- Open Access
The double branching model for earthquake forecast applied to the Japanese seismicity
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. 2011
- Received: 1 April 2010
- Accepted: 1 February 2011
- Published: 4 March 2011
The purpose of this work is to apply the Double Branching Model (DBM) to forecast moderate–large Japanese seismicity. The proposed model is time-dependent, since it assumes that each earthquake can generate or is correlated to other earthquakes, through physical mechanisms acting at different spatio-temporal scales. The model is set up through two sequential steps. In the first step, we estimate the well-established short time clustering. Then, we analyze and characterize the declustered catalog through a second order branching process. The inclusion of the second branching is motivated by the statistically significant departure of the declustered catalog from a time-independent model. From a physical point of view, this new branching accounts for possible long-term earthquake interactions. Some recent applications of this model at global and regional scales (Marzocchi and Lombardi, 2008; Lombardi and Marzocchi, 2009, 2010) have shown that earthquake occurrences tend to have two main time features: a short-term clustering up to months–few years and a longer time modulation of decades (up to few centuries). Here we apply the DBM to the instrumental Japanese database, collected by the Japan Meterological Agency (JMA) (M = 5.0). The purpose of this application is twofold. First, we check the existence of two time branchings previously found in other regions. Second, we provide forecasts to be evaluated by the Japanese CSEP (Collaboratory for the Study of Earthquake Predictability) testing center.
- Earthquake probability
- Japanese seismicity
- stochastic process
Earthquake forecasting has a key role in the geophysical investigation. It has direct implications for planning risk mitigation actions, and it yields important contributions for a better understanding of earthquake generation process. Presently, a large variety of models is available; these models are based on different physical and stochastic components and they cover quite different forecasting time windows, from 1 day to years and decades (see, e.g., Kagan and Knopoff, 1981; Ogata, 1988, 1998; Kagan and Jackson, 2000; Rhoades and Evison, 2004; Gerstenberger et al., 2005; Helmstetter et al., 2006; Marzocchi and Lombardi, 2008, 2009; Lombardi and Marzocchi, 2009; Marzocchi et al., 2009; Console et al., 2010).
Despite the efforts devoted to build models, their reliability has been only partially checked (mostly by the same modelers), often using past data and different statistical methodologies. Moreover, very few attempts have been made to compare the forecasting capabilities of different models. The use of different and inhomogeneous procedures leads to an inherent difficulty to judge what is the best performing model, or more generally, to evaluate relative forecasting performances. Only recently, one important international effort, the Collaboratory for the Study of Earthquake Predictability (CSEP; www.cseptesting.org), has been set to create a common platform for testing and comparing forecasting/prediction models. This initiative is a generalization of the experiment carried out in California, named the Regional Earthquake Likelihood Models (RELM, www.relm.org; Schorlemmer et al., 2007). Specifically, CSEP has established different testing regions and testing center for evaluating and comparing forecasting/prediction models on different forecasting time windows (Schorlemmer et al., 2010). Recently, Japan joined the CSEP initiative establishing a testing center and a testing region (Tsuruoka et al., 2008).
The goal of the present paper is twofold. First, we describe the implementation of a recently proposed model, named the Double Branching Model (DBM hereinafter), to forecast earthquakes in the Japan testing region. Second, the comparison of the parameters of the model estimated for Japan and other regions of the world allows us to get some new insights on the nature of the earthquake occurrence process. The DBM takes into account long-term modulation of earthquakes occurrence, beside of the short-term clustering of earthquakes. In other words, compared to the classical ETAS (Epidemic Type-Aftershocks Sequences) model (Ogata, 1998), we relax the assumption of longterm stationary seismic background that has been questioned by many recent studies (Kagan and Jackson, 1991; Rhoades and Evison, 2004; Lombardi and Marzocchi, 2007; Marzocchi and Lombardi, 2008; Marzocchi et al., 2009). These studies emphasizes the existence of significant long-term time modulation of the earthquake occurrence, probably due to fault interaction and stress perturbations on spatio-temporal scales much larger than the ranges interested by aftershock sequences. Other possible departures from a stationary seismic background on a time scale of few days (Hainzl and Ogata, 2005; Lombardi et al., 2006, 2010) are not taken into account by DBM. Notably, the DBM has shown better earthquake forecasting performances for large earthquakes at both worldwide (Marzocchi and Lombardi, 2008) and regional (Lombardi and Marzocchi, 2009, 2010) scales, with respect to models with a time-independent background rate. The forecast method uses earthquake data only, with no explicit use of tectonic, geologic, or geodetic information. The basis underlying this earthquake forecasting method is the popular concept of epidemic process: every earthquake is regarded as a potential triggering event for subsequent earthquakes (Ogata, 1988, 1998; Helmstetter et al., 2006; Lombardi and Marzocchi, 2007) on different spatio-temporal scales. The method does not deal with single earthquake prediction, but quantifies the chance of an earthquake by estimating the mean rate of future seismicity.
