydrothermal Au-Cu mineralization (HACM) in the study area.

3.1 Fractal analysis of the spatial pattern of prospects Previous works dealing with interpretations of geological controls on mineralization based on the spatial pattern of mineral prospects have applied fractal analysis (Carlson, 1991; Agterberg et al., 1993b; Blenkinsop, 1994, 1995; Cheng & Agterberg, 1995; Cheng et al., 1996; Blenkinsop & Sanderson, 1999; Shen & Zhao, 2002; Weiberg et al., 2004; Hodkiewicz et al., 2005; Kreuzer et al., 2007; Carranza, 2008, 2009a; Ford & Blenkinsop, 2008; Raines, 2008; Zuo et al., 2009a, b; Carranza et al., 2009; Carranza & Sadeghi, 2010; Ford & McCuaig, 2010). The fractal dimension of the spatial pattern of mineral prospects can be measured by the box-counting method. In a GIS, this involves rasterizing of locations of prospects using different cell sizes (d) and then counting in each raster map the number of cells [n(d)] containing at least one prospect. A line segment fitted through a log-log plot of n(d) versus d satisfies a power-law relation (Mandelbrot, 1985):

n (δ ) = Cδ − Db

(1)

where Db is box-count fractal dimension and C is constant of proportionality between n(d) and d. Two line segments fit the log-log plots of n(d) versus d for the 17 prospects of HACD (Fig. 2a), suggesting that spatial pattern of those prospects has two boxcount fractal dimensions: (i) for d of ⱕ10 km, Db is 0.186; and (ii) for d of >10 km, Db is 1.251. These results are consistent with results of previous works mentioned in the preceding paragraph, which suggest that spatial patterns of certain types of mineral deposits have two box-count fractal dimensions—a local-scale

Fig. 2 (a) Log-log plots (white and black dots) of box size versus number of boxes containing prospects of hydrothermal Au-Cu deposits. R2 is coefficient of regression of each fitted line. Black dot represents breakpoint of the fitted lines. (b) Graph of distances and corresponding probabilities that one occurrence of hydrothermal Au-Cu deposit is situated next to a known prospect of hydrothermal Au-Cu deposit. © 2010 The Author Resource Geology © 2010 The Society of Resource Geology

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E. J. M. Carranza

Fig. 3 Fry points (white dots) of locations (black dots) of hydrothermal Au-Cu prospects and rose diagrams trends of pairs of Fry points.

fractal dimension and a regional-scale fractal dimension. The threshold spatial scale of 10 km is also the distance, derived via point pattern analysis (see Boots & Getis, (1988) for details), from every prospect of HACD within which there is at least 0.88 probability that one prospect of HACD is present (Fig. 2b). In Figure 2a, the line segment for d of ⱕ10 km could be due to “roll-off” (Blenkinsop & Sanderson, 1999) related to (i) representation of mineral deposits as points in small-scale maps, (ii) exclusion of noneconomic mineral occurrences around prospects from the analysis, or (iii) the presence of undiscovered mineral deposits. However, the Db of the line segment for d of ⱕ10 km suggests that prospects of HACD in the island occur in clusters at local scales of ⱕ10 km, whereas the Db of the line segment for d of >10 km suggest that clusters of prospects of HACD in the island follow linear trends at regional scales of >10 km. These interpretations can be investigated further via Fry analysis.

3.2 Fry analysis of the spatial pattern of prospects Several previous works have used Fry analysis to infer structural controls on occurrences of certain types of mineral deposits (Vearncombe & Vearncombe, 1999, 2002; Raine & Blenkinsop, 2004; Stubley, 2004; Kreuzer, 2005; Blenkinsop & Kadzviti, 2006; Mondlane et al., 2006; Kreuzer et al., 2007; Carranza, 2008, 2009a, Austin & Blenkinsop, 2009; Carranza et al., 2009; Zuo et al.,

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2009a; Carranza & Sadeghi, 2010) and geothermal fields (Carranza et al., 2008). Fry analysis (Fry, 1979) is a geometrical method of spatial autocorrelation of point objects. It involves translations (so-called Fry points) of point objects by using each point object as origin for translation (see Vearncombe & Vearncombe, (1999) or Carranza (2008, 2009a) for details of creating Fry plots for mineral deposit locations). Orientations and distances between pairs of Fry points can be used for analysis of trends in the spatial pattern of point objects. For analysis of trends between any two neighbouring prospects, it is instructive to use the minimum distance within which there is maximum probability of one prospect next to every known prospect (Carranza, 2008, 2009a). The Fry points of the 17 prospects of HACD show a major WNW trend (Fig. 3). This major trend pertains mainly to the prospects in the southern part of the island, which are mostly hosted in the Yop Formation (Fig. 1b). In that part of the island, the Yop Formation follows a WNW trend, which is not necessarily the major strike of tuffaceous volcaniclastic rocks in that formation. Thus, the major WNW trend in the Fry plot of the 17 prospects of HACD is unlikely due to control on mineralization by WNW-trending geological features. However, all pairs of Fry points of the 17 prospects of HACD also show a subsidiary NNW trend, whereas pairs of Fry points within 15 km of each other show a subsidiary NE trend (Fig. 3). These subsidiary trends in the Fry plot of the 17 prospects of HACD are plausibly related to linear trends of © 2010 The Author Resource Geology © 2010 The Society of Resource Geology


