Generalized inversion of source, site and attenuation parameters using the radiative transfer theory: application to a French dataset

An accurate magnitude estimation is necessary to evaluate properly the seismic hazard. Unfortunately, the magnitudes of small earthquakes are subject to large uncertainties due to high-frequency propagation effects, which are generally not accurately considered. To address this issue, we developed a method to separate source, attenuation and site parameters from the elastic radiative transfer modeling of the full energy envelopes of seismograms. Our separation method is based on a 2-step inversion procedure. First, for each source-station pair, we retrieve the optimal frequency-dependent attenuation parameters (scattering and absorption) fitting the observed energy envelopes in the 0.375-24Hz band. In a second step, we separate the source and site amplification spectra using a joint inversion algorithm. The site amplification is adjusted on reference stations, characterized by approximatively flat H/V ratios. From the source spectra, we estimate the moment magnitude Mw, the corner frequency fc and the apparent stress σapp.
We applied the inversion procedure to around 21000 waveforms recorded by EPOS-FR and LDG stations at hypocentral distances less than 250 km, for earthquakes with magnitudes ML ranging from 2.0 to 5.9. The magnitudes Mw of the extracted 1300 source spectra show a high coherency of our inverted Mw with the unified Euro-Mediterranean catalogue. The comparison with the SI-Hex catalogue shows the role of attenuation variations across France in source parameters estimation. These spatial variations of attenuation are highlighted through scattering and absorption maps. σapp reveals a slight increase with Mw, but no regional differences when preforming the joint inversion. On the contrary, if source and site parameters are estimated for each event independently, σapp presents spatial variations with a systematic higher level in Western France. This regional difference is caused by a regional site effect not considered in a disjoint separation scheme in space and time across the event catalog. These results show the importance of attenuation and site correction in estimating source parameters. In the future, we intend to automate our method and apply it routinely to smaller earthquakes for which traditional methods are not readily applicable due to the complexity of waveforms.