Determining of elastic moduli in multilayered transversely isotropic media with horizontal symmetry axes

1996 ◽  
Author(s):  
S. B. Gorshkalev ◽  
W. V. Karsten
Keyword(s):  
Elastic Moduli ◽  
Transversely Isotropic ◽  
Transversely Isotropic Media ◽  
Horizontal Symmetry ◽  
Isotropic Media

Transverse isotropy of the upper mantle in the vicinity of Pacific fracture zones

1969 ◽  
Vol 59 (1) ◽  
pp. 59-72
Author(s):  
Robert S. Crosson ◽  
Nikolas I. Christensen
Keyword(s):  
Upper Mantle ◽  
Symmetry Axis ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Seismic Wave Propagation ◽  
Fracture Zones ◽  
Mantle Material ◽  
Transversely Isotropic Media ◽  
Horizontal Symmetry ◽  
Isotropic Media

Abstract Several recent investigations suggest that portions of the Earth's upper mantle behave anisotropically to seismic wave propagation. Since several types of anisotropy can produce azimuthal variations in Pn velocities, it is of particular geophysical interest to provide a framework for the recognition of the form or forms of anisotropy most likely to be manifest in the upper mantle. In this paper upper mantle material is assumed to possess the elastic properties of transversely isotropic media. Equations are presented which relate azimuthal variations in Pn velocities to the direction and angle of tilt of the symmetry axis of a transversely isotropic upper mantle. It is shown that the velocity data of Raitt and Shor taken near the Mendocino and Molokai fracture zones can be adequately explained by the assumption of transverse isotropy with a nearly horizontal symmetry axis.

scholarly journals The offset-midpoint traveltime pyramid in 3D transversely isotropic media with a horizontal symmetry axis

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. T51-T62 ◽  
Author(s):  
Qi Hao ◽  
Alexey Stovas ◽  
Tariq Alkhalifah
Keyword(s):  
Symmetry Axis ◽  
Transversely Isotropic ◽  
P Wave ◽  
Analytic Representation ◽  
Velocity Inversion ◽  
Transversely Isotropic Media ◽  
Horizontal Symmetry ◽  
Time Domains ◽  
Isotropic Media ◽  
Hti Media

Analytic representation of the offset-midpoint traveltime equation for anisotropy is very important for prestack Kirchhoff migration and velocity inversion in anisotropic media. For transversely isotropic media with a vertical symmetry axis, the offset-midpoint traveltime resembles the shape of a Cheops’ pyramid. This is also valid for homogeneous 3D transversely isotropic media with a horizontal symmetry axis (HTI). We extended the offset-midpoint traveltime pyramid to the case of homogeneous 3D HTI. Under the assumption of weak anellipticity of HTI media, we derived an analytic representation of the P-wave traveltime equation and used Shanks transformation to improve the accuracy of horizontal and vertical slownesses. The traveltime pyramid was derived in the depth and time domains. Numerical examples confirmed the accuracy of the proposed approximation for the traveltime function in 3D HTI media.

Reflection and transmission responses in a layered transversely isotropic medium with horizontal symmetry axis

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. C143-C157 ◽  
Author(s):  
Song Jin ◽  
Alexey Stovas
Keyword(s):  
Good Accuracy ◽  
Symmetry Axis ◽  
Local Property ◽  
Transversely Isotropic ◽  
Weak Anisotropy ◽  
Reflection And Transmission ◽  
Numerical Tests ◽  
Transversely Isotropic Media ◽  
Horizontal Symmetry ◽  
Isotropic Media

Seismic wave reflection and transmission (R/T) responses characterize the subsurface local property, and the widely spread anisotropy has considerable influences even at small incident angles. We have considered layered transversely isotropic media with horizontal symmetry axes (HTI), and the symmetry axes were not restricted to be aligned. With the assumption of weak contrast across the interface, linear approximations for R/T coefficients normalized by vertical energy flux are derived based on a simple layered HTI model. We also obtain the approximation with the isotropic background medium under an additional weak anisotropy assumption. Numerical tests illustrate the good accuracy of the approximations compared with the exact results.

Reflection and transmission responses for layered transversely isotropic media with vertical and horizontal symmetry axes

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. C181-C203 ◽  
Author(s):  
Song Jin ◽  
Alexey Stovas
Keyword(s):  
Transversely Isotropic ◽  
Model Parameters ◽  
Local Anisotropy ◽  
Weak Anisotropy ◽  
Reflection And Transmission ◽  
Contrast Model ◽  
Transversely Isotropic Media ◽  
Horizontal Symmetry ◽  
Isotropic Media ◽  
Independent Parameters

Reflection and transmission (R/T) responses characterize the energy distributions for incident and generated waves across the subsurface interface. The R/T coefficients are considerably influenced by the local anisotropy, and this implies the significance of the R/T responses analysis for anisotropic media. We have considered the plane interface bounded by two transversely isotropic media with, respectively, vertical and horizontal symmetry axes, and R/T coefficients normalized by the vertical energy flux are obtained in the phase domain. We define two simple anisotropic layered models characterized by fewer independent model parameters. Under the assumption of weak contrast model parameters across the interface, the R/T coefficient approximations are obtained as the perturbations from the simple models’ counterparts. The isotropic background medium is also used to obtain the approximations under an additional weak anisotropy assumption. Compared with approximations degenerated from more general cases, our approximations rely on fewer independent parameters. Numerical tests are implemented to evaluate our approximations.

scholarly journals Bounds of elastic parameters characterizing transversely isotropic media: Application to shales

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. C243-C252 ◽  
Author(s):  
Rune M. Holt
Keyword(s):  
Elastic Moduli ◽  
Laboratory Data ◽  
Transversely Isotropic ◽  
S Wave ◽  
Elastic Parameters ◽  
Reliable Determination ◽  
Transversely Isotropic Media ◽  
Stress Changes ◽  
Isotropic Media ◽  
Engineering Parameters

Several rocks, and in particular shales, are often described as transversely isotropic (TI) materials. Geophysical data coverage does not always permit reliable determination of all five elastic parameters, neither in seismic and sonic data from the field nor in laboratory measurements. Data may, however, be constrained by the existence of bounds on elastic moduli, derived from the fundamental requirement of positive elastic energy. Conditioned bounds are described for engineering parameters such as Poisson’s ratios as well as anisotropy coefficients such as the moveout parameter [Formula: see text] and the anellipticity parameter [Formula: see text]. “Conditioned bounds” means bounds that in general depend on some of the other elastic moduli: The bounds we have evaluated are controlled primarily by P- and S-wave moduli obtained from wave propagation along a symmetry axis and to some extent by P- and S-wave anisotropies. Such data may be acquired more easily from geophysical measurements. We have inspected the laboratory data obtained with various types of shales under different testing conditions, and none of them failed to adapt to the bounds. The data indicate, for instance, clear distinctions between how the proximity to bounds is driven by stress changes for saturated versus nonsaturated shales.

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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