Introduction

In Guitton (2001) I presented an efficient algorithm that attenuates coherent noise based on the spatial predictability of noise and signal. I called this algorithm the subtraction method. In this paper I show that the subtraction approach is closely related to another described method, the filtering method Brown and Clapp (2000); Clapp and Brown (2000); Soubaras (1994); Spitz (1999) if I use a preconditioning strategy Claerbout and Fomel (2001). In a second part I prove that the Spitz estimate for the signal PEF Spitz (1999) makes the inversion of the Hessian stable in the subtraction method.