An empirical Green's function (EGF) technique has been developed to detect the rupture velocity history of a small earthquake. The assumed source model is a circular crack that is characterized by a single and unipolar moment rate function (MRF). The deconvolution is treated as an inverse problem in the time domain, which involves an assumed form of the moment rate function (MRF). The source parameters of the MRF are determined by adopting a global nonlinear inversion scheme. A thorough synthetic study on both synthetic and real seismograms allowed us to evaluate the degree of reliability of the retrieved model parameters. The technique was applied to four small events that occurred in the Umbria-Marche region (Italy) in 1997. To test the hypothesis of a single rupture process, the inversion results were compared with those arising from another EGF technique, which assumes a multiple rupture process. For each event, the best fit model was selected using the corrected Akaike Information Criterion. For all the considered events the most interesting result is that the selected best fit model favors the hypothesis of a single faulting process with a clear variability of the rupture velocity during the process. For the studied events, the maximum rupture speed can even approach the P-wave velocity at the source, as theoretically foreseen in studies of the physics of the rupture and recently observed for high-magnitude earthquakes.