Computation of residual statics using projectors
Koraljka Čaklović, Lavoslav Čaklović · Geophysics · 1985
Abstract 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 (1)Si+Rj+Ck=Tij,k=i+j−1, where i = 1, …, Ns is the shot position index with Ns the number of shot positions,j = 1, …, Nr is the receiver position index with Nr the number of receiver positions,k = 1, …, Nc is the common-depth-point (CDP) position index with Nc the number of common depth points,Si = correction for ith shot position,Rj = correction for jth receiver position, andCk = 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 (2)A˜p=t, where pt = (S1, …, SNs, R1, …, RNr, C1, …, CNc) is the vector of unknown parameters; and tt = (T1 1, T1 2, …, TNsNr) is the vector which consists of the time shifts obtained by crosscorrelation of each trace in CDP gather with the corresponding reference trace.