Finite Difference Method for First-Order Velocity-Stress Equation in Body-Fitted Coordinate System

Abstract

Staircase approximation in simulation of the arbitrarily irregular surface will cause artificial interference of wavefield. The body-fitted coordinate transformation can accurately simulate the arbitrarily irregular surface and avoid the staircase approximation. The finite difference method (FDM) based on body-fitted coordinate system (BFCS) can simulate the propagation process of wavefield in the media with an undulating surface. Currently, the collocated grid is usually used in BFCS. However, adopting this method to simulate waves based on the first-order velocity-stress wave equation in the BFCS will cause oscillation due to the odd-even decoupling, therefore additional filtering operations are required. To solve the above problem, we propose collocate-staggered grid (CSG) to simulate the first-order velocity-stress wave equation in the two-dimensional (2D) BFCS. CSG uses staggered grid scheme to calculate equation parameters, and adopts collocated grid scheme to store these values. We use second-order accuracy spatial and temporal difference for numerical tests. The results show that the elastic wavefield modeling method in the BFCS using CSG difference scheme has the characteristics of high accuracy and stable. This method is suitable for the wavefield simulation in a medium with a large Poisson’s ratio.