To estimate the parameters of the model we use the iteration algorithm developed by Zhuang et al. (2002); the method is based on the Maximum Likelihood Method and on a kernel estimation of total seismic rate. Further details on the model and on estimation of its parameters can be found in Marzocchi and Lombardi (2008).
Maximum Likelihood parameters (with relative errors) of the Double Branching model (seeEq. (1)) for the events of the JMA catalog above 100 km of depth (Mc = 5.0; Jan 1 1965–Dec 31 2008, 5648 events).
61 ± 2 year-1
7.8 ± 0.5 · 10-3 yearp-1
1.17 ± 0.01
7.0 ± 1.0 · 10 -5 year
1.40 ± 0.04
4.6 ± 0.2 km
0.53 ± 0.03
0.013 ± 0.001
30 ± 6 year
82 ± 7 km
1.5 ± 0.2
We argue that the scarce fit of the ETAS model and the lack of improvement with the DBM might be due to two different factors. First, probably there may be a bias into the distance between earthquakes; in fact, both ETAS and DBM consider only epicentral distances, neglecting the depth, whereas the latter can reach up to 100 km. Second, offshore and deep earthquakes may have different features compared to crustal inland earthquakes; this difference may come up from a different resolution in monitoring (Nanjo et al., 2010); or may reflect a real physical difference between these two kind of earthquakes.
Maximum Likelihood parameters (with relative errors) of the Double Branching model (see Eq. (1)) for the events of the JMA catalog above 30 km of depth (Mc = 5.0; Jan 1 1965-Dec 31 2008, 1935 events).
11 ± 1 year-1
1.1 ±0.1 · 10-2 yearp-1
1.16 ± 0.01
6.0 ± 1.0 · 10-5 year
1.20 ± 0.04
4.6 ± 0.2 km
0.53 ± 0.03
0.09 ± 0.01
8 ± 1 year
24 ± 4 km
2.0 ± 0.2
To compare real and simulated values of , we can simply translate the values of IGpe shown in Fig. 6 by the factor . So the conclusions on the significance of the improvement of DBM do not change.
The main goal of the present paper has been to describe the DBM applied to Japanese seismicity. This study has been mainly motivated by the participation to the CSEP experiment for the Japanese testing region. From a seismolog-ical point of view, the results obtained in the present study basically confirm the main finding of previous analyses (Marzocchi and Lombardi, 2008; Lombardi and Marzocchi, 2009, 2010). Large earthquakes in Japan tend to cluster in time and space at different time scales. Besides the short-term clustering described by the ETAS model, we have found also a significant time clustering longer than typical aftershock sequences. Notably, we have found that the DBM has a different forecasting performance on shallow and deep seismicity. Specifically the DBM has a poor reliability on seismicity with a depth up to 100 km, whereas it works significantly better than ETAS model for shallow seismic events (up to 30 km of depth). The scarce fitting with DBM and ETAS model is probably due to the use of epicentral distances; neglecting depth may alter significantly the real distance between earthquakes. Another possibility is that offshore and deeper earthquakes have different features compared to crustal inland earthquakes. The characteristic time of the second branching for the crustal earthquakes (t ~ 8 years) seems to be smaller than the characteristic time found in other regions (Marzocchi and Lombardi, 2008; Lombardi and Marzocchi, 2009, 2010). We explain this shorter time length as due to the high seismic background for Japanese seismicity. In fact, the time decay of the long-term interaction will fade sooner into the background seismicity when the latter is higher. In any case the value of t is in agreement with Lombardi and Marzocchi (2007), which founded a significant variation of background seismicity in Japan about every 10 years.
In all our previous analyses (Marzocchi and Lombardi, 2008; Lombardi and Marzocchi, 2009, 2010), as well as in the present study, we find a low value for a2, not statistically significant from zero. This implies that the postseis-mic triggering capability of an event is independent by its magnitude. By a physical point a view, we explain this finding with the not-suitability of the available data to provide the actual value of a2. In fact, whereas the coseismic stress transfer is a phenomenon spanning all magnitude scales, the postseismic effects are likely mostly caused by the strongest events (Piersanti et al., 1997; Pollitz et al., 1998). The mag-nitudo range recovered by JMA and by all previously analyzed catalogs is rather small and the proportion of giant events (M = 8.0) is negligible. This could be the origin of the indeterminateness of the a2-value. By a statistical point of view, we have shown that a further explanation for the uncertain estimate of the a2-value could be the inefficiency of data to reveal its actual value (Lombardi and Marzocchi, 2009). Specifically we have shown that the probability to estimate a null value for a2 is not negligible also for a class of synthetic catalogs with a2 significantly different from 1.0 and a size comparable with the available real datasets. This is clear evidence that the limited number of data of a catalog might prevent to find a positive value of a2 significantly different from zero.
