Guitton (2003) describes in detail the pattern-based method used in this paper. The main idea is that the patterns of both the noise and the signal can be estimated with time domain non-stationary prediction-error filters. Thanks to the helical boundary conditions Claerbout (1998); Mersereau and Dudgeon (1974), these filters can have any dimension.
The two important components of the proposed method are the noise PEFs and the signal PEFs . Then, in Guitton (2003) I show that the signal can be estimated by minimizing the objective function
To estimate the noise and signal PEFs, we need to derive a model of the noise and a model of the signal. For the multiple attenuation problem, the model given by the Delft approach is the best choice. This choice is not restrictive because we could use other techniques to estimate a model of the multiples. For instance, Haines et al. (2003) show that a Radon transform can give a satisfying model of the multiples while improving on the Radon demultiple result. Another important assumption made with the pattern-based approach is that the model has accurate kinematics and amplitudes. It is well established that with one iteration only, the Delft approach does not properly model amplitudes for high-order multiples Guitton et al. (2001b); Wang and Levin (1994). Guitton (2003) shows that 3-D filters cope better with modeling inaccuracies than 2-D filters. Once the multiple model is computed and the noise PEFs are estimated, I convolve with the data to obtain a signal model from which I estimate the signal PEFs (Spitz, 2001, personal communication).
The proposed pattern-based approach works very well. I show in Guitton (2003) a very detailed comparison of this technique for 2-D and 3-D filters. In the next section, I compare the three multiple attenuation techniques, i.e., Radon, Delft and the pattern-based approach on a Gulf of Mexico dataset provided by WesternGeco. This example proves that the best multiple attenuation result is obtained with the pattern-based approach and 3-D filters.