In seismic exploration of conventional and unconventional energy, we use a seismic source to create seismic waves that travel downward into the Earth and then bounce back by reservoir layers. These reflected waves carry important information about the subsurface oil and gas distribution. Unfortunately, the same seismic source generates not only reflected waves but also surface waves or ground rolls. The surface waves are viewed as noise in reflection seismic imaging and they will degrade the quality of data. We propose a novel approach to extract and suppress the surface waves while maintaining the data quality of the useful reflection events based on the dispersion analysis using the multi-channel nonlinear signal comparison (MNLSC). Our method is data-driven where we first estimate the phase velocities of the surface waves from the recorded data by using the MNLSC method and then we numerically predict the surface waves using the recorded seismic traces based on those estimated phase-velocities. Finally, we subtract the predicted surface waves from the seismic data. Our invention applies to seismic surface Rayleigh and Love wave processing for land acquisition. Our invention applies to seismic Scholte wave processing for marine acquisition where Scholte wave is guided along the sea floor. Our invention applies to Stoneley waves in borehole seismic imaging.