Computing the time-dependent activity rate using non-declustered and declustered catalogues – a first step towards time-dependent seismic hazard calculations for operational earthquake forecasting

Abstract. Probabilistic seismic hazard analysis (PSHA) typically requires tectonic b values and seismic activity rates using declustered catalogues to compute the annual probability of exceedance of a given ground motion (for example, the peak ground acceleration or PGA). In this work, we propose a methodology that includes the spatially gridded time-dependent b value and activity rate computation using seismic clusters in PSHA calculations. To account for the spatial variability and the relationship of the earthquakes with the seismic sources, we incorporate the distance from the centre of the grid cell to the closest fault and the epicentre's uncertainty into the smoothing kernel as the average distance and the variance, respectively. To illustrate this methodology, we selected two scenarios as representatives of the high-seismicity region and low-to-moderate-seismicity region. The first one is located in Central Italy, where the L'Aquila earthquake happened, while the other is in south-eastern Spain, where several earthquakes with a moment magnitude (Mw) greater than 4.0 have taken place over the last 30 years, including two earthquakes with magnitude greater than or equal to 5.0. We compared three different seismic activity models based on the parameters considered in the calculations (distance from spatial cells to faults and epicentral distance uncertainty), and we defined and calculated the changes in the annual probability of exceedance for a given background PGA value. The results reveal noticeable changes in the annual probability of exceedance in the proximity of the occurrence of significant events. In the case of Italy, the annual probability of exceedance increases significantly, but in the case of Spain not all the earthquakes have an associated increase in the exceedance probability. However, we have observed how, for moderate- to low-seismicity regions, the use of a non-declustered catalogue can be appropriate when computing time-dependent PSHA, as in the case of Spain.