Rayleigh wave dispersion curve inversion via genetic algorithms and Marginal Posterior Probability Density estimation

Surface wave dispersion curve inversion is a challenging problem for linear inversion procedures due to its highly non-linear nature and to the large numbers of local minima and maxima of the objective function (multi-modality). In order to improve the reliability of the inversion results, we implemented and tested a two-step inversion scheme based on Genetic Algorithms (GAs). The proposed scheme performs several preliminary "parallel" runs (first step) and a final global run using the previously-determined fittest models as starting population. In this work we focus on the inversion of shear-wave velocity and layer thickness while fixing compressional-wave velocity and density according to user-defined Poisson's ratios and velocity–density relationship respectively. The procedure can nonetheless perform the inversion under different degrees of regularization, depending on the a priori information and the desired degree of freedom of the system. Thanks to the large number of considered models, in addition to the fittest model, a mean model and its accuracy are evaluated by means of a statistical approach based on the estimation of the Marginal Posterior Probability Density (MPPD). We tested the proposed GA-based inversion scheme on three synthetic models reproducing a complex structure with low-to-moderate velocity cover (also including a low-velocity channel) lying over hard bedrock. For all the considered cases the bedrock velocity and depth were properly identified, and velocity inversion was reconstructed with minor uncertainties. The performed tests also investigate the influence of the first higher mode, the reduction of the frequency range of the considered dispersion curve as well as the use of different number of strata. While a limited frequency range of the dispersion curve (maximum frequency reduced from 80 to 40 Hz) does not seem to significantly limit the accuracy of the retrieved model, the adoption of the correct number of strata and the addition of the first higher mode help better focus the final solution. In conclusion, the proposed approach represents an improvement of a purely GA-based optimization scheme and the MPPD-based mean model typically offers a more significant and precise solution than the fittest one. Results of the inversion performed on a field data set were validated by borehole stratigraphy.