We present a wave-equation dispersion spectrum inversion algorithm for near-surface P- and S-wave velocity estimation. We utilize what we often considered in seismic processing as coherent noise, surface waves and guided P-waves, as our inversion data. The dispersion spectrum is calculated using a linear Radon transform. A local-similarity based measurement of the misfit is used as our objective function replacing the conventional L2 norm often used in full waveform inversion. The proposed method does not require picking explicit dispersion curves and is immune to errors in the initial models and source wavelets. One synthetic and two field data examples are used to verify the effectiveness of the proposed method and also reveal some of its limitations.