Application of perturbation theory to a P-wave eikonal equation in orthorhombic media

Stovas, Alexey; Masmoudi, Nabil; Alkhalifah, Tariq

doi:10.1190/geo2016-0097.1

Cited by 28 publications

(5 citation statements)

References 12 publications

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“…A very accurate GMA approximation in ORT media for phase and group velocities is developed by Hao and Stovas (). The perturbation‐based moveout approximation with a traditional elliptic background for ORT media is discussed by Stovas, Masmoudi and Alkhalifah (). The traveltime approximation for the ORT model using perturbation theory by other anellipticity parameters in inhomogeneous background media is developed by Masmoudi and Alkhalifah ().…”

Section: Introductionmentioning

confidence: 99%

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Perturbation‐based moveout approximations in anisotropic media

Stovas

Hao

2016

Geophysical Prospecting

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The moveout approximations play an important role in seismic data processing. The standard hyperbolic moveout approximation is based on an elliptical background model with two velocities: vertical and normal moveout. We propose a new set of moveout approximations based on a perturbation series in terms of anellipticity parameters using the alternative elliptical background model defined by vertical and horizontal velocities. We start with a transversely isotropic medium with a vertical symmetry axis. Then, we extend this approach to a homogeneous orthorhombic medium. To define the perturbation coefficients for a new background, we solve the eikonal equation with horizontal velocities in transversely isotropic medium with a vertical symmetry axis and orthorhombic media. To stabilise the perturbation series and improve the accuracy, the Shanks transform is applied for all the cases. We select different parameterisations for both velocities and anellipticity parameters for an orthorhombic model. From the comparison in traveltime error, the new moveout approximations result in better accuracy comparing with the standard perturbation‐based methods and other approximations.

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Section: Introductionmentioning

confidence: 99%

“…The perturbation series in terms of anellipticity parameters is defined up to the second order (Stovas et al . ):

τ = τ_{0} + \sum_{i} a_{i}^{k} η_{i} + \sum_{i, j} b_{italicij}^{k} η_{i} η_{j}, k = A, B, C, D .

…”

Section: Introductionmentioning

confidence: 99%

Perturbation‐based moveout approximations in anisotropic media

Stovas

Hao

2016

Geophysical Prospecting

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“…The perturbation method using a Taylor series expansion is by far the most widespread approach developed by Alkhalifah (2011a,b) and Stovas & Alkhalifah (2012). Such an approach has been adopted by many researchers (Stovas & Alkhalifah 2012;Alkhalifah 2013;Waheed et al 2013;Stovas et al 2016) for solving anisotropic eikonal equations. Recently, we applied this method to the complex eikonal equation for the seismic complex traveltime .…”

Section: Differences Between Ham and Perturbation Theorymentioning

confidence: 99%

“…Xu et al (2017) have applied perturbation theory to moveout approximations in an anisotropic medium. Later, this approach has been extended to an orthorhombic medium (Stovas et al 2016) and attenuating VTI medium (Hao & Alkhalifah 2017).…”

Section: Introductionmentioning

confidence: 99%

Traveltime approximation for strongly anisotropic media using the homotopy analysis method

Huang

Greenhalgh

2018

Geophysical Journal International

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Traveltime approximation plays an important role in seismic data processing, for example, anisotropic parameter estimation and seismic imaging. By exploiting seismic traveltimes, it is possible to improve the accuracy of anisotropic parameter estimation and the resolution of seismic imaging. Conventionally, the traveltime approximations in anisotropic media are obtained by expanding the anisotropic eikonal equation in terms of the anisotropic parameters and the elliptically anisotropic eikonal equation based on perturbation theory. Such an expansion assumes a small perturbation and weak anisotropy. In a realistic medium, however, the assumption of small perturbation likely breaks down. We present a retrieved zero-order deformation equation that creates a map from the anisotropic eikonal equation to a linearized partial differential equation system based on the homotopy analysis method. By choosing the linear and nonlinear operators in the retrieved zero-order deformation equation, we develop new traveltime approximations that allow us to compute the traveltimes for a medium of arbitrarily strength anisotropy. A comparison of the traveltimes and their errors from the homotopy analysis method and from the perturbation method suggests that the traveltime approximations provide a more reliable result in strongly anisotropic media.

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“…Under the acoustic assumption, different parameterizations for P wave in the ORT medium are defined (Vasconcelos and Tsvankin ; Stovas ; Xu and Stovas ). The corresponding traveltime approximations for the acoustic ORT model are also proposed (Sripanich and Fomel ; Stovas, Masmoudi and Alkhalifah ; Ravve and Koren ; Xu, Stovas and Hao ). The approximations for relative geometrical spreading are proposed in VTI (Xu and Stovas ) and ORT model (Xu and Stovas ; Xu, Stovas and Sripanich ) under the acoustic assumption.…”

Section: Introductionmentioning

confidence: 99%

The kinematics of S waves in acoustic orthorhombic media

Stovas

2019

Geophysical Prospecting

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Orthorhombic models are often used in the seismic industry nowadays to describe azimuthal and polar anisotropy and reasonably realistic in capturing the features of the earth interior. It is challenging to handle so many model parameters in the seismic data processing. In order to reduce the number of the parameters for P wave, the acoustic orthorhombic medium is proposed by setting all on‐axis S wave velocities to zero. However, due to the coupled behaviour for P and S waves in the orthorhombic model, the ‘S wave artefacts’ are still remained in the acoustic orthorhombic model, which kinematics needs to be defined and analysed. In this paper, we analyse the behaviour of S wave in acoustic orthorhombic media. By analysis of the slowness surface in acoustic orthorhombic media, we define the S waves (or S wave artefacts) that are more complicated in shape comparing to the one propagating in an acoustic transversely isotropic medium with a vertical symmetry axis. The kinematic properties of these waves are defined and analysed in both phase and group domain. The caustics, amplitude and the multi‐layered case for S wave in acoustic orthorhombic model are also discussed. It is shown that there are two waves propagating in this acoustic orthorhombic medium. One of these waves is similar to the one propagating in acoustic vertical symmetry axis media, whereas another one has a very complicated shape consisting of two crossing surfaces.

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Application of perturbation theory to a P-wave eikonal equation in orthorhombic media

Cited by 28 publications

References 12 publications

Perturbation‐based moveout approximations in anisotropic media

Perturbation‐based moveout approximations in anisotropic media

Traveltime approximation for strongly anisotropic media using the homotopy analysis method

The kinematics of S waves in acoustic orthorhombic media

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