Trapezoid grid finite difference seismic wavefield simulation with uniform depth sampling interval

In general, seismic wave propagation speed increases along with depth due to compaction of rocks caused by gravity. Trapezoid coordinate design can incorporate the general increasing trend of velocity. The uniform grid sampling in trapezoid coordinate corresponds to a grid interval increasing along with depth in Cartesian coordinate, that is, fine grid in shallow low velocity region and coarse grid in deep high velocity region. The wave equation is derived in trapezoid coordinate and the traditional uniform grid finite difference can be evoked for the calculation. In this work, we achieve a variable grid finite difference seismic wavefield simulation method with linear increasing for lateral grid interval and uniform sampling along depth. Due to the gradual linear increase of the grid interval, this method avoids the artificial reflections caused by transition of regions with different grid size comparing with the discontinuous variable grid mesh finite difference method. The proposed method achieves high accuracy result in shallow region and covers wider apertures in deep area. The trapezoid coordinate is more general and including Cartesian coordinate as one special case. The proposed method has a potential application for accurate and efficient deep seismic wavefield simulation with wide range velocity variation.