It is well known that removing multiples from seismic data is an imperative to producing interpretable images of the subsurface. Multiple attenuation has a rich history in the geophysical literature ranging from methods that try to predict and remove the multiples from the seismic data to methods that use a differential characteristic between primaries and multiples as a discriminator and the basis for separating the two types of events Weglein (1999).
Prediction of the kinematics of multiple reflections by convolution of recorded data was first suggested by Anstey and Newman (1966). Due to amplitude and bandwidth inconsistencies associated with convolution, direct subtraction of multiples thus predicted was not possible. Tsai (1985) suggests modeling the waveform of the multiples to subtract events at times calculated by convolution from the data. The surface-related multiple elimination (SRME) method Berkhout and Verschuur (1997); Verschuur et al. (1992) convolves traces within shot-gathers to predict multiples (surface-related multiple prediction, SRMP) followed by an iterative subtraction scheme to eliminate them from the data. Alternatively, after predicting multiples, via convolution or filter-based methods, Guitton (2005) uses a pattern-based subtraction technique that resembles the match filter application described in Biersteker (2001).
While the above references all operate in the data domain, authors have also suggested removing multiples in the image space, after migration Alvarez et al. (2004); Sava and Guitton (2003, 2005). There are several motivators for attacking multiples in the image space. First, the image space is usually much smaller than the data space. Second, given a reasonably accurate velocity model, the kinematics of the image domain are simplified. Appropriately migrated primary events have little to no residual moveout, and multiples, migrated with velocities that are too fast, have predictable concave-down residual moveout in angle-domain common-image gathers. Alternatively, one could migrate the data and a multiple prediction separately and subtract the two image volumes. This is probably a prohibitively expensive strategy without obvious merit. However, because null-traces are filled during extrapolation steps through wave-front healing, multiple predictions in the image space may be more continuous and accurate in 3D.
We extend the SRMP approach to the image domain through the commutability of wavefield extrapolation and convolution to produce a multiple prediction in the image domain without needing to migrate two data volumes. Our approach is directly analogous to SRMP, though the prediction is calculated during the course of a shot-profile migration. The multiple prediction produced in the image space with this technique is exactly that which would be computed by migrating the multiple prediction produced by SRMP convolutions. The predicted multiples are then removed from the data via adaptive subtraction or pattern-matching techniques. The added cost of IS-SRMP is only a second imaging condition and writing out a second file the size of the migrated image. Because extrapolation dominates the cost of the shot-profile migration scheme, IS-SRMP does not significantly increase the migration cost.
We will develop the image-space surface related multiple prediction (IS-SRMP) technique by combining the SRMP approach with a wave-equation shot-profile depth migration algorithm. The Sigsbee2B synthetic dataset, which represents the multiple problem associated with deepwater seismic imaging in the presence of complex salt bodies, is used to show the efficacy of the approach. Images as a function of reflection angle and deconvolutional variants of the imaging-conditions are presented and we discuss their respective benefits.