clustering of prospects of HACD at spatial scales of >10 km as suggested by the box-count fractal analysis. The Fry and box-count fractal analyses imply linear trends in the spatial pattern of the 17 prospects of HACD, which are plausibly due to controls by linear geological structures such as faults/fractures. This inference can be examined further by analysis of spatial associations between the prospects of HACD and various geological features in the island.

3.3 Analysis of spatial association of prospects with geological features Geological features or data with positive spatial associations with mineral prospects are good spatial evidence of mineral prospectivity. We used point-inpolygon analysis (PPA) and distance distribution analysis (DDA) to examine spatial associations of the prospects with certain geological features and geophysical/geochemical data (cf. Bonham-Carter, 1994; Carranza & Hale, 2002; Carranza, 2008). These two analyses provide similar results as WofE analysis (Bonham-Carter, 1994), but the first two analyses were used here for examining spatial associations of the prospects with different data sets but for calculating weights of spatial evidence. In PPA, spatial association (SA) of prospects (P) with lithologic units (R) is quantified as:

SA = [ n ( P ∩ R) n ( P )] ÷ [ a ( R) a (T )]

(2)

where n(P « R) is number of P in each R, n(P) is total number of prospects, a(R) is area of each R and a(T) is size of study area. The natural logarithm (ln) of SA is akin to the W+ in WofE analysis (Bonham-Carter, 1994),

whereby positive and negative W+ mean, respectively, positive and negative spatial association between P and R. The prospects of HACD in the island have positive spatial associations with the Batalay Intrusives, Yop and Catanduanes Formations, but they have negative spatial association with the sandstone facies of the Payo Formation. (Table 2). Although only two of the prospects occur in the Batalay Intrusives, these rocks have strongest positive spatial association because they occupy smaller areas compared to the other three lithologic formations where the prospects occur. However, prospects of HACD in the Yop and Catanduanes Formations and in the sandstone facies of the Payo Formation are plausibly genetically associated with the Batalay Intrusives because these intrusives likely acted as heat-source controls on HACM in the island. This supposition can be examined via DDA. DDA involves creating graphs of cumulative relative frequency distribution of increasing distances from every location to a set of geological features (denoted as PDD1) and cumulative relative frequency distribution of increasing distances from every prospect location to the same set of geological features (denoted as PDD2). If PDD2 plots above PDD1, there is positive spatial association between the prospects and the geological features being examined. If PDD2 plots below PDD1, there is negative spatial association between the prospects and the geological features being examined. The difference PDD2–PDD1 indicates how much the frequency of prospect occurrence (i.e. PDD2) is higher (in case of positive spatial association) or lower (in case of negative spatial association) than the frequency expected due to chance (i.e. PDD1). The PDD2–PDD1 difference curve in DDA is akin to the contrast (W+–W-)

Table 2 Quantified spatial associations (SA) between prospects of hydrothermal Au-Cu deposits (P) and lithologic units (R) Lithologic units (R) (Fig. 1b)

a(R) in km2

n(P « R)

SA

ln (SA)

Alluvium Viga Formation Santo Domingo Formation San Vicente Formation Buti Hill Limestone Batalay Intrusives Payo Formation (limestone facies) Payo Formation (coal-bearing facies) Payo Formation (sandstone facies) Bonagbonag Limestone Yop Formation Catanduanes Formation

116.21 15.07 55.32 0.98 0.32 16.56 20.46 1.45 535.88 19.93 256.57 408.81

0 0 0 0 0 2 0 0 3 0 7 5

0.00 0.00 0.00 0.00 0.00 10.28 0.00 0.00 0.48 0.00 2.32 1.04

— — — — — 2.33 — — -0.73 — 0.84 0.04

a(T) = 144.56 km2 and n(P) = 17. See text for explanation of variables in the table.


