HEMNO Implementation Issues  

To implement equation () on a computer, we must obtain two quantities. The first, the zero-offset traveltime of the multiple generator, $\tau_m$, may be obtained by hand- or auto-picking, and optionally refined by cross-correlation. However, the second quantity, the zero-offset traveltime to an arbitrary target reflector, $\tau_p$ , cannot realistically be picked. I obtain $\tau_p$ automatically by event tracking, using a smooth estimate of reflector dip obtained from a zero-offset section, in a fashion similar to Lomask's 2003 data flattening method.

How to best obtain this dip estimate is a question still open to debate. Automatic dip estimation techniques like Fomel's 2002 yield good results in regions where reflectors are densely packed, coherent, and do not cross. Unfortunately, below the onset of the first seabed multiple, a zero-offset section will contain crossing events. While previous authors have developed methods to simultaneously estimate two crossing dips Brown (2002); Fomel (2001), the problem is highly nonlinear, and it is difficult to unambiguously associate one dip with the primaries, and the other with multiples.

I have had greater success with a different technique which exploits cubic smoothing splines Hutchinson and De Hoog (1985). On 2-D data, it is easy to pick important reflectors on a zero-offset section, even weak events buried under the multiples. The reflectors are first fit with a cubic smoothing spline, from which the dip, simply the first derivative, can be computed analytically. These computed dips are finally interpolated in time, again using a cubic smoothing spline. This method is somewhat manually intensive, but gives reliable results. In 3-D, the spline technique may have value when crossline aliasing renders automatic dip estimation schemes ineffective. If the data contain many important reflectors, though, the picking may entail considerable manual labor.