Sharp spatially constrained inversion

We present sharp reconstruction of multi-layer models using a spatially constrained inversion with minimum gradient support regularization. In particular, its application to airborne electromagnetic data is discussed. Airborne surveys produce extremely large datasets, traditionally inverted by using smoothly varying 1D models. Smoothness is a result of the regularization constraints applied to address the inversion ill-posedness. The standard Occam-type regularized multi-layer inversion produces results where boundaries between layers are smeared. The sharp regularization overcomes this by allowing a reconstruction with a large number of layers, while preserving abrupt changes in the conductivity distribution. Instead of minimizing the norm of the vertical spatial variation of the model, in the focusing approach, it is the number of layers where the variations occur that is minimized. Thus, the results are compatible with the data and, at the same time, favor sharp transitions. The focusing strategy can also be used to constrain the 1D solutions laterally, guaranteeing that lateral sharp transitions are retrieved without losing resolution. By means of real and synthetic datasets, sharp inversions are compared against classical smooth results and available boreholes. With the focusing approach, the obtained blocky results agree with the underlying geology and allow for easier interpretation by the end-user.