SH wave propagation by discrete wavenumber boundary integral modeling in transversely isotropic medium

1996 ◽  
Vol 86 (2) ◽  
pp. 524-529
Author(s):  
Hayrullah Karabulut ◽  
John F. Ferguson
Keyword(s):  
Transversely Isotropic ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Interface Problem ◽  
Seismic Profiles ◽  
Sh Waves ◽  
Vertical Seismic Profiles ◽  
Flat Interface ◽  
Transversely Isotropic Media ◽  
Isotropic Media

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.

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.

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).

Three-dimensional analysis of cracks in layered transversely isotropic media

1989 ◽  
Vol 424 (1867) ◽  
pp. 307-322 ◽  
Keyword(s):  
Integral Equation ◽  
Green's Functions ◽  
Green’S Functions ◽  
Crack Opening ◽  
Mathematical Formulation ◽  
Transversely Isotropic ◽  
Boundary Integral ◽  
Opening Displacement ◽  
Transversely Isotropic Media ◽  
Isotropic Media

A general mathematical formulation to analyse cracks in layered transversely isotropic media is developed in this paper. By constructing the Green’s functions, an integral equation is obtained to determine crack opening displacements when an applied crack face traction is specified. For the infinite body, the Green’s functions have solutions in a closed form. For layered media, a flexibility matrix in the integral transformed domain is formed that establishes the relation between the traction and the displacement for a single layer; the global matrix is formed by assembling all of the flexibility matrices constructed for each layer. The Green’s functions in the spatial domain are obtained by inversion of the Hankel transform. Finally, the crack opening displacement and the crack-tip opening displacement for a vertical planar crack in a layered transversely isotropic medium are obtained numerically by the boundary integral equation method.

SH waves in layered transversely isotropic media—a wave approach

1979 ◽  
Vol 16 (10) ◽  
pp. 1998-2008 ◽  
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.

Elastic constants of transversely isotropic media from constrained aperture traveltimes

Geophysics ◽  
1994 ◽  
Vol 59 (4) ◽  
pp. 658-667 ◽  
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.

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
Sign in / Sign up

Export Citation Format

Share Document