Focused multi-layer inversion of magnetic resonance sounding data

We present a comparison between two different regularisation schemes for multi-layer inversion of the MRS data. The two regularizations consist of the norm (Occam's inversion) and the support (focused inversion) of the variation of the water content and relaxation time. The focused regularization provides a sharp inversion as it minimizes the area (the support) where the variations of the model parameters occur, and not the (L2) norm of the variations. Clearly, when sharp vertical transitions of the inversion parameters are present, the focused inversion retrieves the interfaces with higher precision and reconstructs more effectively the physical property values as well. This is a quite common situation in hydrogeophysics, e.g. in correspondence with the water table and/or at the boundary between aquifers and aquitards.