Wave-equation skeletonized inversion of dispersion curves and spectra

ABSTRACT Accurate S-wave velocity models are essential for near-surface characterization. A wave-equation surface-wave dispersion spectrum inversion (SWD) method was introduced, which preserved the convexity of the misfit function — a key benefit given the inherent trade-off between data richness and non-convexity in conventional approaches. The dispersion curves were extracted via the ArgMax function that selects the phase velocity from the dispersion spectrum. At the same time, a differentiable approximation was implemented through the SoftMax operator with adjustable sharpness (controlled by β). It allowed the use of additional gradient information from the dispersion spectrum, with the gradient of the misfit function with respect to model parameters derived using the chain rule and adjoint-state method. The convexity of the misfit function mitigated the cycle-skipping problem commonly encountered in full-waveform inversion. Unlike 1D inversion of dispersion curves, SWD offers high lateral resolution without requiring a layered assumption. Synthetic data tests found that SWD reduces dependence on poor or inaccurate initial models, and two field land seismic examples further discovered its reliability in reconstructing near-surface S-wave velocity models.