| 起伏地表弹性波传播的间断Galerkin有限元数值模拟方法 |
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| 引用本文： | 薛昭,董良国,李晓波,刘玉柱.起伏地表弹性波传播的间断Galerkin有限元数值模拟方法[J].地球物理学报,2014,57(4):1209-1223. |
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| 作者姓名： | 薛昭 董良国 李晓波 刘玉柱 |
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| 作者单位： | 1. 同济大学海洋地质国家重点实验室, 上海 200092;
2. 中国石化地球物理重点实验室, 南京 210000 |
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| 基金项目： | 国家油气重大专项(2011ZX05005-005-007HZ);国家油气重大专项(2011ZX05005-005-001);国家973项目(2014CB239201)联合资助 |
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| 摘 要： | 间断Galerkin有限元法（DG-FEM）作为一种有效的高阶有限元法受到了国内外学者的广泛关注.本文基于任意高阶间断Galerkin有限元法对弹性波方程进行空间离散，并将离散后所得的非齐次线性常微分方程系统齐次化，最后结合针对齐次问题的强稳定性保持龙格库塔（SSP Runge-Kutta）算法，将DG-FEM推广至时间任意高阶精度.另外，借鉴近最佳匹配层（NPML）的思想，基于复频移（CFS）拉伸坐标变换推导了一种新的PML吸收边界条件（简称为CFS-NPML），该CFS-NPML能够与DG-FEM算法很好地结合，形成有效的起伏地表地震波传播数值模拟技术.数值试验结果表明，DG-FEM具有高阶精度，可以适应任意复杂起伏地表和复杂构造情况下的弹性波传播数值模拟.同时，CFS-NPML对包括面波等震相的人为边界反射都具有良好的吸收效果.
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| 关 键 词： | 间断Galerkin有限元法 起伏地表 弹性波传播 任意高阶Runge-Kutta时间格式 CFS-NPML |
| 收稿时间： | 2013-02-11 |
Discontinuous Galerkin finite-element method for elastic wave modeling including surface topography |
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| XUE Zhao,DONG Liang-Guo,LI Xiao-Bo,LIU Yu-Zhu.Discontinuous Galerkin finite-element method for elastic wave modeling including surface topography[J].Chinese Journal of Geophysics,2014,57(4):1209-1223. |
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| Authors: | XUE Zhao DONG Liang-Guo LI Xiao-Bo LIU Yu-Zhu |
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| Institution: | 1. State Key Laboratory of Marine Geology, Tongji University, Shanghai 200092, China;
2. SINOPEC Key Laboratory of Geophysics, Nanjing 210000, China |
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| Abstract: | As a powerful high order finite element numerical simulation method, Discontinuous Galerkin finite element method (DG-FEM) has been extensively studied by researchers worldwide. In this paper, we discretize the elastic wave equation based on the arbitrary high order discontinuous Galerkin finite element method in spatial domain, and then transform the final non-homogeneous linear system to a homogeneous one. Finally, combined with strong stability preserved Runge-Kutta integrator aiming at homogeneous system, DG-FEM is extended to arbitrary high order precision in time. A new PML absorbing boundary condition named CFS-NPML is also derived based on the idea of nearly PML (NPML) technology and complex-frequency-shifted(CFS) stretching coordinate transformation. An effective seismic wave numerical simulation method with topography is obtained by combining DG-FEM with the CFS-PML technology. The numerical results show that DG-FEM is characterized by high order accuracy. This method is available for the numerical simulation of elastic wave propagation in the models with arbitrary complicated topography and geologic structures. Meanwhile, CFS-NPML technology has a good absorbing effect on the artificial boundary reflections including the artificial reflections of surface wave. |
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| Keywords: | Discontinuous Galerkin finite element method Topography Elastic wave propagation Arbitrary high order Runge-Kutta CFS-NPML |
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