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E. J. M. Carranza

Fig. 4 Difference between cumulative frequency distributions of distances from every location and from every Au-Cu prospects to (a) Batalay Intrusives (b) NE-trending faults (c) N-trending faults, and (d) NW-trending faults.

curve in WofE analysis (Bonham-Carter, 1994). The higher the difference PDD2–PDD1, the stronger the positive spatial association. Positive spatial association exists between the prospects and the Batalay Intrusives, and the positive spatial association is strongest within 6.5 km of the Batalay Intrusives (Fig. 4a). Within (i.e. at zero distance to) the Batalay Intrusives there is at least 10% higher likelihood of occurrence of HACD than would be expected due to chance. Within 6.5 km of the Batalay Intrusives, there is at most 36% higher likelihood of occurrence of HACD than would be expected due to chance. These results imply that the Batalay Intrusives are not only host-rock controls but are also likely heatsource controls on HACM in the island. Based on the styles of the Au-Cu deposits (Table 1) and based on presence of linear trends in the spatial pattern of the 17 prospects of hydrothermal Au-Du deposits (Fig. 3), linear geological features such as faults/fractures are probable structural controls on HACM in the island. Examination of this supposition via distance distribution analysis of spatial associations between the prospects and faults/fractures is deterred by the paucity of faults/fractures in the regional-scale geological map of the island (Fig. 1a). This problem was overcome by interpreting regional-scale fault/ fractures from shaded-relief images of a digital terrain model (DEM) of the island illuminated from eight dif-

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ferent directions (NW, N, NE, E, SE, S, SW, W). Figure 5 exhibits that Catanduanes Island is cut by mostly NE-, NNW- and NNE-trending faults/fractures and minor NW-trending faults/fractures. For examining the spatial association of the prospects with faults/ fractures, the NNW- and NNE-trending faults/ fractures were considered as one set (hereafter denoted as N-trending faults/fractures) and the NE- and NW-trending faults/fractures were considered as separate sets. The prospects exhibit positive spatial associations with NE- and N-trending faults/fractures and negative spatial association with NW-trending faults (Fig. 4b–d). These results are consistent with the results of the Fry analysis (Fig. 3). Within 2 km of NE-trending faults/fractures, where at least 82% of the prospects are located, there is at most 30% higher likelihood of hydrothermal Au-Cu deposit occurrence than would be expected due to chance. Within 1 km of N-trending faults/fractures, where at least 52% of the prospects are located, there is at most 27% higher likelihood of occurrence of HACD than would be expected due to chance. In contrast, within 3 km of NW-trending faults/fractures, there is at most 22% lower likelihood of occurrence of HACD than would be expected due to chance. At least 94% of the prospects are located at c. 4 km away from NW-trending faults/fractures. These results imply that NE- and © 2010 The Author Resource Geology © 2010 The Society of Resource Geology


Fig. 5 Northwest-illuminated shaded-relief image of DEM of Catanduanes Island and fault/fracture lineaments interpreted from different shaded-relief images of DEM.

N-trending faults/fractures are likely structural controls on vein-style HACM in the island.

3.4 Spatial recognition criteria of regional-scale prospectivity for Au-Cu deposits Based on the preceding spatial association analyses and the analyses of the spatial pattern of the prospects of HACD in the island, regional-scale prospectivity for HACD in the island can be defined by the following spatial recognition criteria. • Presence of rocks of the Catanduanes, Yop and Payo Formations (representing host-rock controls). • Presence of/proximity to the Batalay Intrusives (representing host-rock and heat-source controls). • Proximity to within 2 km of NE-trending faults/ fractures. © 2010 The Author Resource Geology © 2010 The Society of Resource Geology

