Reflection and transmission coefficients of a fracture in transversely isotropic media

2011 ◽  
Vol 56 (2) ◽  
pp. 307-322 ◽  
Author(s):  
José M. Carcione ◽  
Stefano Picotti
1977 ◽  
Vol 67 (3) ◽  
pp. 661-675 ◽  
Author(s):  
P. F. Daley ◽  
F. Hron

abstract It has become necessary in seismology to consider more complicated models of the Earth's structure in order to obtain synthetic seismograms that are more consistent with actual field data. Gassmann (1964) and Postma (1955) have presented results dealing with travel-time methods in anisotropic media—in particular, transversely isotropic media. Kinematic properties alone, however, are not enough to conclusively interpret seismic records. Consequently, dynamic properties must be considered producing a need for synthetic seismograms. One of the most efficient methods for obtaining synthetic seismograms is through the use of asymptotic ray theory (Hron and Kanasewich, 1971; Hron, 1973; Hron, Kanasewich and Alpaslan, 1974). A necessary step in the implementation for layered media displaying transverse isotropy is the computation of reflection and transmission coefficients at the interface between two such layers. Reflection coefficients for a free interface and the corresponding surface conversion coefficients must be computed, as well. Theoretical formulas for reflection, transmission, and surface conversion coefficients corresponding to the zero-order approximation of asymptotic theory are presented for the above-mentioned media.


Geophysics ◽  
1978 ◽  
Vol 43 (3) ◽  
pp. 528-537 ◽  
Author(s):  
Franklyn K. Levin

Assuming media having a velocity dependence on angle which is an ellipse, we have confirmed previously reported time‐distance relations for reflections from single interfaces, for reflections from sections of beds separated by horizontal interfaces, for refraction arrivals, and added the expression for diffractions. We also have derived expressions for plane‐wave reflection and transmission coefficients at an interface separating two transversely isotropic media. None of the properties differs greatly from those for isotropic media. However, velocities found from seismic surface reflections or refractions are horizontal components. There seems to be no way of obtaining vertical components of velocity from surface measurements alone and hence no way to compute depths from surface data.


Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. C143-C157 ◽  
Author(s):  
Song Jin ◽  
Alexey Stovas

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.


Geophysics ◽  
1992 ◽  
Vol 57 (11) ◽  
pp. 1512-1519 ◽  
Author(s):  
Mark Graebner

Numerous investigators have studied the P-SV reflection and transmission coefficients of an isotropic solid (Zoeppritz, 1919; Nafe, 1957; Frasier, 1970; Young and Braile, 1976; Kind, 1976; Aki and Richards, 1980).


Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. C181-C203 ◽  
Author(s):  
Song Jin ◽  
Alexey Stovas

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.


Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. C1-C11 ◽  
Author(s):  
Qi Hao ◽  
Alexey Stovas

We have developed an approximate method to derive simple expressions for the reflection coefficients of P- and SV-waves for a thin transversely isotropic layer with a vertical symmetry axis (VTI) embedded in a homogeneous VTI background. The layer thickness is assumed to be much smaller than the wavelengths of P- and SV-waves inside. The exact reflection and transmission coefficients are derived by the propagator matrix method. In the case of normal incidence, the exact reflection and transmission coefficients are expressed in terms of the impedances of vertically propagating P- and S-waves. For subcritical incidence, the approximate reflection coefficients are expressed in terms of the contrast in the VTI parameters between the layer and the background. Numerical examples are designed to analyze the reflection coefficients at normal and oblique incidence and investigate the influence of transverse isotropy on the reflection coefficients. Despite giving numerical errors, the approximate formulas are sufficiently simple to qualitatively analyze the variation of the reflection coefficients with the angle of incidence.


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