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Practical implementation of the HEMNO equation

To implement equation (3) on a computer, we must obtain two quantities. The first, the zero-offset traveltime of the seabed, $\tau^*(y)$,may be obtained by hand- or auto-picking. Unfortunately, the second quantity, the zero-offset traveltime to an arbitrary subsea reflector at $y=y_0 \pm
(x-x_p)/2$, cannot realistically be picked. Panel c) of Figure [*] motivates the problem; starting at $\tau(y_0)$,the subsea reflector must be followed to y=y0 + (x-xp)/2. My approach to the problem is similar to Lomask and Claerbout's 2002 algorithm for automatically flattening seismic data. It requires a smooth, unambiguous estimate of reflector dip. I summarize this approach (in 2-D; extension to 3-D is more involved but conceptually similar) in pseudocode:

Obtain zero offset section, $\bold d(\tau,y)$, by stacking input data.
		 Use $\bold d(\tau,y)$ to compute smooth reflector dip, $\bold p(\tau,y)$,    using technique of Fomel (2002).
		 Set k=1, y=y0.
		 do while $\left( \; y+\Delta y \leq y_0 + (x-x_p)/2 \; \right)$ 
		 		 Set $\; y = y_0+(k-1)\Delta y$ 
		 		 Set $\; \tau(y+ \Delta y) = \tau(y+ \Delta y) + \bold p(\tau(y),y)$ 
		 		 Set $\; k=k+1$ 
		 end do 		
This approach suffers from some possible pitfalls.
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Next: Examples Up: Traveltime Equation for Pegleg Previous: Traveltime Equation for Pegleg
Stanford Exploration Project
7/8/2003