• Proximity to within 1 km of N-trending faults/ fractures. The absence of pervasive hydrothermal alteration, except for silicification and pyritization adjacent to veins, and the presence of calcite in the veins in several of the Au-Cu deposits (JICA-MMAJ, 1994) suggest that the deposits are replacement vein-type deposits. There are certainly other spatial recognition criteria of regional-scale prospectivity for HACD in the island. For example, subsurface indications of hydrothermally altered rocks as well as unmapped structures or buried plutons can be obtained though airborne or ground magnetic and/or resistivity surveys (e.g. Hoscke & Sexton, 2005; Porwal et al., 2006b; Murakami, 2008). However, airborne geophysical data sets covering the island are unavailable. Nevertheless, multi-element (Au, Ag, As, Cu, Fe, Hg, Mo, Pb, S, Sb and Zn) geochemical data from stream sediment samples in Catanduanes Island are available (JICA-MMAJ, 1994). Catchment basin analysis of the stream sediment geochemical data (Carranza & Hale, 1997; Carranza, 2008, 2009b) results in recognition of an anomalous multi-element (As-S-Au) geochemical signature reflecting presence of HACD (Fig. 6a). To quantify spatial association of the prospects with geochemical anomalies (i.e. third principal component or PC3 scores (representing As-S-Au signature) of the stream sediment geochemical data, DDA was applied via cumulative decreasing value approach rather than via the cumulative increasing distance approach. Stream sediment sample catchment basins characterized by >1.83 (or the upper 30 percentile) PC3 scores of the geochemical data have positive spatial association with the prospects (Fig. 6b). In those stream sediment sample catchment basins (Fig. 6a), there is at most 59% higher likelihood of occurrence of HACD than would be expected due to chance (Fig. 6b). Thus, in addition to the above-mentioned spatial recognition criteria of regional-scale prospectivity for HACD in the island, the following spatial evidence was considered in this study. • Presence of multi-element geochemical anomalies (representing surficial evidence). Because the geochemical data set that was used does not cover the entire island, the derived spatial evidence of multi-element geochemical signature (Fig. 3a) is also incomplete. This certainly causes bias in the results of mineral prospectivity mapping. If an exploration data set is incomplete but is used, however, to derive a spatial evidence layer and integrated with other spatial

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E. J. M. Carranza

evidence layers in order to map mineral prospectivity, a suitable data integration method that allows representation of uncertainty due to missing data must be applied.

4. Predictive mapping of prospectivity for hydrothermal Au-Cu deposits

Fig. 6 (a) Stream sediment catchment basins characterized by an anomalous As-S-Au geochemical signature represented by high PC3 scores. (b) Difference between cumulative frequency distributions of PC3 scores at every location and at every Au-Cu prospect.

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Several GIS-based methods of PMMP are now welldeveloped. Mineral prospectivity maps derived by prudent applications of at least two different methods to a specific area have more-or-less similar fittingand prediction-rates (cf. Agterberg et al., 1993a; Harris & Pan, 1999; Singer & Kouda, 1999; Carranza, 2002, 2008; Harris et al., 2003; Agterberg and BonhamCarter, 2005; Porwal, 2006; Porwal et al., 2010a). However, every GIS-based method of PMMP has certain limitations. For example, WofE analysis (Bonham-Carter et al., 1989; Agterberg et al., 1990) and Bayesian network analysis (Porwal et al., 2006a; Porwal & Carranza, 2008), are disadvantaged by lack of conditional independence (CI) among spatial evidence layers with respect to prospect locations. In this study, lack of CI is expected between an evidence layer based on lithologic units (Fig. 1a) and an evidence layer based on proximity to Batalay Intrusives. Other methods of PMMP (e.g. application of neural networks (Singer & Kouda, 1996, 1999; Porwal et al., 2003, 2004; Nykänen, 2008), support vector machines (Porwal et al., 2010b), genetic programming (Lewkowski et al., 2010) require sophisticated algorithms that are often absent in many publiclyavailable GIS software. In addition, probabilistic neural networks are, like logistic regression (Chung & Agterberg, 1980; Carranza & Hale, 2001; Oh & Lee, 2008), affected by missing data. In this study, some parts of the island lack stream sediment geochemical data (Fig. 6a). Thus, in this work, evidential belief functions (EBFs) were used to derive and integrate maps of indices of mineral prospectivity because of the following reasons. EBFs provide explicit representation of evidence uncertainty as well as missing data (An et al., 1994). EBFs can be used to represent and integrate spatial evidence layers that lack CI among each other with respect to prospect locations, because according to Walley (1987, p. 1460) the “. . . Dempster’s rule should not be used to combine evidence from statistically independent observations . . .”. EBFs can be calculated and integrated easily by using publicly-available GIS software packages. © 2010 The Author Resource Geology © 2010 The Society of Resource Geology


4.1 Evidential belief functions The Dempster-Shafer theory of evidence provides the principle for EBFs (Dempster, 1967, 1968; Shafer, 1976). Estimation of EBFs of spatial evidence, for whatever purpose, always relates to a proposition. Here, EBFs of individual spatial evidence layers were estimated by using the locations of prospects of HACD in order to evaluate the proposition “This location is prospective for HACD”. The formalism of EBFs is complex, so the following discussion for its application here is informal and simplified. The EBFs to be estimated are degree of belief (Bel), degree of disbelief (Dis) and degree of uncertainty (Unc). The values of these EBFs are not necessarily linearly related with each other, but their sum is always unity (i.e. Bel + Unc + Dis = 1). Bel represents belief that evidence supports a proposition. Dis is belief that a proposition is false based on given evidence; it is equal to 1–Unc–Bel. However, if Bel = 0, then Dis = 0; that is because if there is no belief, then there is also no disbelief but only uncertainty. Unc represents ignorance (or doubt) that evidence supports a proposition. Note that if Unc = 0, then Bel = 1–Dis or Dis = 1–Bel as in the probability theory.

