GNGTS 2013 - Atti del 32° Convegno Nazionale

calculating the rupture threshold for each fault every 500 years within an asymmetric Gaussian bell ranging from −3σ to +1σ, where s is assumed equal to 0.3, which is approximately the aleatoric uncertainty in the empirical relationship between the geometry and the moment magnitude M w (e.g., Leonard, 2010; Wells and Coppersmith, 1994). This method begins with a random initialisation of the loading stress values for the faults and, as time advances, is defined by a variable that reproduces the years of observation. The loading mechanism produces a source failure, which in turn changes the stress on all other sources. Additional detail for each source in the loading variable (blue curve in Fig. 1d) is provided here as a function of the slip, which increases from a random ground state d 0 over time as a function of the slip rate. When a source reaches the rupture threshold (red lines in Fig. 1d), its slip instantaneously reverts to zero, creating a perturbation in the state of stress on the other faults through static Coulomb stress interactions (Fig. 1e). To simulate the properties of a realistic fault interac- tion, we assume positive and negative stress transfers as functions of the slip that increase or decrease due to the occurrence of an earthquake on the reaming faults (receiver sources). The ΔCFS contributions from surrounding sources are shown in Fig. 1f and result in instanta- neous changes in the loading curve, as shown in Fig. 1d. For each receiver, the sum of the absolute values of ΔCFS is multiplied by the slip rate of the slipping source to define a parameter that we call the system effect (S E ). The S E quantifies the influence of the presence and slip rate of other neighbour sources over the seismic cycle of each Fig. 1 – a) Three-dimensional view of the nine seismogenic sources in the simulated fault system; b) example of slip rate variability in terms of long-term and short-term variability; c) example of magnitude variability; d–f) examples of simulation results: seismic history. The red lines represent the rupture thresholds and change with the magnitude variability, the blue lines represent the loading variable that changes with time, and the green lines represent the contribution of the ΔCFF when an earthquake occurs; e) example of stress perturbation due to a rupture: the blue lines represent a negative contribution, whereas the red lines represent a positive contribution. 159 GNGTS 2013 S essione 2.1