The first version of the DBM submitted for CSEP Japanese laboratory is focused on providing earthquakes forecast until 100 km depth. The results of this analysis has encouraged us to submit a new version of DBM focused only on the crustal inland earthquakes. We expect that this second version of the DBM should work better than classical ETAS models. The results of the CSEP experiment in the Japanese testing region will provide us interesting insights on this topic.
The authors thank the editor and the two reviewers for useful comments and suggestions.
- Console, R., M. Murru, and G. Falcone, Probability gains of an epidemic-type aftershock sequence model in retrospective forecasting of M > 5.0 earthquakes in Italy, J. Seismol., 14, 9–26, 2010. 10.1007/s10950-009-9161-3View ArticleGoogle Scholar
- Gerstenberger, M., S. Wiemer, L. M. Jones, and P. A. Reasenberg, Realtime forecasts of tomorrow’s earthquakes in California, Nature, 435, 328–331, 2005. 10.1038/nature03622View ArticleGoogle Scholar
- Gibbons, J. D. and S. Chakraborti, Non-parametric Statistical Inference, 4th ed., rev. and expanded, 645 pp, Marcel Dekker, New York, 2003. rev. and expanded,Google Scholar
- Gutenberg, B. and C. F. Richter, Frequency of earthquakes in California, Bull. Seismol. Soc. Am., 34, 185–188, 1954.Google Scholar
- Hainzl, S. and Y. Ogata, Detecting fluid signals in seismicity data through statistical earthquake modeling, J. Geophys. Res., 110, B05S07, doi:10. 1029/2004JB003247, 2005.Google Scholar
- Helmstetter, A., Y. Y. Kagan, and D. D. Jackson, Comparison of short-term and time-independent earthquake forecast models for Southern California, Bull. Seismol. Soc. Am., 96, 90–106, 2006. 10.1785/0120050067View ArticleGoogle Scholar
- Kagan, Y. Y. and D. D. Jackson, Seismic gap hypothesis, ten years after, J. Geophys. Res., 96, 21419–21431, 1991. 10.1029/91JB02210View ArticleGoogle Scholar
- Kagan, Y. Y. and D. D. Jackson, Probabilistic forecasting of earthquakes, Geophys. J. Int., 143, 438–453, 2000. 10.1046/j.1365-246X.2000.01267.xView ArticleGoogle Scholar
- Kagan, Y. Y. and L. Knopoff, Stochastic synthesis of earthquake catalogs, J. Geophys. Res., 86, 2853–2862, 1981. 10.1029/JB086iB04p02853View ArticleGoogle Scholar
- Lombardi, A. M. and W. Marzocchi, Evidence of clustering and nonsta-tionarity in the time distribution of large worldwide earthquakes, J. Geo-phys. Res., 112, B02303, doi:10.1029/2006JB004568, 2007.View ArticleGoogle Scholar
- Lombardi, A. M. and W. Marzocchi, Double Branching model to forecast the next M= 5.5 earthquakes in Italy, Tectonophysics, 475, 514–523, doi:10.1016/j.tecto.2009.06.014, 2009.View ArticleGoogle Scholar
- Lombardi, A. M. and W. Marzocchi, The Double Branching Model (DBM) applied to long-term forecasting Italian seismicity (Ml=5.0) in CSEP experiment, Ann. Geophys., 2010.Google Scholar
- Lombardi, A. M., W. Marzocchi, and J. Selva, Exploring the evolution of a volcanic seismic swarm: the case of the 2000 Izu Islands swarm, Geophys. Res. Lett., 33, L07310, doi:10.1029/2005GL025157, 2006.View ArticleGoogle Scholar
- Lombardi, A. M., M. Cocco, and W. Marzocchi, On the increase of background seismicity rate during the 1997–1998 Umbria-Marche (central Italy) sequence: apparent variation or fluid-driven triggering?, Bull. Seismol. Soc. Am., 100, 1138–1152, 2010. 10.1785/0120090077View ArticleGoogle Scholar
- Marzocchi, W. and A. M. Lombardi, A double branching model for earthquake occurrence, J. Geophys. Res., 113, B08317, doi:10.1029/ 2007JB005472, 2008.Google Scholar
