Relationship between magnitudes commonly calculated by the French observatories and the moment magnitude Mw, and variability of stress drop in the Lesser Antilles subduction zone

Published catalog of instrumental seismicity from French observatories in the Lesser Antilles (OVSG in Guadeloupe and OVSM in Martinique) ranging from 2014 to 2022 is very extensive in space and time but the computed magnitudes are based on various local scales (Saurel et al., 2022; 2024), a common issue for hazard assessment studies. The aim of this study is to unify the magnitudes of this catalog, by establishing a regression relationship between the magnitudes commonly calculated by the observatories and the moment magnitude Mw, and studying the variability of stress drop depending on the tectonic context from trench to depth. The catalog contains 18,784 earthquakes recorded by, with small variations, the same regional seismic stations during the whole period, and with magnitudes ranging from -2.0 to 6.2. Completeness analysis for the entire Lesser Antilles arc reveals two main maximum values: one at M = -0.2, related to volcanic earthquakes from active volcanoes; another at M = 2.5, indicating the approximate completeness magnitude threshold for earthquakes of tectonic origin. In this study we focus on 8,569 earthquakes with M > 2.0. Moment magnitudes Mw were estimated using SourceSpec codes (SSp) (Satriano et al., 2016; 2025), which performs spectral inversion of S-wave displacement spectra. The inversion also provides key parameters such as corner frequency, seismic moment, radiated energy, static stress drop, and apparent stress. Mw values calculated with SSp are consistent with Mw calculated by moment tensor inversion with the Isola software or reported by international agencies, and may support the retroactive inclusion of Mw in older catalogues. Finally, magnitudes Mw computed with SSp codes were validated for 4,238 earthquakes. The relationship between magnitudes does not appear to be linear for the entire M range, and variations in slope and intercept values are observed with depth. Several orthogonal distance regressions with exponential models were then computed for each type of magnitude and for different range of magnitudes and depths. Md appears less stable and, where possible, should be avoided in earthquake location analyses. Uncertainties in magnitude estimations coming from the original catalog were incorporated in the regressions to enhance the results. The different final laws will enable the conversion and incorporation of additional data from instrumental data before 2014. Regarding the preliminary observations of variability of median stress drop values, we observe small differences between the seismotectonic domains from trench to depth.