Structurally constrained inversion by means of a Minimum Gradient Support regularizer: examples of FD-EMI data inversion constrained by GPR reflection data

Many geophysical inverse problems are known to be ill-posed and, thus, requiring some kind of regularization in order to provide a unique and stable solution. A possible approach to overcome the inversion ill-posedness consists in constraining the position of the model interfaces. For a grid-based parameterization, such a structurally-constrained inversion can be implemented by adopting the usual smooth regularization scheme in which the local weight of the regularization is reduced where an interface is expected. By doing so, sharp contrasts are promoted at interface locations while standard smoothness constraints keep affecting the other regions of the model. In this work, we present a structurally-constrained approach and test it on the inversion of frequency-domain electromagnetic induction (FD-EMI) data using a regularization approach based on the Minimum Gradient Support (MGS) stabilizer, which is capable to promote sharp transitions everywhere in the model, i.e., also in areas where no structural a priori information is available. Using 1D and 2D synthetic data examples, we compare the proposed approach to a structurally-constrained smooth inversion as well as to more standard (i.e., not structurally-constrained) smooth and sharp inversions. Our results demonstrate that the proposed approach helps in finding a better and more reliable reconstruction of the subsurface electrical conductivity distribution, including its structural characteristics. Furthermore, we demonstrate that it allows to promote sharp parameter variations in areas where no structural information are available. Lastly, we apply our structurally-constrained scheme to FD-EMI field data collected at a field site in Eastern Germany to image the thickness of peat deposits along two selected profiles. In this field example, we use collocated constant offset ground-penetrating radar (GPR) data to derive structural a priori information to constrain the inversion of the FD-EMI data. The results of this case study demonstrate the effectiveness and flexibility of the proposed approach.