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Numerical Simulation of Wave Propagation in 3D Elastic Media with Viscoelastic Formations

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Abstract

Attenuation is widespread in the Earth’s interior. However, there are several models where viscoelastic formations comprise as few as 10 to 20 % of the volume. They include near-surface and sea-bottom formation due to the low consolidation of the sediments, oil and gas reservoirs due to fluid saturation, etc. At the same time, the major part of the medium is ideally elastic. In this situation, the use of computationally intense approaches for the viscoelastic materials throughout the computational domain is prodigal. So this paper presents an original finite-difference algorithm based on the domain decomposition technique with the individual scheme used inside subdomains. It means that the standard staggered grid scheme approximating the ideally elastic model is used in the main part of the model. In contrast, the attenuation-oriented scheme is utilized inside viscoelastic domains. As the real-size simulations are applied in parallel via domain decomposition technique, this means that the elementary domains assigned to a single core (node) should be different for elastic and viscoelastic parts of the model. The optimal domain decomposition technique minimizing the computational time (core-hours) is suggested in the paper. It is proved analytically and confirmed numerically that for the models with up to 25% of viscoelasticity, the speed-up of the hybrid algorithm is about 1.7 in comparison with purely viscoelastic simulation.

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Funding

D. Vishnevsky implemented the algorithm under the support of the Russian Foundation for Basic Research grant no. 18-05-00031. V. Lisitsa did the optimization of the algorithm under the support of the Russian President Agency grant MD-20.2019.5. S. Soloviev performed numerical experiments using the equipment of the shared research facilities of HPC computing resources at Lomonosov Moscow State University and the using Cluster NKS-30T of the Siberian Supercomputer Center under the support of Russian Science Foundation grant no. 19-77-20004.

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Authors and Affiliations

  1. Institute of Petroleum Geology and Geophysics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    D. M. Vishnevsky & V. V. Lisitsa

  2. Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    S. A. Solovyev

Authors
  1. D. M. Vishnevsky
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  2. S. A. Solovyev
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  3. V. V. Lisitsa
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Correspondence to D. M. Vishnevsky, S. A. Solovyev or V. V. Lisitsa.

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(Submitted by Vl. V. Voevodin)

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Vishnevsky, D.M., Solovyev, S.A. & Lisitsa, V.V. Numerical Simulation of Wave Propagation in 3D Elastic Media with Viscoelastic Formations. Lobachevskii J Math 41, 1603–1614 (2020). https://doi.org/10.1134/S1995080220080211

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