As pointed out by Weglein (1999), the multiple attenuation techniques may be divided into two families: (1) filtering methods which exploit the periodicity and the separability (move-out discrepancies) of the multiples and (2) the wavefield methods, where the multiples are first predicted, for example by autoconvolution of the recorded data, and then subtracted Dragoset and MacKay (1993); Verschhur et al. (1992); Weglein et al. (1997). Traditionally, filtering techniques are the method of choice for multiple processing because of their robustness and cost. However, because these techniques are mainly 1-D methods, they do not extend their multiple attenuation properties very well to higher dimensions, i.e, 2-D or 3-D. Therefore, filtering techniques have some limitations when tackling multiples in complex media. For example predictive deconvolution in the ray parameter domain fails when the water bottom is not flat Treitel et al. (1982).
In this paper I present results of a multiple attenuation technique based on the spatial predictability of both primaries and multiples. The attenuation is based on the assumption that primaries and multiples have different patterns and amplitudes. The pattern is estimated with time-space domain (t-x) multidimensional prediction-error filters (PEFs). In the first section following this introduction, I present the multiple attenuation technique. In the second section I illustrate the proposed method with a Gulf of Mexico field data example. I will show that 3-D PEFs give the best noise attenuation result. More specifically, 3-D PEFs are able to attenuate diffracted multiples better and are also less sensitive to modeling inaccuracies at short offset.