Exact and Asymptotic Solutions for the Field of a Point Source in a Transversely Isotropic Medium

2001 ◽  
Vol 47 (3) ◽  
pp. 252-261
Author(s):  
P. M. Bokov ◽  
A. M. Ionov
Keyword(s):  
Point Source ◽  
Isotropic Medium ◽  
Transversely Isotropic ◽  
Asymptotic Solutions ◽  
Transversely Isotropic Medium

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.

Indentation of a Penny-Shaped Crack by an Oblate Spheroidal Rigid Inclusion in a Transversely Isotropic Medium

1984 ◽  
Vol 51 (4) ◽  
pp. 811-815 ◽  
Author(s):  
Y. M. Tsai
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Contact Stress ◽  
Rigid Inclusion ◽  
Isotropic Medium ◽  
Transversely Isotropic ◽  
Transversely Isotropic Medium ◽  
Penny Shaped Crack ◽  
Shaped Crack

The stress distribution produced by the identation of a penny-shaped crack by an oblate smooth spheroidal rigid inclusion in a transversely isotropic medium is investigated using the method of Hankel transforms. This three-part mixed boundary value problem is solved using the techniques of triple integral equations. The normal contact stress between the crack surface and the indenter is written as the product of the associated half-space contact stress and a nondimensional crack-effect correction function. An exact expression for the stress-intensity is obtained as the product of a dimensional quantity and a nondimensional function. The curves for these nondimensional functions are presented and used to determine the values of the normalized stress-intensity factor and the normalized maximum contact stress. The stress-intensity factor is shown to be dependent on the material constants and increasing with increasing indentation. The stress-intensity factor also increases if the radius of curvature of the indenter surface increases.

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