Volume 28, Issue 1
A Weighted Runge-Kutta Discontinuous Galerkin Method for 3D Acoustic and Elastic Wave-Field Modeling

Xijun He, Dinghui Yang & Xiao Ma

Commun. Comput. Phys., 28 (2020), pp. 372-400.

Published online: 2020-05

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  • Abstract

Numerically solving 3D seismic wave equations is a key requirement for forward modeling and inversion. Here, we propose a weighted Runge-Kutta discontinuous Galerkin (WRKDG) method for 3D acoustic and elastic wave-field modeling. For this method, the second-order seismic wave equations in 3D heterogeneous anisotropic media are transformed into a first-order hyperbolic system, and then we use a discontinuous Galerkin (DG) solver based on numerical-flux formulations for spatial discretization. The time discretization is based on an implicit diagonal Runge-Kutta (RK) method and an explicit iterative technique, which avoids solving a large-scale system of linear equations. In the iterative process, we introduce a weighting factor. We investigate the numerical stability criteria of the 3D method in detail for linear and quadratic spatial basis functions. We also present a 3D analysis of numerical dispersion for the full discrete approximation of acoustic equation, which demonstrates that the WRKDG method can efficiently suppress numerical dispersion on coarse grids. Numerical results for several different 3D models including homogeneous and heterogeneous media with isotropic and anisotropic cases show that the 3D WRKDG method can effectively suppress numerical dispersion and provide accurate wave-field information on coarse mesh.

  • Keywords

Numerical modeling, anisotropy, discontinuous Galerkin method, numerical dispersion, stability.

  • AMS Subject Headings

86-08, 86A15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

hexijun111@sina.com (Xijun He)

dhyang@math.tsinghua.edu.cn (Dinghui Yang)

maxiao@nwpu.edu.cn (Xiao Ma)

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@Article{CiCP-28-372, author = {He , Xijun and Yang , Dinghui and Ma , Xiao }, title = {A Weighted Runge-Kutta Discontinuous Galerkin Method for 3D Acoustic and Elastic Wave-Field Modeling}, journal = {Communications in Computational Physics}, year = {2020}, volume = {28}, number = {1}, pages = {372--400}, abstract = {

Numerically solving 3D seismic wave equations is a key requirement for forward modeling and inversion. Here, we propose a weighted Runge-Kutta discontinuous Galerkin (WRKDG) method for 3D acoustic and elastic wave-field modeling. For this method, the second-order seismic wave equations in 3D heterogeneous anisotropic media are transformed into a first-order hyperbolic system, and then we use a discontinuous Galerkin (DG) solver based on numerical-flux formulations for spatial discretization. The time discretization is based on an implicit diagonal Runge-Kutta (RK) method and an explicit iterative technique, which avoids solving a large-scale system of linear equations. In the iterative process, we introduce a weighting factor. We investigate the numerical stability criteria of the 3D method in detail for linear and quadratic spatial basis functions. We also present a 3D analysis of numerical dispersion for the full discrete approximation of acoustic equation, which demonstrates that the WRKDG method can efficiently suppress numerical dispersion on coarse grids. Numerical results for several different 3D models including homogeneous and heterogeneous media with isotropic and anisotropic cases show that the 3D WRKDG method can effectively suppress numerical dispersion and provide accurate wave-field information on coarse mesh.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0072}, url = {http://global-sci.org/intro/article_detail/cicp/16844.html} }
TY - JOUR T1 - A Weighted Runge-Kutta Discontinuous Galerkin Method for 3D Acoustic and Elastic Wave-Field Modeling AU - He , Xijun AU - Yang , Dinghui AU - Ma , Xiao JO - Communications in Computational Physics VL - 1 SP - 372 EP - 400 PY - 2020 DA - 2020/05 SN - 28 DO - http://doi.org/10.4208/cicp.OA-2018-0072 UR - https://global-sci.org/intro/article_detail/cicp/16844.html KW - Numerical modeling, anisotropy, discontinuous Galerkin method, numerical dispersion, stability. AB -

Numerically solving 3D seismic wave equations is a key requirement for forward modeling and inversion. Here, we propose a weighted Runge-Kutta discontinuous Galerkin (WRKDG) method for 3D acoustic and elastic wave-field modeling. For this method, the second-order seismic wave equations in 3D heterogeneous anisotropic media are transformed into a first-order hyperbolic system, and then we use a discontinuous Galerkin (DG) solver based on numerical-flux formulations for spatial discretization. The time discretization is based on an implicit diagonal Runge-Kutta (RK) method and an explicit iterative technique, which avoids solving a large-scale system of linear equations. In the iterative process, we introduce a weighting factor. We investigate the numerical stability criteria of the 3D method in detail for linear and quadratic spatial basis functions. We also present a 3D analysis of numerical dispersion for the full discrete approximation of acoustic equation, which demonstrates that the WRKDG method can efficiently suppress numerical dispersion on coarse grids. Numerical results for several different 3D models including homogeneous and heterogeneous media with isotropic and anisotropic cases show that the 3D WRKDG method can effectively suppress numerical dispersion and provide accurate wave-field information on coarse mesh.

Xijun He, Dinghui Yang & Xiao Ma. (2020). A Weighted Runge-Kutta Discontinuous Galerkin Method for 3D Acoustic and Elastic Wave-Field Modeling. Communications in Computational Physics. 28 (1). 372-400. doi:10.4208/cicp.OA-2018-0072
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