Bayesian Estimation of Paleoearthquake Magnitudes in the Central Apennines

Paleoseismic data provide critical constraints on earthquake recurrence where instrumental records are limited, but magnitude estimation from geologic evidence requires careful treatment of measurement uncertainties. We develop a Bayesian method with application to the estimation of paleoearthquake magnitudes in the central Apennines, Italy, by jointly analyzing rupture length (L), slip (S), and age (T) data from field investigations. Our framework incorporates empirical scaling relationships with their full uncertainty time-dependent preservation probabilities, and physically informed priors. After the calibration of the best model, our analysis returns magnitude estimates that show agreement with existing parametric catalogs for some historical and instrumental earthquakes while revealing systematic differences with other key events. For the 1915 Fucino earthquake, our result (Mw 6.76±0.07) suggests slight overestimation in past research (Mw ~ 6.8-7.1). The method demonstrates stable performance across 44 paleoevents reported in a new, freshly released database (PaleoECA_2025), with credible intervals mostly in the range ± (0.1-0.3) reflecting measurement uncertainties and preservation bias. We observe that results depend critically on the chosen scaling laws (tested against, e.g., Wells and Coppersmith 1994, Leonard 2010). This approach provides a reproducible framework, also publicly available in the MATLAB software (PaleoBAYES), for quantifying uncertainties in paleoseismic databases. Discrepancies with some historical estimates highlight the importance of systematic, uncertainty-aware methods when deriving magnitudes from paleoseismological data.