<i>Q</i>-compensated reverse-time migration

Zhu, Tieyuan; Harris, Jerry M.; Biondi, B.

doi:10.1190/geo2013-0344.1

Cited by 278 publications

(68 citation statements)

References 32 publications

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“…His formulation captures amplitude loss and velocity dispersion in a single term. Separation of amplitude loss and dispersion operators in the fractional Laplacian wave equation may be preferable because separated forms are more useful in compensating for attenuation loss in inverse problems, e.g., reverse time imaging by only reversing sign of the attenuation operator and leaving the sign of the dispersion operator unchanged Zhu, 2014;Zhu et al, 2014). Zhang et al (2010) also derive the approximate constant-Q wave equation with decoupled amplitude loss and dispersion effects, but their derivation using the normalization transform for decoupling amplitude loss and dispersion is not clearly described in the abstract.…”

Section: Introductionmentioning

confidence: 99%

Modeling acoustic wave propagation in heterogeneous attenuating media using decoupled fractional Laplacians

2014

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We evaluated a time-domain wave equation for modeling acoustic wave propagation in attenuating media. The wave equation was derived from Kjartansson's constant-Q constitutive stress-strain relation in combination with the mass and momentum conservation equations. Our wave equation, expressed by a second-order temporal derivative and two fractional Laplacian operators, described very nearly constant-Q attenuation and dispersion effects. The advantage of using our formulation of two fractional Laplacians over the traditional fractional time derivative approach was the avoidance of time history memory variables and thus it offered more economic computations. In numerical simulations, we formulated the first-order constitutive equations with the perfectly matched layer absorbing boundaries. The temporal derivative was calculated with a staggered-grid finite-difference approach. The fractional Laplacians are calculated in the spatial frequency domain using a Fourier pseudospectral implementation. We validated our numerical results through comparisons with theoretical constant-Q attenuation and dispersion solutions, field measurements from the Pierre Shale, and results from 2D viscoacoustic analytical modeling for the homogeneous Pierre Shale. We also evaluated different formulations to show separated amplitude loss and dispersion effects on wavefields. Furthermore, we generalized our rigorous formulation for homogeneous media to an approximate equation for viscoacoustic waves in heterogeneous media. We then investigated the accuracy of numerical modeling in attenuating media with different Q-values and its stability in largecontrast heterogeneous media. Finally, we tested the applicability of our time-domain formulation in a heterogeneous medium with high attenuation.

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Section: Introductionmentioning

confidence: 99%

Modeling acoustic wave propagation in heterogeneous attenuating media using decoupled fractional Laplacians

2014

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“…Compared to Yan and Liu (2013), they succeeded in decreasing the computation time without affecting accuracy. Zhu et al (2014) analyzed the Q effects on the source and receiver wavefi elds in RTM and decoupled the operator affecting the amplitude and phase in the process of wavefield extrapolation to the viscoelastic wave equation to realize Q-RTM.…”

Section: Introductionmentioning

confidence: 99%

Attenuation compensation in multicomponent Gaussian beam prestack depth migration

Chen

Liu

2015

Appl. Geophys.

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Gaussian beam prestack depth migration is an accurate imaging method of subsurface media. Prestack depth migration of multicomponent seismic data improves the accuracy of imaging subsurface complex geological structures. Viscoelastic prestack depth migration is of practical significance because it considers the viscosity of the subsurface media. We use Gaussian beam migration to compensate for the attenuation in multicomponent seismic data. First, we use the Gaussian beam method to simulate the wave propagation in a viscoelastic medium and introduce the complex velocity Q-related and exact viscoelastic Zoeppritz equation. Second, we discuss PP-and PS-wave Gaussian beam prestack depth migration algorithms for common-shot gathers to derive expressions for the attenuation and compensation. The algorithms correct the amplitude attenuation and phase distortion caused by Q, and realize multicomponent Gaussian beam prestack depth migration based on the attenuation compensation and account for the effect of inaccurate Q on migration. Numerical modeling suggests that the imaging resolution of viscoelastic Gaussian beam prestack depth migration is high when the viscosity of the subsurface is considered.

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“…Treeby and Cox (2010) further explicitly decompose the dispersion and attenuation terms in the viscoelastic FD equation, greatly improving computational efficiency. Viscoelastic seismic imaging of viscosity acoustic media can compensate viscoelastic dispersion and attenuation and has been widely used to improve seismic imaging quality (Zhu 2014;Zhu et al 2014).…”

Section: Introductionmentioning

confidence: 99%

Acoustic viscoelastic modeling by frequency-domain boundary element method

Guan

Sun

2017

Earthq Sci

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Earth medium is not completely elastic, with its viscosity resulting in attenuation and dispersion of seismic waves. Most viscoelastic numerical simulations are based on the finite-difference and finite-element methods. Targeted at viscoelastic numerical modeling for multilayered media, the constant-Q acoustic wave equation is transformed into the corresponding wave integral representation with its Green's function accounting for viscoelastic coefficients. An efficient alternative for full-waveform solution to the integral equation is proposed in this article by extending conventional frequency-domain boundary element methods to viscoelastic media. The viscoelastic boundary element method enjoys a distinct characteristic of the explicit use of boundary continuity conditions of displacement and traction, leading to a semi-analytical solution with sufficient accuracy for simulating the viscoelastic effect across irregular interfaces. Numerical experiments to study the viscoelastic absorption of different Q values demonstrate the accuracy and applicability of the method.

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Q-compensated reverse-time migration

Cited by 278 publications

References 32 publications

Modeling acoustic wave propagation in heterogeneous attenuating media using decoupled fractional Laplacians

Modeling acoustic wave propagation in heterogeneous attenuating media using decoupled fractional Laplacians

Attenuation compensation in multicomponent Gaussian beam prestack depth migration

Acoustic viscoelastic modeling by frequency-domain boundary element method

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