An ordered probit model for seismic intensity data

Seismic intensity, measured through the Mercalli–Cancani–Sieberg (MCS) scale, provides an assessment of ground shaking level deduced from building damages, any natural environment changes and from any observed effects or feelings. Generally, moving away from the earthquake epicentre, the effects are lower but intensities may vary in space, as there could be areas that amplify or reduce the shaking depending on the earthquake source geometry, geological features and local factors. Currently, the Istituto Nazionale di Geofisica e Vulcanologia analyzes, for each seismic event, intensity data collected through the online macroseismic questionnaire available at the web-page www.haisentitoilterremoto.it. Questionnaire responses are aggregated at the municipality level and analyzed to obtain an intensity defined on an ordinal categorical scale. The main aim of this work is to model macroseismic attenuation and obtain an intensity prediction equation which describes the decay of macroseismic intensity as a function of the magnitude and distance from the hypocentre. To do this we employ an ordered probit model, assuming that the intensity response variable is related through the link probit function to some predictors. Differently from what it is commonly done in the macroseismic literature, this approach takes properly into account the qualitative and ordinal nature of the macroseismic intensity as defined on the MCS scale. Using Markov chain Monte Carlo methods, we estimate the posterior probability of the intensity at each site. Moreover, by comparing observed and estimated intensities we are able to detect anomalous areas in terms of residuals. This kind of information can be useful for a better assessment of seismic risk and for promoting effective policies to reduce major damages.