Implicit Splitting Finite Difference Scheme for Multi-dimensional Wave Simulation

In this abstract, we propose a new finite-difference scheme for solving wave equations. This scheme splits the multi-dimensional system into different directions and solves each direction implicitly. Unlike most splitting methods in the literature which produce numerical anisotropy in diagonal directions, this method gives perfect circular impulse responses and allows lateral velocity variations. In this paper, we prove that the proposed scheme is unconditionally stable. In the numerical examples, we show some impulse response tests and compare them with the results from some high-order explicit finite-difference methods. The new method allows larger time step and requires less memory storage during the reverse time migration