A nearly analytic exponential time difference method for solving 2D seismic wave equations |
| |
Authors: | Xiao Zhang Dinghui Yang Guojie Song |
| |
Institution: | 1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China
|
| |
Abstract: | In this paper, we propose a nearly analytic exponential time difference (NETD) method for solving the 2D acoustic and elastic wave equations. In this method, we use the nearly analytic discrete operator to approximate the high-order spatial differential operators and transform the seismic wave equations into semi-discrete ordinary differential equations (ODEs). Then, the converted ODE system is solved by the exponential time difference (ETD) method. We investigate the properties of NETD in detail, including the stability condition for 1-D and 2-D cases, the theoretical and relative errors, the numerical dispersion relation for the 2-D acoustic case, and the computational efficiency. In order to further validate the method, we apply it to simulating acoustic/elastic wave propagation in multilayer models which have strong contrasts and complex heterogeneous media, e.g., the SEG model and the Marmousi model. From our theoretical analyses and numerical results, the NETD can suppress numerical dispersion effectively by using the displacement and gradient to approximate the high-order spatial derivatives. In addition, because NETD is based on the structure of the Lie group method which preserves the quantitative properties of differential equations, it can achieve more accurate results than the classical methods. |
| |
Keywords: | ETD Lie group method Numerical approximations and analysis Computational seismology Numerical dispersion Nearly analytic discrete operator |
本文献已被 SpringerLink 等数据库收录! |
| 点击此处可从《Earthquake Science》浏览原始摘要信息 |
| 点击此处可从《Earthquake Science》下载免费的PDF全文 |
|