Acoustic Reverse-time Migration with Least Squares Staggered-grid Finite-difference Operators

Reverse-time migration (RTM) directly solves the two-way wave equation for wavefield propagation, and for this reason, how to solve the wave equation accurately and quickly is very important in the process of RTM. Staggered-grid finite-difference (SFD) operators have been widely used to solve seismic wave equations. However, the conventional SFD operators are usually based on the Taylor series expansion. If they are used to solve wave equation on a larger frequency zone, a strong dispersion will occur, which directly affects the modelling accuracy and image quality. In this paper, we propose an optimal SFD operator based on least squares to solve acoustic wave equation for prestack RTM, and obtain a new antidispersion RTM algorithm that can use short spatial difference operators. The numerical results demonstrate that the least squares SFD (LSSFD) operator can clearly suppress the numerical dispersion on the larger frequency zone, and the acoustic RTM using the LSSFD operator can effectively improve imaging quality comparing with that using the Taylor-series expansion SFD (TESFD) operator.

Additionally, the LSSFD method can adopt a shorter spatial difference operator to reduce the computing cost while preserving the modelling and imaging accuracy.