DC resistivity Frechet derivatives for a uniform anisotropic medium with a tilted axis of symmetry

Abstract

In this paper we present and analyse DC resistivity sensitivity patterns for uniform anisotropic media. The sensitivity functions (or Fréchet derivatives) give the responsive change in measured electric potential for a perturbation in a model parameter at a particular point in the subsurface for a specific electrode configuration. The anisotropic model investigated is the common tilted transversely isotropic medium (TTI) which is defined by four model parameters. We examine the changes in the Fréchet derivatives of the Green?s functions with respect to both the longitudinal and transverse conductivity and the dip and azimuth angle of the symmetry axis for varying model parameters. Secondly, we wish to illustrate the differences that exist between the sensitivities calculated using an isotropic assumption and those computed with the correct anisotropic formulation. It is shown that in certain cases gross errors in inversion may occur if isotropic Fréchet derivatives are mistakenly used. Here we work with two special forms of the derivatives -one taken with respect to the mean conductivity and the other with respect to the magnitude of the anisotropy- and investigate a range of possible cases.