Very Fast Simulated Annealing Surface Wave Inversion with Model Constraints

Geophysical Inversion is an ill-posed problem that is inherently affected by the non-uniqueness of the solution. Moreover, several peculiar aspects characterize the surface wave inverse problem as the associated forward problem is implicit, modal identification is often difficult and higher mode solutions may not even exist for certain frequency ranges. To this end, the use of a priori information is of great help in reducing the solution ambiguities. In the heuristic inversion algorithm presented in this note, mathematical measures of the desired nature of the inverted models (e.g. smooth or minimum norm solutions) are introduced into the objective function to bias constructively the solution towards realistic estimates of the ID shear wave profile. In the inversion algorithm, two different forward kernels can be alternatively selected for the direct problem computation: the conventional modal inversion based on modal identification, or the direct minimization of the secular function, to avoid possible pitfalls associated with an ambiguous mode identification of the observed dispersion pattern. The versatility of the inversion algorithm is illustrated using both synthetic and real data. In the latter case, the inverted shear velocity profiles are blind compared with crosshole results. Copyright 2009, European Association of Geoscientists and Engineers.