Computation of residual statics using projectors

The residual statics problem, as we know, is treated as the solution of one linear system of equations. If we assume that the static corrections are “surface consistent,” then we know that time shifts of each trace can be written as the sum of three terms [Formula: see text] where i = 1, …, [Formula: see text] is the shot position index with [Formula: see text] the number of shot positions, j = 1, …, [Formula: see text] is the receiver position index with [Formula: see text] the number of receiver positions, k = 1, …, [Formula: see text] is the common‐depth‐point (CDP) position index with [Formula: see text] the number of common depth points, [Formula: see text] = correction for ith shot position, [Formula: see text] = correction for jth receiver position, and [Formula: see text] = correction for each trace in the kth CDP gather. For every pair (i, j) we have one equation. We write system (1) in matrix form as [Formula: see text] where [Formula: see text] is the vector of unknown parameters; and [Formula: see text] is the vector which consists of the time shifts obtained by crosscorrelation of each trace in CDP gather with the corresponding reference trace.