<p>Several authors empirically observed that the scaling between local magnitude ML and moment magnitude Mw computed by spectral methods is not 1:1 for ML<2-4. In particular ML is found to be about proportional to 1.5 Mw but the exact threshold below which this occurs is argued. Such behavior was explained as due to attenuation and scattering along the path or to a minimum limit in the pulse duration or equivalently a maximum limit to the corner frequency of the observed spectra imposed by surface attenuation. The frequency-magnitude distribution of ML estimates provided by the Italian Seismic Instrumental Database (ISIDe) of INGV show a strictly linear behavior with b-value&#187;1.0 down to about ML 1.4 at least. This implies that for Mw the b-value would be about 1.5 below magnitude 2-4 and 1 above. As the frequency magnitude relationship with b-value&#187;1 in terms of Mw is recognized as a general characteristic of seismicity all over the world, based on both empirical and theoretical considerations, the question arises on the reasons of the observed discrepancy for small shocks. One explanation might be the assumption of incorrect seismic wave attenuation properties for the computation of ML, of spectral Mw or both.</p>
Summary In a recent work we computed the relative frequencies with which strong shocks (4.0 ≤ Mw < 5.0), widely felt by the population were followed in the same area by potentially destructive main shocks (Mw ≥ 5.0) in Italy. Assuming the stationarity of the seismic release properties, such frequencies can be tentatively used to estimate the probabilities of potentially destructive shocks after the occurrence of future strong shocks. This allows us to set up an alarm-based forecasting hypothesis related to strong foreshocks occurrence. Such hypothesis is tested retrospectively on the data of a homogenized seismic catalogue of the Italian area against a purely random hypothesis that simply forecasts the target main shocks proportionally to the space-time fraction occupied by the alarms. We compute the latter fraction in two ways a) as the ratio between the average time covered by the alarms in each area and the total duration of the forecasting experiment (60 years) and b) as the same ratio but weighted by the past frequency of occurrence of earthquakes in each area. In both cases the overall retrospective performance of our forecasting algorithm is definitely better than the random case. Considering an alarm duration of three months, the algorithm retrospectively forecasts more than 70 per cent of all shocks with Mw ≥ 5.5 occurred in Italy from 1960 to 2019 with a total space-time fraction covered by the alarms of the order of 2 per cent. Considering the same space-time coverage, the algorithm is also able to retrospectively forecasts more than 40 per cent of the first main shocks with Mw ≥ 5.5 of the seismic sequences occurred in the same time interval. Given the good reliability of our results, the forecasting algorithm is set and ready to be tested also prospectively, in parallel to other ongoing procedures operating on the Italian territory.
Summary In a recent work, we applied the Every Earthquake a Precursor According to Scale (EEPAS) probabilistic model to the pseudo-prospective forecasting of shallow earthquakes with magnitude $M \ge \ 5.0$ in the Italian region. We compared the forecasting performance of EEPAS with that of the Epidemic Type Aftershock Sequences (ETAS) forecasting model, using the most recent consistency tests developed within the Collaboratory for the Study of Earthquake Predictability (CSEP). The application of such models for the forecasting of Italian target earthquakes seems to show peculiar characteristics for each of them. In particular, the ETAS model showed higher performance for short-term forecasting, in contrast, the EEPAS model showed higher forecasting performance for the medium/long-term. In this work, we compare the performance of EEPAS and ETAS models with that obtained by a deterministic model based on the occurrence of strong foreshocks (FORE model) using an alarm-based approach. We apply the two rate-based models (ETAS and EEPAS) estimating the best probability threshold above which we issue an alarm. The model parameters and probability thresholds for issuing the alarms are calibrated on a learning dataset from 1990 to 2011 during which 27 target earthquakes have occurred within the analysis region. The pseudo-prospective forecasting performance is assessed on a validation dataset from 2012 to 2021, which also comprises 27 target earthquakes. Tests to assess the forecasting capability demonstrate that, even if all models outperform a purely random method, which trivially forecast earthquake proportionally to the space-time occupied by alarms, the EEPAS model exhibits lower forecasting performance than ETAS and FORE models. In addition, the relative performance comparison of the three models demonstrates that the forecasting capability of the FORE model appears slightly better than ETAS, but the difference is not statistically significant as it remains within the uncertainty level. However, truly prospective tests are necessary to validate such results, ideally using new testing procedures allowing the analysis of alarm-based models, not yet available within the CSEP.
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