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Volume 32 Issue 2
Apr.  2021
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Emmanuel John M. Carranza. Fuzzy Modeling of Surficial Uranium Prospectivity in British Columbia (Canada) with a Weighted Fuzzy Algebraic Sum Operator. Journal of Earth Science, 2021, 32(2): 293-309. doi: 10.1007/s12583-021-1403-5
Citation: Emmanuel John M. Carranza. Fuzzy Modeling of Surficial Uranium Prospectivity in British Columbia (Canada) with a Weighted Fuzzy Algebraic Sum Operator. Journal of Earth Science, 2021, 32(2): 293-309. doi: 10.1007/s12583-021-1403-5

Fuzzy Modeling of Surficial Uranium Prospectivity in British Columbia (Canada) with a Weighted Fuzzy Algebraic Sum Operator

doi: 10.1007/s12583-021-1403-5
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  • This paper demonstrates knowledge-guided fuzzy logic modeling of regional-scale surficial uranium (U) prospectivity in British Columbia (Canada). The deposits/occurrences of surficial U in this region vary from those in Western Australia and Namibia; thus, requiring innovative and carefully-thought techniques of spatial evidence generation and integration. As novelty, this papers introduces a new weighted fuzzy algebraic sum operator to combine certain spatial evidence layers. The analysis trialed several layers of spatial evidence based on conceptual mineral system model of surficial U in British Columbia (Canada) as well as tested various models of evidence integration. Non-linear weighted functions of (a) spatial closeness to U-enriched felsic igneous rocks was employed as U-source spatial evidence, (b) spatial closeness to paleochannels as fluid pathways spatial evidence, and (c) surface water U content as chemical trap spatial evidence. The best models of prospectivity created by integrating the layers of spatial evidence for U-source, pathways and traps predicted at least 85% of the known surficial U deposits/occurrences in > 10% of the study region with the highest prospectivity fuzzy scores. The results of analyses demonstrate that, employing the known deposits/occurrences of surficial U for scrutinizing the spatial evidence layers and the final models of prospectivity can pinpoint the most suitable critical processes and models of data integration to reduce bias in the analysis of mineral prospectivity.
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Fuzzy Modeling of Surficial Uranium Prospectivity in British Columbia (Canada) with a Weighted Fuzzy Algebraic Sum Operator

doi: 10.1007/s12583-021-1403-5

Abstract: This paper demonstrates knowledge-guided fuzzy logic modeling of regional-scale surficial uranium (U) prospectivity in British Columbia (Canada). The deposits/occurrences of surficial U in this region vary from those in Western Australia and Namibia; thus, requiring innovative and carefully-thought techniques of spatial evidence generation and integration. As novelty, this papers introduces a new weighted fuzzy algebraic sum operator to combine certain spatial evidence layers. The analysis trialed several layers of spatial evidence based on conceptual mineral system model of surficial U in British Columbia (Canada) as well as tested various models of evidence integration. Non-linear weighted functions of (a) spatial closeness to U-enriched felsic igneous rocks was employed as U-source spatial evidence, (b) spatial closeness to paleochannels as fluid pathways spatial evidence, and (c) surface water U content as chemical trap spatial evidence. The best models of prospectivity created by integrating the layers of spatial evidence for U-source, pathways and traps predicted at least 85% of the known surficial U deposits/occurrences in > 10% of the study region with the highest prospectivity fuzzy scores. The results of analyses demonstrate that, employing the known deposits/occurrences of surficial U for scrutinizing the spatial evidence layers and the final models of prospectivity can pinpoint the most suitable critical processes and models of data integration to reduce bias in the analysis of mineral prospectivity.

Emmanuel John M. Carranza. Fuzzy Modeling of Surficial Uranium Prospectivity in British Columbia (Canada) with a Weighted Fuzzy Algebraic Sum Operator. Journal of Earth Science, 2021, 32(2): 293-309. doi: 10.1007/s12583-021-1403-5
Citation: Emmanuel John M. Carranza. Fuzzy Modeling of Surficial Uranium Prospectivity in British Columbia (Canada) with a Weighted Fuzzy Algebraic Sum Operator. Journal of Earth Science, 2021, 32(2): 293-309. doi: 10.1007/s12583-021-1403-5
  • Mineral deposit formation is the product of inter-play of processes that involves sources of metals/fluids, fluid pathways and physical/chemical trap mechanisms. Therefore, in mineral prospectivity modeling or mapping (MPM), the spatial evidence layers that are used to represent each of the relevant processes must to be combined logically and systematically in accordance with knowledge of mineral deposit formation. Therefore, it is beneficial to make use of an inference engine, which expresses one's hypotheses or knowledge on how different germane processes contribute and link to each other during the formation of specific kinds of mineral deposits (Porwal et al., 2015; Carranza and Hale, 2001), hence, a mineral systems methodology of MPM among the various methods of knowledge-driven MPM, fuzzy logic modeling is the most suitable for a mineral systems methodology of MPM (e.g., Porwal et al., 2015). Because, as averred by Bardossy and Fodor (2003), it is highly suitable for depiction of geological processes due to its tractability and straightforwardness.

    The fuzzy set theory (Zadeh, 1965) is the foundation of fuzzy logic modeling, which when knowledge-driven MPM characteristically involves three main feed-forward phases: (1) generation of fuzzy sets (or fuzzification) of spatial evidence; (2) logical assimilation of fuzzy spatial evidence layers with the support of an inference engine and suitable fuzzy operators; and (3) classification (or defuzzification) of the fuzzy logic modeling output to facilitate its elucidation. Among the various fuzzy operators for combining fuzzy sets (Zimmerman, 1991; Zadeh, 1983, 1973, 1965; Thole et al., 1979), the five frequently used fuzzy operators for combining layers of fuzzy spatial evidence for MPM are the fuzzy AND, fuzzy OR, fuzzy algebraic product, fuzzy algebraic sum (FAS) and fuzzy gamma (γ) (Carranza, 2008; Bonham-Carter, 1994). Of these fuzzy operators, the FAS is the most apt for combining layers of fuzzy spatial evidence for MPM that reinforce each other such that the combined fuzzy spatial evidence is more robust compared to the separate layers of fuzzy spatial evidence (Bonham-Carter, 1994). Yet, the FAS does not consider the relative contribution of each fuzzy layer of spatial evidence, and this is incompatible with knowledge that different pertinent geological processes have different relative importance in mineral deposit formation.

    A crucial aspect in the south-central British Columbia (B.C.), Canada, is that data on content of reactive U in probable source rocks exist (Culbert et al., 1984; Boyle, 1982). Thus, this paper addresses the utilization of these data in the generation and integration of layers of U-source spatial evidence to model prospectivity for surficial U in this region based on fuzzy logic modeling. As novelty, this paper proposes a weighted FAS operator for combining certain fuzzy layers of spatial evidence. Another novelty of this paper is that the deposits/occurrences of surficial U in south-central B.C. vary from those in the well-known major uranium provinces in Western Australia and Namibia; thus, requiring innovative and carefully-thought techniques of spatial evidence generation and integration. Accordingly, this paper endeavors to examine the efficacy of the individual layers of spatial evidence for delineating prospective areas for surficial U in south-central B.C.

