PSI - Issue 78

1558 Iunio Iervolino et al. / Procedia Structural Integrity 78 (2026) 1553–1560 like effects exceed 60%. However, absolute differences, that is, [ ( )] − − [ ( )] , are lower than 0.08g for each vibration period. 3 Processes of earthquake occurrence In PSHA, a complementary result to [ ( ) > ] is the probability of occurrence of at least one earthquake in the time interval ( , + Δ ) , given that time zero is when the last earthquake occurred and no earthquakes occurred in (0, ) .This is expressed as [ ( , + Δ ) ≥ 1| (0, ) = 0] , where is the RV counting the occurring earthquakes with magnitude in an interval of interest. Such a probability can be computed as per Eq. (6), in which ( ) is the PDF of the RV, , which defines the interarrival time between earthquakes: [ ( , + ) ≥ 1| (0, ) = 0] = 1 − 1−∫ ( )∙ 0 + 1−∫ ( )∙ 0 Ǥ (6) The formulation of the ( ) distribution depends on the model adopted to describe the processes of earthquake occurrence on the seismic source. Under the classical assumptions used in PSHA, typically applied to large seismic sources, the earthquake occurrence process is modelled as an HPP. In this case, ( ) , as shown in Eq. (7), is completely defined by , the return period, which also corresponds to the mean interarrival time: ( ) = 1 ∙ − . (7) Replacing Eq. (7) in Eq. (6) yields the probability of observing at least an earthquake in a given time interval that depends only on its width, t , neither on the starting point of the interval nor the seismic history prior to it. However, when a single fault is considered, the HPP assumption is often questioned. In such cases, alternative models – featuring different kinds of memory of the earthquake history of the source – can be adopted to model ( ) (e.g., Polidoro et al. 2013). Herein, two such models are considered, both of which have been applied in the literature to the seismic source of interest: the Brownian passage time (BPT) model (Matthews et al. 2002) and the slip-predictable model (SPM) (Kiremidjian and Anagnos 1984). BPT is a Gaussian-distributed loading process on the seismic source, characterized by a constant loading rate over time and a standard deviation. Interarrival times are independent and identically distributed (i.i.d.), where ( ) follows an inverse Gaussian distribution, as given by Eq. (8), that is defined by two parameters: the return period, , and its coefficient of variation, , also known as aperiodicity : ( ) =√ 2∙ ∙ 2 ∙ 3 ∙ − 2(∙ ∙− 2 )∙2 , (8) The SPM assumes that the interarrival times are modelled as Weibull i.i.d. RVs. The corresponding PDF, given in Eq. (9), is defined by a shape and a scale parameter equal to and 1 ⁄ , respectively: ( ) = ∙ ∙ ( ∙ ) −1 ∙ −( ∙ ) . (9) To calibrate the and parameters, the mean and the variance of the interarrival times can be expressed in closed form solutions, which are not reported here for the sake of brevity (Polidoro et al. 2013). Additionally, the model assumes a relationship between the magnitude of the next earthquake and the time elapsed since the last seismic event. 3.1 Probability of earthquake occurrence The work of Akinci et al. (2017) analyzes the seismic sources of the Calabria region and suggests associating the BPT model with each seismic fault of the area, also providing parameter values for each source. Specifically, for the ITIS013 fault, the suggested values of and are equal to 739 years and 0.5, respectively. For the same fault, Faccioli et al. (2008) suggest using SPM with a return period for M7.0 earthquakes ranging between 700 and 1500 years. These values are consistent with the minimum and maximum recurrence time reported in the DISS database for the same source, which are 710 and 1527 years, respectively. A comparison of the PDF of the interarrival times, obtained according to the two cited papers, is provided in Fig. 4a. While the BPT model is fully defined by the two parameters previously reported, the application of the SPM