The purpose of this study is to apply this approach to natural earthquake events, on the example of a moderatesize event (`Mw 4.9) in northeastern France. The main difficulty of such an adjustment lies in the reliability of the minimum phase assumption required by the spectral factorization algorithm. An investigation of the phase properties of earthquake STF indicates that classical singlepatch models such as the Brune model fulfill the minimum phase condition, whereas multiple patch models probably do not. Nevertheless, it is shown that minimum phase wavelets (MPWs) provide reliable information on the actual STF properties such as the duration, seismic moment, and even the actual time history. A statistical study on the timedomain differences between 20,000 arbitrary finite duration wavelets and their minimum phase equivalent supports an a priori minimum phase criterion based on the time-frequency spread of the recovered STF: the lower the latter, the smaller the timedomain discrepancy between the estimated MPW and the unknown actual one. The seismic coda spectral factorization algorithm has then been applied to a moderatesize earthquake Mw 4.9 that occurred near Rambervillers (northeastern France, 22 February 2003). The stability of the retrieved STF from different, distant rock site stations, the correct estimation of the moment magnitude, and the successful comparison with STF obtained by the empirical Green's function deconvolution approach demonstrate the reliability and the robustness of the method as well as the usefulness of the proposed minimum phase criterion.