The invention is a method to predict surface-wave waveforms (306) and subtract them (307) from seismic data. Prediction is done by estimating a set of surface-consistent components (transfer functions in the frequency domain or impulse responses in time domain) that best represent changes in the waveforms for propagation along the surface from source to receiver (303). The prediction uses a mathematical expression, or model, of the earth's filtering effects, both amplitude and phase, as a function of frequency. The desired surface-consistent components are model parameters, and model optimization is used to solve for the surface-consistent components. The surface-consistent components may include filter transfer functions for each source location, each receiver location, and for propagation (302) through each region (301) of the surface that exhibits lateral variation.