Frquency-domain elastic waveform inversion with irregular surface topography

In order to describe the irregular topography that is commonly encountered in land-based seismic exploration, we present a frequency-domain elastic wave modeling algorithm for this phenomenon, incorporated into an elastic waveform inversion algorithm. We use a finite-element method, both for the modeling and for the inversion algorithms, in which the main body is approximated by rectangular elements and irregular topography is described by triangular elements. In common with conventional finite-element modeling algorithms, our finiteelement irregular topography modeling algorithm also naturally satisfies the free-surface boundary condition due to the Neumann boundary condition, which is incorporated when we construct the finite-element formulae. For the inversion algorithm, we use the steepest-descent method, and scale the gradient direction using the diagonal of the pseudo-Hessian matrix rather than the approximate or full Hessian matrix. We apply the inversion technique to the AA-line of the SEG/EAGE salt dome model, modified to account for irregular surface topography. Through numerical examples, we demonstrate that our elastic waveform inversion can reproduce subsurface structures and elastic parameters fairly well, even for a model with irregular topography.