Inversion gradients for acoustic VTI wavefield tomography

Li, Vladimir; Wang, Hui; Tsvankin, Ilya; Díaz, Esteban; Alkhalifah, Tariq

doi:10.1190/geo2016-0624.1

Cited by 12 publications

(15 citation statements)

References 64 publications

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“…The acoustic anisotropic approximation itself can only simulate kinematically-accurate P-waves, so it also has limitations in applications such as full waveform inversion (FWI). Current waveform inversion algorithms in practice are mainly utilizing kinematic information (traveltimes or phases), which means the proposed method still has a potential to be the modeling engine of FWI (Plessix & Cao 2011;Wu & Alkhalifah 2016;Wang & Tsvankin 2016;Li et al 2017;Zhang & Alkhalifah 2017). This is because, considering the complexity of the real earth, exactly fitting the dynamic information (waveforms) is usually not practical for field data sets.…”

Section: Discussionmentioning

confidence: 99%

Efficient anisotropic quasi-Pwavefield extrapolation using an isotropic low-rank approximation

Zhang

Liu

Alkhalifah

et al. 2017

Geophysical Journal International

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2 SUMMARYThe computational cost of quasi-P wave extrapolation depends on the complexity of the medium, and specifically the anisotropy. Our effective-model method splits the anisotropic dispersion relation into an isotropic background and a correction factor to handle this dependency. The correction term depends on the slope (measured using the gradient) of current wavefields and the anisotropy. As a result, the computational cost is independent of the nature of anisotropy, which makes the extrapolation efficient. A dynamic implementation of this approach decomposes the original pseudo-differential operator into a Laplacian, handled using the low-rank approximation of the spectral operator, plus an angular dependent correction factor applied in the space domain to correct for anisotropy. We analyze the role played by the correction factor and propose a new spherical decomposition of the dispersion relation. The proposed method provides accurate wavefields in phase and more balanced amplitudes than a previous spherical decomposition. Also, it is free of SVwave artifacts. Applications to a simple homogeneous transverse isotropic medium with a vertical symmetry axis (VTI) and a modified Hess VTI model demonstrate the effectiveness of the approach. The Reverse Time Migration (RTM) applied to a modified BP VTI model reveals that the anisotropic migration using the proposed modeling engine performs better than an isotropic migration.

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Section: Discussionmentioning

confidence: 99%

Efficient anisotropic quasi-Pwavefield extrapolation using an isotropic low-rank approximation

Zhang

Liu

Alkhalifah

et al. 2017

Geophysical Journal International

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“…The general sequence of steps for deriving the IDT gradients in VTI media is described in Li et al . (). Here, we extend their results to TTI models parameterized by V nmo (0), δ, η and the symmetry‐axis tilt θ.…”

Section: Theorymentioning

confidence: 97%

Image‐domain wavefield tomography for tilted transversely isotropic media

Tsvankin

Guitton

et al. 2019

Geophysical Prospecting

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Transversely isotropic models with a tilted symmetry axis have become standard for imaging beneath dipping shale formations and in active tectonic areas. Here, we develop a methodology of wave‐equation‐based image‐domain tomography for acoustic tilted transversely isotropic media. We obtain the gradients of the objective function using an integral wave‐equation operator based on a separable dispersion relation that takes the symmetry‐axis tilt into account. In contrast to the more conventional differential solutions, the integral operator produces only the P‐wavefield without shear‐wave artefacts, which facilitates both imaging and velocity analysis. The model is parameterized by the P‐wave zero‐dip normal‐moveout velocity, the Thomsen parameter δ, anellipticity coefficient η and the symmetry‐axis tilt θ. Assuming that the symmetry axis is orthogonal to reflectors, we study the influence of parameter errors on energy focusing in extended (space‐lag) common‐image gathers. Distortions in the anellipticity coefficient η introduce weak linear defocusing regardless of reflector dip, whereas δ influences both the energy focusing and depth scale of the migrated section. These results, which are consistent with the properties of the P‐wave time‐domain reflection moveout in tilted transversely isotropic media, provide important insights for implementation of velocity model‐building in the image‐domain. Then the algorithm is tested on a modified anticline section of the BP 2007 benchmark model.

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“…Partial stack power has proved to be more suitable for typical TI models than differential semblance optimization (V. Li et al, 2017).…”

Section: Objective Functionmentioning

confidence: 99%

“…It is convenient to invert for the parameters V 2 nmo , 2V 2 nmo η, and V 2 P0 , which form a linear parameter set for the dispersion relation employed in the integral extrapolator. The gradients for these parameters can be obtained from the ones described in V. Li et al (2017) by applying the chain rule. Because this parameterization is linear, the gradients are computed just from wavefield correlation and do not involve any model-parameter terms.…”

Section: Inversion Algorithmmentioning

confidence: 99%

“…Their results, however, show that realistic errors in the covariance matrix result in insufficient updates in the anisotropy coefficients. Here, we combine P-wave surface and VSP data to simultaneously estimate all three relevant VTI parameters using the adjointstate gradients derived by V. Li et al (2017) for the image-and data-domain objective functions.…”

Section: Introductionmentioning

confidence: 99%

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Acoustic VTI wavefield tomography of P-wave surface and VSP data

Tsvankin

Guitton

et al. 2017

SEG Technical Program Expanded Abstracts 2017

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CitationLi V, Tsvankin I, Guitton A, Alkhalifah T (2017) Acoustic VTI wavefield tomography of P-wave surface and VSP data. SUMMARYTransversely isotropic (TI) models have become standard in depth imaging and are often used in waveform inversion. Here, we develop a robust wave-equation-based tomographic algorithm for building acoustic VTI (transversely isotropic with a vertical symmetry axis) velocity models from P-wave surface reflection and vertical seismic profiling (VSP) data. Wavefield extrapolation is performed with an integral operator to avoid generating shear-wave artifacts. Focusing energy in extended images produced by reverse-time migration (RTM) makes it possible to update the zero-dip NMO velocity V nmo and the anellipiticity parameter η. To constrain the anisotropy coefficient δ and improve the accuracy in V nmo and η, we employ borehole information by introducing an additional objectivefunction term designed to fit VSP data. Image-guided smoothing is applied to both data-and image-domain gradients to steer the inversion towards geologically plausible solutions.Testing on the VTI Marmousi model shows that the joint inversion of surface and VSP data helps estimate all three relevant medium parameters.

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Inversion gradients for acoustic VTI wavefield tomography

Cited by 12 publications

References 64 publications

Efficient anisotropic quasi-Pwavefield extrapolation using an isotropic low-rank approximation

Efficient anisotropic quasi-Pwavefield extrapolation using an isotropic low-rank approximation

Image‐domain wavefield tomography for tilted transversely isotropic media

Acoustic VTI wavefield tomography of P-wave surface and VSP data

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