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A Fourth-Order Compact Numerical Scheme for Three-Dimensional Acoustic Wave Equation with Variable Velocity

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Recent Advances in Mathematical and Statistical Methods (AMMCS 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 259))

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Abstract

In this paper we proposed an accurate and efficient numerical algorithm for solving the acoustic wave equation in three-dimensional heterogeneous media. Numerical solution of the wave equation has been used in various science and engineering applications, such as the seismic full waveform inversion (FWI) problem. FWI is a computationally intensive procedure, in which the acoustic wave equation is numerically solved (forward modelling) repeatedly during the iterative process. Therefore, efficiency and accuracy of the numerical method for solving the acoustic wave equation is critical in the success of seismic full waveform inversion. The new method is obtained by combining the Padé approximation and a novel algebraic manipulation with the Alternative Directional Implicit (ADI) method. Numerical experiments have shown that the new method is accurate, efficient and stable.

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Acknowledgements

The work of the first author is supported by the Natural Sciences & Engineering Research Council of Canada (NSERC) individual Discovery Grant program.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Calgary, Calgary, AB, T2N 1N4, Canada

    Wenyuan Liao

  2. Department of Computer Science, Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Ou Wei

Authors
  1. Wenyuan Liao
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  2. Ou Wei
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Corresponding author

Correspondence to Wenyuan Liao .

Editor information

Editors and Affiliations

  1. Department of Mathematics & MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, ON, Canada

    D. Marc Kilgour

  2. Department of Mathematics & Statistics, University of Guelph, Guelph, ON, Canada

    Herb Kunze

  3. Department of Mathematics & MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, ON, Canada

    Roman Makarov

  4. Department of Mathematics & MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, ON, Canada

    Roderick Melnik

  5. Department of Mathematics & MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, ON, Canada

    Xu Wang

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Liao, W., Wei, O. (2018). A Fourth-Order Compact Numerical Scheme for Three-Dimensional Acoustic Wave Equation with Variable Velocity. In: Kilgour, D., Kunze, H., Makarov, R., Melnik, R., Wang, X. (eds) Recent Advances in Mathematical and Statistical Methods . AMMCS 2017. Springer Proceedings in Mathematics & Statistics, vol 259. Springer, Cham. https://doi.org/10.1007/978-3-319-99719-3_26

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