Long‐wave elastic anisotropy in transversely isotropic media

Geophysics ◽  
1979 ◽  
Vol 44 (5) ◽  
pp. 896-917 ◽  
Author(s):  
James G. Berryman
Keyword(s):  
Elastic Anisotropy ◽  
Transversely Isotropic ◽  
Layered Media ◽  
Seismic Signal ◽  
Perturbation Scheme ◽  
Low Velocity ◽  
Compressional Waves ◽  
Long Wave ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Compressional waves in horizontally layered media exhibit very weak long‐wave anisotropy for short offset seismic data within the physically relevant range of parameters. Shear waves have much stronger anisotropic behavior. Our results generalize the analogous results of Krey and Helbig (1956) in several respects: (1) The inequality [Formula: see text] derived by Postma (1955) for periodic isotropic, two‐layered media is shown to be valid for any homogeneous, transversely isotropic medium; (2) a general perturbation scheme for analyzing the angular dependence of the phase velocity is formulated and readily yields Krey and Helbig’s results in limiting cases; and (3) the effects of relaxing the assumption of constant Poisson’s ratio σ are considered. The phase and group velocities for all three modes of elastic wave propagation are illustrated for typical layered media with (1) one‐quarter limestone and three‐quarters sandstone, (2) half‐limestone and half‐sandstone, and (3) three‐quarters limestone and one‐quarter sandstone. It is concluded that anisotropic effects are greatest in areas where the layering is quite thin (10–50 ft), so that the wavelengths of the seismic signal are greater than the layer thickness and the layers are of alternately high‐ and low‐velocity materials.

On: “Long‐wave elastic anisotropy in transversely isotropic media” by J. G. Berryman, and “Seismic velocities in transversely isotropic media” by F. K. Levin (GEOPHYSICS, v. 44, May 1979, p. 896–917 and p. 918–936, respectively).

Geophysics ◽  
1981 ◽  
Vol 46 (3) ◽  
pp. 336-338 ◽  
Author(s):  
Felix M. Lyakhovitskiy
Keyword(s):  
Poisson’S Ratio ◽  
Elastic Anisotropy ◽  
Transversely Isotropic ◽  
Layered Media ◽  
Thin Layers ◽  
Poisson's Ratio ◽  
Seismic Velocities ◽  
Long Wave ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Berryman and Levin made an assumption about constancy or limited variations of Poisson’s ratio in the thin layers, in their analyses of elastic anisotropy in thin‐layered media. Berryman states (p. 913): “Rare cases can occur with large variations in Poisson’s ratio.” However, on p. 911 Berryman does point out (with reference to Benzing) that range of variations of the parameter γ = VS/VP from 0.45 to 0.65 is typical of rocks. That corresponds to a range of variations of Poisson’s ratio of 0.373 to 0.134 (i.e., almost three times as much).

On: “Long‐wave elastic anisotropy in transversely isotropic media” by James G. Berryman (GEOPHYSICS, May 1979, p. 896–917).

Geophysics ◽  
1980 ◽  
Vol 45 (5) ◽  
pp. 977-980
Author(s):  
K. Helbig
Keyword(s):  
Isotropic Material ◽  
Significant Contribution ◽  
Elastic Anisotropy ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Homogeneous Material ◽  
Long Wave ◽  
Transversely Isotropic Media ◽  
Horizontal Stratification ◽  
Isotropic Media

Berryman shows elegantly that the “inequality [Formula: see text] is true for any horizontally stratified, homogeneous material whose constituent layers are isotropic…” However, the final clause of this sentence “…, i.e., any homogeneous, transversely isotropic material,” is, if taken at face value, misleading. It is clear from the proof in the section “A fundamental inequality” that this statement is only shown to hold for lamellated media with isotropic lamellae, and that Berryman chooses arbitrarily and without any warning the phrase homogeneous, transversely isotropic to stand as a synonym for what Backus (1962) painstakingly describes as “smoothed, transversely isotropic, long‐wave equivalent (STILWE).” In view of the fact that even within the context of exploration seismics transverse isotropy can be due to causes other than horizontal stratification with isotropic constituents (e.g., schists can be intrinsically anisotropic, anisotropy might be due to preferential orientation of sandgrains or joints), I believe this choice to be unfortunate. It leads the unsuspecting reader to assume a wider applicability of the fundamental inequality than Berryman really intends to claim, and thus makes it unnecessarily difficult to understand this significant contribution.

