Solving fractional Laplacian viscoelastic wave equations using domain decomposition

Zhiguang Xue, Hyoungsu Baek, Houzhu Zhang, Yang Zhao, Tieyuan Zhu, Sergey Fomel

Research output: Contribution to conferencePaper

Abstract

Fractional Laplacian viscoacoustic/viscoelastic wave equations offer separate controls over amplitude loss and phase dispersion, and have been used in Q-compensated reverse-time migration and full waveform inversion. Previously, the spatially varying-order fractional Laplacians have been solved with the global Fourier pseudo-spectral method by representing the spatially varying order with an average value, which introduces numerical errors into simulations. To reduce the errors, we propose a local pseudo-spectral method, which uses a large number of block-variable values instead of just one to represent the spatially varying order. A numerical implementation scheme for parallel computing, domain decomposition, has been adopted to take advantage of the local pseudo-spectral method, which improves both numerical accuracy and computing efficiency. A tapering internal boundary condition is used to reduce the Fourier artifacts caused by wavefield truncation at subdomain boundaries. An overlap-add communication scheme bewteen subdomains is applied for reducing the additional cost associated with boundary padding and for interpolating the wavefields from different subdomains within the overlapping boundaries. Numerical examples verify the effectiveness of the domain decomposition strategy in improving the accuracy of solving fractional Laplacians in the viscoelastic wave equations.

Original languageEnglish (US)
Pages3943-3947
Number of pages5
DOIs
StatePublished - Jan 1 2019
Event88th Society of Exploration Geophysicists International Exposition and Annual Meeting, SEG 2018 - Anaheim, United States
Duration: Oct 14 2018Oct 19 2018

Other

Other88th Society of Exploration Geophysicists International Exposition and Annual Meeting, SEG 2018
CountryUnited States
CityAnaheim
Period10/14/1810/19/18

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spectral methods
wave equation
wave equations
decomposition
parallel computing
tapering
reaction time
artifact
artifacts
waveforms
boundary condition
communication
inversions
boundary conditions
costs
approximation
cost
simulation
method

All Science Journal Classification (ASJC) codes

  • Geophysics

Cite this

Xue, Z., Baek, H., Zhang, H., Zhao, Y., Zhu, T., & Fomel, S. (2019). Solving fractional Laplacian viscoelastic wave equations using domain decomposition. 3943-3947. Paper presented at 88th Society of Exploration Geophysicists International Exposition and Annual Meeting, SEG 2018, Anaheim, United States. https://doi.org/10.1190/segam2018-2998547.1
Xue, Zhiguang ; Baek, Hyoungsu ; Zhang, Houzhu ; Zhao, Yang ; Zhu, Tieyuan ; Fomel, Sergey. / Solving fractional Laplacian viscoelastic wave equations using domain decomposition. Paper presented at 88th Society of Exploration Geophysicists International Exposition and Annual Meeting, SEG 2018, Anaheim, United States.5 p.
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Xue, Z, Baek, H, Zhang, H, Zhao, Y, Zhu, T & Fomel, S 2019, 'Solving fractional Laplacian viscoelastic wave equations using domain decomposition' Paper presented at 88th Society of Exploration Geophysicists International Exposition and Annual Meeting, SEG 2018, Anaheim, United States, 10/14/18 - 10/19/18, pp. 3943-3947. https://doi.org/10.1190/segam2018-2998547.1

Solving fractional Laplacian viscoelastic wave equations using domain decomposition. / Xue, Zhiguang; Baek, Hyoungsu; Zhang, Houzhu; Zhao, Yang; Zhu, Tieyuan; Fomel, Sergey.

2019. 3943-3947 Paper presented at 88th Society of Exploration Geophysicists International Exposition and Annual Meeting, SEG 2018, Anaheim, United States.

Research output: Contribution to conferencePaper

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Xue Z, Baek H, Zhang H, Zhao Y, Zhu T, Fomel S. Solving fractional Laplacian viscoelastic wave equations using domain decomposition. 2019. Paper presented at 88th Society of Exploration Geophysicists International Exposition and Annual Meeting, SEG 2018, Anaheim, United States. https://doi.org/10.1190/segam2018-2998547.1