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Weak dispersion wave-field simulations: A predictor-corrector algorithm for solving acoustic and elastic wave equations

NIAN WANG1 ,  DINGHUI YANG1 ,  FAQI LIU2
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1 Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P.R. China. dhyang@math.tsinghua.edu.cn,
2 Hess Corporation, One Allen Center, Houston, Texas 77002, U.S.A. fliu@hess.com,
JSE 2012, 21(2), 125–152;
Submitted: 3 October 2011 | Accepted: 19 February 2012 | Published: 1 May 2012
© 2012 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

Wang, N., Yang, D. and Liu, F., 2012. Weak dispersion wave-field simulations: A predictor-corrector algorithm for solving acoustic and elastic wave equations. Journal of Seismic Exploration, 21: 125-152. A new predictor-corrector algorithm (PCA) based on the implicit Runge-Kutta method is proposed to solve the acoustic and elastic wave equations. We transform the wave equation into a system of first-order partial differential equations (PDEs) with respect to time, convert the transformed wave equation into a semi-discrete ordinary differential equation (ODE) system by using the high-order interpolation method to approximate the spatial derivatives (Yang et al., 2003, 2007), and finally use the proposed PCA which is a time discretization method to solve the semi-discrete ODE system. We investigate the theoretical properties of the PCA such as its numerical convergence, stability criteria, and numerical dispersion for solving 1-D and 2-D scalar wave equations. The computational efficiency of the PCA in simulating acoustic wave fields is also investigated, and is compared with that of the staggered-grid method and the fourth-order Lax-Wendroff correction method (LWC). The effectiveness of the PCA is also demonstrated by its well matched waveforms to the analytic solution for modeling both acoustic and elastic models. Promising numerical simulation results indicate that the proposed PCA provides a useful method for the large-scale wave-field simulations because it can effectively suppress numerical dispersions even when coarse modeling grids are used or large velocity contrasts exist in geological models.

Keywords
predictor-corrector algorithm
numerical dispersion
wave field simulation
implicit Runge-Kutta method
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Journal of Seismic Exploration, Print ISSN: 0963-0651, Published by AccScience Publishing
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