APPLICATION OF THE PROJECTED LANDWEBER METHOD TO THE ESTIMATION OF THE SOURCE TIME FUNCTION IN SEISMOLOGY

The empirical Green function (EGF) model, which is used in this paper for the analysis of the waveforms of low-energy earthquakes, consists in assuming that the propagating medium and the recording instrument c an be treated as a linear system and that the impulse response functio n of the system can be approximated by the waveform of a very small ea rthquake. The deconvolution of the Green function event from the wavef orm of a larger one, located at approximately the same position, provi des information about the source time function (STF) of the latter. Li near inversion methods do not yield satisfactory estimations of the ST F which must be positive and causal. Moreover, an estimate of the dura tion (support) of the STF should be desirable. In this paper we apply to this problem the so-called projected Landweber method, which is an iterative nonlinear method allowing for the introduction of constraint s on the solution. The implementation of the method is easy and effici ent. We first validate the method by means of synthetic data, generate d by the use of waveforms of a seismic swarm that occurred in the Ligu rian Alps (north-western Italy) during July 1993. Then, taking into ac count the indications provided by the simulations, the method has been applied to the inversion of real data, yielding satisfactory results also in the case of quite complex events.