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Type: Journal article
Title: Electric Potential and Fréchet Derivatives for a Uniform Anisotropic Medium with a Tilted Axis of Symmetry
Other Titles: Electric Potential and Frechet Derivatives for a Uniform Anisotropic Medium with a Tilted Axis of Symmetry
Author: Greenhalgh, S.
Marescot, L.
Zhou, B.
Greenhalgh, M.
Wiese, T.
Citation: Pure and Applied Geophysics, 2009; 166(4):673-699
Publisher: Birkhauser Verlag Ag
Issue Date: 2009
ISSN: 0033-4553
Statement of
S. A. Greenhalgh, L. Marescot, B. Zhou, M. Greenhalgh and T. Wiese
Abstract: In this paper we develop analytic solutions for the electric potential, current density and Fréchet derivatives at any interior point within a 3-D transversely isotropic medium having a tilted axis of symmetry. The current electrode is assumed to be on the surface of the Earth and the plane of stratification given arbitrary strike and dip. Profiles can be computed for any azimuth. The equipotentials exhibit an elliptical pattern and are not orthogonal to the current density vectors, which are strongly angle dependent. Current density reaches its maximum value in a direction parallel to the longitudinal conductivity direction. Illustrative examples of the Fréchet derivatives are given for the 2.5-D problem, in which the profile is taken perpendicular to strike. All three derivatives of the Green's function with respect to longitudinal conductivity, transverse resistivity and dip angle of the symmetry axis (dG/dσl, dG/dσt, dG/dθ0) show a strongly asymmetric pattern compared to the isotropic case. The patterns are aligned in the direction of the tilt angle. Such sensitivity patterns are useful in real-time experimental design as well as in the fast inversion of resistivity data collected over an anisotropic earth. © Birkhäuser Verlag, Basel, 2009.
Keywords: Resistivity
electric potential
DOI: 10.1007/s00024-009-0465-6
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