The hydraulic and electrical fractal dimension of regolith

Abstract

Electrical and electromagnetic (EM) geophysical data from a line or grid are usually converted into two- or three-dimensional resistivity models of the Earth. In regions of relatively uniform geology, variability of measurements are assumed to be random and Gaussian, such that the Earth models are found from a maximum likelihood approach. In this paper, we show that such variability is not Gaussian, and has a scale-length dependence, expressed as a fractal dimension. We argue that the fractal dimension of electrical and EM data is causally determined from Earth heterogeneity, which provides a link with hydraulic conductivity in porous and fractured media that also has a fractal dimension. This paper presents initial analyses of data from two sites within South Australia. NanoTEM time domain electromagnetic (TEM) data were collected at Tunkillia in the Gawler Craton with a target of identifying palaeochannels for gold exploration. Analysis of survey data revealed a good correlation between regions of low resistivity and high fractal dimension. On the other hand, a river-borne NanoTEM survey of the River Murray sediments showed much lower correlation. We conclude that analysis of the variability of EM data may provide useful additional constraints on subsurface properties.