Читать книгу Statistical Methods and Modeling of Seismogenesis - Eleftheria Papadimitriou - Страница 32

In order to test the potential use of the simulation algorithm for drawing conclusions about the predictability of large earthquakes, one should make a comparison between the synthetic and the real catalog. The analysis was based on some arbitrary criteria to attribute a specific earthquake to one or more segments. The rules adopted for this purpose are: the earthquake must have a minimum magnitude of 6.0; the earthquake is first assigned to the segment that contains the largest number of fractured cells; the same earthquake can also be assigned to other segments if the number of cells ruptured by the event exceeds the number of 600 or at least 80% of the total number of cells for the specific segment. Examples of time-space plots of the synthetic catalogs obtained after applying the above-mentioned criteria to the first 2,500 years are shown by blue bars in Figure 2.6. For the sake of comparison, this figure also shows the 17 earthquakes that are reported in the real catalog since 1700 CE (red squares).

A visual inspection of Figure 2.6 does not reveal any systematic behavior that can be recognized as substantial discrepancy between the synthetic and the real catalogs. Note that Figure 2.6 displays all the ruptures that constitute a single earthquake as individual events. This justifies the apparent larger number of synthetic events with respect to those reported in the real catalog (which assigns each earthquake to a single segment, independently of its size). We observe a non-periodical time distribution, with interevent times ranging from a few years to hundreds of years on the same segment. We can also see earthquakes that rupture different segments as a unique event or more events that occur with very short time separation. This feature is consistent with historical observations.

Figure 2.6. Space-time features of synthetic catalogs concerning earthquakes with M > 6.0 for the first 2,500 years (blue bars). Red squares show the occurrence time and location of the observed earthquakes in the last 300 years (based on Console et al. 2015). For a color version of this figure, see www.iste.co.uk/limnios/statistical.zip

In order to assess whether the earthquake occurrence time on the same segments in the synthetic catalogs behaves as a Poisson process or not, we carried out a statistical analysis of the interevent times for the entire 100,000 years simulation. In this respect, Figure 2.7 shows the interevent time distribution of the simulation. Table 2.1 displays the mean interevent time, the standard deviation and the coefficient of variation for each segment. The relatively short average interevent times of the simulations can be justified by the circumstance that often two or more segments rupture simultaneously in a single earthquake. Along with the above-mentioned temporal parameters, Table 2.1 also reports the results of the difference between the log-likelihood computed by the BPT renewal model and the Poisson time-independent model (dlogL). For the likelihood estimation, we have adopted the values obtained for Tr and Cν reported in Table 2.1 for each fault segment.

Both Figure 2.7 and Table 2.1 show, as expected, that the most active segments are those characterized by larger size and higher slip rate (such as Psathopyrgos, Aigion, Eliki and Xylokastro). The simulation also shows that, especially for the less active segments (offshore Perachora, Skinos and Alepochori), interevent times of several hundreds of years are possible. The coefficient of variation Cν is typically close to 0.6, which would be associated with moderately time-predictable behavior of the seismicity. The log-likelihood difference denotes an outstanding better performance of the renewal model against the time-independent hypothesis. The exception to this pseudo-periodical behavior is presented by segment #4 (offshore Akrata), which exhibits a coefficient of variation slightly larger than 1 and a modest log-likelihood difference.

Figure 2.7. Interevent time distribution from a simulation of 100,000 years of seismic activity across the CGFS (based on Console et al. 2015). For a color version of this figure, see www.iste.co.uk/limnios/statistical.zip

Table 2.1. Statistical parameters of the synthetic catalog (based on Console et al. 2015).