Imaging reflections in elliptically anisotropic media

Geophysics ◽  
1988 ◽  
Vol 53 (12) ◽  
pp. 1616-1618 ◽  
Author(s):  
Joe Dellinger ◽  
Francis Muir
Keyword(s):  
Point Source ◽  
Isotropic Medium ◽  
Short Note ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Virtual Image ◽  
Transversely Isotropic Medium ◽  
Sh Waves ◽  
Special Case

In an isotropic medium, waves reflected from a mirror form a virtual image of their source. This property of planar reflectors is generally not true in the presence of anisotropy. In their short note, Blair and Korringa (1987) show that for the special case of SH waves from a point source in a transversely isotropic medium, an aberration‐free image is formed for any orientation of the mirror. While their proof is mathematical, we show the same result in an intuitive, pictorial fashion and in the process discover that although the image is indeed aberration free, it is still distorted.

Elastic waves in anisotropic media

1959 ◽  
Vol 253 (1275) ◽  
pp. 563-580 ◽  
Keyword(s):  
Point Source ◽  
Elastic Medium ◽  
Elastic Waves ◽  
Isotropic Medium ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Transversely Isotropic Medium ◽  
Anisotropic Elastic Medium ◽  
Anisotropic Elastic ◽  
Fourier Integrals

The displacements due to a radiating point source in an infinite anisotropic elastic medium are found in terms of Fourier integrals. The integrals are evaluated asymptotically, yielding explicit expressions for displacements at points far from the source. The relative amplitudes of waves from a point source are thus determined, and it is found that although in general the decay of wave amplitudes is proportional to the distance from the source, it is possible that in certain directions the decay is less than this. The method used in this paper is also shown to be an alternative way of deriving known results concerning the geometry of the propagation of disturbances. As an example, the radiation in a transversely isotropic medium from an isolated force varying harmonically with time is discussed.

Estimating SV‐wave stacking velocities for transversely isotropic solids

Geophysics ◽  
1991 ◽  
Vol 56 (10) ◽  
pp. 1596-1602 ◽  
Author(s):  
Patricia A. Berge
Keyword(s):  
Shear Wave ◽  
Isotropic Medium ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Vertical Axis ◽  
Transversely Isotropic Medium ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Snell’S Law ◽  
Snell's Law

Conventional seismic experiments can record converted shear waves in anisotropic media, but the shear‐wave stacking velocities pose a problem when processing and interpreting the data. Methods used to find shear‐wave stacking velocities in isotropic media will not always provide good estimates in anisotropic media. Although isotropic methods often can be used to estimate shear‐wave stacking velocities in transversely isotropic media with vertical symmetry axes, the estimations fail for some transversely isotropic media even though the anisotropy is weak. For a given anisotropic medium, the shear‐wave stacking velocity can be estimated using isotropic methods if the isotropic Snell’s law approximates the anisotropic Snell’s law and if the shear wavefront is smooth enough near the vertical axis to be fit with an ellipse. Most of the 15 transversely isotropic media examined in this paper met these conditions for short reflection spreads and small ray angles. Any transversely isotropic medium will meet these conditions if the transverse isotropy is weak and caused by thin subhorizontal layering. For three of the media examined, the anisotropy was weak but the shear wave-fronts were not even approximately elliptical near the vertical axis. Thus, isotropic methods provided poor estimates of the shear‐wave stacking velocities. These results confirm that for any given transversely isotropic medium, it is possible to determine whether or not shear‐wave stacking velocities can be estimated using isotropic velocity analysis.

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