The key assumption of the proposed multiple attenuation technique is that the primaries and multiples have different multidimensional spectra that PEFs can approximate Claerbout (1992); Spitz (1999). In this approach, the multiple attenuation is similar to Wiener filtering Abma (1995). One important approximation is that the multiples and primaries are uncorrelated so that the cross-spectrum between them is not needed. Multiple attenuation with multidimensional PEFs is performed in two steps. First the PEFs for the multiples and primaries are estimated. Then multiples are separated from the primaries. In the next section, I describe the multiple removal step first, assuming that the PEFs for both the primaries and multiples are known. Then I describe how PEFs are estimated and show how the signal PEFs can be computed when no signal model is given, leading to the Spitz approximation.