Surface-Wave Dispersion Curve Computation and Inversion: A Framework Integrating Quadratic Extrema Interpolation and Randomized Layering with Multiple Initial Models

Surface-wave dispersion curve computation is a fundamental tool for seismic wavefield simulation and subsurface characterization. However, models containing low-velocity layers (LVLs) present persistent challenges due to the “mode-kissing” phenomenon, in which adjacent dispersion curve branches converge closely, leading to missed critical roots in conventional root-finding methods and compromising inversion completeness. To address this, we propose a quadratic extrema interpolation method that strategically augments sampling points at mode-kissing zones, thereby resolving previously undetected roots while maintaining computational efficiency by focusing on function morphology rather than conducting additional forward simulations. Comparative analyses against the widely used Computer Programs in Seismology package demonstrate that the proposed method significantly reduces root-omission rates and achieves substantial speed improvements in computing dispersion curves. For inversion, we adopt a wavelength-constrained layering scheme that adapts to the depth-dependent resolution of surface-wave data, combined with depth-zoned empirical relationships; this design balances geophysical plausibility and computational efficiency, whereas statistical aggregation of results from multiple initial models addresses inversion nonuniqueness. Validation through numerical simulations (near-surface and crustal LVL models) and real data applications (Mirandola site and USArray) confirms the method’s robustness: it accurately resolves LVLs and key structural features, with results consistent with independent measurements and existing models, providing a reliable tool for subsurface characterization in engineering and geological studies. To facilitate the adoption and application of this workflow, an open-source program QEDispInv, encompassing both forward computation and inversion of dispersion curves, has been developed and released in conjunction with this work.