THE REFLECTION, REFRACTION, AND DIFFRACTION OF WAVES IN MEDIA WITH AN ELLIPTICAL VELOCITY DEPENDENCE

Geophysics ◽  
1978 ◽  
Vol 43 (3) ◽  
pp. 528-537 ◽  
Author(s):  
Franklyn K. Levin
Keyword(s):  
Wave Reflection ◽  
Transversely Isotropic ◽  
Velocity Dependence ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Transversely Isotropic Media ◽  
Surface Data ◽  
Isotropic Media ◽  
Surface Measurements ◽  
Time Distance

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.

Reflection and transmission coefficients for transversely isotropic media

1977 ◽  
Vol 67 (3) ◽  
pp. 661-675 ◽  
Author(s):  
P. F. Daley ◽  
F. Hron
Keyword(s):  
Dynamic Properties ◽  
Transversely Isotropic ◽  
Synthetic Seismograms ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Conversion Coefficients ◽  
Surface Conversion

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.

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.

Plane‐wave reflection and transmission coefficients for a transversely isotropic solid

Geophysics ◽  
1992 ◽  
Vol 57 (11) ◽  
pp. 1512-1519 ◽  
Author(s):  
Mark Graebner
Keyword(s):  
Plane Wave ◽  
Wave Reflection ◽  
Transversely Isotropic ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Isotropic Solid

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).

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.

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