Application of Fuzzy Set Theory to Integrated Mineral Exploration

Geological intelpretationofmuluple geophysical and other auxiliary data sets has always ken a mnpler and ambiguous experience, even with good quality data sets. lhre are ~ever.4 quantitative methods of integrating gedogical and geophysical data sets for specific exploration targets: classical @ayesian) probability approach, Dempster-Shafer approach, kmy logic approach and AImpen system methods. In this study, apx! from geophysical interpretation an* inversion theories, the problem is focused on the geophysical infomation representation and quantitative integration Of Spatial *am sets far chosen expkxamn proposirions. Fuzzy set theory using *e algebraic-sum and y operators is investigated and tested wicb nine sets of geological and geophysical data from the Farlcy L*e area, Canada. The possibility distribution maps derived trsing both the algebraic and ~operators have successfully outlined fa”o”rdJ,e areas for “base metal deposits” and“irotl formation deposits”. Furlher evaluation using the jack!aife estimation approach indicates that the fuzzy logic approach provides an effective too1 for integrating gmlogical. geochemical and geophysical data sets for resources exploration. The results overlain with bands I and 2 of MEIS-II (Multi-detector Ektro-optical Image Scanner-It) image *emOnStlate that the digitally outlined favourable ueas can funher be utilized with recently available high-resolution images of the exploration area. In resource exploration, and in geophysical research in general, there has always been urgent need for further development of new techniques for geophysical inversion and for integrated geological interpretation of the observed field data. Recently, there has appeared a new problem in processing and integration of large volumes of multiple geophysical data sets. This problem has been intensified with rapidly increasing size of geophysical data sets, particularly from airborne and space-borne sensors. One of the most popular new approaches taken to resolve this problem is the commonly available digital GIS’s (Geographical Information System). The GIS works well with simple geographic and map information. Geophysical information from various sensors, however, requires more precise representation for subsequent spatial reasoning and interpretation (An, 1989; Moon, 1989; Moon, 1990). In this study, the fuzzy logic approach of representing geological and geophysical information is reviewed and investigated. The classical set theory founded by Georg Cantor (1845. 1918) is defined on a collection of objects (elements) which have cenain common properties (Kuratowski and Moslowski, 1976). An object can be either a member of the set with a membership I or not a member with membership 0. There is no third option in the classical set theory. In the cases where the information to be processed is possibilistic and transient in nature, one needs a mathematical tool which can adequately represent the information with a degree of possibility and/or uncertainty. The traditional mathematical approach has commonly employed the statistical and probabilistic approach with specific information theoretical framework (Chug and Moon, 1990: Moon et al., 1990). The fuzzy membership function is not, by definition, a probability and there is some advantage to using the fuzzy logic approach in geophysical problems. There have recently been several repotted applications of fuzzy logic theory in remote sensing and other geographical information processing. Among them are Wang (1989) who applied fuzzy set theory in an expert system for remote sensing image analysis and Blonda et al. (1989) who used a fuzzy logic technique in classifying multitemporal remotely sensed imagery. In geophysical exploration, certain measurements and/or observations, such as measurements of Earth’s gravitational anomalies or observation ofcertain rock types, form a “data set” or “data sets”. This information usually has been treated, i.e., hented at the C.S.E.G. National Co”“e”tim, Calgary, AlLww May 16, 1991. Manuscript receive* by the Editor Rebruary 5, ,991: revise* manuacnpr receive* April IO, ,991. irxp”me”t of Ckopbysics, The ““iWSity of Manitoba, Winn@& Manitoba R3T 2x2 hm. Oeological Suney Of Canada. maw. ontano KI.4 OE8 This research is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) operating grant A-7400 to W.M. Moon. Drs. Mark Fedikow and lfti Hosein 81 the Dep. of Energy and Mines, Province of Manitoba, and geologists at Manitoba Mineral Resources Ltd. kindly provided the test da** for tie.7 study. CSEG ,o”md 1 ~e,,,hcr IWI P. AN. W.M. MOON and A. REWZ processed and interpreted, in the framework of classical sets. Even though the information very seldom is discrete, it is discretized for convenience to facilitate digital processing. Let us consider a subset of a gravity data, which is defined as B = “Bouguer gravity anomalies greater than 31.52 mCal”. One can define this as a subset with only “31.52 mGal”. However, we know that it is not practical tu create an infinite number of subsets to represent certain information. A more logical choice to subset such data sets would be to include a family of observations whose values are close to this particular measurement. The elements in this subset can have varying degrees of information content as well as varying degrees of uncertainty. Further. a subset of the geological map can be defined as F = “felsic intrusives”. This spatial subset of a geological map has a number of uncertainties such as boundary errors, identifying the rock, and scale and drawing errors onto a map. Similarly, most geological and geophysical information cannot be precisely represented using the classical set theory, neither in temporal nor spatial domains. Suppose an explorationist is searching for a favourable area for base metal deposits in a survey arca, and he has an aeromagnetic map. Analysis of the map will provide a subset of several anomalies, some of which may be indicative of base metal deposits. However, physical size, shape and degree of magnetic induction associated with each anomaly may be more appropriately represented hy some other method than the classical set approach. The uncertainties of interpreting each anomaly and of correlating the results with the physical parameters, representative of a base metal, also pose problems. If there are more than one data sets, anomalies and/or evidences indicative of base metal deposits with varying degrees of uncertainties, they can first be quantitatively integrated and then reassessed. Similar anomalous features may then be identified from different data sets at the same or different location, as expert explorationists often do. One of the major tasks of today’s integrated exploration is to include mathematically proper representation of the information from different data sets and to develop an effective tool for accurate and efficient combination of the evidences from each data set to obtain the most reasonable and realistic interpretation. For this purpose, fuzzy set theory pxvides a more precise method of representing the information content of different data sets and of combining them with a choice of processing operations. Application of the furry set theory investigated below is tested with the remote sensing and geophysical data sets COIlected over the Farley Lake area of Manitoba. The study area is mapped using variousgeophysical andgeochemical techniques and also using airborne MEIS-II (Multi-detector Electro-optical Imaging Scanner-II) and airborne MSS (Multi-spectral Scanner). Detailed comlation of the various geochemical and remote-sensing data was reported by Singh et al. (1989). In this study, integrated information of nine geological and geophysical data sets is correlated with only hands I and 2 of MEW11 image data because, according to the previous study (Singh et al., 1989), only these two bands have positive correlation with iron and copper concentration anomalies in the study area. Quenouille (1956) introduced a mathematical technique for reducing the information bias, which can result during the data processing, by splitting the sample into M groups if the sample is composed of n pieces. This was later nicknamed the ‘jackknife technique” by Tukey (1958). As mentioned above, integration steps involve operationsofcombininginformation from different data sets. Aside from some difficulties in choosing appropriate combination operators, the jackknife technique can be easily applied to the above~described overall process to reduce the bias of combination and, in turn, to evaluate the degree of the operational bias. In this paper, furry set theory and the jackknife technique are briefly reviewed and applied to a mineral exploration example from the Parley Lake area of Manitoba. This test area was also the site of an integrated exploration study to determine the feasibility of using airborne MEIS-II and MSS data as a potential biogeochemical mineral exploration tool (Singh et al., 1989). The final results of this work are digitally overlaid on bands I and 2 of the MEIS-II image of the test area for further effective utiliration of the digital information.