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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, ,may be obtained by hand- or auto-picking. Unfortunately, the second quantity, the zero-offset traveltime to an arbitrary subsea reflector at , cannot realistically be picked. Panel c) of Figure motivates the problem; starting at ,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, , by stacking input data.
Use  to compute smooth reflector dip, ,    using technique of Fomel (2002).
Set k=1, y=y0.
do while
Set
Set
Set
end do

This approach suffers from some possible pitfalls.
• In the  to zone'', consists of primary events only, and to a (normally) lesser extent, other coherent noise modes (e.g. locally-converted shear waves, internal multiples). For , contains both peglegs and primaries, as well as other possibly strong unmodeled multiple reflection modes, and the dip of these events is unlikely to be equal.

Previous authors Brown (2002b); Fomel (2001) have developed methods to simultaneously estimate two crossing dips. The problem is inherently nonlinear, and thus highly dependent on initial guesses for the two dips. Assuming weak non-primary/pegleg noise, a possible strategy might be to seed the pegleg dip with primary dip from above.

In current implementation, however, I ignore this problem by setting the dip to zero in the zone. I justify this assumption by noting that as increases, the distance from y0 to shrinks asmyptotically to zero, so unless the reflector dip is severe (inconsistent with the derivation of equation(3)), this omission will not present a large problem.

• Faults and other event discontinuities in are inconsistent with the smooth'' mentioned above. The current implementation ignores any possible faulting, although the dip estimation algorithm used can handle steeply folding reflectors.

Next: Examples Up: Traveltime Equation for Pegleg Previous: Traveltime Equation for Pegleg
Stanford Exploration Project
7/8/2003