Abstract. The knowledge of the crustal strain rate tensor provides a description of geodynamic processes such as fault strain accumulation, which is an important parameter for seismic hazard assessment, as well as anthropogenic deformation. In the past two decades, the number of observations and the accuracy of satellite based geodetic measurements like GPS greatly increased, providing measured values of displacements and velocities of points. Here we present a method to obtain the full continuous strain rate tensor from dense GPS networks. The tensorial analysis provides different aspects of deformation, such as the maximum shear strain rate, including its direction, and the dilatation strain rate. These parameters are suitable to characterize the mechanism of the current deformation. Using the velocity fields provided by SCEC and UNAVCO, we were able to localize major active faults in Southern California and to characterize them in terms of faulting mechanism. We also show that the large seismic events that occurred recently in the study region highly contaminate the measured velocity field that appears to be strongly affected by transient postseismic deformation. Finally, we applied this method to coseismic displacement data of two earthquakes in Iceland, showing that the strain fields derived by these data provide important information on the location and the focal mechanism of the ruptures.