3-D Theory  

In marine environments, three-dimensional reflection seismic data is normally acquired in a so-called ``wide tow'' streamer configuration, illustrated in Figure . Ironically, the crossline offset range of this data is less than with most land acquisition geometries, so geophysicists often call towed streamer data ``narrow azimuth'' data. Note that the crossline shot interval, $\Delta s_y$, is chosen such that the outermost receiver line on one swath overlaps the innermost receiver line on the previous swath. Figure illustrates that such an acquisition geometry produces a regularly sampled crossline CMP axis, if cable feathering is absent. In one sense, this geometry boasts some degree of optimality, as it produces a well-sampled 3-D image at a minimum cost.

 

narrow-az
Figure 1 Wide tow marine geometry. The acquisition boat tows many (usually 4-12) receiver lines and steams in parallel sail lines.

 

cgg-midpoints
Figure 2 Midpoint locations from two adjacent sail lines of the CGG Green Canyon 3-D dataset. The boat tows four streamers and fires two sources alternatively in a ``flip-flop'' configuration. Midpoints from shot ``A'' are labeled ``a'', and so on. Two shot pairs from each sail line are shown. For a fixed ship speed, this geometry doubles crossline midpoint density, at the cost of reduced inline resolution, compared to a single-source configuration. Flip-flop shooting allows one airgun to be recharged while the other shoots, thereby allowing the ship to sail faster than would be possible with one gun. Cable feathering is evident, though not severe.

Unfortunately, geometry shown in Figure causes the 3-D extension of the SRME method of multiple prediction to fail spectacularly. SRME requires $\Delta s_y$ to be relatively small-in practice, roughly the same as commonly chosen crossline receiver line spacing parameters van Borstelen (2003). 3-D field datasets commonly have a crossline shot interval of up to ten times the crossline receiver line spacing. Workarounds for the 3-D sampling problem include: ignoring crossline structure and using a 2-D prediction, massive (270,000 CPU hours) shot interpolation Kleemeyer et al. (2003), sparse inversion of the crossline multiple contribution gathers Hokstad and Sollie (2003); van Dedem and Verschuur (2002), and novel acquisition geometries Paffenholz (2003). Currently, none of these methods combines proven accuracy with computational/cost efficiency.

The LSJIMP method has good potential to separate 3-D peglegs from wide tow marine data. In Section , I demonstrated how, in a fairly complex 2-D setting, the HEMNO equation can model some complex multiples as accurately as SRME. In this chapter, I outline a practical extension of my implementation of LSJIMP to work on 3-D wide tow marine data.