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

CHAOYUAN ZHANG1 ,  LI CHEN2
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1 College of Mathematics and computer, Dali University, Dali 671003, P.R. China. zcy_km@163.com,
2 College of Engineering, Dali University, Dali 671003, P.R. China.,
JSE 2016, 25(3), 229–255;
Submitted: 19 July 2015 | Accepted: 27 January 2016 | Published: 1 June 2016
© 2016 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

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.

Keywords
Runge-Kutta method
NAD operator
seismic wave equation
numerical dispersion
wave simulation
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Journal of Seismic Exploration, Print ISSN: 0963-0651, Published by AccScience Publishing
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