Comparison Between the Pseudo-Analytical and Finite Difference Method for Seismic Modelling and Imaging

Seismic forward modelling is typically done using the finite difference (FD) approach. However, this method suffers from numerical dispersion problems which translates into less focused stacks and a decrease in bandwidth coverage. To mitigate this problem, the pseudo analytical method formulated by Etgen and Brandersberg-Dahl in 2009 was utilized. This paper demonstrates that pseudo analytics’ pseudo differential operator that utilizes velocity interpolation allows it to be more robust towards varying velocity and grid sizes while providing better amplitudes for shot gathers compared to the FD modelling scheme. FD and pseudo analytically generated gathers were then migrated using the reverse time migration (RTM) algorithm and showed that the pseudo analytically generated shot gathers were better at preserving shallower and higher frequency reflectors while at the same time better suppressed migration artifacts at the steeply dipping salt flank. The pseudo analytically generated gathers also provided an improved amplitude spectrum compared to FD especially in the lower frequency range of around 25-50 Hz. Various test cases demonstrate that the pseudo analytical method was shown to be a viable alternative to the typically used FD method in imaging at challenging geological environments such as salt.