Optimization for nonlinear inverse problem

The non-linear inversion of geophysical data in general does not yield a unique solution, but a single model representing the investigated field, and is preferred for an easy geological interpretation of observations. The analyzed region is constituted by a number of sub-regions where multi-valued non-linear inversion is applied, which leads to a multi-valued solution. Therefore, combining the values of the solution in each sub-region, many acceptable models are obtained for the entire region and this complicates the geological interpretation of geophysical investigations. In this paper new methodologies are presented, capable of selecting one model among all acceptable ones, that satisfies different criteria of smoothness in the explored space of solutions. In this work we focus on the non-linear inversion of surface wave dispersion curves, which gives structural models of shear-wave velocity versus depth.