Seismic-Velocity / Electrical-Conductivity Relations

Cross-property relations are useful when some rock properties can be more easily measured than other properties. Relations between electrical conductivity and seismic velocity, stiffness moduli and density can be obtained by expressing the porosity in terms of those properties. There are many possibilities to combine the constitutive equations to obtain a relation, each one representing a given type of rock, depending on the assumptions to obtain the involved constitutive equations. Mainly, these involve Archie's law and its modifications for a conducting frame, the Hashin-Shtrikman bounds, the selfsimilar and CRIM (complex refraction index) models in the electromagnetic case, and the timeaverage, the Hashin-Shtrikman bounds, and Gassmann equation in the elastic case. Also, expressions for dry rocks and for anisotropic media, using Backus averaging, are analyzed. The relations are applied to the a shale saturated with brine (overburden) and to a sandstone saturated with oil (reservoir).