Anisotropic parameters and <i>P</i>‐wave velocity for orthorhombic media

Tsvankin, Ilya

doi:10.1190/1.1444231

Cited by 616 publications

(461 citation statements)

References 28 publications

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“…The elastic properties of most hydrocarbon reservoirs can be wellapproximated using orthorhombic anisotropy (Schoenberg & Helbig 1997;Tsvankin 1997;Ivanov & Stovas 2016) on the scale of common exploration seismic wavelengths. Systems of orthogonal fractures or vertical layering within a reservoir can be described by macroscale orthorhombic media; see Fig.…”

Section: Introductionmentioning

confidence: 99%

Waveform inversion for orthorhombic anisotropy with P waves: feasibility and resolution

Kazei

Alkhalifah

2018

Geophysical Journal International

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Summary Various parameterizations have been suggested to simplify inversions of first arrivals, or P −waves, in orthorhombic anisotropic media, but the number and type of retrievable parameters have not been decisively determined. We show that only six parameters can be retrieved from the dynamic linearized inversion of P −waves. These parameters are different from the six parameters needed to describe the kinematics of P −waves. Reflection-based radiation patterns from the P − P scattered waves are remapped into the spectral domain to allow for our resolution analysis based on the effective angle of illumination concept. Singular value decomposition of the spectral sensitivities from various azimuths, offset coverage scenarios, and data bandwidths allows us to quantify the resolution of different parameterizations, taking into account the signal-to-noise ratio in a given experiment. According to our singular value analysis, when the primary goal of inversion is determining the velocity of the P −waves, gradually adding anisotropy of lower orders (isotropic, vertically transversally isotropic, orthorhombic) in hierarchical parameterization is the best choice. Hierarchical parametrization reduces the tradeoff between the parameters and makes gradual introduction of lower anisotropy orders straightforward. When all the anisotropic parameters affecting P −wave propagation need to be retrieved simultaneously, the classic parameterization of orthorhombic medium with elastic stiffness matrix coefficients and density is a better choice for inversion. We provide estimates of the number and set of parameters that can be retrieved from surface seismic data in different acquisition scenarios. To set up an inversion process, the singular values determine the number of parameters that can be inverted and the resolution matrices from the parameterizations can be used to ascertain the set of parameters that can be resolved.

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Section: Introductionmentioning

confidence: 99%

Waveform inversion for orthorhombic anisotropy with P waves: feasibility and resolution

Kazei

Alkhalifah

2018

Geophysical Journal International

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“…Figure 1 a) A diagram of an orthorhombic reservoir (Tsvankin, 1997) in an isotropic background within the context of a potential acquisition scenario. b).…”

Section: Theorymentioning

confidence: 99%

“…Specifically, it describes a system of orthogonal fractures or layering (vertical) at the microscale level within the reservoir. P-wave velocity analysis for orthorhombic media (Tsvankin, 1997) defines the resolution limits of most ray-based methods. Recently, the interest in the dynamic components of the wavefield, despite the additional acquisition and computational requirements, has grown as we seek the higher resolution potential of wavefields.…”

Section: Introductionmentioning

confidence: 99%

On the Resolution of Inversion for Orthorhombic Anisotropy

Kazei

Alkhalifah²

2017

Proceedings

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SummaryWe investigate the resolution of elastic anisotropic inversion for orthorhombic media with P-waves by remapping classic radiation patterns into the wavenumber domain. We show analytically that dynamic linearized inversion (linearized reverse-time migration and full-waveform inversion) for orthorhombic anisotropy based on longitudinal waves is fundamentally sensitive to emph{six} parameters only and density, in which the perturbing effects can be represented by particular anisotropy configuration. Singular value decomposition of spectral sensitivities allows us to provide estimates of the number of parameters one could invert in specific acquisition settings, and with certain parametrization. In most acquisition scenarios, a hierarchical parameterization based on the $P$, and $S$-wave velocities, along with dimensionless parameters that describe the anisotropy as velocity ratio in the radial and azimuthal directions, minimizes the tradeoff and increases the sensitivity of the data to velocity compared to the standard (stiffness, density) parametrization. These features yield more robust velocity estimation, by focusing the inversion on a subset of invertible parameters.

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“…Here, we focus on the parameterization, which includes three VTI parameters: the horizontal velocity v h1 , ϵ 1 , η 1 , which are defined in the ðx; zÞ vertical plane, and three azimuthal anisotropy parameters: two deviation parameters ϵ d , η d , and the parameter δ 3 defined from the x-axis TI plane (Tsvankin, 1997). The horizontal velocity is related to the vertical P-wave velocity v v and to the NMO velocity v n1 in the ðx; zÞ plane through the equations given by…”

Section: A Suitable Choice Of Parametersmentioning

confidence: 99%

“…Orthorhombic anisotropy is usually regarded as the most practical realistic approximation of the earth subsurface because it combines the anisotropy admitted by the natural, mostly horizontal layering of the earth (due to gravity), as well as the vertical aligned fractures, usually found in fractured reservoirs or horizontal stresses caused by the tectonic regime or salt intrusions (Cheadle et al, 1991;Wild and Crampin, 1991;Schoenberg and Helbig, 1997;Tsvankin, 1997;Bakulin et al, 2000). Contrary to the VTI case, orthorhombic media incorporate velocity variations with azimuths (azimuthal anisotropy), therefore, 3D wide-azimuth acquisitions are essential to estimate these variations (Tsvankin and Grechka, 2011).…”

Section: Introductionmentioning

confidence: 99%

Full-waveform inversion in acoustic orthorhombic media and application to a North Sea data set

Masmoudi

Alkhalifah

2018

GEOPHYSICS

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Full-waveform inversion (FWI) in anisotropic media is challenging, mainly because of the large computational cost, especially in 3D, and the potential trade-offs between the model parameters needed to describe such media. By analyzing the trade-offs and understanding the resolution limits of the inversion, we can constrain FWI to focus on the main parameters the data are sensitive to and push the inversion toward more reliable models of the subsurface. Orthorhombic anisotropy is one of the most practical approximations of the earth subsurface that takes into account the natural horizontal layering and the vertical fracture network. We investigate the feasibility of a multiparameter FWI for an acoustic orthorhombic model described by six parameters. We rely on a suitable parameterization based on the horizontal velocity and five dimensionless anisotropy parameters. This particular parameterization allows a multistage model inversion strategy in which the isotropic, then, the vertical transverse isotropic, and finally the orthorhombic model can be successively updated. We applied our acoustic orthorhombic inversion on the SEG-EAGE overthrust synthetic model. The observed data used in the inversion are obtained from an elastic variable density version of the model. The quality of the inverted model suggests that we may recover only four parameters, with different resolution scales depending on the scattering potential of these parameters. Therefore, these results give useful insights on the expected resolution of the inverted parameters and the potential constraints that could be applied to an orthorhombic model inversion. We determine the efficiency of the inversion approach on real data from the North Sea. The inverted model is in agreement with the geologic structures and well-log information.

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Anisotropic parameters and P‐wave velocity for orthorhombic media

Cited by 616 publications

References 28 publications

Waveform inversion for orthorhombic anisotropy with P waves: feasibility and resolution

Waveform inversion for orthorhombic anisotropy with P waves: feasibility and resolution

On the Resolution of Inversion for Orthorhombic Anisotropy

Full-waveform inversion in acoustic orthorhombic media and application to a North Sea data set

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