3-D Surface Multiple Attenuation
Authors: Dragoset W.H. 
Published: October 2008

Abstract
Surface multiples were removed from an irregularly sampled Gulf of Mexico 3-D seismic data set using a 2-D wave equation-based algorithm. Accomplishing that task required facing several challenges: the project's potentially high processing cost, the 2-D algorithm's inability to accommodate 3-D effects directly, and the algorithm's need to have an input wavefield with regular spatial sampling. The first two challenges were addressed by predicting surface multiples in a 2-D fashion for half of the 2-D lines in the 3-D data set. The predicted multiples were then subtracted from the original lines using a process called adaptive noise cancellation to correct the predictions for ignored 3-D effects such as those due to cable feathering and cross dip. In addition, the adaptive process was able to subtract multiples predicted for one subsurface line not only from that line, but also from an adjacent line, thereby almost halving the cost of the project. The spatial sampling problem, which arose mostly because the survey was designed without surface multiple prediction in mind, was solved by regularizing the 2-D lines with an assortment of interpolation processes before multiple prediction. The interpolation increased the processing cost by about a factor of four.

Introduction
Imaging structures below complex, Gulf of Mexico salt bodies, like those in the Mississippi Canyon's Pluto prospect (Fig. 1), is a major geophysical challenge. Although 3-D data acquisition combined with 3-D prestack depth migration has dramatically improved the seismic industry's ability to image such structures, in many areas, including Pluto, obtaining a good interpretable image below salt is still problematic.
Subsalt imaging problems occur for several reasons, among them: improper or poor illumination of reflectors below the salt, weak penetration of the acoustic signal through the salt, and poor signal-to-noise ratio due to high-amplitude multiples. The first two reasons are chiefly data acquisition issues, while the problem with interfering multiples is mainly a data processing issue. In reality, of course, any particular imaging problem is likely a combination of these reasons. Thus, when reflectors below salt are properly illuminated with strong signals, the multiple problem seems less severe, and vice-versa. For the Pluto prospect, modeling experiments indicate that strong surface multiples definitely contribute to the subsalt-imaging problem. Furthermore, processing experiments have shown that traditional, moveout discrimination-based approaches to multiple attenuation are generally ineffective at removing those multiples.
In 1988, Verschuur, et al.1 introduced a wave equation-based method of attenuating surface multiples in marine seismic data that does not depend on moveout discrimination. Since then, many different implementations of that algorithm have been applied to 2-D data sets, with some excellent results.2 Developing a practical full 3-D version of the wave equation method of attenuating surface multiples, however, is not straightforward; a variety of difficulties arise due to the nature of the algorithm and that of the typical 3-D data set.3 If those difficulties could be overcome somehow, then wave equation-based surface multiple elimination would be a good candidate for solving the Pluto prospect's multiple problem.