DC resistivity sensitivity for tilted transversely isotropic media

Summary: Many rocks possess electrical properties with a clearly expressed anisotropy. The anisotropic character of the rocks has usually been overlooked in the inversion (and interpretation) of apparent resistivity data with the direct current method. In this study we firstly present an analytic expression for the Green's function for a special case of anisotropy: tilted transversely isotropic (TTI) media. We then present a formulation for sensitivity of anisotropic model parameters in terms of the presented Green's functions. Finally we directly compare the sensitivity patterns for an isotropic, homogeneous model with that for a uniform TTI (anisotropic) model using a pole-pole array. In order to make a direct comparison the sensitivity functions for anisotropic media are expressed with respect to the average conductivity (geometric mean of the longitudinal and transverse conductivities). The anisotropic sensitivity patterns are very different from the isotropic one, especially for strongly anisotropic rocks and for steep dips. There are prominent differences in both the sign and the magnitude of the sensitivities between the two cases, and so the possibility for error in interpretation is considerable.