  • Deposits of surficial uranium (U) comprise just 4% of the world's resources of U (IAEA, 2000), but they are attractive to the mining industry because they exist close the surface and so they are fairly cheap to mine. In south-central B.C. (Fig. 1) there are few deposits (n=4) and many minor occurrences (i.e., prospects, showings) (n=32) of surficial U. Descriptions of the few deposits of surficial U (with tonnages in the 24-629 kt range and U grades in the 0.01%–0.5% range) can be found in Boyle (1982) and Culbert et al. (1984). Descriptions of individual prospects/showings (with U grades in the 0.007%–0.297% range) exist in the B.C. MINFILE mineral inventory (http://minfile.gov.bc.ca/). The region's prospectivity for surficial U has not been comprehensively evaluated yet.

    Figure 1.  Deposits/occurrences (white dots) of surficial U in south-central B.C. (Canada).

    The oldest rocks that mostly underlie the region comprise the Shuswap metamorphic complex (comprised of limestones, schists, quartzites, and gneisses) (Fig. 2) (Cui et al., 2017). These rocks are overlain by Mesozoic metavolcanic-metasedimentary rocks. Intruding all these older rocks are granitoids (comprised of granodiorite, diorite, granite, monzonite and pegmatite belonging to the Okanagan Highlands intrusive complex) of Jurassic to Early Cretaceous age. All these pre-existing rocks were intruded by granitoids (porphyritic granite, quartz monzonite, and pegmatite) of Late Cretaceous to Paleocene age. Then, volcanic-sedimentary rocks (conglomerates, sandstones, mudstones, shales, basalts, andesites, rhyolites, rhyodacites, and trachytes) of Paleocene–Oligocene age deposited in separate basins on all the pre-existing rocks. Contemporary with the volcanic rocks of Paleocene–Oligocene age are granitoid intrusions of Eocene age.

    Figure 2.  Simplified map of lithostratigraphic units (modified from Cui et al., 2017, 2013) showing locations (white dots) of deposits/occurrences of surficial U in south-central B.C. (Canada).

    The deposits of surficial uranium (U) in the region occur in the form of riverine and/or playa/lacustrine U mineralization. The deposits exist within loose, permeable fluvial sediments of Late Miocene age occupying (paleo)depressions or (paleo)channels (Boyle, 1982). The age of sediments is most likely not older compared to 10 000 years (Tixier and Beckie, 2001; Culbert and Leighton, 1988; Culbert et al., 1984). The U mineralization is composed chiefly of uranous phosphate minerals such as autunite (Ca(UO2)2(PO4)2·8-10H2O), ningoyite (U, Ca)2(PO4)·1-2H2O), and saleeite (Mg(UO2)2(PO4)2·8-10H2O) (Boyle, 1982) and/or uranyl carbonates (UO2(CO3)) (Culbert et al., 1984). However, characteristic U ore minerals (e.g., carnotite (K2(UO2)2(VO4)2·3H2O), uraninite (UO2)) have still not been recognized in the region. Therefore, the region's U mineralization is seemingly still in development since U is merely fixed loosely onto sediments, from which it is remobilized easily, as there exists no favorable material (e.g., calcrete) that could play the role of both trap as well as host to surficial U mineralization (Culbert et al., 1984; Boyle, 1982).

  • Felsic volcanic or intrusive rocks with reactive U are the usual U-sources for surficial and other kinds of U mineralization (Boyle, 1984). This is seemingly true in the study region because the known deposits/occurrences of surficial U show good spatial relationship with volcanic rocks of Early Tertiary age and with granitoids of Jurassic to Early Cretaceous age (Fig. 2).

    The likely U-source in the region are volcanic rocks (rhyolite, trachyte) of Eocene age, granitoid intrusions (Coryell Monzonite) of Eocene–Oligocene age, granitoids of Jurassic to Early Cretaceous age, and the Shuswap Metamorphic Complex (composed of, among others, minor units of uraniferous pegmatites) of Paleozoic age (Culbert et al., 1984; Boyle, 1982). The Coryell Monzonite appears to be the utmost contributor of U (Table 1); however, taking into consideration the proportion of reactive U, the Okanagan pegmatites and granites are the most important U-sources in the study region.

    Rock type Average U in rock (ppb) Average reactive U (ppb) Reactive U* (%)
    Coryell Monzonite (Eocene–Oligocene) 6 200 43 0.69
    Trachyte/rhyolite (Eocene) 5 600 12 0.21
    Okanagan Granite (Jurassic–Cretaceous) 5 400 59 1.09
    Okanagan Granodiorite (Jurassic–Cretaceous) 2 300 9 0.39
    Okanagan Pegmatite (Jurassic–Cretaceous) 5 200 192 3.69
    Shuswap Gneiss (Paleozoic) 1 600 - -
    Data in the first three columns are from (Boyle, 1982). *. Each last column value is a ratio of a third column value to its corresponding second column value, and multiplied by 100.

    Table 1.  South-central B.C.: reactive U content of probable U-source rocks

  • Fabric-loosened intrusive rocks intersected by inter-connected faults/fractures benefit broadly-dispersed and entrenched flow of U-carrying groundwater, which in due course permeate pervious sediments in (paleo)channels or (paleo)depressions (Culbert et al., 1984). In these near-surface environs, U is carried by oxygenated alkaline groundwater as soluble uranyl carbonate complexes (Culbert and Leighton, 1988). The flow of water, which is concentrated in permeable (paleo)topographic lows filled with pervious riverine sediments, is driven chiefly by hydrological gradient.

  • As groundwater bearing soluble complexes of U enters trapping areas, precipitation and accumulation of U minerals may take place through a variety of ways contingent upon the kind of surficial environment of the areas where trapping occurs. In playa/lacustrine environs, lake sediments furnish both chemical and physical traps, and precipitation/accumulation may ensue chiefly by evaporation and/or by reduction owing to bacteria or organic-rich lake sediments (Culbert et al., 1984). In pervious zones of riverine (or channel) environs, precipitation and accumulation of U minerals may take place as upwelling groundwater come upon sediments or soils that are organic-rich. Because no characteristic minerals of U have been recognized yet in the study region, precipitation/accumulation of U takes place possibly because of adsorption, reduction or evaporation (Tixier and Beckie, 2001; Culbert et al., 1984). However, based on geochemical calculations by Tixier and Beckie (2001), evaporation is unlikely as groundwater has not achieved saturation relative to typical U phosphates. Tixier and Beckie (2001) also argued that reduction is somewhat unlikely because no minerals of U have been recognized even though groundwater showed changes in Eh. It follows that, in the study region, the most possible prevalent control on U mineralization in riverine (or channel) systems is adsorption, followed by reduction (Tixier and Beckie, 2001).

