A Monte Carlo multimodal inversion of surface waves

The analysis of surface wave propagation is often used to estimate the S-wave velocity profile at a site. In this paper, we propose a stochastic approach for the inversion of surface waves, which allows apparent dispersion curves to be inverted. The inversion method is based on the integrated use of two-misfit functions. A misfit function based on the determinant of the Haskell–Thomson matrix and a classical Euclidean distance between the dispersion curves. The former allows all the modes of the dispersion curve to be taken into account with a very limited computational cost because it avoids the explicit calculation of the dispersion curve for each tentative model. It is used in a Monte Carlo inversion with a large population of profiles. In a subsequent step, the selection of representative models is obtained by applying a Fisher test based on the Euclidean distance between the experimental and the synthetic dispersion curves to the best models of the Monte Carlo inversion. This procedure allows the set of the selected models to be identified on the basis of the data quality. It also mitigates the influence of local minima that can affect the Monte Carlo results. The effectiveness of the procedure is shown for synthetic and real experimental data sets, where the advantages of the two-stage procedure are highlighted. In particular, the determinant misfit allows the computation of large populations in stochastic algorithms with a limited computational cost.