Multifractal modelling and spatial analysis with GIS: Gold potential estimation in the Mitchell-Sulphurets area, northwestern British Columbia.

In combination with statistical modelling and GIS-based (Geographic Information Systems) spatial analysis, fractal and multifractal theory can be used for various purposes in the geosciences. Two multifractal models have previously been developed. One of these is based on the fractal dimension spectrum f($\alpha$) and the other one on the codimension function C($\gamma$). It can be shown that these two multifractal models are identical if $\gamma\ >$ D-$\alpha$(0). For $\gamma $ D$\sb{\rm L}.$ Similar relations hold true for surface areas and volumes of fractal geometries in three-dimensional space. The multifractal model provides new types of functions for modelling the covariance and semivariogram in spatial statistics as well as a new type of second-order intensity function for two-dimensional point processes. These functions are used to describe the underlying spatial structure of Au mineral occurrences in the Iskut River map sheet and for three relatively well known data sets: (1) Cochran's example of the number of tree seedlings per foot along a 200 ft long bed, (2) De Wijs's example of zinc values from a sphalerite-quartz vein near Pulacayo in Bolivia, and (3) Gerrard's example of trees in Lansing Woods. A new version of the weights of evidence technique based on the box-counting method is proposed for integrating various nonfractal and fractal patterns in mineral potential mapping, and is demonstrated with a case study of Au potential estimation in the Iskut River map sheet. The ordinary weights of evidence method is used for geochemical anomaly separation in the Mitchell-Sulphurets mineral district and gives results similar to those obtained with the fractal element concentration-area method. As another nonfractal method of geochemical anomaly separation, a new spatial statistical approach based on U-statistics is proposed which uses a moving average with optimal window radius. This method is tested by computer simulation and for geochemical anomaly separation of Au and Au-associated elements in stream sediment samples from the Iskut River map sheet. (Abstract shortened by UMI.