Introduction

In complex geology, multiples and primaries can be accurately separated by estimating a model of the multiples and subtracting it from the data Verschuur et al. (1992). The subtraction of a given model is usually made by assuming that the signal (the primaries) has minimum energy. As exemplified by numerous authors (e.g., Guitton and Verschuur (2004); Guo (2003); Kelamis et al. (2002); Lu (2003); Spitz (1999)), the minimum energy assumption might not hold and other norms or subtraction techniques might be needed.

In Guitton (2003a), I demonstrated on a field data example that the pattern recognition technique presented in Guitton (2003b) gives the best multiple attenuation result for complex geology, thus providing an alternative to the popular adaptive subtraction method. In addition, I showed that 3D prediction error filters (estimated in the time, shot, offset domain) were more effective in characterizing the multivariate spectra of the noise and data than a series of 2D filters (time, offset) Guitton (2003a, 2004).

In this paper, I investigate both the adaptive subtraction technique with the $\ell^2$ norm and the pattern-based method for a 2D synthetic data example. This example is perfectly suited for the adaptive subtraction since all the recorded events are propagating in the inline direction. In this comparison, I show that the pattern-based method performs generally better than the adaptive subtraction technique. However, where the noise and signal have similar patterns, I demonstrate that the pattern-based technique damages some primary reflections. This problem is mainly caused by the Spitz approximation which only provides an accurate signal model where the noise and signal are uncorrelated.

In the next section I briefly present the two subtraction techniques and the parameters used for the modeling of the multiples. Then I show the multiple attenuation results on a 2D synthetic model provided by BP.