Bayesian Estimation of Paleoearthquake Magnitudes in the Central Apennines

ABSTRACT Paleoseismic data provide critical constraints on earthquake recurrence where instrumental records are limited, but magnitude estimation from geological 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), throw (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 calibrating the best model, our analysis yields magnitude estimates that show agreement with existing parametric catalogs for some historical and instrumental earthquakes. The method is applied to 44 paleoevents reported in a new database (PaleoEcA), with 2σ credible intervals mostly in the range ±(0.3–0.7), 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 as a MATLAB software (PaleoBAYES), for quantifying uncertainties in paleoseismic databases. Discrepancies with some catalog estimates highlight the importance of systematic, uncertainty-aware methods when deriving magnitudes from paleoseismological data.