  • Because published knowledge exists about the study region's deposits/occurrences of surficial U and because data of locations of these deposits/occurrences exist, either knowledge- or data-driven methodology of MPM may be followed to outline targets for surficial U exploration in the region. Yet, several researchers have debated that expert knowledge of geological features, which are geogenically and spatially related to mineral deposits of interest, is quite biased and convey systemic uncertainty in knowledge-driven MPM. Such kind of uncertainty can also originate from "black-box" methods of data-driven MPM. In contrast, insufficient or low-quality evidential data and scarce locational data of mineral deposit/occurrence convey stochastic uncertainty in data- or knowledge-driven MPM. Clearly, ample and high-quality evidential data are required for data- or knowledge-driven MPM. Nevertheless, recently, several researchers have propositioned to take up a mineral systems methodology for modeling/mappin prospectivity in order to reduce chiefly systemic uncertainty (Occhipinti et al., 2016; Kreuzer et al., 2015; Joly et al., 2015; Lisitsin et al., 2013; McCuaig et al., 2010; Porwal and Kreuzer, 2010). A formative study on the use of mineral systems methodology to analyze prospectivity for six kinds of U systems was discussed by Kreuzer et al. (2010), and a formative study on the use of such methodology to analyze prospectivity for surficial U was discussed by Porwal et al. (2015).

    The mineral systems methodology for modeling of prospectivity needs expert knowledge of the source-transport-trap system of formation of mineral deposits under study and its use to generate and combine spatial layers (or evidential images) from appropriate spatial geoscience data. Porwal et al. (2015) initially demonstrated a mineral systems methodology using a geographic information system (GIS) for modeling prospectivity for surficial U in Yeelirrie area (Western Australia). There, deposits/occurrences of surficial U exist as calcrete-hosted carnotite (Cameron, 1984); but, deposits/occurrences of surficial U in south-central B.C. vary from those in Western Australia and Namibia. Mineralization of surficial U in south-central B.C. is on-going and no characteristic minerals of U have been formed yet. The reason is that U is attached loosely to sediments, from which it is remobilized easily, as no suitable matter (e.g., calcrete) exists there to act both/either as trap for and/or host to surficial U mineralization (Boyle, 1984; Culbert et al., 1984). Thus, the surficial U system in south-central B.C. varies from those in Western Australia or Namibia. Accordingly, the GIS-based methodology propositioned by Porwal et al. (2015) to model regional-scale prospectivity for surficial U in Yeelirrie is modified in this paper for usage in south-central B.C.

  • The mineral system of the region's deposits/occurrences of surficial U exhibits similarities to as well as differences from the mineral systems of the world's most significant surficial U deposits, which exist as calcrete-hosted carnotite (K2(UO2)2(VO4)2·3H2O) (Khoury, 2014; Misra et al., 2011; Cameron, 1984; Carlisle, 1984). Therefore, targeting criteria and layers of spatial evidence for the analysis and modeling of the study region's prospectivity for surficial U will vary to some extent from those discussed by Porwal et al. (2015) for analysis and modeling of surficial U prospectivity in the Yeelirrie area (Australia).

  • The targeting criterion for U-sources considered appropriate here for modeling the study region's regional-scale prospectivity for surficial U is described in Table 2.

    Targeting criterion Spatial evidence Source of data Justification
    Felsic (volcanic or intrusive) rocks that contain reactive U Presence of or closeness to felsic rocks that contain reactive U 1. Regional-scale lithologic map (Cui et al., 2013)
    2. Total and reactive U contents of felsic rocks (Boyle, 1982)
    Felsic (intrusive or volcanic) rocks are characteristically enriched in U and are generally regarded as chief U-sources for majority of mineral systems of U, however, not all felsic rocks have significant amounts of reactive U

    Table 2.  South-central B.C. (Canada): spatial evidence of U-source targeting criterion of regional-scale prospectivity for surficial U

    Closeness (i.e., Euclidean distance) to U-rich granites has been used by Porwal et al. (2015) as spatial evidence of U-rich Archean granites to represent U-source targeting criterion for surficial U systems in the Yeelirrie area. This strategy is insightful because reactive U is transported, by groundwater, from source rocks and mineralization of surficial U may take place either on areas with underlying U-source rocks or on areas in the vicinity of such rocks. However, in this paper, Euclidean distance was converted into fuzzy closeness to depict probability-like values (i.e., 1 for closest and 0 for farthest distance in an image) so that, as in Porwal et al. (2015), the fuzzy set theory can be used for MPM. To transform Euclidean distance into fuzzy closeness, a non-linear function was used here instead of a linear function because favorability for mineralization is not a linear function of closeness to geological features that control mineral deposit formation. A non-linear function that is usually applied to represent layers of spatial evidence for MPM is the logistic function (Sanusi and Amigun, 2020; Yousefi and Carranza, 2015; Carranza, 2010, 2008; Nyknen et al., 2008; Porwal et al., 2006, 2003). The logistic function applied herein was

    In this equation, x represents the values (e.g., distances) being transformed to the range [0, 1], m the selected inflection point of the function, s the slope of the function, and e the Euler number.

    In this study, for representation of closeness to U-source rocks, m was selected to be 10 km to depict that in locations of at most 10 km from a source (or a pathway, or a trap) there is 0.5–1.0 possibility of mineralization for surficial U but in locations farther than 10 km from a source (or a pathway, or a trap) there is < 0.5 possibility of U mineralization for surficial. The selection of m is subjective and definitely needs expert opinion; the use of 10 km for m here to model closeness to U-source rocks was intended for illustrating the method rather than a tender of expert knowledge. The images of fuzzy closeness to mapped units of U-source rocks obtained from the corresponding images of Euclidean distance to these units are shown in Figs. 3, 4, 5.

    Figure 3.  Distance transformed (a), using Eq. (1), to fuzzy closeness (b), proximity to Coryell plutonic suite (represented by polygons in black outlines) in south-central B.C. (Canada). White dots depict deposits/occurrences of surficial U. Image coordinates are the same as in Figs. 1 or 2.

    Figure 4.  Distance transformed (a), using Eq. (1), to fuzzy closeness (b), proximity to Eocene volcanic rocks (represented by polygons in black outlines) in south-central B.C. (Canada). White dots depict deposits/occurrences of surficial U. Image coordinates are the same as in Figs. 1 or 2.

    Figure 5.  Distance transformed (a), using Eq. (1), to fuzzy closeness (b), proximity to Okanagan batholith (represented by polygons in black outlines) in south-central B.C. (Canada). White dots depict deposits/occurrences of surficial U. Image coordinates are the same as in Figs. 1 or 2.

