Calculation of the warp function

The previous authors Grubb and Tura (1997); Rickett and Lumley (1998) determined the warp function by calculating local cross-correlation functions at certain node points within the image space. The warp function at those node points is then taken to be the lag associated with the maxima of the cross-correlelograms. Node values may then be smoothed and interpolated to fill the image volume.

Unfortunately because seismic data is band-limited, cross-correlelograms have multiple local maxima, and in noisy data situations, the maxima may have similar amplitude. Simply picking maxima is, therefore, prone to cycle-skipping problems. The problem of cycle-skipping is fundamental to the process of automated (and even manual) seismic interpretation. Rickett and Lumley (1998) addressed it by heavy smoothing and median filtering of the warp functions before the image resampling itself.

In this paper, I exploit the link between shaping filters and cross-correlation functions to incorporate the smoothing within the matching process. I pick shaping filter maxima as opposed to cross-correlelogram maxima, reducing the need for ad hoc smoothing after the fact.