Numerical Simulation of Wave Propagation in 3D Elastic Media with Viscoelastic Formations
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Numerical Simulation of Wave Propagation in 3D Elastic Media with Viscoelastic Formations D. M. Vishnevsky1* , S. A. Solovyev2** , and V. V. Lisitsa1*** (Submitted by Vl. V. Voevodin) 1
Institute of Petroleum Geology and Geophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia 2 Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia Received April 13, 2020; revised April 19, 2020; accepted April 24, 2020
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 nearsurface 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. DOI: 10.1134/S1995080220080211 Keywords and phrases: wave propagation, viscoelastic media, seismic attenuation, finite differences, domain decomposition, high-performance computing.
1. INTRODUCTION Nowadays numerical simulation is a common approach to study peculiarities of complex physical processes which precedes field data acquisition. Moreover, numerical solution of the forward problems is a major part of inversion and imaging algorithms [7, 17, 33, 34, 37, 42]. The finite-difference method is the most widely used approach in seismic modeling, because it combines implementation simplicity, including parallel implementation of the algorithms, with sufficient accuracy [41]. However, each physical aspect of media or the wave propagation process requires design of a new mathematical model and its finite-difference approximation. In particular, multi-scale media (fractured reservoirs) require the use of the locally refined meshes [22, 23, 27]; anisotropic media require specific finite-difference approximation [29, 30, 36]; to account for seismic attenuation one needs to use the model of viscoelastic media [12, 21, 32]; also for poro
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