    The U-rich granite map used by Porwal et al. (2015) was prepared by combining radiometric data, geochemical map of U content, and lithologic map. This practice was, however, skipped here as the existing lithologic map (Fig. 2) was a product of combining surficial and bedrock geology, and geochemical and geophysical data analyses (Cui et al., 2017). Yet, here, data on total and reactive U content of felsic rocks (Boyle, 1982) were available and these data posed a new task for spatial data fusion in this situation because the previous work of Kreuzer et al. (2010) and Porwal et al. (2015) did not deal with such kind of data.

    Even though total and reactive U data exist for various latent U-source rocks (Table 1), the existing regional-scale geological map (Cui et al., 2017) shows only the (a) Coryell Plutonic Suite, comprising other felsic plutonic rocks aside from monzonite, (b) Eocene volcanic rocks, comprising other felsic volcanic rocks aside from rhyolite/trachyte, and (c) Okanagan Batholith or intrusive complex, comprising other felsic intrusive rocks aside from pegmatite, granodiorite, and granite. However, because the particular rocks for which reactive U data exist are typical of the aforesaid mapped rock units, it was shown in this study how such data can be employed as weights for closeness to mapped units of latent U-source rocks. Accordingly, the percentage of reactive U data of Coryell monzonite was assigned to the Coryell Plutonic Suite, the percentage of reactive U data of Eocene trachyte/rhyolite to the Eocene volcanic rocks, and the mean percentage of reactive U data of Okanagan pegmatite, granodiorite and granite (Table 1) to the Okanagan Batholith (Table 3). Then, to derive the weights, each percentage was divided by their sum (Table 3).

    Rock type % of reactive U (*1) Spatial weight (*3)
    Coryell Plutonic Suite (monzonite) 0.69 0.28
    Eocene volcanic rocks (rhyolite/trachyte) 0.21 0.08
    Okanagan Batholith (pegmatite, granodiorite, granite) 1.72 (*2) 0.66
    Except where indicated, data in this column are from the last column of Table 1. Mean % of reactive U in rocks in the Okanagan Batholith given in Table 1. Figures in this column are ratios of each value in the second column to their sum.

    Table 3.  South-central B.C. (Canada): weights of closeness to rock units as probable sources of reactive U for mineralization of surficial U

    Because there are now three images of distances to every mapped unit of latent U-source rocks (Figs. 3 (left panel), 4 (left panel), 5 (left panel)) and their respective weights (Table 3), the following task was concerned with how to integrate these images, employing their weights, into one image of fuzzy closeness to all latent U-source rocks. Integrating these images is insightful as the reactive U derived from the different source rocks is ultimately blended together in groundwater. For this image integration task, the FAS was deemed the most appropriate among the five frequently applied fuzzy operators (see An et al. (1991), Bonham-Carter (1994), Carranza (2008)) because it is appropriate when more than two layers of evidence (here, images of closeness to latent U-source rocks) for a proposition (here, prospectivity for surficial U) support one another and the combined evidence layer is more robust compared to each of the separate evidence layers (cf. Bonham-Carter, 1994). However, the outcome of applying the existing equation for FAS (see Bonham-Carter (1994), Carranza (2008)), shown in Fig. 6a, is seemingly poor because the image look like chiefly the image of fuzzy closeness to Eocene volcanic rocks (Fig. 4, right panel) hinting that the volcanic rocks of Eocene age are the most significant U-source. Even though rhyolites are commonly regarded as significant U-sources (Bonnetti et al., 2017; Chabiron et al., 2003; Page, 1983; Zielinski, 1983, 1978; Cunningham et al., 1982; Lindsey, 1982; Kazanskiy et al., 1977), this common fact conflicts with the reactive U information regarding the latent U-source rocks in the study region (Tables 1 and 3). Therefore, to apply the weights (symbolized as w) to integrate the three evidence layers of fuzzy closeness to latent U-source rocks (symbolized as μi, i=1, 2, 3), the existing FAS equation (see Bonham-Carter (1994), Carranza (2008)) was adapted here into a weighted FAS (hereafter denoted as wFAS) as

    Figure 6.  Images of combined fuzzy closeness to probable U-source rocks (a), using conventional FAS (see Bonham-Carter (1994), Carranza (2008)) and combined fuzzy closeness to probable U-source rocks (b), using the propositioned wFAS, Eq. (2)) in south-central B.C. (Canada). White dots depict deposits/occurrences of surficial U. Image coordinates are the same as in Figs. 1 or 2.

    The image resulting from the application of Eq. (2) (Fig. 6b) is seemingly reasonable because it depicts the Okanagan Batholith as the most significant latent source rock of U (cf. Fig. 5 (right panel), Table 3), while the Eocene volcanic rocks and the Coryell Plutonic Suite have minor significance. Yet, the quantified spatial relationships of the known deposits/occurrences of surficial U with each of the images in Fig. 6 suggest that both images have nearly-equal quality as spatial predictors of the study region's prospectivity for surficial U (Fig. 7). Thus, this gives the impression that applying the weights derived from the reactive U data was frivolous for modeling of spatial evidence of latent U-source rocks. As no previous study has examined this issue, this initial appraisal of the efficiency of the derived (non-weighted and weighted) layers of U-source spatial evidence for modeling of the study region's surficial U prospectivity will be reconsidered in the following section, in which all the individual layers of spatial evidence were combined for that purpose.

    Figure 7.  Plots portraying the spatial relationship of the known deposits/occurrences of surficial U with image of combined fuzzy closeness to probable U-source rocks (Fig. 6a) and with the image of combined fuzzy weighted closeness to probable U-source rocks (Fig. 6b). The method for creating these plots is described in Agterberg and Bonham-Carter (2005).

  • As what Porwal et al. (2015) have done, one criterion for pathways is appropriate for modeling of the study region's regional-scale prospectivity for surficial U (Table 4).

    Targeting criterion Spatial evidence Source of data Justification
    Tertiary–recent p aleochannels Closeness to paleochannels (1) SRTM digital elevation model
    (2) ASTER thermal infrared data
    Driven by gravity, near-surface (U-carrying) groundwater flows through pervious soils/sediments in (paleo)topographic lows. An image of river/stream network is usable as evidence for pathways if major river/stream systems are already dormant.

    Table 4.  South-central B.C. (Canada): spatial evidence of pathways targeting criterion of regional-scale prospectivity for surficial U

    Using a digital elevation model (DEM) and night-time thermal infrared data obtained by ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer) enables interpretation/mapping of topographic features in the near-subsurface (e.g., paleochannels) (Thakur et al. 2016; Stamoulis, 2006). ASTER data are available for free from NASA (http://asterweb.jpl.nasa.gov/data.asp). ASTER DEM or SRTM (Shuttle Radar Topography Mission) DEM are likewise available for free from the USGS (http://gdex.cr.usgs.gov/gdex/). As the MPM work described here is regional in scale, SRTM DEM with 90-m pixel size was utilized rather than ASTER DEM with 30-m pixel size. An image of Euclidean distance to detected paleochannels was then created, and it was transformed using Eq. (1) (with m=10 km) into an image of fuzzy closeness to paleochannels as pathways spatial evidence. Majority of the known deposits/occurrences of surficial U exists near paleochannels (Fig. 8). However, Fig. 9 informs that mineralization of surficial U is nearly absent in 20% of the region's areas within ~2 km of detected paleochannels, although many (i.e., 10%–90%) of the known deposits/occurrences surficial U exist in the next 20%–50% of the region's areas within 2-5 km of detected paleochannels.

    Figure 8.  Distance transformed (a), using Eq. (1), to fuzzy closeness (b), proximity to interpreted paleochannels (black lines) in south-central B.C. (Canada). White dots depict deposits/occurrences of surficial U. Image coordinates are the same as in Figs. 1 or 2.

    Figure 9.  Plot portraying the spatial relationship of the known deposits/occurrences of surficial U with image of fuzzy closeness to interpreted paleochannels (Fig. 8, right panel). The method for creating this plot is described in Agterberg and Bonham-Carter (2005).

    Three conceivable reasons can be offered for the modeled spatial relationship between detected paleochannels and the study region's known deposits/occurrences of surficial U (Fig. 9). Firstly, as mineralization of surficial U in the study region is most likely not older than 10 000 years (Tixier and Beckie, 2001; Culbert and Leighton, 1988; Culbert et al., 1984) and is seemingly still developing and because U is remobilized easily, it is probable that the known deposits/occurrences of surficial U have "migrated from their initial depositional sites at/near paleochannels to their present locations". Secondly, the data of surficial U deposits/occurrences (Tixier and Beckie, 2001; Culbert and Leighton, 1988, 1978; Boyle, 1984, 1982; Carlisle, 1984; Culbert et al., 1984) are not current, but the DEM and ASTER data employed to detect paleochannels are current and have good accuracy. Thirdly, the detected paleochannels are not accurate and imprecise. As the second and third conceivable reasons are more confirmable and are mendable, future/further work of modeling the study region's prospectivity for surficial U must nonetheless endeavor to create map of paleochannels with better accuracy and precision. The reason for that is paleochannel sediment-fills provide aquifers needed to transport U from probable sources.

  • Mineralization of surficial U needs traps, both physical and chemical ones. The former restrict where surficial U deposition occurs, whereas the latter make available the chemical conditions that favor the accumulation and amelioration of U and for the development of U deposits.

  • For modeling of the study region's regional-scale prospectivity for surficial U, layers of spatial evidence for two targeting criteria for physical traps can be generated bearing in mind available regional-scale data (Table 5).

    Targeting criteria Spatial evidence Source of data Justification
    Almost-torpid water in channels (Porwal et al., 2015) Almost-plain topographic depressions SRTM DEM U precipitates at/near surface from almost-torpid water in channels (Porwal et al., 2015), and thus in topographic depressions with plain or almost-plain slopes, as it is likely that rates of evaporation and fluid modification in such locales are higher than in locales with dissimilar topographic features (e.g., ridges)
    Size of source area (Porwal et al., 2015) Flow accumulation (Porwal et al., 2015) SRTM DEM Locales that collect river/stream water flow from large U-source rock areas will possibly accumulate, enhance, and collect more U. An image of flow accumulation is a sound spatial evidence that approximates extents of areas with underlying probable U-source rocks from which specific locales accumulate water

    Table 5.  South-central B.C. (Canada): spatial evidence of physical traps targeting criteria of regional-scale prospectivity for surficial U

    The SRTM DEM with 90-m pixel size (Fig. 10a) was used to create a regional-scale image of channel slopes as spatial evidence for almost-torpid water in channels. Channels (or topographic depressions) can be detected from a second vertical derivative image of the SRTM DEM (Fig. 10b); in such image, values > 0 and < 0 depict depressions and ridges, respectively, and values $ \cong $0 depict somewhat plain areas. From Fig. 10b, it can be seen that the region's deposits/occurrences of surficial U are sited largely in locales with values > 0 (i.e., depressions) or values $ \cong $0 (i.e., plain areas).

    Figure 10.  Images of SRTM DEM with elevation in meters (a) and 2nd-derivative of SRTM DEM (b) in south-central B.C. (Canada). White dots depict deposits/occurrences of surficial U. Image coordinates are the same as in Figs. 1 or 2.

    To reveal slopes in topographic depressions, slope was calculated for every pixel in the SRTM DEM (Fig. 11a). Examination of the 2nd-derivative image of the SRTM DEM (Fig. 10b) and the slope image (Fig. 11a) shows that, in the former image, plain areas have values in the range [-2, 2] whereas depressions have values > 2. This information is taken as basis for creation of an image of fuzzy almost-plain topographic depressions (Fig. 11b); that is, allocation of 0 to non-plain areas and non-depressions (i.e., with 2nd-derivative values of ≤-2) and then transformation of slopes in locales with 2nd-derivative values of more than -2 into the fuzzy range [0, 1] using Eq. (1) with m specified as 10 (degrees). The study region's deposits/occurrences of surficial U are sited largely in locales with values of ~1 in the image of fuzzy almost-plain topographic depressions (Fig. 11b).

    Figure 11.  Images of slope calculated from SRTM DEM (a) and fuzzy almost-plain topographic depressions (b) in south-central B.C. (Canada). White dots depict deposits/occurrences of surficial U. Image coordinates are the same as in Figs. 1 or 2.

    With a DEM, flow accumulation can be calculated (e.g., O'Callaghan and Mark (1984) so as to create an image of catchments that can be used spatial evidence for size of source area from which water flow. This entails six steps (O'Callaghan and Mark, 1984): (1) sinks in a DEM were filled, (2) flow direction was calculated, (3) flow accumulation was calculated according to flow direction, (4) streams were extricated according to flow accumulation, (5) stream orders were labeled according to flow direction and elevation, and finally (6) catchments were extricated for the same highest stream order. Figure 12a shows the catchments extricated from the study region's SRTM DEM. No catchments were extricated along the study region's edges, especially the eastern parts, as no streams with the same highest order were labeled in those areas. Then, the areas of individual catchments were established and the range of smallest-largest catchment sizes was re-scaled linearly into a fuzzy range of 0.100–0.999. The preference for this fuzzy range is subjective and, although expert opinion is needed in practice for the preference of a fuzzy range, it was intended for instructing the method here but not a tender of expert knowledge. The linearly re-scaled fuzzy scores were subsequently assigned to the corresponding catchments, and areas external to the extricated catchments were given a fuzzy score of 0.001. Similarly, the preference here for this minimum fuzzy score is subjective and not a tender of expert knowledge but simply for demonstrating the method. Figure 12b shows the created image of fuzzy flow accumulation (or catchment area).

