Go to previous page

A Weighted Runge-Kutta Discontinuous Galerkin Method for 3D Acoustic and Elastic Wave-Field Modeling

A Weighted Runge-Kutta Discontinuous Galerkin Method for 3D Acoustic and Elastic Wave-Field Modeling

Year:    2020

Author:    Xijun He, Dinghui Yang, Xiao Ma

Communications in Computational Physics, Vol. 28 (2020), Iss. 1 : pp. 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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2018-0072

Communications in Computational Physics, Vol. 28 (2020), Iss. 1 : pp. 372–400

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    29

Keywords:    Numerical modeling anisotropy discontinuous Galerkin method numerical dispersion stability.

Author Details

Xijun He Email

Dinghui Yang Email

Xiao Ma Email

  1. A novel hybrid method based on discontinuous Galerkin method and staggered‐grid method for scalar wavefield modelling with rough topography

    Huang, Jiandong | Hu, Tianyue | Song, Jianyong | Li, Yandong | Yu, Zhenzhen | Liu, Lichao

    Geophysical Prospecting, Vol. 70 (2022), Iss. 3 P.441

    https://doi.org/10.1111/1365-2478.13171 [Citations: 8]
  2. Solving elastic wave equations in 2D transversely isotropic media by a weighted Runge-Kutta discontinuous Galerkin method

    He, Xi-Jun | Li, Jing-Shuang | Huang, Xue-Yuan | Zhou, Yan-Jie

    Petroleum Science, Vol. 20 (2023), Iss. 2 P.827

    https://doi.org/10.1016/j.petsci.2022.10.007 [Citations: 4]
  3. Modeling 3-D Elastic Wave Propagation in TI Media Using Discontinuous Galerkin Method on Tetrahedral Meshes

    He, Xijun | Yang, Dinghui | Huang, Jiandong | Huang, Xueyuan

    IEEE Transactions on Geoscience and Remote Sensing, Vol. 61 (2023), Iss. P.1

    https://doi.org/10.1109/TGRS.2023.3247540 [Citations: 5]
  4. High-order Runge-Kutta discontinuous Galerkin methods with multi-resolution WENO limiters for solving steady-state problems

    Zhu, Jun | Shu, Chi-Wang | Qiu, Jianxian

    Applied Numerical Mathematics, Vol. 165 (2021), Iss. P.482

    https://doi.org/10.1016/j.apnum.2021.03.011 [Citations: 9]
  5. A nodal discontinuous Galerkin method for wave propagation in coupled acoustic–elastic media

    Li, Ruiqi | Zhang, Yijie | Liu, Naihao | Gao, Jinghuai

    Geophysical Prospecting, Vol. 72 (2024), Iss. 6 P.2282

    https://doi.org/10.1111/1365-2478.13520 [Citations: 0]
  6. Investigation of the Elastic Waves Anisotropy Using the Grid-characteristic Computational Method and Explicit Treatment of Cracks

    Khokhlov, N. I. | Favorskaya, A. V.

    Lobachevskii Journal of Mathematics, Vol. 44 (2023), Iss. 1 P.341

    https://doi.org/10.1134/S1995080223010201 [Citations: 0]
  7. Comprehensive Structural Integrity

    Discontinuous Galerkin Methods for Solids and Structures

    Gulizzi, Vincenzo | Benedetti, Ivano | Milazzo, Alberto

    2023

    https://doi.org/10.1016/B978-0-12-822944-6.00024-4 [Citations: 0]