2D Laplace‐domain waveform inversion using adaptive finite element method

Abstract

Summary Waveform inversion in the Laplace domain has been proposed recently. The Laplace-domain waveform inversion is robust, is not sensitive to the initial model, and generates a long-wavelength velocity model for field data as it exploits a well behaved objective function. To improve the applicability of the waveform inversion, we adopted the adaptive finite element method to deal with the sources and receivers at shallow depths. Since the Laplace-domain wavefield damps out rapidly as a receiver becomes sufficiently far from a source, we applied the Dirichlet boundary condition on the edges of the extended model instead of using an absorbing boundary condition. By these two improvements in forward modeling, a numerical test was conducted on a time-domain original BP benchmark dataset. The Laplace-domain waveform inversion using the adaptive mesh successfully provided a long-wavelength velocity model of the true model. The inverted smooth velocity model was used as a good initial model for the frequency-domain waveform inversion. The followed frequency-domain inversion recovered almost every features of the BP model except some sub-salt structures.