LSJIMP and wide tow marine data

For the particular geometry shown in Figures 1 and 2, notice that each crossline midpoint gather is occupied by one, and only one receiver line. Therefore, we can conceptualize a 3-D CMP gather as a 2-D CMP gather with nonzero crossline offset, and thus remove the crossline offset axis from five-dimensional CMP-sorted data, saving considerable memory and computational waste. This approach is similar in spirit to Biondi's 1997 combination of azimuth moveout (AMO) Biondi et al. (1998) and common-azimuth wave equation depth migration Biondi and Palacharla (1996) for the prestack imaging of primaries in data with narrow-azimuth geometries. Unfortunately, the AMO transformation is not generally valid for multiples.

HEMNO is well-suited to image multiples with the data geometry described above, primarily because HEMNO images pegleg multiples with a vertical time shift. Rather than correlating wavefields across possibly-undersampled axes like migration, HEMNO uses a measurement of the data's zero-offset time dip to account for structure-induced moveout variations. Because the crossline offset axis is removed, the computational cost increase of applying HEMNO to 3-D data versus 2-D data is only proportional to the number of crossline midpoints.

My particular LSJIMP implementation, outlined in two previous works Brown (2003a,c), uses HEMNO, an extension of the NMO equation for multiples, in conjunction with three amplitude normalization operators to produce a ``true relative amplitude'' image of pegleg multiples. One of these, the Snell Resampling operator, moves multiple energy across offset to make the multiple's AVO response comparable to its primary. However, the use of Snell Resampling in the crossline direction on narrow azimuth data runs contrary to the stated assumption that we store only one crossline offset bin per 3-D CMP gather. Therefore, for the results shown in this paper, I do not apply crossline Snell Resampling. In practice, little useful angular information is anyway obtained in the crossline direction, since in most cases the data will have a maximum crossline offset of only a few hundred meters.