To the uninitiated, LSJIMP may seem at best a perplexing idea; at worst, an egregious display of circular reasoning. Signal/noise separation and imaging have traditionally occupied mutually exclusive domains. Usually multiple suppression is performed as a prerequisite to imaging. While some recent approaches do the multiple suppression after imaging Sava and Guitton (2003), the two steps are still largely independent.
With LSJIMP, the multiple separation and imaging steps are innately intertwined. Figure motivates the fundamental difference between LSJIMP and conventional multiple suppression and imaging. The ``NMO for primaries'' panel is the usual domain of multiple suppression/imaging algorithms. There, the signal is the primary reflections and the noise is the multiples. LSJIMP expands the dimensionality of the problem. In the other two panels, the signal is not the primaries, but instead the flattened multiples. The key observation is that the signal in each panel is consistent with the signal in the other panels.
Nearly every existing multiple suppression technique exploits differences between multiples and primaries in the left panel only. LSJIMP does that, but the novelty of the method is that it also exploits similarities between signal across panels to improve the separation. ``Noise'' is sometimes ``signal'', and vice versa, depending on which image one views. Why not use all the information at our disposal?
Figure 1 Solid lines in each panel are ``signal''; dashed lines are ``noise''. Left: A CMP gather after NMO. The seabed (WB) produces pegleg multiples WBM and RPL. Reflector R also produces pegleg RM. Center: After NMO for seabed peglegs, WBM and RPL are aligned with WB and R. Right: After NMO for R's peglegs, RM is aligned with R and RPL.