DC resistivity sensitivity patterns for tilted transversely isotropic media

Abstract

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 (dG / dσ l , dG / dσ t , dG / dθ 0 , dG / dφ 0 ) 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.

Comparison Between Hydraulic Conductivity Anisotropy and Electrical Resistivity Anisotropy From Tomography Inverse Modeling

“…As in the isotropic case presented in section 3, it is crucial to adapt the data acquisition protocol given that electrode configurations are not necessarily sensitive to the same subsurface features. Different electrodes configurations do not have the same sensitivity to anisotropy (Wiese et al, 2009;Greenhalgh et al, 2010;Kenkel and Kemna, 2016). In particular, Bing and Greenhalgh (2000) have detailed the use of cross-hole ERT.…”

Comparison of DC sensitivity patterns for anisotropic and isotropic media

“…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. In a companion paper (Wiese et al, 2009) we illustrate in greater detail the influence of dip angle, out of plane effects (azimuth angle) and coefficient of anisotropy on four more conventional Fréchet derivatives, namely those with respect to longitudinal conductivity, transverse conductivity, dip and azimuth of the axis of symmetry (see Section 3). The companion paper also examines the sensitivity patterns produced with four electrode arrays (e.g.…”

Prediction Model for Advanced Detection of Water-Rich Faults Using 3D Anisotropic Resistivity Modeling and Monte Carlo Methods

“…The anisotropic coefficient of resistivity usually varies from 1 to 3, and it also could be up to 3.7 or 4.5 in limestone strata [21]. Even if the anisotropic coefficient were 1.1, the effect of anisotropy could not be ignored [22]. If a medium with a relatively large anisotropic coefficient is simplified as isotropy, it could bring nonignorable errors in predicting water-bearing structures.…”