Fractal-mechanical network based time-domain viscoacoustic wave equation

Xing, Guangchi; Zhu, Tieyuan

doi:10.1190/segam2018-2995782.1

Cited by 11 publications

(5 citation statements)

References 32 publications

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“…If the Q heterogeneity becomes even stronger in practice, we can choose more Q values for implementing PSFLPI to maintain the numerical accuracy. Also, several advanced numerical schemes have been reported to further improve the accuracy of calculating the fractional Laplacian operators, e.g., low-rank approximation (Sun et al, 2015), analytic wave propagator plus low-rank approximation (Chen et al, 2016), Hermitian-distributed approximation functional (Yao et al, 2017), and fixed-order fractional Laplacian (Xing and Zhu, 2018). These three methods have the potential to improve the accuracy of solving the viscoelastic-TI wave equation proposed in this study.…”

Section: Accuracy Of Computing Fractionalmentioning

confidence: 99%

“…These three methods have the potential to improve the accuracy of solving the viscoelastic-TI wave equation proposed in this study. Among them, a fixed-order power term of the fractional Laplacian using an ad-hoc approximation presented by Chen et al (2016) and Xing and Zhu (2018) may further simplify the formulation of the viscoelastic-VTI wave equation and will be investigated in upcoming studies.…”

Section: Accuracy Of Computing Fractionalmentioning

confidence: 99%

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

Zhu

Bai

2019

GEOPHYSICS

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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 ([Formula: see text]), where the frequency-independent [Formula: see text] 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 [Formula: see text], we select several [Formula: see text] 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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Section: Accuracy Of Computing Fractionalmentioning

confidence: 99%

Section: Accuracy Of Computing Fractionalmentioning

confidence: 99%

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

Zhu

Bai

2019

GEOPHYSICS

Self Cite

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“…For heterogeneous media, the order of the fractional Laplacian may be spatially variable, which suffer from the mixed-domain problems and can also introduce strong noises because of the Gibb's phenomenon in the inverse Fourier transform, especially for models with sharp Q contrasts (Li et al, 2016). Several strategies are proposed to cope with the problem of the spatially variable-order fractional Laplacian (Chen et al, 2016;Yao et al, 2017;Xing and Zhu, 2018;Wang et al, 2018). In addition, with the decoupled dispersion and attenuation effects, fractional Laplacian wave equations have been widely used to achieve Q-compensated reverse-time migration Guo et al, 2016;Zhu and Sun, 2017) and waveform inversion (Xue et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Modelling of viscoacoustic wave propagation in transversely isotropic media using decoupled fractional Laplacians

Qiao

Sun

Jie

2020

Geophysical Prospecting

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A new wave equation is derived for modelling viscoacoustic wave propagation in transversely isotropic media under acoustic transverse isotropy approximation. The formulas expressed by fractional Laplacian operators can well model the constant‐Q (i.e. frequency‐independent quality factor) attenuation, anisotropic attenuation, decoupled amplitude loss and velocity dispersion behaviours. The proposed viscoacoustic anisotropic equation can keep consistent velocity and attenuation anisotropy effects with that of qP‐wave in the constant‐Q viscoelastic anisotropic theory. For numerical simulations, the staggered‐grid pseudo‐spectral method is implemented to solve the velocity–stress formulation of wave equation in the time domain. The constant fractional‐order Laplacian approximation method is used to cope with spatial variable‐order fractional Laplacians for efficient modelling in heterogeneous velocity and Q media. Simulation results for a homogeneous model show the decoupling of velocity dispersion and amplitude loss effects of the constant‐Q equation, and illustrate the influence of anisotropic attenuation on seismic wavefields. The modelling example of a layered model illustrates the accuracy of the constant fractional‐order Laplacian approximation method. Finally, the Hess vertical transversely isotropic model is used to validate the applicability of the formulation and algorithm for heterogeneous media.

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“…They subsequently apply this equation to compensate attenuation effects in reverse-time migration (RTM) (Zhu, 2014;, reflectivity inversion (Sun et al, 2016), and FWI (Xue et al, 2018). Based on a modified constant-Q wave equation (Xing & Zhu, 2018), Xing and Zhu (2019) derive the corresponding Fréchet kernels and misfit gradients for traveltime, amplitude, and waveform measurements. Yang et al (2016) give a systematic review of the viscoelastic wave equations and the corresponding applications in FWI.…”

Section: Introductionmentioning

confidence: 99%

Estimating P Wave Velocity and Attenuation Structures Using Full Waveform Inversion Based on a Time Domain Complex‐Valued Viscoacoustic Wave Equation: The Method

Yang

Zhu

et al. 2020

JGR Solid Earth

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To complement velocity distributions, seismic attenuation provides additional important information on fluid properties of hydrocarbon reservoirs in exploration seismology, as well as temperature distributions, partial melting, and water content within the crust and mantle in earthquake seismology. Full waveform inversion (FWI), as one of the state-of-the-art seismic imaging techniques, can produce high-resolution constraints for subsurface (an)elastic parameters by minimizing the difference between observed and predicted seismograms. Traditional waveform inversion for attenuation is commonly based on the standard-linear-solid (SLS) wave equation, in which case the quality factor (Q) has to be converted to stress and strain relaxation times. When using multiple attenuation mechanisms in the SLS method, it is difficult to directly estimate these relaxation time parameters. Based on a time domain complex-valued viscoacoustic wave equation, we present an FWI framework for simultaneously estimating subsurface P wave velocity and attenuation distributions. Because Q is explicitly incorporated into the viscoacoustic wave equation, we directly derive P wave velocity and Q sensitivity kernels using the adjoint-state method and simultaneously estimate their subsurface distributions. By analyzing the Gauss-Newton Hessian, we observe strong interparameter crosstalk, especially the leakage from velocity to Q. We approximate the Hessian inverse using a preconditioned L-BFGS method in viscoacoustic FWI, which enables us to successfully reduce interparameter crosstalk and produce accurate velocity and attenuation models. Numerical examples demonstrate the feasibility and robustness of the proposed method for simultaneously mapping complex velocity and Q distributions in the subsurface.

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Fractal-mechanical network based time-domain viscoacoustic wave equation

Cited by 11 publications

References 32 publications

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

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

Modelling of viscoacoustic wave propagation in transversely isotropic media using decoupled fractional Laplacians

Estimating P Wave Velocity and Attenuation Structures Using Full Waveform Inversion Based on a Time Domain Complex‐Valued Viscoacoustic Wave Equation: The Method

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