- Marzocchi, W., J. Selva, A. Piersanti, and E. Boschi, On the long-Term interaction among earthquakes: Some insights from a model simulation, J. Geophys. Res., 108(B11), 2538, doi:10.1029/2003JB002390, 2003.View ArticleGoogle Scholar
- Marzocchi, W., J. Selva, F. R. Cinti, P. Montone, S. Pierdominici, R. Schivardi, and E. Boschi, On the occurrence of large earthquakes: New insights from a model based on interacting faults embedded in a realistic tectonic setting, J. Geophys. Res., 114, B01307, doi:10.1029/2008JB005822, 2009.Google Scholar
- Mogi, K., Recent seismic activity in the Tokai (Japan) region where a large earthquake is expected in the near future, Tectonophysics, 138, 255–268, 1987. 10.1016/0040-1951(87)90043-6View ArticleGoogle Scholar
- Nanjo, K. Z., T. Ishibe, H. Tsuruoka, D. Schorlemmer, Y. Ishigaki, and N. Hirata, Analysis of the completeness magnitude and seismic network coverage of Japan, Bull. Seismol. Soc. Am., 100, doi:10. 1785/0120100077, 2010.Google Scholar
- Ogata, Y., Statisticals Models for Earthquake Occurrences and Residual Analysis for Point Processes, J. Amer. Statist. Assoc., 83(401), 9–27, 1988. 10.1080/01621459.1988.10478560View ArticleGoogle Scholar
- Ogata, Y., Space-Time Point-Process Models for Earthquake Occurrences, Ann. Inst. Statist. Math., 50(2), 379–402, 1998. 10.1023/A:1003403601725View ArticleGoogle Scholar
- Papangelou, F., Integrability of expected increments of point processes and related random change of scale, Trans. Am. Math. Soc., 165, 483–506, 1972. 10.1090/S0002-9947-1972-0314102-9View ArticleGoogle Scholar
- Piersanti, A., G. Spada, R. Sabadini, and M. Bonafede, Global postseismic deformation, Geophys. J. Int., 120, 544–566, 1995. 10.1111/j.1365-246X.1995.tb01838.xView ArticleGoogle Scholar
- Piersanti, A., G. Spada, and R. Sabadini, Global postseismic rebound of a viscoelastic Earth: Theory for finite faults and application to the 1964 Alaska earthquake, J. Geophys. Res., 102, 477–492, 1997. 10.1029/96JB01909View ArticleGoogle Scholar
- Pollitz, F. F., Postseismic relaxation theory on the spherical Earth, Bull. Seismol. Soc. Am., 82, 422–453, 1992.Google Scholar
- Pollitz, F. F., R. Bürgmann, and B. Romanowicz, Viscosity of oceanic asthenosphere inferred from remote triggering of earthquakes, Science, 280, 1245–1249, 1998. 10.1126/science.280.5367.1245View ArticleGoogle Scholar
- Rhoades, D. A. and F. F. Evison, Long-range earthquake forecasting with every earthquake a precursory according to scale, Pure Appl. Geophys., 161, 47–72, 2004. 10.1007/s00024-003-2434-9View ArticleGoogle Scholar
- Rikitake, T., Probability of a great earthquake to recur in the Tokai district, Japan: reevaluation based on newly-developed paleoseismology, plate tectonics, tsunami study, micro-seismicity and geodetic measurements, Earth Planets Space, 51, 147–157, 1999. 10.1186/BF03352219View ArticleGoogle Scholar
- Schorlemmer, D., M. C. Gerstenberger, S. Wiemer, D. D. Jackson, and D. A. Rhoades, Earthquake likelihood model testing, Seismol. Res. Lett., 78(1), 17–29, 2007. 10.1785/gssrl.78.1.17View ArticleGoogle Scholar
- Schorlemmer, D., J. D. Zechar, M. J. Werner, E. H. Field, D. D. Jackson, T. H. Jordan, and the RELM Working Group, First results of the regional earthquake likelihood models experiment, Pure Appl. Geophys., 167(8–9), 859–876, 2010. 10.1007/s00024-010-0081-5View ArticleGoogle Scholar
- Tsuruoka, H., N. Hirata, D. Schorlemmer, F. Euchner, and T. H. Jordan, CSEP Earthquake Forecast Testing Center for Japan, AGU, Fall Meeting 2008, 2008.Google Scholar
- Zhuang, J., Y. Ogata, and D. Vere-Jones, Stochastic declustering of spacetime earthquake occurrence, J. Am. Stat. Assoc., 97, 369–380, 2002. 10.1198/016214502760046925View ArticleGoogle Scholar