Introduction

In the presence of complex geology where multipathing, illumination gaps, and coherent noise are present, the most advanced techniques need to be used for both preprocessing and imaging. For multiple attenuation, it has been established that methods that take the wavefield propagation into account (e.g., Verschhur et al. (1992); Weglein et al. (1997)) are the most successful in complex geology Bishop et al. (2001); Matson et al. (1999); Paffenholz et al. (2002).

For multiple removal in complicated geology, the standard processing workflow is usually divided into a prediction step (i.e., modeling of the multiples) and a subtraction step. In the subtraction step, multiples are removed according to some assumptions made on the signal distribution (primaries) in the data. Assuming that the signal has minimum energy, the multiple model is often simply subtracted by adaptive subtraction with a $\ell^2$ norm. However, the least-squares assumption might not hold all the time Spitz (1999). For instance, Guitton and Verschuur (2004) show that when primaries are much stronger than the multiples, the $\ell^1$ norm should be used instead. In Guitton (2003b), I showed that a subtraction scheme based on the assumption that both primaries and multiples have different patterns leads to a successful separation. This technique approximates the multivariate spectrum (patterns) of the noise and signal with non-stationary multidimensional prediction-error filters (PEFs).

In this paper, I investigate the multiple attenuation technique with multidimensional PEFs with the Sigsbee2B dataset. This dataset is particularly challenging due to the complex geometry of the salt body. In the ideal case where an accurate noise (multiples) and signal model are known in advance, the PEF processing leads to an excellent attenuation of the multiples. If only a multiple model is known such as with the Delft approach, 3D filters should be used instead of 2D filters. This result is consistent with the conclusions in Guitton (2003b).

Often in the processing of multiples, the final results are displayed on common shot gathers, common offset sections or stacks. Because the end-product of the seismic processing workflow is always a migrated image, the outcome of a multiple attenuation technique should be analyzed in the image space (after migration) as often as possible. Therefore, I will concentrate most of my efforts in displaying multiple attenuation results in the image space with migrated images at zero-offset and angle domain common-image gathers (ADCIG).

In the next section, I derive the basic equations governing the multiple attenuation technique with multidimensional PEFs. Then, I present the results of multiple attenuation on the Sigsbee2B dataset with or without a known signal model and when 2D or 3D filters are used.