Abstract
Abstract. This paper presents a new model proposed on the basis of multiplicative cascade process (MCP) theory for integrating spatial information to be used for mineral resources prediction and environmental impact assessment. Probability of a spatial point event is defined as the probability that a small map calculating unit (map unit) randomly selected from a study area contains one or more points. The probability that such unit randomly selected from a subarea with known spatial binary map patterns (evidential layers) contains one or more points is defined as the posterior point event probability. In this paper, processes of integrating multiple binary map patterns that divide the study area into smaller areas with updated posterior probabilities are viewed as multiplicative cascade processes resulting in a new log-linear model for calculating conditional probabilities from the multiple evidential input layers. The coefficients (weights) involved in this model measuring degree of spatial correlation between point event and the evidential layers are found to be associated with singularity indices involved in multifractal modeling. It is demonstrated that the model is simple and easy to be implemented in comparison with the existing weights of evidence model which is commonly applied in spatial decision modeling. In addition, the posterior probability as the end product of a multiplicative cascade process can be used to describe multifractality and singularity which are useful properties for characterizing spatial distribution of predicted point events. A case study of tin mineral potential mapping in the Gejiu mineral district in China is used to illustrate principles and use of the modeling process. Four binary layers: formation of limestone, buffer distance for intersections of three groups of faults, local and regional geochemical anomalies of elements As, Sn, Cu, Pb, Zn and Cd, were combined for mapping potential areas for occurrence of tin mineral deposits.
Highlights
Singular physical, chemical and biological processes can result in anomalous energy release, mass accumulation or matter concentration that, generally, are all confined to narrow intervals in space or time (Cheng, 2007a)
This paper aims to demonstrate that the concepts of multiplicative cascade processes (MCP) and singularities as the end products of MCP can be applied to model the processes of combining multiple geo-variables to map potential areas for discovering new mineral deposits
There are a total of 11 units occupied by Sn mineral deposits, from which the prior probability of a 3ra6ndomly chosen square from the area containing mineral deposits can be estimated as P [D] = 0.0065
Summary
Chemical and biological processes can result in anomalous energy release, mass accumulation or matter concentration that, generally, are all confined to narrow intervals in space or time (Cheng, 2007a). Hydrothermal mineral deposits often exhibit non-linear features with respect to ore element and associated toxic element concentration values in rock and related surface media such as water, soil, stream sediment, till, humus and vegetation (Cheng et al, 1994a; Turcotte, 2002; Xie and Bao, 2004; Agterberg, 2007a; Xie et al, 2007; Cheng and Agterberg 2009; Ford and Blenkinsop, 2009; Hronsky, 2009) These properties can be used for delineating target areas for finding undiscovered mineral deposits in support of mineral exploration and mineral resources planning. These posterior probabilities can be considered as resulting from multiplicative cascade processes that may depict multifractality and singularities which can be characterized by fractal and multifractal models
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