    Figure 12.  Images of drainage catchment calculated from SRTM DEM (a) and fuzzy flow accumulation (b). Streams of the same highest order are depicted as black lines in south-central B.C. (Canada). White dots depict deposits/occurrences of surficial U. Image coordinates are the same as in Figs. 1 or 2.

    The maximum fuzzy score of 0.999 corresponds to the largest flow accumulation in the study region's north-eastern portion. However, majority of the known deposits/occurrences of surficial U exists in the catchment with the second next largest flow accumulation in the study region's south-central part; the fuzzy score of this catchment is 0.883. The catchment with the smallest flow accumulation, and thus assigned the minimum fuzzy score of 0.1, in the study region's north-western portion encloses a couple of known occurrences of surficial U.

    It can be seen from Fig. 13 that the image of fuzzy almost-plain depressions is a weaker physical trap spatial evidence compared to the image of fuzzy flow accumulation. That is, 36% of the region with the maximum chance of being almost-plain depression encloses only 60% of the known deposits/occurrences of surficial U while the same percentage of the region with the maximum flow accumulation encloses 94% of the known deposits/occurrences of surficial U. This is quite insightful because there are likely numerous areas in the study region with almost-plain depression, although it is doubtful if all or most of these areas are linked to groundwater whereas catchments with streams/rivers of the same highest order are conceivably likely linked to groundwater. Confining slope calculation to palaeochannels only is likely better, but that would need thorough and precise mapping of palaeochannels, which is not the scope of this paper. However, this preliminary assessment of the effectiveness of these layers of physical trap spatial evidence will be returned to after all the layers of spatial evidence have been combined to model prospectivity for surficial U.

    Figure 13.  Plots portraying the spatial relationship of the known deposits/occurrences of surficial U with image of fuzzy almost-plain topographic depressions (Fig. 11b) and the image of fuzzy flow accumulation (Fig. 12b). The method for creating this plot is described in Agterberg and Bonham-Carter (2005).

  • Because this case study involves analysis of regional-scale prospectivity for surficial U, prospectivity for lacustrine or riverine sub-type of deposits is distinguished. Thus, control by reduction on either lacustrine or riverine sub-type of surficial U mineralization (Tixier and Beckie, 2001; Culbert et al., 1984) is modeled here. For district- to local-scale modeling of prospectivity for surficial U, it is crucial to create a layer of spatial evidence of evaporation for lacustrine systems (Culbert et al., 1984) and to create a layer of spatial evidence of adsorption for riverine systems (Tixier and Beckie, 2001).

    For analysis of the study region's regional-scale prospectivity for surficial U, layers of spatial evidence representing two targeting criteria for chemical trap can be generated based on available regional-scale data (Table 5). Both of the layers of spatial evidence created here for modeling of regional-scale prospectivity, stream water alkalinity and U-richness (Table 6), essentially indicate amelioration of aqueous uranyl complexes in surface waters. Thus, it can be argued that these layers of spatial evidence are perhaps more suggestive of the presence of good complexing ligands and good U-sources instead of chemical traps (i.e., near-surface alkaline waters would transport U as soluble complexes of uranyl carbonates/phosphates). However, whereas stream waters depict mixtures of sources upslope/upstream of every sample site, the physical and chemical properties of stream waters that were recorded at the time sampling pertain to the physical and chemical conditions at every sample site. It follows that alkalinity and U-richness of stream waters measured at sampling sites can be regarded as results of chemical trapping processes at those sites rather than upslope/upstream of such sites. All the same, a detailed soil classification image would be a desirable source of spatial evidence for chemical traps pertinent to surficial U mineralization but such image was not available for this study.

    Targeting criteria Spatial evidence Source of data Justification
    Bicarbonate contents of river/stream waters Alkalinity of river/stream waters pH of river/stream waters (Lett, 2011) Strongly alkaline waters typically contain bicarbonates in the range of 50 ppm–600 ppm, which boost considerably the capacity of soils/sediments along (paleo)topographic lows to collect U (Culbert et al., 1984).
    U-rich groundwater U-richness of river/stream waters U content of river/stream waters (Lett, 2011) Dispersal of U from sources and concentration of U in surface water as well as groundwater permits huge quantities of this metal to be transported to traps, where deposits of surficial U form.

    Table 6.  South-central B.C. (Canada): spatial evidence of chemical traps targeting criteria of regional-scale prospectivity for surficial U

    To create layers of spatial evidence depicting variations in bicarbonate (representing alkalinity) and U contents (representing U-richness) of stream waters in the study region, data on stream water pH and U concentration (Lett, 2011) were used. The pH and U stream water data pertain to 3 338 samples collected from the study region (Lett, 2011), (Fig. 14a), denoting a mean sampling density of 1 sample per 13 km2, which is conventional for geochemical surveys at regional-scales. The semi-variograms of these data show very strong spatial autocorrelations stream water pH and U (Figs. 14b, 14c), signifying defensibility of interpolating the individual point data to depict the spatial patterns of the variables as continuous-value images (Fig. 15 left panel, Fig. 16 left panel).

    Figure 14.  (a) stream water samples (dots) overlain on shaded-relief image of SRTM DEM; (b) semi-variogram of stream water pH; (c) semi-variogram of stream water U content in south-central B.C. (Canada). Image coordinates are the same as in Figs. 1 or 2.

    Figure 15.  Stream water pH (a) transformed, using Eq. (1) with a negative value for s and a pH=7 for m, to fuzzy stream water alkalinity (b) in south-central B.C. (Canada). White dots depict deposits/occurrences of surficial U. Image coordinates are the same as in Figs. 1 or 2.

    Figure 16.  Stream water U content (a) transformed, using Eq. (1) with a negative value for s and a value of 2 ppb for m, to fuzzy U-richness of stream water (b) in south-central B.C. (Canada). White dots depict deposits/occurrences of surficial U. Image coordinates are the same as in Figs. 1 or 2.

    Figures 15 and 16 show that the known deposits/occurrences of surficial U are present in locales where stream waters are alkaline and U-rich, which either overlap or are close to interpreted paleochannels (Fig. 8). However, Fig. 17 shows the image of fuzzy stream water alkalinity is a weaker chemical trap spatial evidence compared to the image of fuzzy U-richness of stream waters. This is plausible, as, even though alkaline stream waters may exist in numerous places in the region particularly in the western portions (Fig. 15, left panel), the most important source rocks that release reactive U into the stream waters are present mostly in the study region's south-eastern to south-central portions (Fig. 6b).

    Figure 17.  Plots portraying the spatial relationship of the known deposits/occurrences of surficial U with image of fuzzy stream water alkalinity (Fig. 15, right panel) and the image of fuzzy U-richness of stream waters (Fig. 16, right panel. The method for creating this plot is described in Agterberg and Bonham-Carter (2005).

