Fuzzy Weights of Evidence Method and Its Application in Mineral Potential Mapping

This paper proposes a new approach of weights of evidence method based on fuzzy sets and fuzzy probabilities for mineral potential mapping. It can be considered as a generalization of the ordinary weights of evidence method, which is based on binary or ternary patterns of evidence and has been used in conjunction with geographic information systems for mineral potential mapping during the past few years. In the newly proposed method, instead of separating evidence into binary or ternary form, fuzzy sets containing more subjective genetic elements are created; fuzzy probabilities are defined to construct a model for calculating the posterior probability of a unit area containing mineral deposits on the basis of the fuzzy evidence for the unit area. The method can be treated as a hybrid method, which allows objective or subjective definition of a fuzzy membership function of evidence augmented by objective definition of fuzzy or conditional probabilities. Posterior probabilities calculated by this method would depend on existing data in a totally data-driven approach method, but depend partly on expert's knowledge when the hybrid method is used. A case study for demonstration purposes consists of application of the method to gold deposits in Meguma Terrane, Nova Scotia, Canada.     

Application of singularity mapping technique to identify local anomalies using stream sediment geochemical data,a case study from Gangdese,Tibet, western China

Identifying geochemical anomalies from background is a fundamental task in exploration geochemistry. The Gangdese mineral district in western China has complex geochemical surface expression due to complex geological background and was chosen as a study area for recognition of the spatial distribution of geochemical elements and separating anomalies from background using stream sediment geochemical data. The results illustrate that weak anomalies are hidden within the strong variance of background and are not well identified by means of inverse distance weighted; neither are they clearly identified by the C–A method if this method is applied to the whole study area. On the other hand, singularity values provide new information that complements use of original concentration values and can quantify the properties of enrichment and depletion caused by mineralization. In general, producing maps of singularities can help to identify relatively weak metal concentration anomalies in complex geological regions. Application of singularity mapping technique in Gangdese district shows local anomalies of Cu are not only directly associated with known deposits in the central part of the study area, but also with E–W and N–E oriented faults in the north of the study area. Both types of anomalies should be further investigated for undiscovered Cu mineral deposits.     

Two-stage least-squares model for the relationship between mappable geological variables

A method is developed for expressing a dependent variable that is subject to systematic regional variations (trend) in terms of a set of independent geological variables. Trend surfaces are fitted to the independent variables, and the dependent variable is regressed on both the fitted trend values and the original observations for the independent variables. The method is applied to evaluate the areal distribution of gold occurrences in the Greenbelt of western Quebec as a function of a set of lithological variables.     

Past and Future of Mathematical Geology

This is a brief review of alternative methods of problem-solving in geoscience with emphasis on the role of mathematical geology. It is desirable to maintain a clear-cut distinction between reliable facts which can be stored in data banks and concepts that can be incorporated in the speciflcations of sta-tistical models designed for specific purposes. If possible, subjective probabilities shclld be incorporated in hypotheses that are to be tested by statistical inference.     

A spatial analysis method for geochemical anomaly separation

One purpose of using statistical methods in exploration geochemistry is to assist exploration geologists in separating anomalies from background. This always involves two types of negatively associated errors of misclassification: type I errors occur when samples with background levels are rejected as background; and type II errors occur when samples with anomalous values are accepted as background. A new spatial statistical approach is proposed to minimize errors of total misclassification using a moving average technique with variable window radius. This method has been applied for geochemical anomaly enhancement and recognition as demonstrated by a case study of Au and Au-associated data for 698 stream sediment samples in the Iskut River area, northwestern British Columbia. Similar results were obtained using the fractal concentration-area method on the same data. By employing spatial information in the analysis, the process of selecting anomalies becomes less subjective than in more traditional approaches.     

Spatial relationships of multivariate data

Spatial factor analysis (SFA) is a multivariate method that determines linear combinations of variables with maximum autocorrelation at a given lag. This is achieved by deriving estimates of auto-/cross-correlations of the variables and calculating the corresponding eigenvectors of the covariance quotient matrix. A two-point spatial factor analysis model derives factors by the formation of transition matrixU comparing auto-/cross-correlations at lag 0,R ₀, with those at a specified lag d,R _d, expressed asU _d=R ₀ ^–1 R_d. The matrixU _d can be decomposed into its spectral components which represent the spatial factors. The technique has been extended to include three points of reference. Spatial factors can be derived from the relationship: