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In a constantvelocity medium, the expression for x_{p} derived earlier, equation
(4), simplifies to:
 
(9) 
Then xx_{p}, which will be needed later, simplifies to:
 
(10) 
Using equations (9) and (10), we can directly write the
(twoway) zero offset traveltime of the seabed and subsea reflection as a
function of midpoint location, y_{0}:
 

 (11) 
 
 (12) 
where the small angle approximation was employed as before. Utilizing equations
(9)(12), we can now manipulate equation
(3) to make it resemble Levin and Shah's moveout equation
(8):
 
(13) 
 (14) 
Equation (14) is equivalent to equation (8).
Therefore, we have proven the equivalence of the moveout equations of the true and
approximate raypaths shown in Figure , subject to the small
dip angle approximation. As before, and terms were dropped
in going from equation (13) to equation (14).
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Previous: Levin and Shah's Traveltime
Stanford Exploration Project
7/8/2003