The relationship between the physical properties and the effective electrical conductivity of porous structures is studied using three-dimensional (3-D) models of random porosity. Synthetic electric (DC) and electromagnetic (EM) field data are calculated for a 3-D electrical conductivity model with a random porosity p (p = 2 - 70%) embedded in a homogeneous half-space. The effective conductivity of the random porosity model is obtained from inversion of the synthetic data and agrees with a modified Archie's law. We applied percolation theory to our random porosity model to explain the variation of effective conductivity with p. We found that EM and DC data do not provide the same effective conductivity at a particular porosity but they do provide the same volume fraction of interconnected conductive elements. This volume fraction depends on the percolation threshold pc. It follows a law of the form ~p above pc and ~p2.2 below pc.