Separation of Source, Site, and Path Effects Based on Elastic Radiative Transfer Theory, Part 2: Generalized Inversion of Source and Site Parameters and Application to Metropolitan France

Magnitudes of small earthquakes are subject to large uncertainties due to high-frequency (>1 Hz) propagation effects. Reliable estimates of magnitudes and source properties are essential for hazard assessment. To address this, we developed a two-step inversion procedure to separate source, attenuation, and site properties. First, path effects are extracted from data envelopes in the 0.375–24 Hz band for each source–station pair, as detailed in the companion article (Heller et al., 2026). Second, source and site amplification spectra are separated using a generalized inversion algorithm, with site amplification adjusted on reference stations exhibiting approximately flat horizontal-to-vertical (H/V) ratios. From the source spectra, we infer the moment magnitude Mw, corner frequency fc, apparent stress σapp, and stress drop Δσ. We apply the inversion procedure to approximately 21,000 waveforms recorded by the European Plate Observing System - France and Commissariat à l’Énergie Atomique et aux Énergies Alternatives stations at hypocentral distances less than 250 km, for earthquakes of magnitude ML 2.0–5.9. The magnitudes Mw deduced from 1279 source spectra are in strong agreement with the unified Euro-Mediterranean catalog. The comparison with the SI-Hex catalog illustrates the impact of attenuation variations across France on source parameter estimation. We also highlight the role of the inversion strategy. In the generalized inversion, σapp moderately increases with seismic moment M0, with a scaling exponent of 0.24 ± 0.08, without regional differences. In contrast, a single-event (SE) inversion scheme yields spatial variations of σapp with a systematically higher level in western France. This regional difference is caused by a regional site effect that is not considered in a SE separation scheme. The choice of reference for site amplification also matters. Using all stations for reference instead of stations with approximately flat H/V ratios, magnitudes are overestimated by 0.1–0.2 units and σapp increases more rapidly with M0. These results show the importance of properly accounting for attenuation and site effects when estimating source parameters.