Application of vertical velocity analysis for a vertically transversely isotropic medium

2002 ◽  
Author(s):  
Sherman Yang ◽  
Chung‐Chi Shih ◽  
Niranjan C. Banik ◽  
Jeff Chen ◽  
George Schultz ◽  
...  
Keyword(s):  
Vertical Velocity ◽  
Isotropic Medium ◽  
Transversely Isotropic ◽  
Velocity Analysis ◽  
Transversely Isotropic Medium

Generalized moveout approximation for qP- and qSV-waves in a homogeneous transversely isotropic medium

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. D79-D84 ◽  
Author(s):  
Alexey Stovas
Keyword(s):  
Isotropic Medium ◽  
Symmetry Axis ◽  
Transversely Isotropic ◽  
Velocity Analysis ◽  
Kinematic Modeling ◽  
Transversely Isotropic Medium ◽  
Time Migration ◽  
Special Cases ◽  
Higher Order Terms ◽  
Vti Medium

The moveout approximations can be used in kinematic modeling, velocity analysis, and time migration. The generalized moveout approximation involves five approximation parameters and has several known approximations as special cases. A method is demonstrated for determining parameters of the generalized nonhyperbolic moveout approximation for qP- and qSV-waves in a homogeneous transversely isotropic medium with vertical symmetry axis (VTI medium). The additional parameters for the generalized approximation are computed from the hyperbolic asymptote at infinite offset. Comparison with a few well-known moveout approximations for higher-order terms in the Taylor series and asymptotic behavior shows that the generalized moveout approximation is superior to other nonhyperbolic approximations. A few numerical examples for qP- and qSV-waves in a VTI medium also indicate that the generalized approximation performs the best.

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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