Lowrank approximation for time domain viscoacoustic wave equation with spatially varying order fractional Laplacians

Abstract

PreviousNext No AccessSEG Technical Program Expanded Abstracts 2014Lowrank approximation for time domain viscoacoustic wave equation with spatially varying order fractional LaplaciansAuthors: Hanming Chen*Hui ZhouShan QuHanming Chen*China U of PetroleumSearch for more papers by this author, Hui ZhouChina U of PetroleumSearch for more papers by this author, and Shan QuChina U of PetroleumSearch for more papers by this authorhttps://doi.org/10.1190/segam2014-0055.1 SectionsSupplemental MaterialAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InRedditEmail Abstract Recently a time domain nearly constant Q (NCQ) wave equation derived from Kjartansson's constant Q model has been developed for modeling viscoacoustic wavefield. The wave equation introduces decoupled attenuation and dispersion terms based on two separate fractional Laplacians, which can be easily calculated by spatial Fourier pseudo-spectral method. The fractional orders of the Laplacians are related to Q, and that means the orders are actually spatially varying. However, no desirable approach is presented in the current literatures to handle the varying orders. The fractional Laplacian with a spatially varying order can be exactly represented by a wavenumber-space domain operator. In this abstract we use a lowrank decomposition method to approximate the mixed-domain operator, thus making the NCQ wave equation adapt to large Q contrasts. Additionally, we reformulate the existing velocity-stress-strain NCQ formulation as an equivalent compact velocity-pressure system. The staggered-grid pseudo-spectral (SGPS) method and unsplit convolutional perfectly matched layer (CPML) are adopted in numerical simulations. Keywords: Fourier, acoustic, modeling, time-domain, viscoelasticPermalink: https://doi.org/10.1190/segam2014-0055.1FiguresReferencesRelatedDetailsCited ByViscoelastic Wave Simulation with High Temporal Accuracy Using Frequency-Dependent Complex Velocity8 September 2020 | Surveys in Geophysics, Vol. 42, No. 1The asymptotic local finite-difference method of the fractional wave equation and its viscous seismic wavefield simulationGuojie Song, Xinmin Zhang, Zhiliang Wang, Yali Chen, and Puchun Chen16 April 2020 | GEOPHYSICS, Vol. 85, No. 3Optimal approximation of internal controls for a wave-type problem with fractional Laplacian using finite-difference method10 March 2020 | Mathematical Models and Methods in Applied Sciences, Vol. 30, No. 03A matrix-transform numerical solver for fractional Laplacian viscoacoustic wave equationHanming Chen, Hui Zhou, Ying Rao, Pengyuan Sun, Jianlei Zhang, and Yangkang Chen19 June 2019 | GEOPHYSICS, Vol. 84, No. 4Effective Q-compensated reverse time migration using new decoupled fractional Laplacian viscoacoustic wave equationQingqing Li, Li-Yun Fu, Hui Zhou, Wei Wei, and Wanting Hou11 February 2019 | GEOPHYSICS, Vol. 84, No. 2A stable approach for Q-compensated viscoelastic reverse time migration using excitation amplitude imaging conditionXuebin Zhao, Hui Zhou, Yufeng Wang, Hanming Chen, Zheng Zhou, Pengyuan Sun, and Jianlei Zhang29 August 2018 | GEOPHYSICS, Vol. 83, No. 5A constant fractional-order viscoelastic wave equation and its numerical simulation schemeNing Wang, Hui Zhou, Hanming Chen, Muming Xia, Shucheng Wang, Jinwei Fang, and Pengyuan Sun5 December 2017 | GEOPHYSICS, Vol. 83, No. 1Estimating velocity and Q by fractional Laplacian constant-Q wave equation-based full-waveform inversionHanming Chen and Hui Zhou17 August 2017Full-Waveform Inversion II Complete Session17 August 2017Comparison of two viscoacoustic propagators for Q-compensated reverse time migrationPeng Guo, George A. 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