Weak elastic anisotropy

Thomsen, Leon

doi:10.1190/1.1442051

Cited by 3,927 publications

(2,611 citation statements)

References 11 publications

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“…Reflection-based radiation patterns were used to analyze the ability of anisotropic elastic FWI to estimate VTI parameters using only P-waves in various parameterizations (Gholami et al 2013b;Alkhalifah & Plessix 2014). Podgornova et al (2015) proved that only three VTI parameters are invertible from P-P waves under the assumption of weak anisotropy, by using SVD analysis to investigate the FWI resolution possibilities with P-P and P-SV waves in Thomsen's well-known parameterization for VTI media (Thomsen 1986). …”

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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“…Here, δ 1 and δ 2 are the Thomsen's (1986) parameters in the ðx; zÞ and ðy; zÞ vertical planes, respectively. These values correspond to v h1 ≈ 2366,…”

Section: Forward Modelingmentioning

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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“…For this purpose, we built a VTI model using Thomsen's (1986) parameters from an initial isotropic model. The orthorhombic model is built from the VTI model by introducing a system of synthetic vertical cracks in the medium.…”

Section: P-s Conversion Point In Anisotropic Mediamentioning

confidence: 99%

Comparing P-S conversion point location in isotropic and anisotropic media

et al. 2006

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ABSTRACT. The determination of the exact position of the P-S conversion point (CP) is an important issue in converted-wave seismology. Frequently, this issue is approached considering that the rock formation is isotropic. This simple approach may lead to significant errors due to the anisotropic features of the subsurface. This paper presents a comparison between the position of the CP obtained from the isotropic solution and the position of the CP considering two types of anisotropy: the transversely isotropic medium with vertical axis of symmetry, the so-called VTI, and an orthorhombic medium. In order to determine the location of the CP, the modeling program ANRAY, based on ray tracing method, was used. It is shown that for the VTI case the discrepancy between the true position of the CP and the one found by assuming isotropy can be in the order of hundreds of meters, even for offset/depth ratio, (X/Z), less than 2. On the other hand, for some particular values of Thomsen's parameters and δ, it can be demonstrated that, the position of the CP practically coincides with the isotropic case. For orthorhombic symmetry (azimuthal anisotropy), the CP, in general, is no longer located in the vertical plane defined by the source-receiver positions, i.e., the discrepancy between CP locations is expressed by an inline and an offline components. The offline component value depends on the anisotropic nature of the medium. This observation is not valid only for orthorhombic models since similar discrepancies can also be observed in cases where the anisotropy is induced by cross-dipping structures or in models with lower anisotropic symmetries.Keywords: Converted wave, Conversion point, Anisotropy. RESUMO.A determinação exata do ponto de conversão (PC) do modo convertido PSé um aspecto relevante da sismologia da onda convertida. Geralmente, este problemaé abordado considerando-se modelos isotrópicos. Mas esta simplificação pode induzir erros significativos devidoà desconsideração das características anisotrópicas do subsolo. O presente artigo apresenta uma comparação no que diz respeitoà posição do PC nos casos isotrópico e anisotrópico. No caso anisotrópico consideram-se as seguintes simetrias: transversalmente isotrópica com eixo de simetria vertical (VTI) e ortorrômbica. Os PC's são calculados mediante a teoria do raio.Mostra-se que para a simetria VTI a discrepância entre a verdadeira posição do PC e o calculado, supondo isotropia, pode ser da ordem de centenas de metros, mesmo para uma relação afastamento-profundidade menor que 2. Por outro lado, para alguns valores dos parâmetros de Thomsen ( e δ), demonstra-se que a posição do PC praticamente coincide com o caso isotrópico. Para a simetria ortorrômbica queé um caso de anisotropia azimutal, o PC, em geral, não se localiza no plano vertical definido pelas posições da fonte e do receptor, istoé, a discrepância entre a locação do PC isotrópico ou VTI com relaçãoà ortorrômbica possui componentes paralelas e normais ao referido plano. A componente normal depende da intens...

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Weak elastic anisotropy

Cited by 3,927 publications

References 11 publications

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

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

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

Comparing P-S conversion point location in isotropic and anisotropic media

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