Multiple attenuation: Theory and Practice

Chapter expands the filtering technique of Chapter to the problem of multiple attenuation with 2-D data. The basic idea is to separate multiples from primaries according to their pattern, or multivariate spectra. To do so, I approximate covariance operators for both the data and the model with multidimensional prediction-error filters. These PEFs can be seen as proxies for the primaries and multiples. This method is a two steps technique. First, the PEFs for the multiples and the primaries are estimated. The noise PEFs (multiples) are estimated from a multiple model, generally derived by convolving shot gathers Verschuur et al. (1992). To estimate the signal PEFs, I introduce the Spitz approximation Spitz (1999). Then, the multiples and primaries are separated in a least-squares sense with the PEFs for covariance operators. One important result of this Chapter is that 3-D filters lead to a better multiple removal than 2-D filters. Comparing with the adaptive subtraction technique of Chapter , I also show that the pattern-based technique is less sensitive to modeling errors present in the multiple model.