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Efficient electric resistivity inversion using adjoint state of mixed finite-element method for Poisson’s equation

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Authors
Ha, Taeyoung; Pyun, Sukjoon; Shin, Changsoo
Issue Date
2005-10-25
Publisher
Elsevier
Citation
Journal of Computational Physics 214 (2006) 171-186
Keywords
Resistivity inversionMixed finite-element methodSteepest descent method
Abstract
We propose an electric resistivity inversion method that is similar to the reverse time migration technique applied to
seismic data. For calculating model responses and inversion, we use the mixed finite-element method with the standard
P1 P0 pair for triangular decompositions, which makes it possible to compute both the electric potential and the electric
field vector economically. In order to apply the adjoint state of the Poisson equation in the resistivity inverse problem, we
introduce an apparent electric field defined as the dot product between the computed electric field vector and a weighting
factor and then defining a virtual source to compute the partial derivative of the electric field vector. We exploit the adjoint
state (the symmetry of Green s function) of matrix equations derived from solving the Poisson equation by the mixed finiteelement
method, for the calculation of the steepest descent direction of our objective function. By computing the steepest
descent direction by a dot product of backpropagated residual and virtual source, we can avoid the cumbersome and
expensive process of computing the Jacobian matrix directly. We calibrate our algorithm on a synthetic of a buried conductive
block and obtain an image that is compatible with the limits of the resistivity method.
ISSN
0021-9991
Language
English
URI
http://hdl.handle.net/10371/6119
DOI
https://doi.org/10.1016/j.jcp.2005.09.007
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College of Engineering/Engineering Practice School (공과대학/대학원)Dept. of Energy Systems Engineering (에너지시스템공학부)Journal Papers (저널논문_에너지시스템공학부)
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