We now apply the concepts developed in the previous sections for equalizing a seismic dataset before imaging. An application that is of interest to us is the reduction of the size of prestack data while correcting for the effects of its irregular geometry. The example presented in this section was designed to illustrate the two steps in our method and demonstrate the effects of fold variations on prestack imaging.
We consider the application of partial stacking by offset continuation of a 2D synthetic data example. The model consists of a horizontal bed, a dipping reflector, and a point diffractor in a constant velocity medium of 2.5/sec. The input data represents eight constant-offset sections between 500 and 1200 meter offsets with a 100 meter offset spacing. To simulate the fold variations between CMP bins, we randomly deleted about half the total input traces. An area of missing coverage (zero fold) is generated around CMP bin 80, as indicated on the fold chart (Figure fold). Figures input24 and input68 show four out of the eight irregularly sampled input sections.
To illustrate the effects of the irregular geometry on the imaging operator, we show in Figure amo-600 the output of an offset continuation from 500 to 850 meter offset, whereas in Figure amo-1200 we show the results of AMO from 1000 meters offset to an effective offset of 850 meters. Both results suffer poor resolution and severe amplitude and phase distortions. The aliasing effects strongly contaminated the dipping events and destroyed their phase. The non-aliased implementation of the offset continuation operator following Bevc and Claerbout (1992) eliminated that noise around the flat reflector even in presence of irregular sampling.
For the sake of consistency, all the results are displayed after NMO correction since the AMO transformation operates on moveout-corrected data.