Efficient modeling of wave propagation in a vertical transversely isotropic attenuative medium based on fractional Laplacian

Tieyuan Zhu, Tong Bai

Research output: Contribution to journalArticle

Abstract

To efficiently simulate wave propagation in a vertical transversely isotropic (VTI) attenuative medium, we have developed a viscoelastic VTI wave equation based on fractional Laplacian operators under the assumption of weak attenuation (Q≫1), where the frequency-independent Q model is used to mathematically represent seismic attenuation. These operators that are nonlocal in space can be efficiently computed using the Fourier pseudospectral method. We evaluated the accuracy of numerical solutions in a homogeneous transversely isotropic medium by comparing with theoretical predictions and numerical solutions by an existing viscoelastic-anisotropic wave equation based on fractional time derivatives. To accurately handle heterogeneous Q, we select several Q values to compute their corresponding fractional Laplacians in the wavenumber domain and interpolate other fractional Laplacians in space. We determined its feasibility by modeling wave propagation in a 2D heterogeneous attenuative VTI medium. We concluded that the new wave equation is able to improve the efficiency of wave simulation in viscoelastic-VTI media by several orders and still maintain accuracy.

Original languageEnglish (US)
Pages (from-to)T121-T131
JournalGeophysics
Volume84
Issue number3
DOIs
StatePublished - May 1 2019

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wave equation
Wave equations
Wave propagation
wave propagation
Viscoelastic Substances
modeling
seismic attenuation
Derivatives
prediction
simulation

All Science Journal Classification (ASJC) codes

  • Geochemistry and Petrology

Cite this

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abstract = "To efficiently simulate wave propagation in a vertical transversely isotropic (VTI) attenuative medium, we have developed a viscoelastic VTI wave equation based on fractional Laplacian operators under the assumption of weak attenuation (Q≫1), where the frequency-independent Q model is used to mathematically represent seismic attenuation. These operators that are nonlocal in space can be efficiently computed using the Fourier pseudospectral method. We evaluated the accuracy of numerical solutions in a homogeneous transversely isotropic medium by comparing with theoretical predictions and numerical solutions by an existing viscoelastic-anisotropic wave equation based on fractional time derivatives. To accurately handle heterogeneous Q, we select several Q values to compute their corresponding fractional Laplacians in the wavenumber domain and interpolate other fractional Laplacians in space. We determined its feasibility by modeling wave propagation in a 2D heterogeneous attenuative VTI medium. We concluded that the new wave equation is able to improve the efficiency of wave simulation in viscoelastic-VTI media by several orders and still maintain accuracy.",
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Efficient modeling of wave propagation in a vertical transversely isotropic attenuative medium based on fractional Laplacian. / Zhu, Tieyuan; Bai, Tong.

In: Geophysics, Vol. 84, No. 3, 01.05.2019, p. T121-T131.

Research output: Contribution to journalArticle

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