Considering uncertainties in the determination of earthquake source parameters from seismic spectra.

In this paper, we present a method for handling uncertainties in the determination of the source parameters of earthquakes from spectral data. We propose a robust framework for
estimating earthquake source parameters and relative uncertainties, which are propagated down to the estimation of basic seismic parameters of interest such as the seismic moment,
the moment magnitude, the source size and the static stress drop. In practice, we put together a Bayesian approach for model parameter estimation and a weighted statistical mixing of multiple solutions obtained from a network of instruments, providing a useful framework for extracting meaningful data from intrinsically uncertain data sets. The Bayesian approach used to estimate the source spectra parameters is a simple but powerful mechanism for non-linear model fitting, providing also the opportunity to naturally propagate uncertainties and to assess the quality and uniqueness of the solution. Another important added value of such an approach is the possibility of integrating information from the expertise of seismologists. Such data can be encoded in a prior state of information that is then updated with the information provided by seismological data. The performance of the proposed approach is demonstrated analysing data from the 1909 April 23 earthquake occurred near Benavente (Portugal).