A probabilistic approach for integrating macroseismic data and its application to estimate the data completeness

One of the most common practice to estimate the effects of a past earthquakes at given localities when the documented ones present important gaps in space and time is through the use of Intensity Prediction Equations – IPEs. However, these attenuation models can present some limitations. For example, they generally model an isotropic decay of intensity with distance disregarding lateral heterogeneities induced by the fracture process and geological/geomorphological features. In this regard, the main scope of this research was to develop an alternative approach for estimating the intensity values at the considered sites capable of minimizing these limitations. The proposed approach relies on the probabilistic Bayesian formalization in order to take into account the uncertainties resulting from the intensity attenuation models and the nature of macroseismic intensity data (ordinal, discrete and range-limited value). In detail, the key element of the presented approach is a combination of probabilistic estimates provided by an Intensity Prediction Equation (IPE) constrained by observed intensities that are spatially close to the site of interest. In this way, this approach makes it possible to modify the isotropic decay of intensity with distance resulting from IPEs modelling the pattern of predicted intensities in a more realistic way. The proposed methodology was developed in order to integrate the scattered macroseismic intensity distributions of past earthquakes and to enrich the seismic histories (i.e., the list of documented effects observed through time) of a single locality. The approach has been developed with a thorough analysis of the distances among the 15332 Italian localities contained in the Italian Macroseismic Database - DBMI15 (Locati et al., 2019). The performance of the proposed approach has been first applied to 28 Italian sites homogeneously distributed over the Italian area with long and rich seismic histories. The results obtained in terms of predicted number of occurrences are then tested with the intensities observed at the considered sites. Furthermore, the outcomes of the approach for two recent and well know events (i.e., 1980 Southern Italy and 2009 Central Italy events) have been compared with the intensity values obtained with two IPEs (Pasolini et al., 2008; Gomez et al., 2017). The scatter and poor macroseismic intensity distributions of two past earthquakes i.e., 1542 North-Central Italy and 1794 Southern Italy events) have been integrated with this approach. In addition, the proposed methodology was used for integrating and enriching the single seismic history of 228 Italian localities selected according to the number of macroseismic observations with intensity greater than or equal to 5 contained in DBMI15 and to their geographical distribution, spread over the Italian area. The number of data observed at the sites, integrated with those calculated with the proposed approach has been compared with the intensity computed with the IPE in order to estimate the completeness of the data of each seismic history. With this analysis, it was possible to identify a minimum completeness time for each considered locality and for intensity greater than or equal to 5, estimating a time period in which all the effects of a certain intensity degree are likely to be completely reported at the site. Finally, the minimum completeness times estimated at the single localities have been used to define the completeness of the epicentral intensity of an earthquake catalogue. The estimates of the minimum completeness time at the site have been interpreted in terms of epicentral intensity as the completeness starting year for an event with its epicenter at the same place or at a given location in function of the distance. The outcomes of this analysis have produced different estimates in function of the epicentral intensity of the catalogue greater than or equal to 6 assuming as the epicenter location the node of a regular grid of 40*40 km covering all the Italian area. Moreover, the results obtained have been then compared with the completeness times provided by Meletti and Marzocchi (2019) and Meletti et al. (2021)