Numerical simulation of wave equations based on minimum-norm optimization of staggered-grid finite-difference coefficients
TANG Chao1, WEN Xiaotao1,2, WANG Wenhua1
1. College of Geophysics, Chengdu University of Technology, Chengdu, Sichuan 610059, China; 2. Key Laboratory of Earth Exploration and Information Techniques of Ministry of Education(Chengdu University of Technology), Chengdu, Sichuan 610059, China
Abstract：When the finite difference method is used for numerical simulation of wave equations, the inhe-rent numerical dispersion affects the accuracy of calculation results. Most of the existing constant coefficient optimization approaches suppress the numerical dispersion by solving the difference coefficient that satisfies the broadest wavenumber cove-rage under a given error threshold. This, however, increases the dispersion error in a small wavenumber interval, resulting in a significant error accumulation effect during the wavefield propagation. In view of this, this paper proposes a new finite difference forward simulation method for staggered grid optimization of acoustic equations. First, the objective function of the spatial first derivative is established with L1 norm in the wavenumber domain, and then the staggered-grid finite-difference coefficients are solved using the alternating direction multiplier method (ADMM). The comparison of the numerical dispersion curves shows that the ADMM has a better control effect on the dispersion error in the low and middle wavenumber domains at the error tolerance of one ten-thousandth. The numerical experiments on homogeneous and complex models show that the L1 norm has better control over the error accumulation among diffe-rent norms for optimization.
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