4.2 Calculation and integration of indices of hydrothermal Au-Cu prospectivity In PMMP, a suitable unit cell size (denoted as (•)), is chosen for dividing a study area (T) into a regular grid in order to calculate indices of likelihood of mineral deposit occurrence in every unit cell. The chosen (•) is roughly related to the lateral extents of every prospect (P). Based on the method proposed by Carranza (2008, 2009c) for objective selection of (•), it was found that 50 m is the most suitable (•) for spatial representation of every prospect of hydrothermal Au-Cu deposit in the island at the same 1:50,000 scale of the geological maps in Miranda and Vargas (1967) and JICA-MMAJ (1994). Thus, all maps used in this study were either rasterized (i.e. gridded) or re-sampled using a cell size of 50 m. With this cell size, total number of unit cells in the island is N(T) = 579,258 and total number of unit cells with one prospect each is N(P) = 17. The maps used as spatial evidence layers for predictive mapping of prospectivity for HACD in the island are the lithologic map (Fig. 1a), maps of distances to Batalay Intrusives, NE- and N-trending faults/fractures and catchment basin map of anomalous geochemical signature (Fig. 6a). The variables used for estimation of EBFs (Bel, Dis and Unc) of every spatial evidence layer are N(T), N(P), number of unit cells in each evidence © 2010 The Author Resource Geology © 2010 The Society of Resource Geology

class (N(Cij)) and number of unit cells with at least one prospect in each evidence class (N(Cij艚P)). In each distance-based spatial evidence layer, cell values were classified into spatial evidence classes by using certain percentile intervals of distances. Thus, for each Xi (i = 1,2, . . . n number of) spatial evidence layer, each Cij (j = 1,2, . . . ,m number of) spatial evidence class has N(Cij) number of unit cells. In the spatial evidence layer of anomalous geochemical signature (Fig. 6a), unit cells with missing geochemical data were classified as “no data”. The binary map of P is overlaid on each classified spatial evidence map to determine N(Cij艚P)]. The equations for calculation of EBFs based on a training set of prospect locations are not given here but can be found in Carranza and Hale (2003), Carranza et al. (2005) or Carranza (2002, 2008). In the island, only areas underlain by the Batalay Intrusives, Yop Formation, Catanduanes Formation and Payo Formation (sandstone facies) have Bel values of >0 and Unc values of 1 km from every prospect, estimates of PDr decrease abruptly and then monotonically (Fig. 10a). The spatial distribution of estimates of PDr reflects that areas proximal to known prospects are relatively more explored than distal areas (Fig. 10b). 5.1.3 Control unit cells for calibration of OLP OLP assumes that the geology in the control unit cells are representative of the geology associated with mineral deposits of the type sought (McCammon & Kork, 1992). The choice of control unit cells in OLP is subjective (i.e. based on expert opinion) and, thus, different choices of control unit cells are likely to yield different estimates of the number of undiscovered prospects. To avoid this problem in this work: (i) a

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Fig. 10 Degree of exploration (a) derived as prospect density in areas defined by distance from prospects and (b) depicted in a map.



neighbourhood of unit cells containing and surrounding every P was used to represent control unit cells, (ii) OLP was calibrated by using different sets of control unit cells defined by certain values of PDr, and (iii) the final estimate of the number of undiscovered prospects was derived as the average of estimates based on every set of control unit cells. This approach was followed because estimates of the number of undiscovered prospects are a function of not only geology and mineral prospectivity but also degrees of exploration (cf. McCammon & Kork, 1992). 5.1.4 Calibration of OLP parameters In the study area, there are k (= 1,2, . . . ,l) number of unit cells. The two binary classifications described above result in four classes of unit cells, namely: prospective-endowed (pM); prospective-unendowed ( pM ); unprospective-endowed ( pM); unprospectiveunendowed ( pM). The total number of Au-Cu prospects [N(TPCI)] in Catanduanes Island is then defined as:

