A physical model study of the travel times and reflection points of SH-waves reflected from transversely isotropic media with tilted symmetry axes

Abstract An extension of the boundary integral method for SH waves is given for transversely isotropic media. The accuracy of the method is demonstrated for a simple flat interface problem by comparison to the Cagniard-de Hoop solution. The method is further demonstrated for a case with interface topography for both surface and vertical seismic profiles. The new method is found to be both accurate and effective.

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Synthetic seismograms for SH waves in anelastic transversely isotropic media

Geophysical Journal International ◽

10.1111/j.1365-246x.1994.tb03283.x ◽

1994 ◽

Vol 116 (3) ◽

pp. 598-604 ◽

Cited By ~ 15

Author(s):

Lawrence H. T. Le ◽

E. S. Krebes ◽

Gerardo E. Quiroga-Goode

Keyword(s):

Transversely Isotropic ◽

Synthetic Seismograms ◽

Sh Waves ◽

Transversely Isotropic Media ◽

Isotropic Media

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SH waves in layered transversely isotropic media—a wave approach

Canadian Journal of Earth Sciences ◽

10.1139/e79-186 ◽

1979 ◽

Vol 16 (10) ◽

pp. 1998-2008 ◽

Cited By ~ 1

Author(s):

P. F. Daley ◽

F. Hron

Keyword(s):

Layered Medium ◽

Transversely Isotropic ◽

Integral Transforms ◽

Earth Model ◽

Sh Waves ◽

Transversely Isotropic Media ◽

Head Waves ◽

Isotropic Media ◽

Ray Series ◽

Insight Into

There are many reports in the literature of anomalies in traveltime data when an isotropic homogeneous Earth model is used to interpret field data. In several cases, the introduction of a layered transversely isotropic model has successfully explained these kinematic irregularities. However, it is useful, in fact essential, to confirm the kinematic fit with a dynamic (amplitude) comparison.In this paper the problem of SH waves propagating in a transversely isotropic plane layered medium is discussed through the use of integral transforms and evaluation by steepest descents. This procedure yields not only the asymptotic solution which is also attainable using an asymptotic ray series approach, but also allows for the investigation of the interference of the reflected and head waves in the vicinity of the critical point (point of critical refraction). It is in this region that asymptotic ray theory breaks down or at least introduces significant error in the displacement amplitudes.It can be shown that a simple transformation will reduce this problem to one that may be solved exactly by the Cagnaird de Hoop technique but it is instructive to examine nonspherical wave-fronts in order to obtain an insight into more complicated anisotropic media.

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Elastic constants of transversely isotropic media from constrained aperture traveltimes

Geophysics ◽

10.1190/1.1443625 ◽

1994 ◽

Vol 59 (4) ◽

pp. 658-667 ◽

Cited By ~ 1

Author(s):

Reinaldo J. Michelena

Keyword(s):

Elastic Constants ◽

Heterogeneous Media ◽

Transversely Isotropic ◽

System Of Equations ◽

Sh Waves ◽

Velocity Models ◽

Transversely Isotropic Media ◽

Isotropic Media ◽

P And Sv Waves ◽

Homogeneous Media

The elastic constants that control P‐ and SV‐wave propagation in a transversely isotropic media can be estimated by using P‐ and SV‐wave traveltimes from either crosswell or VSP geometries. The procedure consists of two steps. First, elliptical velocity models are used to fit the traveltimes near one axis. The result is four elliptical parameters that represent direct and normal moveout velocities near the chosen axis for P‐ and SV‐waves. Second, the elliptical parameters are used to solve a system of four equations and four unknown elastic constants. The system of equations is solved analytically, yielding simple expressions for the elastic constants as a function of direct‐ and normal‐moveout velocities. For SH‐waves, the estimation of the corresponding elastic constants is easier because the phase velocity is already elliptical. The procedure, introduced for homogeneous media, is generalized to heterogeneous media by using tomographic techniques.

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Travel times and reflection points for reflected P-waves in transversely isotropic media

Terrestrial Atmospheric and Oceanic Sciences ◽

10.3319/tao.2005.16.5.1061(t) ◽

2005 ◽

Vol 16 (5) ◽

pp. 1061 ◽

Cited By ~ 2

Author(s):

Young-Fo Chang ◽

Yu-Ting Kuo

Keyword(s):

Transversely Isotropic ◽

Travel Times ◽

P Waves ◽

Transversely Isotropic Media ◽

Isotropic Media

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A Fast Sweeping Scheme for Calculating P Wave First-Arrival Travel Times in Transversely Isotropic Media with an Irregular Surface

Pure and Applied Geophysics ◽

10.1007/s00024-014-0836-5 ◽

2014 ◽

Vol 171 (9) ◽

pp. 2199-2208 ◽

Cited By ~ 5

Author(s):

Haiqiang Lan ◽

Jingyi Chen ◽

Zhongjie Zhang

Keyword(s):

Transversely Isotropic ◽

P Wave ◽

Irregular Surface ◽

Travel Times ◽

Transversely Isotropic Media ◽

Fast Sweeping ◽

First Arrival Travel Times ◽

Isotropic Media ◽

First Arrival

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Reverse time migration in tilted transversely isotropic media

Brazilian Journal of Geophysics ◽

10.22564/rbgf.v38i2.2041 ◽

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.

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