Magnitude and source spectra estimation using an elastic radiative transfer modelling of seismic wave-field attenuations: application to a French dataset.

Accurate magnitude estimates and reliable propagation models are essential for seismic hazard assessment. Unfortunately, the magnitudes of small earthquakes remain subject to significant uncertainties, primarily due to complex high-frequency propagation effects. Similarly, spatial variations in attenuation properties are crucial for refining ground motion models and reducing epistemic uncertainties in seismic hazard assessment. This study proposes (1) to map attenuation properties (scattering and absorption) in Metropolitan France using the radiative transfer theory of elastic waves, and (2) to simultaneously estimate source and site spectra through a generalized inversion. The recovered source spectra provide access to the moment magnitude Mw​, corner frequency fc​, and apparent stress σ_app​.

We apply the entire inversion procedure to approximately 21,000 recordings from the EPOS-FR and CEA databases, including events with local magnitudes ML​ ranging from 2.0 to 5.9, and stations with hypocentral distances of less than 250 km. The estimated attenuation maps reveal strong spatial and frequency-dependent variations. Scattering dominates absorption at low frequencies (< 1 Hz), while absorption prevails at high frequencies. Strong scattering anomalies are concentrated in recent sedimentary basins at low frequencies and in deformed regions or deep sedimentary basins at medium and high frequencies. Conversely, Variscan units exhibit low scattering attenuation, especially at low frequencies. Absorption is highest in the French Alps and the western Pyrenees and lowest in the Armorican Massif. Concurrently, a catalog of 1,279 Mw​ magnitudes and 577 site terms is established for Metropolitan France. The obtained magnitudes are consistent with those in the unified Euro-Mediterranean catalog. Its comparison with the SI-Hex catalog highlights the importance for correcting the attenuation variations before extracting source parameters and especially the magnitude. The analysis of the apparent stress σ_app​ reveals a moderate increase with the seismic moment M0​ (scaling exponent of 0.24±0.08), without any marked regional trend. Finally, we emphasize the importance of rigorously correcting for site effects, using reference stations on bedrock and of ensuring inter-event connectivity during the generalized inversion process through the existence of common stations across event records. The next step is to integrate this approach and related results in CEA seismic alert operational framework.