The data-space alternative is SRME Verschuur et al. (1992). Since SRME uses the data itself to predict the multiples, the complexity of the multiple trajectory is not an issue. Furthermore, no knowledge whatsoever is required about the subsurface. The problem with SRME, specially with 3D data, is that it requires regular, fine sampling, and large apertures in both the inline and cross-line directions. With standard streamer acquisition, and in the presence of cable feathering, these conditions are unlikely to be met in practice. In the cross-line direction in particular, cost and logistic considerations dictate that sampling be coarse and apertures small. The remedy is to apply large-scale interpolation of near offsets and streamers and extrapolation of cross-line offsets. In addition, data regularization is required to deal with cable feathering. A lot of research is currently being carried out on how to address these issues in a way that allows fast and accurate estimation of the multiple model.
An alternative to data-space methods is to attenuate the multiples after migration, i.e. in the image domain Sava and Guitton (2003). The main advantage of the image domain is that prestack migration can unravel the complex propagation of both primaries and multiples. In Subsurface Offset Domain Common Image Gathers (SODCIGs), the primaries are focused near the zero subsurface-offset line whereas the multiples are smeared along a curve toward the negative subsurface offsets Alvarez (2005). Although identification of the multiples is simple in SODCIGs, they are not the ideal domain to attenuate them. Instead, we can transform the SODCIGs to Angle Domain Common Image Gathers (ADCIGs) that are a function of the reflection and azimuth angle Biondi and Tisserant (2004). In this domain, the primaries will be flat as a function of the aperture angle for the azimuth of the reflection plane, but will have curvature for other azimuths. The multiples, on the other hand, will not be flat even for the azimuth of the multiple-generating interface, but will instead exhibit a residual moveout that in 2D can be approximated, to a first order, by a simple trigonometric equation Alvarez (2005). This equation in turn can be used as the kernel of a Radon transform to focus the primaries and multiples to separate regions of the Radon domain, thereby allowing for their attenuation.
Here I use a real 3D dataset from the Gulf of Mexico to illustrate the mapping of the multiples to image space. The dataset, provided by VeritasDGC, was acquired over a complex salt body with structure in both the inline and the cross-line directions. The water-bottom itself dips about 11 degrees in the cross-line direction making the mapping of the multiples in the image-space cube difficult to predict. The presence of the salt distorts the multiples so much that in many cases it is difficult to discern with certainty which events are multiples and which events are primaries in the migrated cube. An important tool for that purpose are the SODCIGs where the multiples can be identified by their tendency to map to toward the negative subsurface offsets. I illustrate this situation by computing SODCIGs for one sail-line. The goal is to compute SODCIGs inline and crossline for the entire area, but at the time of writing this report the results are not yet available. I show that even in the SODCIGs for one sail-line, however, the multiples are identifiable and clearly distinguishable from the primaries.