Multimodal inversion of Rayleigh wave dispersion curves based on a generalized misfit function

Fundamental mode dispersions, particularly higher ones obtained from weak and hard interlayers, are usually used for inversion to obtain the S-wave velocity profile. Higher mode dispersions are more informative for surface-wave inversion, thus benefiting both inversion stability and model resolution. In the multimodal inversion of the Rayleigh wave dispersion curves, the conventional root-mean-square based misfit function (RMF) is often deviated when the dispersion modes are misidentified. Alternatively, the inversion based on the determinant misfit function (DMF) may avoid misidentifications, but will still be limited to its inherent local minima. In order to reduce this complexity, the paper presents a generalized misfit function (GMF) for estimating the S-wave velocity profile. The generalized function allows for the inversion of both fundamental and higher modes dispersion, without mode-numbering. Before the inversion, the dispersion points are divided into the recognizable fundamental mode dispersion points and others. The RMF is then calculated using data from distinct fundamental mode dispersion, while the DMF was calculated using data from other points. Lastly, the RMF and the DMF were combined to form the GMF by normalizing. The results are based on both theoretical and real data sets and confirm the advantages of GMF in mode identification and inversion accuracy compared to both RMF and DMF.