Conclusions on basic LSJIMP theory  

In the following section, I discuss some potential future issues surrounding the LSJIMP method in general.

• Which Multiples? I cast the LSJIMP method in the fashion of explicit multiple imaging, e.g., one order, split, and multiple generator per operator. Implicit multiple imaging techniques like Guitton's 2002 or Shan's 2003 implicitly image all multiples with a reflection at the free surface. While the conceptual simplicity of the implicit methods is enticing, they have the same problems as the SRME method of multiple modeling. Because the imaging is done by correlating events, each of which has finite bandwidth, the wavelet of the imaged multiple will change, and may complicate the combination of multiple and primary images. Furthermore, the SRME method requires dense area source coverage, which is highly uncommon in today's 3-D marine geometries.
• Regularization: The regularization operators presented in section exploit two forms of signal multiplicity in the image space: that along offset/angle and that between multiple and primary images. An unexplored possibility is to exploit the multiplicity of signal events across nearby midpoints, in the same fashion as Prucha-Clapp and Biondi (2002), by applying a differential operator along the dominant local reflector dip. As those authors showed, however, the quality of the result is sensitive to the prior estimate of reflector dip.
• Imaging or Inversion in Image Space? In section , I discussed some requirements for and existing choices of multiple imaging operators. Out of many choices, which is the best? The answer is hardly black and white, and the ``correct'' answer for one user or application may not suit others. For instance, prestack depth migration produces more accurate imaging results than, for instance, normal moveout or time migration. However, it is widely known that the lack of an accurate depth velocity model negatively affects prestack depth migration. Moreover, in practice, the velocity estimation and depth imaging methods are generally intertwined tightly, and make up the final step before well selection.

  Users may (reasonably) cast LSJIMP as a multiple separation algorithm. LSJIMP outputs a multiple-free estimate of the primaries, which have been enhanced by the inversion. Conventionally, such multiple-free data is a prerequisite to velocity model building and depth migration. Stacking velocities, on the other hand, are available almost at the beginning of the processing flow, so in these situations, users may prefer to use imaging techniques which are less sensitive to velocity, like any method which uses stacking velocity instead of interval velocity.

  One important point to emphasize is this: LSJIMP is an inversion algorithm which operates in an image space, not simply an imaging technique or a multiple separation technique. There are many choices of image space, but the central premises and potential of the LSJIMP method remain strong, regardless of the choice.