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Many seismic experiments result in multiple time series which can be decomposed into signal and additive noise, where the noise has both a coherent and an incoherent component. The signal and the two noise components are stationary second-order random functions. The time shifts, called moveouts, of the signal and coherent noise are random variables with known distributions. Wiener filter theory is used to design the filter system that gives the optimal signal estimate, based upon the moveout distributions and the power spectra of the various components of the data. Velocity filters are useful in seismic data processing to separate signal from noise on the basis of moveout (velocity) differences without distorting the basic shape of the signal.