N (TPCI )) = known prospects + unknown prospects q l ⎛ ⎞ (4) = ∑ Mk + ⎜ C × ∑ pp M (1 − PDp M )⎟ ⎝ ⎠ k =1 p M =1 where Mk is endowment score in every kth unit cell, pp M is prospectivity score and PDp M is explored portions (i.e. PDr) of individual pM (= 1,2, . . . ,q number of) unit cells. The first term in the right-hand side of Equation 4 is total number of known prospects in unit cells regardless of their prospectivity scores. The second term in the right-hand side of Equation 4 means that the number of undiscovered prospects is derived only from unexplored portions (i.e. 1 − PDp M ) of pM cells, since ppM = 0 and, thus, ppM (1 − PDpM ) = 0. Thus, the OLP assumes absence of undiscovered prospects in explored portions of individual pM cells (McCammon & Kork, 1992). The constant C in Equation 4 is derived from control unit cells, in which the number of known prospects [N(KPc)known] is the sum of endowment scores in c (=1,2, . . . d number of) control unit cells (cf. McCammon & Kork, 1992): d

N ( KPc )known = ∑ Mc = 17

(5)

c =1

The number of known prospects in control unit cells can be calculated as a function of C, p and PD of each control unit cell, thus: © 2010 The Author Resource Geology © 2010 The Society of Resource Geology

d

N ( KPc )calculated = C × ∑ pc PDc

(6)

c =1

By setting N(KPc)known = N(KPc)calculated, Equations 5 and 6 can be solved to derive C. The assumption and application of a calibration constant C to every unit cell in a study area introduces Type I and Type II errors (McCammon & Kork, 1992; McCammon et al., 1994). Type I error pertains to pM unit cells, whereas Type II error pertains to pM unit cells. Like C, estimates of Type I and Type II errors associated with C are derived from control unit cells. Formulas for estimation of Type I and Type II errors can be found in McCammon and Kork (1992), McCammon et al. (1994), Carranza et al. (2009) or Carranza and Sadeghi (2010). An area-normalized error measure (ANEM) is then defined as the absolute difference between estimates of Type I and Type II errors (McCammon & Kork, 1992). Finally, by using the ANEM, the total error associated with C for estimation of the number of undiscovered prospects in pM (=1,2, . . . ,s number of) unit cells in a study area is obtained (see formula in McCammon & Kork, [1992], McCammon et al. [1994], Carranza et al. [2009] or Carranza and Sadeghi [2010]) and then subtracted from the related estimate of the number of undiscovered prospects (i.e. the second term of the right-hand side of Eqn 4). 5.1.5 Results of OLP Based on values of PD (Fig. 10), the OLP was calibrated to estimate the number of undiscovered prospects using six sets of control unit cells. Application of calibrated C over-estimates the number of undiscovered prospects, which are corrected for total error (Table 4). Different sets of control unit cells result in different estimates of the number of undiscovered prospects (Table 5). Control unit cells with extremely low to moderate PD (i.e. ⱖ0.02) result in a high number of undiscovered prospects because such control unit cells cover large areas where many prospects are possibly undiscovered. Control unit cells with low to moderate PD (i.e. ⱖ0.06) result in a low number of undiscovered prospects because such control cells cover moderatelysized areas where many prospects probably have already been discovered. Control unit cells with moderate degrees PD (i.e. ⱖ0.20) result in a high number of undiscovered prospects because such control unit cells cover small areas and many prospects are still possibly undiscovered outside those areas.

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Table 4 Example of calibration of OLP parameters using known prospects and control unit cells with degrees of exploration ⱖ6% (i.e. with PD ⱖ 0.06), and corresponding estimate of number of unknown prospects based on the calibrated OLP parameters. Values in bold pertain to all control unit cells Calibration of OLP parameters: Variables in control unit cells Predicted prospectivity Endowment classification Number of control unit cells Number of known prospects Total number of known prospects SPD of control unit cells Total SPD of control unit cells Sp ¥ PD of control unit cells Total Sp ¥ PD of control unit cells C (= 17 ⫼ 8282.05) Type I error (=C*8277.40 ⫼ 13,708.92) Type II error (=C*0 ⫼ 13,708.92) ANEM Application of calibrated OLP parameters: Variables in study area Predicted prospectivity Endowment classification Number of unit cells Number of known endowed unit cells Sp(1 - PD) in pM cells Uncorrected number of undiscovered prospects in pM cells = [C ¥ Sp(1 - PD)] Total error = [ANEM ¥ (117,254 ¥ 10,7141.79)1/2] Corrected number of undiscovered prospects

Data and/or results in control unit cells with PD ⱖ 0.06 Prospective (p) Unprospective (p ) Endowed (M) Unendowed (M ) Endowed (M) Unendowed (M ) 13 45,764 4 39,088 13 — 4 — 17 4.65 8277.40 1.43 5425.44 13,708.92 4.65 8277.40 0 0 8282.05 0.0021 — 0.0013 — — — — 0.000 — 0.0013 Data and/or results in all unit cells in the study area Prospective (p) Unprospective (p ) Endowed (M) Unendowed (M ) Endowed (M) Unendowed (M ) 13 117,254 4 461,986 13 — 4 — — 107,141.79 — — — 225 — — — —

