Linking electrical and hydraulic conductivity through models of random resistor networks

Abstract

We present models of random resistor networks to relate electrical resistivity to fracture permeability in the upper crust. In this approach, the upper crust is modelled as a network of resistors that are randomly assigned to be either electrically and hydraulically conductive or resistive based on a network-wide probability of connection. In the models presented here, the conductive resistors are assigned resistance values based on a constant fracture diameter of 1 mm and a fluid resistivity of 0.1 Om, with variable fault length distributions and probabilities of connection. We have found that the permeability is very sensitive to both of these parameters, increasing to 8.33 × 108 times the matrix permeability in the fully connected case. The resistivity is less sensitive, increasing by a factor of 1000.