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

Zhu, Tieyuan; Bai, Tong

doi:10.1190/geo2018-0538.1

Cited by 35 publications

(18 citation statements)

References 43 publications

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“…By employing the fractional Laplacian to approximate the fractional time derivatives, the stress (σ ij )-strain (ε ij ) relationship for attenuative VTI media can be written as (Zhu and Bai, 2019):…”

Section: Methodology Anisotropic Viscoelastic Modeling Based On Fractmentioning

confidence: 99%

“…On the other hand, setting γ ij ¼ 0 only in equation 4 eliminates the velocity dispersion, while setting γ ij ¼ 0 only in equation 5 removes the dissipation. A more detailed description of the decoupled viscoelastic VTI wave equation can be found in Zhu and Bai (2019).…”

Section: Methodology Anisotropic Viscoelastic Modeling Based On Fractmentioning

confidence: 99%

“…However, these wave propagators include coupled effects of dissipation and dispersion, which poses a challenge for Q-compensated TR imaging. Zhu and Bai (2019) develop a formulation with fractional Laplacians for viscoelastic VTI media that decouples the attenuation terms into those responsible for amplitude loss and dispersion.…”

Section: Introductionmentioning

confidence: 99%

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Attenuation compensation for time-reversal imaging in VTI media

Bai

Zhu

Tsvankin

2018

SEG Technical Program Expanded Abstracts 2018

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Time reversal is a key component in reverse-time migration (RTM) and source localization using wavefield extrapolation. The successful implementation of time reversal depends on the time symmetry (reversibility) of the wave equation in acoustic and elastic media. This symmetry in time, however, is no longer valid in attenuative media, and attenuation is often anisotropic. Here, we employ a viscoelastic anisotropic wave equation that decouples the influence of energy dissipation and velocity dispersion. That equation helps compensate for anisotropic attenuation and restore the time symmetry by changing the signs of the dissipation-dominated terms in time-reversed propagation, while keeping the dispersion-related terms unchanged. We test the Q-compensated time-reversal imaging algorithm on synthetic microseismic data from a 2D transversely isotropic medium with a vertical symmetry axis (VTI). After back-propagating multicomponent data acquired in a vertical borehole, we image microseismic sources using wavefield focusing. The source excitation times are estimated by picking the maximum amplitude of the squared shear strain component ϵ 13 at the source locations. Accounting for attenuation anisotropy produces superior source images and more accurate excitation times compared to those obtained without attenuation compensation or with purely isotropic attenuation coefficients. The algorithm is also applied to a modified BP TI model to investigate the influence of such factors as survey geometry, errors in velocity and attenuation, noise, and limited aperture.

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Section: Methodology Anisotropic Viscoelastic Modeling Based On Fractmentioning

confidence: 99%

Section: Methodology Anisotropic Viscoelastic Modeling Based On Fractmentioning

confidence: 99%

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Attenuation compensation for time-reversal imaging in VTI media

Bai

Zhu

Tsvankin

2018

SEG Technical Program Expanded Abstracts 2018

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“…In addition, Zhu (2017) derives the viscoelastic wave equations based on the fractional time derivatives. By transforming the fractional time derivatives into fractional Laplacians, Zhu and Bai (2019) further implement the wave propagation in VTI attenuating media using the PSM. Following Zhu's work, we derive the corresponding viscoacoustic wave equations in VTI attenuating media and develop an effective approach to implement the numerical modelling based on the arbitrary-order Taylor series expansion (TE) approximation.…”

Section: Introductionmentioning

confidence: 99%

Arbitrary‐order Taylor series expansion‐based viscoacoustic wavefield simulation in 3D vertical transversely isotropic media

Zhang

Liu

2020

Geophysical Prospecting

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Taking the anisotropy of velocity and attenuation into account, we investigate the wavefield simulation of viscoacoustic waves in 3D vertical transversely isotropic attenuating media. The viscoacoustic wave equations with the decoupled amplitude attenuation and phase dispersion are derived from the fractional Laplacian operator and using the acoustic approximation. With respect to the spatially variable fractional Laplacian operator in the formulation, we develop an effective algorithm to realize the viscoacoustic wavefield extrapolation by using the arbitrary‐order Taylor series expansion. Based on the approximation, the mixed‐domain fractional Laplacian operators are decoupled from the wavenumbers and fractional orders. Thus, the viscoacoustic wave propagation can be conveniently implemented by using a generalized pseudospectral method. In addition, we perform the accuracy and efficiency analyses among first‐, second‐ and third‐order Taylor series expansion pseudospectral methods with different quality factors. Considering both the accuracy and computational cost, the second‐order Taylor series expansion pseudospectral method can generally satisfy the requirements for most attenuating media. Numerical modelling examples not only illustrate that our decoupled viscoacoustic wave equations can effectively describe the attenuating property of the medium, but also demonstrate the accuracy and the high robustness of our proposed schemes.

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“…Extending some of these models to the anisotropic case can be seen in Carcione (2015), Bai and Tsvankin (2016), Bai et al (2017) Zhu (2017), Zhu and Bai (2019).…”

Section: Introductionmentioning

confidence: 99%

Viscoacoustic anisotropic wave equations

Hao

Alkhalifah

2019

SEG Technical Program Expanded Abstracts 2019

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Running head: Viscoacoustic anisotropic wave equations ABSTRACT The wave equation plays a central role in seismic modeling, processing and inversion. Incorporating the attenuation anisotropy into the acoustic anisotropic wave equations provides a choice for acoustic modeling and imaging in fluid-filled anisotropic reservoirs. However, the existing viscoacoustic anisotropic wave equations are obtained for a specified viscoacoustic model. In this paper, we present a relatively general representation of the scalar and vector viscoacoustic wave equations for orthorhombic anisotropy. We also show the viscoacoustic wave equations for transverse isotropy as a special case. The viscoacoustic orthorhombic wave equations are flexible for multiple viscoacoustic models. We take into account the classic visocoacoustic models such as the Kelvin-Voigt, Maxwell, standard-linear-solid 1 and Kjartansson models, and derive the corresponding viscoacoustic wave equations in differential form. To analyze the wave propagation in viscoacoustic models, we derive the asymptotic acoustic point-source radiation. Numerical examples show a comparison of the acoustic waveforms excited by a point source in the viscoacoustic orthorhombic models and the corresponding nonattenuating model, and the effect of the attenuation anisotropy on the acoustic waveforms.

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

Cited by 35 publications

References 43 publications

Attenuation compensation for time-reversal imaging in VTI media

Attenuation compensation for time-reversal imaging in VTI media

Arbitrary‐order Taylor series expansion‐based viscoacoustic wavefield simulation in 3D vertical transversely isotropic media

Viscoacoustic anisotropic wave equations

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