kt. LVe denote by Dfc the (complex) Fourier coefficient of frequency f (f = 1, . . . , Nj) for trace t, t = 1, . . . , N, 5 NrNS. Ideally, after they have been corrected for normal move-out (18), all traces corresponding to the same midpoint carry coherent information. If there were no need for statics corrections, all signals, stacked by their common midpoint, should be in phase and yield a maximum for the total powerE(S, R) In Eq. 7, the statics corrections S = (S,, . . . , S,?) and R = (R, . . . , Rhrr) are now considered independent variables. Their ootimum values are found bv maximizing ;he power E. Equation 7 highlights the multimodal nature of E, which, even for relatively lorn-dimensional s and R, exhibits a very large number of local minima. This is illustrated in Fig. 1. To assess the performance of TRUST, we considered a problem Involving N5 = 77 shots and N, = 77 receivers. A data set consisting of N, = 1462 synthetic se~smic traces folded over Ni, = 133 common midpoint gathers was obtained from CognlSeis Corporation (20). The data set uses Nf = 49Fourier comwonents for data reoresentation. Even though this set is somewhat smaller than typical collections obtained during seismic surveys by the oil industry, it is representative of the extreme comwlexitv underlying residual statics problems. T o herive a auantitative estimate of TRUST'S oerformance, let E, denote the total contribution to the stack power arising from midpoint It, and let Bk refer to the upper bound of Ei, in terms of S and R. Using. a oolar coordinates representation for the trace data Djc, that is, Dfc = aft exp(ieufc), we can prove (21 ) thatThe TRUST results, illustrated in Fig. 2, show the significant improvement in the coherence factor of each common gather.This factor is the ratio EJB, and characterizes the overall quality of the seismic image.In conclusion, the TRUST methodology for solving unconstrained global function optimization problems proves to be a powerful tool not only for academic problems; it has the robustness and consistency required by large-scale, real-life applications.