  The analysis of surface wave dispersion curves is a way to infer the vertical
distribution of shear-wave velocity. The range of applicability is extremely
wide going, for example, from seismological studies to geotechnical
characterizations and exploration geophysics. However, the inversion of the
dispersion curves is severely ill-posed and only limited efforts have been put
into the development of effective regularization strategies. In particular,
relatively simple smoothing regularization terms are commonly used, even when
this is in contrast with the expected features of the investigated targets. To
tackle this problem, stochastic approaches can be utilized, but they are too
computationally expensive to be practical, at least, in the case of large
surveys. Instead, within a deterministic framework, we evaluate the
applicability of a regularizer capable of providing reconstructions
characterized by tunable levels of sparsity. This adjustable stabilizer is
based on the minimum support regularization, applied before on other kinds of
geophysical measurements, but never on surface wave data. We demonstrate the
effectiveness of this stabilizer on i) two benchmark - publicly available -
datasets at crustal and near-surface scales, ii) an experimental dataset
collected on a well-characterized site. In addition, we discuss a possible
strategy for the estimation of the depth of investigation. This strategy relies
on the integrated sensitivity kernel used for the inversion and calculated for
each individual propagation mode. Moreover, we discuss the reliability, and
possible caveats, of the direct interpretation of this particular estimation of
the depth of investigation, especially in the presence of sharp boundary
reconstructions.
