Software and Data P P Divisor Reclassi cations Divide FM_Categorical P P Reclass Field Reclassify Reclass_kbge5 Float Float_Rec 1234 P Categorical Evidence Divisor Figure 2: Diagram of the Categorical Weights tool available in the Spatial Data Modeller toolbox Geologic-Map Evidence P Categorical kbgeol3 Rock-Geochemical Evidence Categorical Fuzzy Membership AND Lithologic Factor Gamma 0.9 P Small 3,4 Fuzzy Overlay (3) Lithologic-adjusted Geochemical Factor Carlin Possibility kjenks Geochemical Evidence Fuzzy Membership (3) OR FuzzyMe_kjen2 Fuzzy Overlay (2) P Large 15,2 as_std Fuzzy Membership (2) Large 4,5 FuzzyMe_as_s1 Fuzzy Overlay Mineralization Factor P sbnb Fuzzy Membership FuzzyMe_sbn10 Figure 3: A demonstration of a simple fuzzy logic model. Categorical membership is described in Figure 2. The other tools are Overlay tools in ArcGIS 10. Mineralization Geochemical Factor Use the Large Fuzzy Membership tool for assigning fuzzy membership values to Sb and As. Tune the parameters for the Large Fuzzy Membership tool to produce fuzzy evidence maps acceptable to the expert. Combine the Sb and As fuzzy maps with a Fuzzy OR operator. Use the Fuzzy Membership tool for K, again tuning the parameters for the Small Fuzzy Membership tool to make an acceptable map. Lithologic-Adjusted Geochemical Factor Use the Fuzzy AND operator to combine the mineralization geochemical factor with the K membership. Lithologic Factor Assign the fuzzy memberships to the various lithologies present on the geologic map following guidance from the expert and using the Categorical Fuzzy Membership tool in the Spatial Data Modeller toolbox and diagrammed in Figure 2. Combine the lithologic-adjusted geochemical factor with the litho- logic factor using the Gamma combination operator to produce the Carlin-type gold possibility map. Tune the gamma parameter value to produce an acceptable combination. Once the model shown in Figure 3 is assembled, it will be necessary to adjust the fuzzy membership parameters to tune fuzzy memberships to represent properly the expert’s concepts. This tuning can be done graphically in a spreadsheet or, more often, spatially by inspecting rasters. Using iteration methods in separate tuning models is useful for quickly computing a selection of rasters with a range of parameters. Experts will recognize the best representation of the spatial data. When disagreements occur about the optimal tuning of the fuzzy memberships, multiple models can be built quickly representing different opinions and tested during model validation. Figure 4 provides a comparison of the Boolean and fuzzy logic models. A weighted sum model would be more similar to—but not the same as—the fuzzy logic model. Divisor Geologic-Map Evidence Categorical P kbgeol3 Rock-Geochemical Evidence Categorical Fuzzy Membership AND FM_Cat Fuzzy Gamma Output Raster FLCarlinNew P P Small 3,4 kjenks Fuzzy Membership (3) OR OR FuzzyMe_kje n2 Fuzzy Overlay (2) P Large 15,2 as_std Fuzzy Membership (2) P Large 4,5 FuzzyMe_as_ s1 Fuzzy Overlay FuzzyOv_Fuzz z2 sbnb Fuzzy Membership FuzzyMe_sbn 10 Figure 4: The simple fuzzy logic model for Carlin-type gold deposits Continued on page 12 www.esri.com ArcUser Spring 2010 11