The surface-related multiple elimination (SRME) technique Verschuur et al. (1992) is a wavefield method that (1) uses the data as prediction operators to generate a model of the multiples (the noise), and (2) adaptively subtract the model from the data in order to estimate the primaries (the signal). Both steps are equally important for successfully attenuate the multiples. The prediction of the multiples requires a dense sampling of both shots and receivers across the whole survey. With modern acquisition geometries, especially in 3-D, this condition is rarely met in practice. In marine seismic, for example, a boat usually tows four to twelve streamers with two to six shots. While the shots and receivers are usually well sampled in the inline direction, e.g., every twenty five meters for the receivers and every fifty meters for the shots, they are not in the crossline direction where the spacing between adjacent sail lines might go up to 150 meters, or more. This creates a lack of crossline offsets that can damage the prediction. In addition, cable feathering, cross-line aperture, and other factors Dragoset and Jericevic (1998) make the acquisition geometry irregular. Therefore, 3-D geometries cause serious problems to the applicability of SRME.
To make SRME work with 3-D data, both the prediction and the subtraction steps should be looked at. The prediction can be improved by devising strategies for regularizing the data by interpolation or extrapolation. The subtraction can be improved by designing methods that are less sensitive to modeling errors. However, most of today's research is focused on the prediction. For instance, Biersteker (2001) interpolates the missing data before the multiple prediction to insure dense sampling of both shots and receivers. This technique is computationally expensive but leads to very good prediction results because the multiples can be estimated in a 3-D sense. Hill et al. (2002) predict the multiples with a beam method from a 3-D model of the subsurface. This method is much faster than the full interpolation because it relies on a depth model to kinematically predict the multiples. However, being model based, this technique can only attenuate a limited number of multiples from interpreted 3-D surfaces. Recently, van Dedem (2002) showed how a 3-D Fresnel zone reconstruction method could postpone the interpolation step within the multiple prediction itself. Once the multiple model is estimated, these authors rely on adaptive subtraction with matching filters to subtract the estimated model. However, this technique is known to suffer from leakage problems Berkhout and Verschuur (2004); Spitz (1999) and to be quite sensitive to modeling errors (i.e., Chapter ).
Although being an important part of the process, very little is done to improve the subtraction step. For 3-D data, Dragoset et al. (2000) propose predicting the multiples streamer by streamer in 2D and subtracting them with flexible adaptive subtraction schemes with time-varying filters. The main problem with these methods is that they can damage primaries. The obvious advantage is that dealing with the prediction in a 2-D sense makes the computation of the multiples affordable for large surveys, relying on the subtraction step to deal with slight variations between the modeled and recorded multiples. The major drawback is that out of plane multiples, e.g., diffracted multiples, are not properly modeled, if at all. Herrmann and Verschuur (2004) separate multiples from primaries in the Curvelet domain by thresholding the data where the noise is present.
In 2003, CGG donated 3-D marine data from a non-exclusive survey in the Gulf of Mexico from the Green Canyon area (Figure ). The acquisition consists of four streamers placed every 150 m with a flip-flop source interval of 37.5 m, the same source being repeated every 75 m. The receiver spacing is 25 m and the maximum offset equals 8.1 km. In addition, the presence of salt bodies with complex structure generate multiple events bouncing outside the 2-D plane between a given source and receiver. Thus, the acquisition geometry and the geology make the multiple removal with SRME very challenging. The goal of this Chapter is to illustrate on one seismic line for one streamer a multiple attenuation strategy based on a 2-D prediction of the multiples Dragoset et al. (2000) and a subtraction with the pattern-based approach of Chapter . This subtraction technique is robust to modeling errors and does not suffer from leakage problems. Application of this method to this dataset proves that the pattern-based method gives far better multiple attenuation results than adaptive subtraction with matching filters.
This Chapter starts by a description of an interpolation technique for shots and near-offset traces used before 2-D surface-related multiple prediction (SRMP) Verschuur et al. (1992). The interpolation is done in the CMP domain with a hyperbolic radon transform with and without sparseness constraints. Inversion with the sparseness constraint yields better interpolation results. Then, the multiple model obtained from the 2-D prediction is presented. Compared with the actual multiples present in the data, kinematic and amplitude errors are clearly visible in the multiple model. Finally, the multiples are attenuated with the pattern-based approach of Chapter and with adaptive subtraction. The data are then prestack migrated with and without multiples for the two subtraction techniques. Comparisons of the migration results illustrate that the pattern-based technique gives the best multiple attenuation results while preserving the primaries.