A fourth-order Runge-Kutta method with eighth-order accuracy and low numerical dispersion for solving the seismic wave equation

JSE

Journal of Seismic Exploration

0963-0651

AccScience Publishing

Article

A fourth-order Runge-Kutta method with eighth-order accuracy and low numerical dispersion for solving the seismic wave equationhttps://geophysical-press.com/journal/JSE/articles/242ZHANGCHAOYUAN,CHENLI

2016

253

2016-06-01

Zhang, C. and Chen, L., 2016. A fourth-order Runge-Kutta method with eighth-order accuracy and low numerical dispersion for solving the seismic wave equation. Journal of Seismic Exploration, 25: 229-255. 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.Runge-Kutta method, NAD operator, seismic wave equation, numerical dispersion, wave simulation

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