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Dispersion and cost analysis of some finite difference schemes in one-parameter acoustic wave modeling

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Abstract

Given a precision threshold to be imposed on the group velocity error and a finite difference scheme for the acoustic wave equation, it is possible to determine time-step and grid-spacing in an optimal manner, i.e., so as to minimize the computational cost. Using this optimal cost as a criterion, it becomes easy to compare schemes for efficiency in homogeneous media.

Heterogeneous media with constant density can be accommodated to a certain extent by minimizing the cost over a range of Courant numbers. Such analysis shows that, amongst the second-order Taylor series schemes in time, higher-order schemes are generally more efficient than lower-order schemes. However, this result does not extend to very high order schemes.

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Authors and Affiliations

  1. Institut Français du Pétrole, DIMA-DER, B.P. 311, F-92506, Rueil-Malmaison, France

    Laurent Anné & Quang Huy Tran

  2. Department of Computational and Applied Mathematics, Rice University, P.O. Box 1892, Houston, TX, 77251, USA

    William W. Symes

Authors
  1. Laurent Anné
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  2. Quang Huy Tran
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  3. William W. Symes
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Anné, L., Tran, Q.H. & Symes, W.W. Dispersion and cost analysis of some finite difference schemes in one-parameter acoustic wave modeling. Computational Geosciences 1, 1–33 (1997). https://doi.org/10.1023/A:1011576309523

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  • DOI: https://doi.org/10.1023/A:1011576309523

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