Electric resistivity inversion via reverse time migration algorithm of seismic data

Abstract

We propose an electric resistivity inversion method that is similar to reverse time migration technique applied to seismic data. In order to apply the adjoint state of Poisson equation in resistivity inverse problem, we introduce apparent electric field defined as the scalar product between computed electric field and weighting factor. In our algorithm, we use the adjoint state of matrix equation originated from solving Poisson equation by the mixed finite-element mehtod, and introduce a virtual source and backpropagation term as in seismic inverse problem. Since we can compute steepest descent direction by an inner prodect of backpropagated residual and virtual source, we can circumvent the cumbersome process of computing Jacobian matrix directly.