Structurally-constrained FD-EMI data inversion using a Minimum Gradient Support (MGS) regularization

In geophysical data inversion, one way to decrease the non-uniqueness of the solutions is to incorporate structural constraints. Such structural constraints are typically derived from collocated geophysical data, which are more sensitive to subsurface structures and parameter contrasts than the to-be-inverted data. When using a smooth regularization operator, a straightforward approach is to reduce the local weight of the smoothness constraints in model regions where we expect an interface. However, when using such an inversion approach, the capability to reconstruct a sharp interface relies only on the structural a priori information; i.e., model areas where no structural a priori information is available are solely controlled by the standard smoothness constraints. Therefore, this approach is not optimal in practice, as the structural a priori information is often not complete.

In this study, we evaluate a structurally-constrained inversion approach based on the Minimum Gradient Support (MGS) regularization, which is capable to promote sharp interfaces also in areas where no structural a priori information is explicitly specified. We test and evaluate this regularization approach for the inversion of frequency-domain electromagnetic induction (FD-EMI) data, where we use a constant-offset 3D GPR data set to derive structural a priori information. Our field data set covers an area of about 120 m x 50 m and has been collected at a field site in Kremmen, Germany, to explore peat deposits. Our results demonstrate that the proposed structurally-constrained inversion approach helps in finding a reliable subsurface structures (e.g., peat thickness) as well as a reliable reconstruction of the subsurface electrical conductivity distribution within the peat formation (e.g., related to varying degrees of peat decomposition) and within the sandy substratum.