DC resistivity sensitivity patterns for tilted transversely isotropic media

Abstract

<jats:title>ABSTRACT</jats:title><jats:p>In this paper we present and analyse DC resistivity sensitivity patterns for uniform anisotropic media and for various surface electrode arrays. 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, 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 <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/nsg2009003-math-0011.png" xlink:title="urn:x-wiley:15694445:nsg2009003:equation:nsg2009003-math-0011" /> for varying model parameters. Anisotropic sensitivities are vastly different in strength and shape compared to the isotropic sensitivity pattern. The various arrays (pole‐pole, dipole‐dipole, Wenner and square array) produce distinctive patterns that are important in assessing resolution. Valuable insights were gained: the anisotropic Fréchet derivatives can vary greatly from the isotropic pattern in both strength and shape depending on the nature of the anisotropy. Also it was found that the relationship between components of current density (parallel and perpendicular to the symmetry axis) and the sensitivity patterns is somewhat akin to the dot product of the true source and adjoint source current density vectors in isotropic media. Understanding of the anisotropic sensitivity pattern variations will enable, through further analysis, computation of model resolution matrices and improvement of experimental design. Appreciation of the significant differences between isotropic and anisotropic sensitivities should help avoid errors in using inappropriate isotropic inversion schemes to interpret measurements made over anisotropic ground.</jats:p>