146 79

— —

— —

Table 5 Summary of OLP of number of undiscovered prospects based on calibrated values of C and ANEM obtained from different sets of control unit cells with degrees of exploration (i.e. values of PD) greater than or equal to a certain threshold PD of control unit cells

C

ⱖ0.02 0.0017 ⱖ0.04 0.0018 ⱖ0.06 0.0021 ⱖ0.08 0.0022 ⱖ0.10 0.0028 ⱖ0.20 0.0039 Average corrected number of undiscovered prospects =

Thus, it is important to calibrate C and ANEM by using different sets of control unit cells. On average, the results of OLP suggest that there are still 89 undiscovered prospects of HACD in the island. Validation of this result by further mineral exploration would take a sufficiently long time to find out if estimates of the number of undiscovered hydrothermal Au-Cu prospects in the island based on the OLP are accurate. However, another empirical method for estimation of the number of undiscovered prospects can be applied to cross-check the results of OLP.

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ANEM

Corrected number of undiscovered prospects

0.0008 0.0010 0.0013 0.0014 0.0019 0.0027

93 82 79 80 88 112 89

5.2 Radial-density fractal analysis of undiscovered deposits Radial-density fractal analysis of the spatial pattern of mineral deposits of a certain type can be used for estimation of undiscovered deposits (Raines, 2008). The radial-density fractal dimension of the spatial pattern of point objects can be derived according to the following power-law relation (Mandelbrot, 1983):

d = Cr Dr −2

(7)



In relation to QMRA, the radial-density power-law equations of line segments fitted by least-squares method through a log-log plot of PDr versus r can be used to estimate the total number of prospects (cf. Raines, 2008; Zuo et al., 2009b). That is, by setting PDr in Equation 3 equal to d in Equation 11, the total number of prospects, N(P)r, within areas defined by distance r (in km) from every known prospect of deposit-type, can be estimated as (adapted from Raines, [2008]):

N ( P )r = Cr Dr −2 × ( cell count )r × ( cell size ) × 0.000001 (8) 2

Fig. 11 Log-log plot (white and black dots) of prospect density versus distance r from every prospect (Eqn 3). The individual lines fitted by least-squares method through the plots satisfy the power-law relation in Equation 11. R2 is coefficient of regression of each fitted line. Black dot represents breakpoint of the fitted lines.

where d is the density of point objects in areas defined by circles of radius r from each point object, C is the constant of proportionality between d and r, and Dr is the radial-density fractal dimension of the spatial pattern of the point objects. Note therefore that the C in Equation 7 is different from the C in Equation 4, but d in Equation 7 is computationally equivalent to PDr in Equation 3. A log-log plot of d versus r, or a log-log plot of PDr versus r, allows estimation of the radial-density fractal dimensions of a set of point objects, which are roughly similar to the box-count fractal dimensions (cf. Carlson, 1991). If the plot of PDr versus r in Figure 10a is converted into a log-log plot (Fig. 11), the latter can be fitted with two line segments with a common breakpoint at r = 6.6 km. Thus, the log-log plot of PDr versus r suggests two radial-density fractal dimensions of the spatial pattern of the hydrothermal Au-Cu prospects: Dr = 0.268 for r ⱕ 6.6 km and Dr = 0.749 for r > 6.6 km. These two radial-density fractal dimensions have the same interpretations as the two box-count fractal dimensions derived earlier (Fig. 2a). Thus, the Dr for r of ⱕ6.6 km is probably due to “roll-off” effect (Blenkinsop & Sanderson, 1999) or it likely represents geological controls on HACM at local-scales, whereas the Dr for r of >6.6 km likely represents geological controls on HACM at regional-scales (cf. Agterberg et al., 1993b; Raines, 2008; Zuo et al., 2009a). © 2010 The Author Resource Geology © 2010 The Society of Resource Geology

where the constant 0.000001 converts the area of every unit cell from m2 to km2. By using the breakpoint at r = 6.6 km as regional-scale reference and, thus, by using in Equation 8 the right-hand side of the power-law equations for the two line segments in Figure 11, the following estimates are derived:

N ( P )r ≤ 6.6 = 0.327 × 6.6 −1.732 × [( cell count )r ≤ 6.6 ] × 50 2 × 0.000001 = 63; and N ( P )r > 6.6 = 0.1 × 6.6 −1.080 × [( cell count )r > 6.6 ] × 50 2 × 0.000001 = 68. These results suggest that there are 63 and 68 prospects of HACD, respectively, within and beyond 6.6 km of every known prospect of the same deposit-type and therefore the total number of prospects of this deposittype in the island is 130. Since there are 17 known prospects of HACD, the results of radial-density fractal analysis suggest there are still 113 undiscovered prospects of HACD.

