A FOURTH-ORDER RUNGE-KUTTA METHOD WITH EIGHTH-ORDER ACCURACY AND LOW NUMERICAL DISPERSION FOR SOLVING THE SEISMIC WAVE EQUATION

In this paper, we give a fourth-order Runge-Kutta method with the eighth-order accuracy and low numerical dispersion for solving the seismic wave equation, which is called the ENAD-FRK method in brief. We first give the theoretical deduction and stability conditions for this new method in detail. And, we derive numerical dispersion relations of the ENAD-FRK method in 2D acoustic case and compare numerical dispersions against the eighth-order Lax-Wendroff correction (LWC) scheme and the eighth-order Staggered-grid (SG) finite difference method. Meanwhile, we compare the memory requirement and the computational efficiency of the proposed method against the eighth-order LWC scheme for modeling 2D seismic wave fields in a two-layer heterogeneous acoustic medium. Last, we apply the ENAD-FRK method to simulate 2D seismic wave propagating in a three-layer homogenous transversely isotropic elastic medium, a two-layer homogenous isotropic elastic medium and a Marmousi model. Simulation results indicate that the ENAD-FRK method can greatly save both computational costs and storage space as contrasted to the eighth-order LWC scheme. Meanwhile; Both comparisons of numerical dispersion analysis and numerical experimental results show that the ENAD-FRK method can effectively suppress numerical dispersion caused by discretizing the seismic wave equation when too coarse grids are used against the eighth-order LWC scheme and the eighth-order SG method.