Analysis of Spreading Loss for Refracted/Reflected Rays in Constant‐Velocity‐Gradient Media

1964 ◽  
Vol 36 (12) ◽  
pp. 2298-2305 ◽  
Author(s):  
M. J. Jacobson
Keyword(s):  
Velocity Gradient ◽  
Constant Velocity

Fresnel-zone binning: Fresnel-zone shape with offset and velocity function

Geophysics ◽  
2010 ◽  
Vol 75 (1) ◽  
pp. T9-T14 ◽  
Author(s):  
David J. Monk
Keyword(s):  
Velocity Gradient ◽  
Constant Velocity ◽  
Fresnel Zone ◽  
Geometric Approach ◽  
Velocity Function ◽  
Zero Offset ◽  
Limiting Case ◽  
Fresnel Zones

The concept of the Fresnel zone has been explored by many workers; most commonly, their work has involved examining the Fresnel zone in the limiting case of zero offset and constant velocity. I have examined the shape of the Fresnel zone for nonzero offset and in the situation of constant velocity gradient. Finite-offset Fresnel zones are not circular but are elliptical and may be many times larger than their zero-offset equivalents. My derivation takes a largely geometric approach, and I suggest a useful approximation for the dimension of the Fresnel zone parallel to the shot-receiver azimuth. The presence of a velocity gradient (velocity increasing with depth) in the subsurface leads to an expansion of the Fresnel zone to an area that is far larger than may be determined through a more usual straight-ray determination.

Reflection of rays in a constant gradient medium: CRP geometry

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 707-712
Author(s):  
Franklyn K. Levin
Keyword(s):  
Velocity Gradient ◽  
Seismic Data ◽  
Constant Velocity ◽  
Finite Range ◽  
Velocity Increase ◽  
Rate Of Increase ◽  
Constant Gradient ◽  
Gradient Medium

In a medium having a velocity that increases linearly with depth (constant gradient), rays are arcs of circles (Slotnick, 1936). A constant gradient medium is not a good approximation to a real subsurface. Not only does velocity increase without limit with depth, but the rate of increase is constant. Nonetheless, over a finite range of depths, a constant gradient medium is closer to reality than a medium having constant velocity down to reflector of interest. For that reason, a number of investigators have considered the changes in processes applied to seismic data when a constant velocity gradient other than zero is assumed.

Motions with Constant Velocity Gradient

2012 ◽  
pp. 107-108
Author(s):  
Morton E. Gurtin ◽  
Eliot Fried ◽  
Lallit Anand
Keyword(s):  
Velocity Gradient ◽  
Constant Velocity
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