Laboratory results for the features of body‐wave propagation in a transversely isotropic media

Geophysics ◽  
2001 ◽  
Vol 66 (6) ◽  
pp. 1921-1924 ◽  
Author(s):  
Young‐Fo Chang ◽  
Chih‐Hsiung Chang
Keyword(s):  
Wave Propagation ◽  
Shear Wave ◽  
Elastic Anisotropy ◽  
Body Wave ◽  
Transversely Isotropic ◽  
Sedimentary Basins ◽  
Seismic Profiles ◽  
Vertical Seismic Profiles ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Much of the earth’s crust appears to have some degree of elastic anisotropy (Crampin, 1981; Crampin and Lovell, 1991; Helbig, 1993). The phenomena of elastic wave propagation in anisotropic media are more complex than those in isotropic media. Shear‐wave propagation in an orthorhombic physical model is most complex when the direction of the wave is close to the neighborhood of the cusp on the group velocity surfaces (Brown et al., 1991). The first identification of singularities in wave propagation through sedimentary basins occurred in the examination of shear‐wave splitting in multioffset vertical seismic profiles (VSPs) at a borehole site in the Paris Basin (Bush and Crampin, 1991), where large variations in shear‐wave polarizations in propagation directions close to point singularities were observed. Computation of synthetic seismograms for layer sequences showed that the shear‐wave polarizations and amplitudes were irregular near point singularities (Crampin, 1991).

Reverse time migration in tilted transversely isotropic media

2020 ◽  
Vol 38 (2) ◽  
Author(s):  
Razec Cezar Sampaio Pinto da Silva Torres ◽  
Leandro Di Bartolo
Keyword(s):  
Seismic Anisotropy ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Computer Clusters ◽  
Time Migration ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Tti Media

ABSTRACT. Reverse time migration (RTM) is one of the most powerful methods used to generate images of the subsurface. The RTM was proposed in the early 1980s, but only recently it has been routinely used in exploratory projects involving complex geology – Brazilian pre-salt, for example. Because the method uses the two-way wave equation, RTM is able to correctly image any kind of geological environment (simple or complex), including those with anisotropy. On the other hand, RTM is computationally expensive and requires the use of computer clusters. This paper proposes to investigate the influence of anisotropy on seismic imaging through the application of RTM for tilted transversely isotropic (TTI) media in pre-stack synthetic data. This work presents in detail how to implement RTM for TTI media, addressing the main issues and specific details, e.g., the computational resources required. A couple of simple models results are presented, including the application to a BP TTI 2007 benchmark model.Keywords: finite differences, wave numerical modeling, seismic anisotropy. Migração reversa no tempo em meios transversalmente isotrópicos inclinadosRESUMO. A migração reversa no tempo (RTM) é um dos mais poderosos métodos utilizados para gerar imagens da subsuperfície. A RTM foi proposta no início da década de 80, mas apenas recentemente tem sido rotineiramente utilizada em projetos exploratórios envolvendo geologia complexa, em especial no pré-sal brasileiro. Por ser um método que utiliza a equação completa da onda, qualquer configuração do meio geológico pode ser corretamente tratada, em especial na presença de anisotropia. Por outro lado, a RTM é dispendiosa computacionalmente e requer o uso de clusters de computadores por parte da indústria. Este artigo apresenta em detalhes uma implementação da RTM para meios transversalmente isotrópicos inclinados (TTI), abordando as principais dificuldades na sua implementação, além dos recursos computacionais exigidos. O algoritmo desenvolvido é aplicado a casos simples e a um benchmark padrão, conhecido como BP TTI 2007.Palavras-chave: diferenças finitas, modelagem numérica de ondas, anisotropia sísmica.

Variation of stacking velocity in transversely isotropic media

1995 ◽  
Vol 26 (2-3) ◽  
pp. 431-436 ◽  
Author(s):  
Patrick N.(Jr). Okoye ◽  
N. F. Uren ◽  
W. Waluyo
Keyword(s):  
Transversely Isotropic ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Elastic Least-Squares Imaging in Tilted Transversely Isotropic Media for Multicomponent Land and Pressure Marine Data

2020 ◽  
Vol 41 (4) ◽  
pp. 805-833 ◽  
Author(s):  
Jidong Yang ◽  
Biaolong Hua ◽  
Paul Williamson ◽  
Hejun Zhu ◽  
George McMechan ◽  
...  
Keyword(s):  
Least Squares ◽  
Transversely Isotropic ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Marine Data
Sign in / Sign up

Export Citation Format

Share Document