Comparison of different regularization schemes for the 1D laterally constrained inversion of seismic surface wave data

The 1D layered inversion of surface wave dispersion data is a powerful tool to characterize the vertical distribution of S-wave velocity. Its applications span from seismology to geotechnical engineering, going through exploration geophysics. As many others, also this non-linear inverse problem is considerably ill-posed. Thus, in the Tikhonov’s regularization framework, the associated non-uniqueness and instability of the solution with respect to the data and their uncertainty can be tackled by including prior information in the inversion process. However, for the case of the gradient-based deterministic inversion problem, only constraints enforcing smooth spatial variations of the S-velocities have been used, even when blocky targets were expected. This, clearly, generates results that might fit the observed data, but that are often not compatible with other sources of information. On the other hand, probabilistic approaches can be used to properly map the model space; however, they are still very computationally expensive to be used routinely, or to be easily integrated in a multi-physical inversion procedure involving other geophysical methods.

Our goal is to combine computer efficiency, capability of integration with other geophysical methods, and some exhaustiveness regarding the non-uniqueness of the inverse problem. For this, we developed a coherent set of tools for the deterministic inversion of dispersion curves that is capable of applying a quite large spectrum of constraints. This includes, for example, vertically and laterally constrained inversions with different levels and kinds of regularization (sharpness and/or smoothness). In this study, we evaluate the capabilities and the possible limitations of the different regularization approaches on various datasets.