  • Because surficial U mineralization is the end-product of the interaction of processes that depict sources, pathways and traps, the layers of spatial evidence created to represent these processes must be integrated methodically to model their interactions. Therefore, it is beneficial to implement an inference engine, which replicates one's understanding or suppositions regarding the interactions of processes associated with the development of specific kinds of minerals deposits (Porwal et al., 2015; Carranza and Hale, 2001). Thus, a mineral system approach, as in Porwal et al. (2015), a fuzzy inference engine (Fig. 18) was used here for modeling of the study region's prospectivity for surficial U according to the arguments in the previous sections with regard to the surficial U system and the layers of spatial evidence representing the regional-scale criteria for targeting surficial U. Accordingly, the theory of fuzzy set (Zadeh, 1965) was applied here because, as claimed by Bardossy and Fodor (2003), it is the most suitable for depiction of geological processes by reason of its straightforwardness and tractability.

    Figure 18.  Inference engine for combining layers of spatial evidence for modeling of the study region's regional-scale prospectivity for surficial U.

    Every part of a fuzzy inference engine, whereby no less than a couple layers of spatial evidence are combined with the use of an appropriate fuzzy operator, relates to a proposition about the interaction of no less than a couple of processes associated with mineral deposit formation. Hence, a fuzzy inference engine establishes a sequence of coherent rules, which successively combines (through the use of appropriate fuzzy operators) images of fuzzy spatial evidence. It likewise functions to negate the influence of ambiguous spatial evidence. For instance, topographic depressions that are almost-plain are nearly ubiquitous in the region (Fig. 11). However, it is definitely unlikely that each almost-plain topographic depression is associated with mineralization of surficial U. Thus, by rationally combining the fuzzy spatial evidence of almost-plain depression with another fuzzy spatial evidence, such as fuzzy flow accumulation, just the involvements of both or either of the two images of fuzzy spatial evidence are recorded in the result conditional to the proposition of mineral deposit formation. There are no customary rules for hypothesizing a fuzzy inference engine but it must model sufficiently one's understanding of the pertinent system of mineralization. Therefore, as considered in the previous section, the following operations were performed according to the fuzzy inference engine portrayed in Fig. 18.

    The individual layers of spatial evidence of probable U-source rocks (Figs. 35) were integrated into an image of combined spatial evidence of probable U-source rocks (Fig. 6b) by applying the propositioned wFAS operator (Eq. (2)). This image of combined spatial evidence of probable U-source rocks was assessed if it is more effectual than an image of combined spatial evidence of probable U-source rocks (Fig. 6a) produced by applying the conventional FAS (see Bonham-Carter (1994), Carranza (2008)).

    The layers of fuzzy spatial evidence of stream water alkalinity and U-richness (Figs. 15 and 16, respectively) were integrated into an image of combined spatial evidence of chemical traps (Fig. 19a) via fuzzy AND operator (Fig. 18) as both U-richness and alkalinity of stream water are needed to form and concentrate deposits of surficial U.

    Figure 19.  Images of combined fuzzy chemical traps (a) and combined fuzzy physical traps (b) in south-central B.C. (Canada). White dots depict deposits/occurrences of surficial U. Image coordinates are the same as in Figs. 1 or 2.

    The layers of fuzzy spatial evidence of almost-plain depressions (Fig. 11b) and flow accumulation (Fig. 12b) were integrated into an image of spatial evidence of physical traps (Fig. 19b) via fuzzy OR operator as either almost-plain depressions or catchments with large flow accumulation may be adequate to confine where deposits of surficial U may develop. Yet, almost-plain depressions are apparently suitable spatial evidence for local-scale rather than regional-scale physical traps. Thus, it was assessed if it was more effectual to employ an image of combined spatial evidence of physical traps than to employ only spatial evidence of flow accumulation in modeling of the study region's regional-scale prospectivity for surficial U.

    Lastly, the spatial evidence of pathways (Fig. 8, right panel) was integrated with the images of combined spatial evidence of U-sources and chemical/physical traps via fuzzy AND operator, as the corresponding processes signified by these layers of spatial evidence are all needed to form surficial U deposits.

    Figure 20a shows the output of integrating the layer of combined spatial evidence of U-sources obtained via the propositioned wFAS operator (Eq. (2)) with the layer of spatial evidence of pathways, combined layer of fuzzy chemical traps and combined layer of fuzzy physical traps; this output is denoted fuzzy prospectivity model 1a. Figure 20b shows the output of integrating the layer of combined spatial evidence of U-sources obtained via the conventional FAS operator (see Bonham-Carter (1994), Carranza (2008)) with the layer of spatial evidence of pathways, combined layer of fuzzy chemical traps and combined layer of fuzzy physical traps; this output is designated fuzzy prospectivity model 2a. Among these outputs, the latter is worse as its maximum fuzzy scores, which occupy 10% of the region, predict just 36% of the known deposits/occurrences of surficial U but the maximum fuzzy scores of the former, which also occupy 10% of the region, predict 92% of the known deposits/occurrences surficial U. Thus, the combined spatial evidence of U-sources obtained via the propositioned wFAS operator (Eq. (2)) was more effectual compared to the combined spatial evidence of U-sources obtained via the conventional FAS operator (see Carranza, 2008; Bonham-Carter, 1994).

    Figure 20.  Fuzzy prospectivity model 1a derived by integrating the combined spatial evidence of U-sources obtained via the propositioned wFAS operator (Eq. (2)), spatial evidence of pathways, combined fuzzy chemical traps and combined fuzzy physical traps (a); and fuzzy prospectivity model 2a (b) derived by integrating the combined spatial evidence of U-sources obtained via the conventional FAS operator (see Bonham-Carter (1994), Carranza (2008)), spatial evidence of pathways, combined fuzzy chemical traps and combined fuzzy physical traps (right) in south-central B.C. (Canada). White dots depict deposits/occurrences of surficial U. Image coordinates are the same as in Figs. 1 or 2.

    Figure 22b shows the output of integrating the layer of combined spatial evidence of U-sources obtained via the propositioned wFAS operator (Eq. (2)) with the layer of spatial evidence of pathways, layer of combined fuzzy chemical traps and layer of fuzzy flow accumulation; this output is denoted as fuzzy prospectivity model 1b. Figure 22a shows the result of integrating the layer of combined spatial evidence of U-sources obtained via the conventional FAS operator (see Bonham-Carter (1994), Carranza (2008)) with the layer of spatial evidence of pathways, layer of combined fuzzy chemical traps and layer of fuzzy flow accumulation; this output is denoted as fuzzy prospectivity model 2b. Among these outputs, the first one is worse as its maximum fuzzy scores, which occupy 10% of the region, predict just 83% of the known deposits/occurrences of surficial U but the maximum fuzzy scores of the second one, which also occupy 10% of the region, predict 92% of the known deposits/occurrences of surficial U. Thus, the combined spatial evidence of U-sources obtained via the propositioned wFAS operator (Eq. (2)) was more effectual compared to the combined spatial evidence of U-sources obtained via the conventional FAS operator (see Bonham-Carter (1994), Carranza (2008)).

