Frequency-domain Waveform Inversion with Irregular Surface Based on Variable Grid Finite Difference Method

Irregular topography is common in onshore seismic exploration, and this has a significant influence on the accuracy of inversion. It is essential to introduce the effect of surface topography in the full waveform inversion to improve the accuracy of inversion. We develop a variable-grid finite-difference frequency-domain modeling algorithm with the irregular topography, and incorporate it into a full waveform inversion algorithm for the first time. The finite-difference method (FDM) can be applied to forward modeling with higher efficiency and simplicity, compared with classical finite-element method and finite-volume method. However, the conventional FDM suffers from severe dispersion. To balance the artificial diffractions and the computational cost, the computational domain containing the surface is discretized by fine rectangular grids, while the rest of the model is discretized by coarse grids. In the full waveform inversion algorithm with irregular surface, the strong nonlinearity arising from free-surface multiples is another challenging issue. We apply successive inversions of frequency overlapping group and layer stripping method to improve the stability of iterative procedure. In the meantime, the pseudo-Hessian matrix is used to scale the gradient to accelerate convergence. We validated the accuracy of our algorithm by numerical tests.