A gelation analogy of crustal formation derived from fractal conductive structures

Abstract

The statistical evaluation of numerical random media models and of electromagnetic array data provides evidence of fractal conductive structures in the middle and lower crust. During the search for an electrical conduction mechanism that is compatible with the geophysical anomalies in the middle and lower crust, random resistor networks were developed. These networks contain two types of resistors, representing the rock matrix and the conductive phase. Here we demonstrate that random resistor network models can also explain the statistical properties of the electric field distortion measured in large‐scale electromagnetic array experiments. Correspondence between measured and modeled distortion statistics is obtained if the structures formed by the two resistor types in the networks have a fractal geometry. This can indicate that the natural conductive networks also have a fractal geometry and stay close to a percolation threshold. A simple scale model of crust formation mechanics is considered in order to find an analog medium and an analog process that creates such a geometry. We suggest gelation as a rheological analogy that allows for a coexistence of ductile and brittle behavior of material in the lower crust. This process forms fractal structures in the host matrix and fractal conductive networks, provided that conductive material is available at that time of crustal evolution. The statistical evaluation of the field data provides evidence for a fractal structure with an upper bound of the size of Fennoscandia.