We discuss in this paper the possibility of detecting slow slip events (such as silent earthquakes, or earthquake nucleation phases) in the vicinity of geological faults, and the possible localization of those faults from GPS observations. An eigenvalue problem (of Steklov type), modelling the slow evolution of the slip, is stated as a direct problem. The recovery of an active fault from surface observations is formulated as the related inverse problem.

We use an asymptotic formula for the observed surface displacement to infer two inversion techniques for the recovery of faults from surface observations. The first one involves a least-square minimization method; the second one uses the momentum method. The recovered information contains only the depth of the fault, its horizontal position and the 'normalized seismic moment', which is related to the fault shape. We test the two inversion methods for line segment faults in numerical simulations. We are led to conclude that the momentum method gives a very good initial guess for the least-square minimization method, which turns out to be sharp, robust and computationally inexpensive. Unexpectedly, the latter method is also very efficient for faults that are close to the observation surface, despite the fact that our asymptotic approximation may not be valid in that region. Finally we assess how our method for detecting active faults is affected by the sensitivity of the observation apparatus and the stepsize for the grid of surface observation points. The maximum permissible stepsize for such a grid is computed for different values of fault depth and orientation.