3. EM/GPR Imaging Technologies
Electric Resistivity Inversion using Adjoint State of Poisson Equation
Taeyoung Ha(1) and Changsoo Shin(2)
(1) Department of Mathematical Sciences, Korea. (2) School of Civil, Urban and Geosystem Engineering, Korea.
Abstract
We propose an electric resistivity inversion method that is similar to the reverse time migration technique applied to seismic data. 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's equation by the mixed finite element 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.
Last modified: Wed May 10 08:29:24 2006