Spectral-element method based on optimal numerical integration for seismic waveform modeling
MENG Xueli1,2, LIU Shaolin1, YANG Dinghui3, WANG Wenshuai2, XU Xiwei1, LI Xiaofan4
1. National Institute of Natural Hazards, Ministry of Emergency Management of China, Beijing 100085, China; 2. School of Mathematics and Statistics, Ningxia University, Yinchuan, Ningxia 750021, China; 3. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China; 4. Institute of Geophysics & Geomatics, China University of Geoscience, Wuhan, Hubei 430074, China
Abstract：High-accuracy seismic waveform modeling for complex media is a difficult issue in the geophysics community,and developing a high-accuracy and efficient numerical algorithm is crucial to the research on the forward modeling and inversion of seismic waveforms. At present, the spectral-element method (SEM) has been successfully applied to seismic wave simulation by models on different scales. However,the Gauss-Lobatto-Legendre (GLL) numerical integration algorithm used by the conventional SEM is not able to accurately calculate the polynomial integration involved in the mass and stiffness matrices, which thus decreases the accuracy of SEM. Here we propose an optimal numerical integration algorithm to solve the abovementioned problem. We first construct the least-square formation of the objective functions for numerical integration and exact integration. After that,we utilize the conjugate gradient method to solve the weight coefficient of optimal numerical integration,which increases the accuracy of the numerical integration and thereby improves the numerical accuracy of SEM. Theoretical analyses and numerical examples verify that the spectral-element method based on optimal numerical integration performs better in suppressing numerical dispersion and increasing calculation accuracy.
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