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A generalized time-domain velocity-stress seismic wave equation for composite viscoelastic media with a topographic relief and an irregular seabed

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Abstract

Accurate seismic wave modeling of viscoelastic anisotropic medium is a fundamental tool for seismic data processing, interpretation and full waveform inversion. Also, free water surface, topographic relief and irregular seabed are often encountered in practical seismic surveys. Thus, basing on the General Maxwell Body, we proposed a generalized matrix form of the velocity-stress seismic wave equation, which becomes valid for composite viscoelastic anisotropic media and satisfies the boundary conditions in presence of topographic free surfaces and irregular fluid–solid interfaces. We theoretically show that the viscoelastic effect of a medium may be considered as the intrinsic body sources accumulated in wavefield history and computed by a recursive convolution formula accurately and efficiently. We also demonstrated that such a generalized viscoelastic wave equation may be solved with the curvilinear MacCormack finite difference method and validated the accuracy and feasibility of the proposed method. The modeling results in homogeneous and heterogeneous media match well with the analytical solutions and the references yielded by the spectral element solutions.

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Data availability

Data sharing not applicable to this article as no datasets were generated during the current study.

Code availability

The analytical solution code is download from Seismic wave Propagation and Imaging in Complex media: a European network (SPICE) website (EX2DDIR/ EX2DELEL package, http://www.spice-rtn.org/library/software.1.html) The spectral element code is downloaded from the Computational Infrastructure for Geodynamics (CIG) website (SPECFEM2D package, https://geodynamics.org/cig/software/ specfem2d/).

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Acknowledgements

C. J. thanks the Chinese Scholarship Council and Khalifa University for the financial support.

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Authors and Affiliations

  1. Department of Earth Science, Khalifa University of Science and Technology, 127788, Abu Dhabi, United Arab Emirates

    Chao Jin & Bing Zhou

  2. Department of Mathematics, Khalifa University of Science and Technology, 127788, Abu Dhabi, United Arab Emirates

    Mohamed Kamel Riahi

  3. Department of Electrical Engineering and Computer Science, Khalifa University of Science and Technology, 127788, Abu Dhabi, United Arab Emirates

    Mohamed Jamal Zemerly

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  1. Chao Jin
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Jin, C., Zhou, B., Riahi, M.K. et al. A generalized time-domain velocity-stress seismic wave equation for composite viscoelastic media with a topographic relief and an irregular seabed. Comput Geosci (2024). https://doi.org/10.1007/s10596-024-10273-2

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