On the reflection of plane waves in transversely isotropic media

Many real rocks and sediments relevant to seismic exploration can be described by elastic, transversely isotropic media. The properties of plane waves propagating in a transversely isotropic medium can be given in an analytically exact form. Here the polarization is recast into a comprehensive form that includes Daley and Hron’s normalization and Helbig’s full range of elastic constants. But these formulas are rather lengthy and do not easily reveal the features caused by anisotropy. Hence Thomsen suggested an approximation scheme for weak transverse isotropy. His derivation of the approximate polarization, however, is based on a property that is not suitable to measure small differences between an isotropic and a weakly transversely isotropic medium. Therefore the approximation of the polarization is recast. The corrected approximation does show a dependence on weak transverse isotropy. This feature can be viewed as an additional rotation of the polarization with respect to the wavenormal. It depends on the anisotropy as well as the inverse velocity ratio. An approximate condition of pure polarization, which occurs in certain directions, is also obtained. The corrected approximation results in a better match of the approximate polarization with the exact one, providing the assumption of weak transverse isotropy is met. When comparing the additional rotation with the deviation of the (observable) ray direction from the wavenormal, the qSV‐wave indicates transverse isotropy most clearly.

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Wave propagation in transversely isotropic elastic media - I. Homogeneous plane waves

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1989.0019 ◽

1989 ◽

Vol 422 (1862) ◽

pp. 23-66 ◽

Cited By ~ 67

Keyword(s):

Elastic Waves ◽

Plane Waves ◽

Transversely Isotropic ◽

Reference Plane ◽

Slowness Surface ◽

Transversely Isotropic Media ◽

Isotropic Media ◽

Homogeneous Plane ◽

Broad Structure ◽

Complete Account

In relation to transversely isotropic media, this paper presents a detailed study of those aspects of the propagation of homogeneous plane elastic waves which are essential to a basic understanding of the behaviour of surface waves. It is first shown how the ordering of the speeds of plane waves provides, directly and simply, a means of classifying the chosen materials, with the class label specifying the broad structure of the slowness surface and the location of its singular points. An examination of the shape of the outer sheet of the slowness surface follows, providing inter alia a complete account of the incidence of the various types of transonic states. The discussion turns next to exceptional waves, that is homogeneous plane waves which leave free of traction some family of parallel planes. The subset of the plane waves possessing this property is determined, after which the subset of the exceptional waves serving as limiting waves for an exceptional transonic state is picked out. Exceptional transonic states occur only when the axis of material symmetry lies either in the reference plane or at right angles to the reference vector and these orientations of the axis are referred to as α and β configurations respectively. The exceptional states are arranged in a threefold classification, one class consisting of a continuous set of α configurations and the others discrete β configurations. The paper ends with calculations of the limiting speed of the transonic state for the totality of α and β configurations.

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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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