Traditional approaches of utilizing the dispersion curves in S-wave velocity reconstruction have many limitations, namely, the 1D layered model assumption and the automatic/manual picking of dispersion curves. On the other hand, conventional full-waveform inversion (FWI) can easily converge to one of the local minima when applied directly to complicated surface waves. Alternatively, a wave equation dispersion spectrum inversion can avoid these limitations, by inverting the slopes of arrivals at different frequencies. A local-similarity objective function is used to avoid possible cycle skipping. We apply the proposed method on the large-scale ambient-noise data recorded at a large-N array with over 3000 recorders. So we can estimate the shear-wave velocities down to 1.8 km depth. The main benefits of the proposed method are 1) it handles lateral variations; 2) it avoids picking dispersion curves; 3) it utilizes both the fundamental- and higher-modes of Rayleigh waves, and 4) it can be solved using gradient-based local optimizations. A good match between the observed and predicted dispersion spectra also leads to a reasonably good match between the observed and predicted waveforms, though the inversion does not aim to match the waveforms.


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