Abstract
We present a new filtering method for potential fields, based on modelling the fields in terms of very compact solutions, i.e., the sources are expected to occupy the smallest allowable volume in the source domain. The selected solutions, which we call "Extremely Compact Sources" (ECS) form a sort of atomized model, which still satisfies the non-unique inverse problem of gravity and magnetic fields. The ECS model is not only characterized by sparsity, but also by large values of the physical property (density or magnetic susceptibility). The sparse nature of the model allows for the definition of a highly localized filter, which can be obtained by simply specifying the atoms to be selected in a given area. This feature allows managing tasks normally impossible with traditional filters, such as the separation of interfering anomalies having a similar wavenumber content. In addition, the procedure can perform a very effective regional/residual separation. We demonstrate the method on synthetic cases and apply it in the real case of gravity data of Campi Flegrei volcanic area (Italy), where we use the ECS filtering to isolate the gravity effect of the Mount Olibano dome.