Wave equation dispersion inversion using a difference approximation to the dispersion-curve misfit gradient

•We proposed a new method for 2D S-wave velocity inversion of the dispersion curve for the Rayleigh-wave.•The dispersion curve is picked automatically for the predicted data.•The proposed method is free of local minima problem.•Both synthetic and field data show its effectiveness.

We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh wave dispersion curve using a difference approximation to the gradient of the misfit function. We call this wave equation inversion of skeletonized surface waves because the skeletonized dispersion curve for the fundamental-mode Rayleigh wave is inverted using finite-difference solutions to the multi-dimensional elastic wave equation. The best match between the predicted and observed dispersion curves provides the optimal S-wave velocity model. Our method can invert for lateral velocity variations and also can mitigate the local minimum problem in full waveform inversion with a reasonable computation cost for simple models. Results with synthetic and field data illustrate the benefits and limitations of this method.