General love solution in the linear inhomogeneous transversely isotropic theory of radius-dependent elasticity

2010 ◽  
Vol 46 (4) ◽  
pp. 367-376 ◽  
Author(s):  
M. Yu. Kashtalyan ◽  
J. J. Rushchitsky
Keyword(s):  
Transversely Isotropic ◽  
Isotropic Theory

On Cagniard's problem for a qSH line source in transversely isotropic media

1993 ◽  
Vol 83 (2) ◽  
pp. 529-541 ◽  
Author(s):  
Lawrence H. T. Le
Keyword(s):  
Line Source ◽  
Transversely Isotropic ◽  
Time Shift ◽  
Plane Boundary ◽  
Seismic Profiles ◽  
Wave Speeds ◽  
Vertical Seismic Profiles ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Isotropic Theory

Abstract This paper studies the response to a qSH pulse generated by a line source, of two homogeneous half-spaces (transversely isotropic elastic or viscoelastic) separated by a plane boundary. For a simple model of two transversely isotropic half-spaces in welded contact, all the arrivals, including the incident, reflected, head, transmitted, and evanescent waves, that are predicted by the isotropic theory are present. For the 15% change in wave speeds considered here, anisotropy changes the dynamic and kinematic characteristics of the pulses. Depending on the anisotropy factor, the change can be pronounced. Because of the significant time shift and amplitude variation of the first arrivals due to anisotropy, proper consideration of the anisotropy of the medium is necessary in interpreting vertical seismic profiles or crosshole seismic data by means of any travel time or amplitude tomographic scheme.

INVESTIGATION OF SHEAR WAVES

Geophysics ◽  
1956 ◽  
Vol 21 (4) ◽  
pp. 905-938 ◽  
Author(s):  
R. N. Jolly
Keyword(s):  
Shear Waves ◽  
Practical Importance ◽  
Transversely Isotropic ◽  
Compressional Wave ◽  
Fundamental Properties ◽  
Theoretical Predictions ◽  
Weathered Layer ◽  
Complex Variation ◽  
Shearing Motion ◽  
Isotropic Theory

A series of measurements was made to investigate some of the fundamental properties of shear waves and to explore the possibility of using horizontally polarized (SH) shear waves for reflection prospecting. A special source was devised to produce a shearing motion which was detectable as far as 400 feet vertically and 1,000 feet horizontally. Direct, refracted, and reflected SH and SV (vertically polarized) shear waves were identified on a series of surface and subsurface recordings. A strong, highly dispersive surface wave, which satisfies the theoretical criteria of Love waves, was also observed. Certain anomalous features of the data which did not conform to the predictions of simple isotropic theory were readily explained by considering the stratified section under observation to be transversely isotropic. It was found that horizontal SH velocity exceeded vertical SH velocity by 100 percent whereas the corresponding compressional wave velocities differed by only 12 percent. SV anisotropy was manifested by a complex variation of velocity at intermediate directions of travel. Other theoretical predictions were confirmed in detail by the experimental data. An evaluation of SH reflection recording was made in four different areas. It was possible at one location, using multiple horizontal geophones and the shear source, to obtain an SH reflection from the base of a thick weathered layer. However, the results in general indicate that the method is not likely to have much practical importance.

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.

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