Solving fractional laplacian viscoacoustic wave equation using hermite distributed approximating functional method

Jie Yao, Tieyuan Zhu, Fazle Hussain, Donald J. Kouri

Research output: Contribution to journalConference article

1 Citation (Scopus)

Abstract

Accurate seismic modeling in realistic media severs the basis of seismic inversion and imaging. Recently viscoacoustic seismic modeling incorporating attenuation effects was done by solving a fractional Laplacian viscoacoustic wave equation. In this equation, attenuation, being spatially heterogeneous, is represented partially by the spatially varying power of the fractional Laplacian operator previously approximated by the global Fourier method. In this paper, we present a local spectral approach, based on Hermite distributed approximating functional (HDAF) method, to implement the fractional Laplacian in the viscoacoustic wave equation. The proposed approach combines local methods' simplicity and global methods' accuracy. Several numerical examples are presented to demonstrate the feasibility and accuracy of using the HDAF method for the frequency-independent Q fractional Laplacian wave equation.

Original languageEnglish (US)
Pages (from-to)3966-3971
Number of pages6
JournalSEG Technical Program Expanded Abstracts
Volume35
DOIs
StatePublished - Jan 1 2016
EventSEG International Exposition and 86th Annual Meeting, SEG 2016 - Dallas, United States
Duration: Oct 16 2011Oct 21 2011

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wave equation
Wave equations
wave equations
attenuation
inversions
Imaging techniques
operators
modeling
method

All Science Journal Classification (ASJC) codes

  • Geotechnical Engineering and Engineering Geology
  • Geophysics

Cite this

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title = "Solving fractional laplacian viscoacoustic wave equation using hermite distributed approximating functional method",
abstract = "Accurate seismic modeling in realistic media severs the basis of seismic inversion and imaging. Recently viscoacoustic seismic modeling incorporating attenuation effects was done by solving a fractional Laplacian viscoacoustic wave equation. In this equation, attenuation, being spatially heterogeneous, is represented partially by the spatially varying power of the fractional Laplacian operator previously approximated by the global Fourier method. In this paper, we present a local spectral approach, based on Hermite distributed approximating functional (HDAF) method, to implement the fractional Laplacian in the viscoacoustic wave equation. The proposed approach combines local methods' simplicity and global methods' accuracy. Several numerical examples are presented to demonstrate the feasibility and accuracy of using the HDAF method for the frequency-independent Q fractional Laplacian wave equation.",
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Solving fractional laplacian viscoacoustic wave equation using hermite distributed approximating functional method. / Yao, Jie; Zhu, Tieyuan; Hussain, Fazle; Kouri, Donald J.

In: SEG Technical Program Expanded Abstracts, Vol. 35, 01.01.2016, p. 3966-3971.

Research output: Contribution to journalConference article

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T1 - Solving fractional laplacian viscoacoustic wave equation using hermite distributed approximating functional method

AU - Yao, Jie

AU - Zhu, Tieyuan

AU - Hussain, Fazle

AU - Kouri, Donald J.

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N2 - Accurate seismic modeling in realistic media severs the basis of seismic inversion and imaging. Recently viscoacoustic seismic modeling incorporating attenuation effects was done by solving a fractional Laplacian viscoacoustic wave equation. In this equation, attenuation, being spatially heterogeneous, is represented partially by the spatially varying power of the fractional Laplacian operator previously approximated by the global Fourier method. In this paper, we present a local spectral approach, based on Hermite distributed approximating functional (HDAF) method, to implement the fractional Laplacian in the viscoacoustic wave equation. The proposed approach combines local methods' simplicity and global methods' accuracy. Several numerical examples are presented to demonstrate the feasibility and accuracy of using the HDAF method for the frequency-independent Q fractional Laplacian wave equation.

AB - Accurate seismic modeling in realistic media severs the basis of seismic inversion and imaging. Recently viscoacoustic seismic modeling incorporating attenuation effects was done by solving a fractional Laplacian viscoacoustic wave equation. In this equation, attenuation, being spatially heterogeneous, is represented partially by the spatially varying power of the fractional Laplacian operator previously approximated by the global Fourier method. In this paper, we present a local spectral approach, based on Hermite distributed approximating functional (HDAF) method, to implement the fractional Laplacian in the viscoacoustic wave equation. The proposed approach combines local methods' simplicity and global methods' accuracy. Several numerical examples are presented to demonstrate the feasibility and accuracy of using the HDAF method for the frequency-independent Q fractional Laplacian wave equation.

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