5.3 Discussion In one-level prediction, high uncorrected estimates (Table 5) are due not only to assumption of fixed metal endowment per control unit cell but also to binary classification of mineral prospectivity. The latter is considered in one-level prediction because indices of prospectivity (e.g. integrated Bel) tend to lack correlation with presence/absence of mineral deposits, although locations at/around prospects generally coincide with higher indices of prospectivity compared to locations away from mineral deposits (cf. McCammon et al., 1994). However, because those two assumptions in OLP are certainly not true, the method allows for estimation and correction of errors associated with them. In Catanduanes, the average estimate of the number of undiscovered prospects of HACD obtained via

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one-level prediction is about 27% lower than the estimate obtained via radial-density fractal analysis. The main reason for this is that the average estimate obtained via one-level prediction pertains only to prospective unit cells based on the results of the predictive mapping of mineral prospectivity, whereas the estimate obtained via radial-density fractal analysis pertains to all unit cells. Thus, in Catanduanes, the different results obtained via one-level prediction and radial-density fractal analysis suggest that 24 undiscovered prospects of HACD possibly exist in areas predicted non-prospective areas that were used in the application of one-level prediction. These nonprospective areas, which have high uncertainty of prospectivity for HACD (Figs 7, 8), are likely not completely barren of this type of deposits. Although one-level prediction and radial-density fractal analysis provide comparable estimates of the number of undiscovered prospects, the former is advantageous because it considers mineral prospectivity as a function of geology and locations of prospects whereas the latter considers only locations of prospects. Thus, mineral prospectivity mapping and onelevel prediction result in geologically-sound estimates of the number of undiscovered prospects. However, it is useful to apply radial-density fractal analysis to cross-validate the results of the one-level prediction. Locations of known prospects of the deposit-type sought, which are a function of not only geology but also of mineral exploration, provide proxy measures for degree of exploration that can be used in one-level prediction of the number of undiscovered prospects. Estimates of prospect density (Eqn 3) and radialdensity fractal dimensions (Eqn 8), which relate to the spatial pattern of prospects, carry, however, some unquantifiable errors derived from mineral exploration (e.g. missed prospects due to false-negative evidence [or Type II error]). In addition, in a poorly-explored area, like Catanduanes, the spatial pattern of known prospects of the deposit-type sought is probably not representative of the spatial pattern of known and undiscovered prospects of the deposit-type sought. Therefore, estimates obtained in this study are likely conservative and must be revised as up-to-date data about mineral prospects and exploration data sets become available. Implicit in one-level prediction is the assumption that undiscovered and discovered prospects have analogous geology. Implicit in both one-level prediction and radial-density fractal analysis is the assumption that undiscovered and discovered prospects have

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analogous spatial patterns. These assumptions of analogy between undiscovered and discovered prospects are also inherent in a variety of existing methods for quantitative mineral resource assessment (cf. Bliss, 1992; Bliss & Menzie, 1993; Cox, 1993; Drew & Menzie, 1993; Singer et al., 2001, 2005; Singer, 2008; Mamuse et al., 2010). However, the geology and spatial pattern of undiscovered prospects of the type sought may differ, to some extents, from those of discovered prospects. Therefore, predictive maps of mineral prospectivity and estimates of the number of undiscovered prospects derived by any existing quantitative technique must be updated in the light of advances in geological knowledge or exploration techniques that will be made in the future. This is particularly important in Catanduanes Island where detailed genetic studies of the Au-Cu deposits are lacking.

6. Conclusions Catanduanes Island is not well-explored for hydrothermal Au-Cu deposits. The results of the present study suggest that there are still substantial undiscovered prospects for hydrothermal Au-Cu deposits. Analyses of the spatial pattern of known prospects and analysis of their spatial associations with different sets of evidential data layer are useful in predictive mapping of mineral prospectivity, the results of which can be used for estimation of the number of undiscovered prospects via the one-level prediction. Prospect density, which is a function of the spatial pattern of known prospects, can be used as proxy data for degree of exploration of individual cells for the application of the one-level prediction. One-level prediction and radialdensity fractal analysis provide comparable estimates of the number of undiscovered prospects. The present study shows therefore that (i) analysis of the spatial pattern of known prospects provides a link between predictive mapping of mineral prospectivity and quantitative mineral resource assessment, and therefore (ii) predictive mapping of mineral prospectivity can be a part of quantitative mineral resource assessment.

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