Minimal-norm RKHS solution of an integral model in geo-electromagnetism

In this paper, a numerical method is developed for approximating the solution of a linear integral model in a reproducing kernel Hilbert space (RKHS). The model is typical of frequency domain electromagnetic (FDEM) induction methods in applied geophysics. The original problem is reformulated as a new one whose solution has the same smoothness properties as the original one. Then, the minimal-norm solution of such a model is computed through a numerical method that combines Riesz's theory with regularization tools. Several numerical tests illustrate the performance of the proposed approach.