    Comparing fuzzy prospectivity models 1a and 1b, the former is the worse model as its maximum fuzzy scores, which occupy 5% of the region, predict 83% of the known deposits/occurrences of surficial U (Fig. 22) but the maximum fuzzy scores of the latter model, which also occupy 5% of the region, predict 89% of the known deposits/occurrences of surficial U (Fig. 21). Comparing fuzzy prospectivity models 2a and 2b, the former is the worse model as its maximum fuzzy scores, which occupy 10% of the region, predict just 36% of the known deposits/occurrences of surficial U (Fig. 23) but the maximum fuzzy scores of the latter, which also occupy 10% of the region, predict 83% of the known deposits/occurrences of surficial U (Fig. 21). These outcomes demonstrate that omitting the spatial evidence of almost-plain depressions (Fig. 11b) and employing only the spatial evidence of flow accumulation (Fig. 12b) to model physical trap did not worsen but improved modeling of the study region's regional-scale prospectivity for surficial U. This shows moreover that the spatial evidence of flow accumulation was more effectual compared the spatial evidence of almost-plain depressions. These outcomes imply furthermore that almost-plain depressions were more suitable as physical trap spatial evidence for local-scale but not regional-scale development of surficial U.

    Figure 21.  Plots portraying the spatial relationship of the known deposits/occurrences of surficial U with image images of fuzzy prospectivity models 1a and 2a (Fig. 20). The method for creating this plot is described in Agterberg and Bonham-Carter (2005).

    Figure 22.  Fuzzy prospectivity model 1b (a) derived by integrating the combined spatial evidence of U-sources obtained via the propositioned wFAS operator (Eq. (2)), spatial evidence of pathways, combined fuzzy chemical traps and combined fuzzy physical traps; and fuzzy prospectivity model 2b (b) derived by integrating the combined spatial evidence of U-sources obtained via the conventional FAS operator (see Bonham-Carter (1994), Carranza (2008)), spatial evidence of pathways, combined fuzzy chemical traps and combined fuzzy physical traps in south-central B.C. (Canada). White dots depict deposits/occurrences of surficial U. Image coordinates are the same as in Fig. 1 or 2.

    Figure 23.  Plots portraying the spatial relationship of the known deposits/occurrences of surficial U with images of fuzzy prospectivity models 1b and 2b (Fig. 22). The method for creating this plot is described in Agterberg and Bonham-Carter (2005).

  • The two best prospectivity images obtained in this work, fuzzy prospectivity models 1a (Fig. 20a) and 1b (Fig. 22a), take into account the spatial evidence of weighted closeness to probable U-source rocks (Fig. 6b). This indicates (a) the significance of reactive U data in modeling of prospectivity for surficial U and (b) the efficacy of the propositioned adaptation of the conventional FAS operator (i.e., Eq. (2)) so as to assimilate into the analysis the reactive U data.

    The two best prospectivity images do not take into account the spatial evidence of almost-plain depressions (Fig. 11b). This indicates (a) the ineffectiveness and perhaps unsuitability of this spatial evidence in modeling of the study region's regional-scale prospectivity for surficial U, or (b) the relatively superior effectiveness of the spatial evidence of flow accumulation (Fig. 12b). However, if, among the layers of trap spatial evidence, only the spatial evidence of stream water U-richness (Fig. 16, right panel) is employed jointly with the layers of spatial evidence for pathways (Fig. 8, right panel) and the spatial evidence of weighted probable U-source rocks, the resultant prospectivity image, fuzzy prospectivity model 3 (Fig. 24), is just very faintly worse compared to fuzzy prospectivity models 1a (Figs. 20b, 1b, 22a). This shows that the layers of spatial evidence of stream water alkalinity (Fig. 15, right panel) and flow accumulation (Fig. 12b) provide scanty contribution to better the predictive ability of prospectivity analysis in spite of their [theoretical] significance as criteria for targeting surficial U in the region. Conversely, the outcomes suggest that stream water alkalinity is a more effective spatial evidence of U-transporting capacity of surface waters (under oxidizing conditions) but not of U-trapping, and that stream water U-richness is a less effective spatial evidence of U-trapping. These limitations necessitate revision of the prospectivity modeling as more appropriate data emerge.

    Figure 24.  (a) Fuzzy prospectivity model 3 (left) derived by integrating the combined spatial evidence of U-sources derived via the propositioned wFAS operator (Eq. (2)), spatial evidence of pathways, fuzzy U-richness of stream waters. White dots depict deposits/occurrences of surficial U. Image coordinates are the same as in Figs. 1 or 2. (b) Plot portraying the spatial relationship of the known deposits/occurrences of surficial U with fuzzy prospectivity model 3, compared with plots portraying the spatial relationships of the known deposits/occurrences of surficial U with fuzzy predictive models 1a (Fig. 20b) and 1b (Fig. 22b) in South-central B.C. (Canada). The method for creating these plots is described in Agterberg and Bonham-Carter (2005).

    However, according to the two best prospectivity images obtained here (i.e., Figs. 20a, 22a) there is yet possibility for undiscovered deposits surficial U in the study region's south-central part. Then again, this is the same portion of the study region where most of the known deposits/occurrences of surficial U are present. It follows, on the one hand, that these two best prospectivity images possibly comprise "false-negative" bias relative to undiscovered deposits of surficial U that may likely be present in the study region's other parts. On the other hand, the two worst prospectivity images obtained in this study (Figs. 20b, 22b) comprise substantial "false-positive" bias relative to the known deposits/occurrences surficial U in the region. These "false-positive" and "false-negative" biases represent, correspondingly, methodical over- and under-estimation of prospectivity. Nevertheless, among them, it is more important to eschew "false-positive" bias as this will not lead to discovery of new deposits but will incur loss of financial outlay on exploration while "false-negative" bias will just lead to lost chance to discover new deposits. Porwal et al. (2015) employed gamma-ray spectrometric data to verify likely "false-positive" prospective areas. Yet, the surficial U system in the region is geologically youthful to yield daughter products measurable by radiometric survey. Otherwise, the trustworthiness of the prospectivity images obtained here may be examined further by employing past exploration data (cf. Kreuzer et al., 2015). Another potential alternate assessment is to contrast the outcomes with a spatio-temporal examination of changes in distribution of exploration/mining claims in the study region (cf. Coyan et al., 2017). However, these alternative approaches to cross-validate the results are outside the focus of this study.

    The research discussed here for modeling of the study region's regional-scale prospectivity for surficial U is quite effortlessly implementable in a geographic information system. A more intricate fuzzy inference system to model expert opinion for modeling of prospectivity of surficial U (cf. Porwal et al. 2015) will perhaps be as beneficial for analysts with expert understanding of the surficial U system in the study region.

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