GNGTS 2022 - Atti del 40° Convegno Nazionale

196 GNGTS 2022 Sessione 2.1 Determination ofmodel parameters. The high number of free parameters to be determined (in principle about 20), considering the parameters of the background model, the aftershock model, and the adjustment factor due to the missing contribution of earthquakes below the minimum completeness magnitude m c the maximization of the log-likelihood function is very time consuming and subject to numerical instability. However, according to Rhoades and Evison (2004), simultaneous optimization of all parameters is not necessary because some of them, such as the b-value of the Gutenberg and Richter (1944) relation and other parameters can be, in fact, separately fitted or even be simply assigned based on previous works in the same area. For parameters that need to be fitted, the likelihood optimization was carried out using the downhill simplex method (Nelder and Mead, 1965), which is the same optimization method used by the authors for the application of EEPAS to New Zealand (Rhoades and Evison, 2004). Forecasting skills evaluation and comparisonwith other forecastingmodels. We compared the obtained optimal log-likelihood and other statistic as the number of expected earthquake in the time period 1990-2021 obtained with the optimal fitted parameters, the information gain per earthquake (IGPE), AIC, AIC and the information Gain obtained by the EEPAS model with to ones obtained by other rate-based model like Space Uniform Poisson model (SUP), Space Varying Poisson model (SVP), Past to Proximity Earthquake (PPE) and Epidemic Type Aftershock Sequence (ETAS) applied for Italy territory region using the same dataset and the same analysis grid (Table 1). Tab. 1 - Comparison of skills statistics obtained by each model involved. SUP SVP PPE EEPAS ETAS-SUP ETAS-SVP Expected 54.1/54 54.5/54 54/54 42.7/54 52.0/54 54.1/54 earthquakes log-likelihood -1030.8 -915.1 -1009.5 -983.1 -681.6 -672.8 IGPE 0 2.14 0.39 0.88 6.47 6.63 AIC 2063.7 1832.13 2027.05 1992.12 1379.25 1361.61 ΔAIC 0 2.14 0.34 0.66 6.34 6.50 G 1 8.53 1.48 2.42 643.63 757.84 References Evison, F., & Rhoades, D. (2005). Multiple ‐ mainshock events and long ‐ term seismogenesis in Italy and New Zealand. New Zealand Journal of Geology & Geophysics , 48 , 523–536. https://doi.org/0028-8306/05/4803-0523. Gasperini, P., Lolli, B., & Vannucci, G. (2013). Empirical calibration of local magnitude data sets versus moment magnitude in Italy. Bulletin of the Seismological Society of America , 103 (4), 2227–2246. https://doi. org/10.1785/0120120356. Lolli, B., Randazzo, D., Vannucci, G., & Gasperini, P. (2020). The homogenized instrumental seismic catalog (HORUS) of Italy from 1960 to present. Seismological Research Letters , 91 (6), 3208–3222. https://doi. org/10.1785/0220200148. Nelder, J. A., & Mead, R. (1965). A Simplex Method for Function Minimization. The Computer Journal , 7 (4), 308–313. https://doi.org/10.1093/comjnl/7.4.308. Rhoades, D. A. (2007). Application of the EEPAS Model to Forecasting Earthquakes of Moderate Magnitude in Southern California . 78 (1), 110–115. Rhoades, D. A. (2011). Application of a long-range forecasting model to earthquakes in the Japan mainland testing region. Earth, Planets and Space , 63 (3), 197–206. https://doi.org/10.5047/eps.2010.08.002. Rhoades, D. A., & Evison, F. F. (2004). Long-range earthquake forecasting with every earthquake a precursor according to scale. Pure and Applied Geophysics , 161 (1), 47–72. https://doi.org/10.1007/s00024-003-2434-9. Rovida, A., Locati, M., Camassi, R., & Lolli, B. (2020). The Italian earthquake catalogue CPTI15. In Bulletin of Earthquake Engineering (Issue 0123456789). Springer Netherlands. https://doi.org/10.1007/s10518-020-00818-y.