Comparison of DC sensitivity patterns for anisotropic and isotropic media |
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| Authors: | Stewart Greenhalgh Tim Wiese Laurent Marescot |
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| Institution: | 1. VIRG-Rudgeofizika, Petrogradskaya nab. 18, korp. 3V, St. Petersburg, 197046, Russia;2. Institute of Earth Sciences, St. Petersburg State University, per. Dekabristov 16, St. Petersburg, 199155, Russia;1. G360 Centre for Applied Groundwater Research, University of Guelph, Canada;2. School of Engineering, University of Guelph, Canada;3. School of Environmental Sciences, University of Guelph, Canada |
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| Abstract: | Many rocks possess electrical properties with a clearly expressed anisotropy. The anisotropic character of the rocks is often overlooked in forming the Fréchet derivatives or sensitivity functions for parameter updating during the inversion of DC resistivity data. In this study we have compared the sensitivity patterns for an isotropic, homogeneous model with that for a transversely isotropic (i.e. anisotropic) model having a tilted axis of symmetry using a pole–pole array. The sensitivity functions are expressed in terms of the derivatives of the electric potential U with respect to the average conductivity σm (geometric mean of the longitudinal and transverse conductivities) and the coefficient of anisotropy λ. Results are plotted in both cross-section form and plan view for various dip and strike angles of the axis of symmetry. The derivative dU/dλ decreases more rapidly than the isotropic value dU/dσ, and shows pronounced asymmetry and weakening of magnitude with increasing dip of the plane of symmetry. The derivative dU/dσm also exhibits the asymmetric pattern (except for vertical and horizontal dip cases). The positive region between the electrodes only extends to a small depth compared to the isotropic derivative, even in the case of a vertical axis of symmetry (VTI medium). The ratio of this anisotropic derivative to the isotropic derivative, when plotted as a function of position and depth shows prominent differences in both the sign and the magnitude of the sensitivities, especially for steep dips and for strongly anisotropic rocks. The plot highlights the dangers of an isotropic assumption. Even for mildly anisotropic rocks (λ < 1.2) the possibility for error in interpretation is considerable. Combined borehole and surface measurements are needed to diagnose anisotropy. Further work is needed to design optimal electrode configurations in anisotropic situations. |
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