We propose a two-step inversion of three-component seismograms that ( 1) recovers the far-field source time function at each station and (2) estimates the distribution of co-seismic slip on the fault plane for small earthquakes (magnitude 3 to 4). The empirical Green’s function (EGF) method consists of finding a small earthquake located near the one we wish to study and then performing a deconvolution to remove the path, site, and instrumental effects from the main-event signal. The deconvolution between the two earthquakes is an unstable procedure: we have therefore developed a simulated annealing technique to recover a stable and positive source time function (STF) in the time domain.