Inversion of relative motion data for estimates of the velocity gradient field and fault slip

A new method is presented for a purely kinematic analysis of relative motion data of crustal deformation. We start by developing a general integral formulation that links the relative motion between two positions to the velocity gradient field. Next, fault slip is explicitly incorporated, leading to the final observation equation. This equation provides a new, complete and, in practice, exact description of the time-dependent relation between surface motion and the underlying kinematics. The combination of equations belonging to pairs of observation sites (e.g. of a geodetic network) leads in a natural way to a linear inverse problem from which the velocity gradient field and slip on active faults can be estimated. The method is successfully tested in a synthetic experiment.