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.

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.

Normal moveout from dipping reflectors in anisotropic media

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 268-284 ◽  
Author(s):  
Ilya Tsvankin
Keyword(s):  
Symmetry Axis ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Weak Anisotropy ◽  
Anisotropic Models ◽  
Transversely Isotropic Media ◽  
Wide Range ◽  
Isotropic Media ◽  
The Difference

Description of reflection moveout from dipping interfaces is important in developing seismic processing methods for anisotropic media, as well as in the inversion of reflection data. Here, I present a concise analytic expression for normal‐moveout (NMO) velocities valid for a wide range of homogeneous anisotropic models including transverse isotropy with a tilted in‐plane symmetry axis and symmetry planes in orthorhombic media. In transversely isotropic media, NMO velocity for quasi‐P‐waves may deviate substantially from the isotropic cosine‐of‐dip dependence used in conventional constant‐velocity dip‐moveout (DMO) algorithms. However, numerical studies of NMO velocities have revealed no apparent correlation between the conventional measures of anisotropy and errors in the cosine‐of‐dip DMO correction (“DMO errors”). The analytic treatment developed here shows that for transverse isotropy with a vertical symmetry axis, the magnitude of DMO errors is dependent primarily on the difference between Thomsen parameters ε and δ. For the most common case, ε − δ > 0, the cosine‐of‐dip–corrected moveout velocity remains significantly larger than the moveout velocity for a horizontal reflector. DMO errors at a dip of 45 degrees may exceed 20–25 percent, even for weak anisotropy. By comparing analytically derived NMO velocities with moveout velocities calculated on finite spreads, I analyze anisotropy‐induced deviations from hyperbolic moveout for dipping reflectors. For transversely isotropic media with a vertical velocity gradient and typical (positive) values of the difference ε − δ, inhomogeneity tends to reduce (sometimes significantly) the influence of anisotropy on the dip dependence of moveout velocity.

scholarly journals Nonlinear amplitude versus angle inversion for transversely isotropic media with vertical symmetry axis using new weak anisotropy approximation equations

2020 ◽  
Vol 17 (3) ◽  
pp. 628-644 ◽  
Author(s):  
Lin Zhou ◽  
Zhuo-Chao Chen ◽  
Jing-Ye Li ◽  
Xiao-Hong Chen ◽  
Xing-Ye Liu ◽  
...  
Keyword(s):  
Symmetry Axis ◽  
Transversely Isotropic ◽  
Weak Anisotropy ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Amplitude Versus
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