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Turing-Style Tests for UCERF3 Synthetic Catalogs by Morgan T

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Turing-Style Tests for UCERF3 Synthetic Catalogs by Morgan T Bulletin of the Seismological Society of America, Vol. XX, No. XX, pp. –, – 2018, doi: 10.1785/0120170223 Ⓔ Turing-Style Tests for UCERF3 Synthetic Catalogs by Morgan T. Page and Nicholas J. van der Elst Abstract Epidemic-type aftershock sequence (ETAS) catalogs generated from the third Uniform California Earthquake Rupture Forecast (UCERF3) model are unique in that they are the first to combine a complex, fault-based long-term forecast with short-term earthquake clustering statistics. We present Turing-style tests to examine whether these synthetic catalogs can successfully imitate observed earthquake behav- ior in California. We find that UCERF3-ETAS is more spatially diffuse than the ob- served historic catalog in California and that it lacks quiet periods that are present in the real catalog. Although mean aftershock productivity of the observed catalog is matched closely by UCERF3-ETAS, the real catalog has more intersequence produc- tivity variability and small mainshocks have more foreshocks. In sum, we find that UCERF3-ETAS differs from the observed catalog in ways that are foreseeable from its modeling simplifications. The tests we present here can be used on any model that produces suites of synthetic catalogs; as such, in addition to providing avenues for future improvements to the model, they could be incorporated into testing platforms such as Collaboratory for the Study of Earthquake Predictability (CSEP). Electronic Supplement: Five 1000-yr third Uniform California Earthquake Rup- ture Forecast epidemic-type aftershock sequence (UCERF3-ETAS) synthetic catalogs, and figures showing aftershock decay rates for M 5.5–6.5 mainshocks, mean fore- shock and aftershock productivity as a function of differential magnitude, and results from the clustering analysis. Introduction Traditionally, earthquake probability models have the model, the long-term time-dependent model (UCERF3- largely been in two separate time domains. Probabilistic haz- TD) (Field et al., 2015), includes elastic rebound effects ard analysis employing fault-based information and elastic related to the time of the last event on major faults. Finally, rebound has operated on time scales of decades to centuries, short-term time dependence is added to this model in the whereas empirical statistical models incorporating clustering form of epidemic-type aftershock sequence (ETAS) modeling due to aftershocks have operated on the scale of days to (Ogata, 1988) to make UCERF3-ETAS (Field et al., 2017). years. Bringing these different models into alignment re- UCERF3-ETAS differs from conventional ETAS due to quires bridging the “medium-term forecasting gap” (Jordan, the explicit modeling of faults. In particular, although 2012) that separates them as well as reconciling inherent stat- conventional ETAS employs the Gutenberg–Richter (G-R) istical and spatial differences. magnitude distribution (Gutenberg and Richter, 1944)at The third Uniform California Earthquake Rupture the smallest spatial scales, the magnitude distributions in Forecast (UCERF3) model is the first unified earthquake fore- UCERF3 are more variable. UCERF3 is constrained to fol- casting model to include elastic rebound effects, fault-based low G-R scaling in large regions (northern California and ruptures, and clustering driven by Omori–Utsu statistics southern California), but in smaller regions it deviates from (Omori, 1895; Utsu, 1972). The base of the model is the time- this scaling. On average, the magnitude distributions on the independent model (UCERF3-TI) (Field et al., 2014), which major modeled faults are characteristic (Wesnousky et al., usesaninversionmethod(Page et al.,2014) to relax segmen- 1983; Schwartz and Coppersmith, 1984), meaning that the tation and solve for the rates of hundreds of thousands of rates of M ⪆ 6:5 earthquakes are higher than a G-R extrapo- potential ruptures on an interconnected network of faults. To lation from small earthquake rates would predict. However, these fault-based ruptures, off-fault seismicity is added from there is considerable variation—in addition to faults with smoothed historical seismicity data. The next progression of varying degrees of characteristic magnitude behavior, some BSSA Early Edition / 1 2 M. T. Page and N. J. van der Elst faults have magnitude distributions that are approximately Early in the UCERF3-ETAS catalogs, these spontaneous G-R and still others are somewhat anticharacteristic. events account for 30% of all events; after 1000 yrs, they The variable magnitude distributions in the UCERF3 account for 20%. Thus, it is possible for the catalogs to have model have a substantial effect on the triggering probabilities different statistical behavior as they evolve. Also, because all for large earthquakes. For potential foreshocks that occur in synthetic catalogs include aftershocks from the same histori- close proximity to characteristic faults, the probability of cal events, we expect the catalogs to be more similar at the triggering a large earthquake is elevated relative to the fore- start of 1000-yr simulations than at the end. For these rea- shock probabilities in conventional ETAS; similarly, the sons, in many of our tests we compare the 28-yr observed model predicts that earthquakes occurring near anticharacter- catalog to 28-yr snapshots taken from both the beginning istic faults have a lower probability of triggering a large and end of 1000-yr synthetic catalogs. (M ⪆ 6:5) earthquake. This effect is in agreement with a sim- ilar effect seen in the Agnew and Jones (1991) model that is also due to the adoption of characteristic magnitude distribu- Seismological Turing Tests tions (Michael, 2012). A fault with a sufficiently character- Seismicity Rate istic magnitude distribution, could, in theory, cause a runaway sequence of aftershocks for parameters that would The mean seismicity rate in UCERF3 is 8.3 M ≥ 5 be subcritical in conventional ETAS; however, in UCERF3- earthquakes per year. By design, this is a bit higher than the ETAS this effect is mitigated by elastic rebound, which historical (1850–2011) seismicity rate in California of 7.9 effectively removes many large earthquakes from the pool of M ≥ 5 earthquakes per year, and higher still than the recent potential aftershocks following rupture of a fault. (1984–2011) seismicity rate of 5.8 M ≥ 5 earthquakes per By modeling faults, elastic rebound, and short-term year (Felzer, 2013b). Although there are several logic-tree clustering, UCERF3-ETAS marries previously disparate branches with different seismicity rates in UCERF3, more types of earthquake forecasting and bridges the medium- weight was given to high-seismicity rates in the model be- term forecasting gap. Given both the complexity and novelty cause the true long-term seismicity rate in California is likely of the model, testing is required to ensure that results are con- to be higher than the historical rates due to the lack of M ≥ 8 sistent with observed seismicity. To this end, we devise a events in the post-1850 era (Felzer, 2013d). The difference in series of seismological Turing tests. The original Turing test mean seismicity rate is evident in Figure 1, which shows the was proposed by mathematician Alan Turing to sidestep range of small earthquake rates for 10-day windows in both what he saw as the poorly defined question of whether or not the real and synthetic UCERF3-ETAS catalogs. However, machines could truly think. Instead, he devised a game to even when the rates are normalized by the mean rate (Fig. 1c), determine whether a machine could successfully imitate the the distributions are still different. The real California catalog language behavior of a human (Turing, 1950). In our seis- from 1984 to 2012 (Felzer, 2013a) has more quiet periods mological Turing tests, we ask whether synthetic catalogs than synthetic catalogs. This difference is significant given produced by UCERF3-ETAS can successfully imitate the the scatter seen in shorter UCERF3-ETAS catalogs as well statistical behavior seen in the real California earthquake (Fig. 1c). This may be because of the spontaneous back- catalog. Although the observed California catalog is quite ground events in UCERF3-ETAS, which account for limited in duration, we have many long synthetic catalogs. ∼30% of the events early in synthetic catalogs and 20% We can thus construct many synthetic-catalog snapshots that of events 1000 yrs into a synthetic catalog (the fraction of match the duration of the real catalog. These snapshots can events that are spontaneous diminishes as the catalogs are be used to construct error bounds for various metrics; run for longer, because there are more previous events UCERF3-ETAS fails the Turing test if the observed data producing aftershocks). These spontaneous events are Pois- are outside of those bounds. sonian in time, but in reality many of them represent or- We compare the statistics of one hundred 1000-yr phaned aftershocks of parent earthquakes that occur prior synthetic UCERF3-ETAS catalogs to the observed catalog to the start, outside the spatial bounds of the catalog, or be- in California for a 28-yr period from 1984 to 2011 (Felzer, low the minimum magnitude used (van der Elst, 2017). Thus, 2013a). These tests are fully retrospective, because we com- they may be more temporally clustered than is assumed in pare UCERF3-ETAS to an observational catalog that was the modeling. At the high end of seismicity rates, UCERF3- available at the time of its construction. Both observed and ETAS and the observed catalog
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