1. Abstract The space-time epidemic-type aftershock sequence (ETAS) model is a stochastic process in which seismicity is classified into background and clustering components and each earthquake triggers other earthquakes independently according to some rules. Given an earthquake catalog, we can stochastically decluster it according to the estimated probabilities that one event is produced by another previous event or produced from the background seismicity. According to our previous studies, we propose an improved model, where the background event has a different productivity and a different magnitude distribution. We classify the earthquakes into four types: Type I (foreshock), Type II, Type I ' and Type-II ', where a foreshock (Type-I event) is defined as a background event that has at least more than one child of a larger magnitude. Properties associated with these 4 types of events are deriverd analytically based on the improved model. We verify these theoretic results by applying the stochastic reconstruction method to the JMA catalogue. Fall Meeting 2004 Paper Number: S43B-1079 The largest events in earthquake clusters and their relationship to foreshocks Jiancang Zhuang and Yosihiko Ogata Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo, Japan Stochastic reconstruction (Zhuang et al. 2004)  Background probability: the probability that an event is a background event  Triggering probability: the probability that event j is directly triggered by i. Hypotheses associated with clustering features of earthquakes can be tested by building empirical functions with the events weighted by the above probabilities. Definitions of 4 types of events Type-I (foreshock): background event that has at least one larger descendent; Type-II: background event that has no larger descendent; Type-I': non-background event that has at least one larger descendent; Type-II': non-background event that has no larger descendent. Conclusion: Based on the theory of the ETAS model and an improved version, we obtain the probabilities associated with the background events which have larger descendents (defined as foreshocks here). The theoretical results are compared to data analysis by using the stochastic reconstruction method. The behaviors of foreshocks can well described by the improved model. Moreover, we may over-predict if we predict earthquakes based on an assumption that foreshocks trigger mainshocks in the same way as mainshocks trigger aftershocks. Main references: (1)Kagan Y. and Knopoff L. (1976). Statistical search for non-random features of the seismicity of strong earthquakes. Phys. Earth Planet. Inter., 12, 291-318. (2)Ogata Y., Utsu T. and Katsura K. (1995). Statistical features of foreshocks in comparison with other earthquake clusters. Phys. Earth Planet. Inter., 12, 291-318. (3)Ogata Y. (1998) Space-time point-process models for earthquake occurrences. Ann. Inst. Statist. Math., 50 (401): 379-402. (4)Zhuang J., Ogata Y. and Vere-Jones D. (2002). Stochastic declustering of space-time earthquake occurrences. J. Amer. Statist. Assoc., 97: 369-380. (5)Zhuang J., Ogata Y., Vere-Jones D. (2004). Analyzing earthquake clustering features by using stochastic reconstruction. J. Geophys. Res., 109, No. B5, B05301, doi:10.1029/2003JB002879. (6)Zhuang J. and Ogata Y. (2005) Properties of the probability distribution associated with the largest event in an earthquake cluster and their implications to foreshocks. Submitted to Physics Review, E. Problems on foreshocks 1. How to define a foreshock? 2. Are foreshocks different from the mainshocks whose aftershocks happened to be bigger? 3. How to use foreshocks in prediction? Space-Time Epidemic Type Aftershock Sequence (ETAS) model  Time varying seismicity rate = "background" + “Triggered seismicity":  Magnitudal distribution: the G-R law  Time distribution: the Omori-Utsu law  Spatial location distribution of children:  Triggering ability: mean number of children t : time ( x, y ): spatial location m : magnitude An improved model Zhuang et al. (2004) found that background seismicity is different from triggered seismicity in the magnitude distribution and in triggering children. Mean numbers of children background seismicity: triggered seismicity: Magnitude distributions background seismicity: triggered seismicity: Distributions in a cluster based on ETAS models  Pr { no event greater than m in an arbitrary cluster }  Pr { no descendant greater than m' from an ancestor of m}  Pr { an ancestor of m having at least 1 larger descendants}  Probability density for magnitudes of events having more than 1 larger descendants Distributions in a cluster based on the improved model  Pr { no event greater than m in an arbitrary cluster starting from a non-background event}  Pr { no descendant greater than m' from a background ancestor of m}  Pr { no descendant greater than m' from a non-background ancestor of m}  Probability densities of magnitudes of Type I, II, I' and II' events  Average numbers of children from Types I, II, I' and II' events Analysis of the Japanese JMA catalog Data selection l ocation : 121º-155ºE 21º-48ºN depth : 0-100 km time : 1/Jan/1926~31/Dec/1999 magnitude : M J ≥4.2 Target space-time range time : 10000 days after 1/Janm/1926 location : 130º~146ºE, 33º~42.5ºN Fig. 2. (a) Comparison between average numbers of children from an arbitrary parent (black circles), background events (green), triggered events (red) and the theoretical from model fitting (black solid line) (b) Comparison between magnitude distributions of all evetns, background events and triggered events. Fig. 1. Seismicity in the Japan region and nearby during 1926-1999 (M J ≥4.2). (a)Epicenter locations. (b)Latitudes of epicenter locations versus occurrence times. The shaded region represents the target space-time range. Fig. 3. Probabilities of having a larger descendant in the JMA catalogue. Circles, triangles and crosses represent the reconstructed Ĥ(m), Ĥ b (m) and Ĥ c (m), for all the events, background events and triggered events, respectively. The black, red and orange solid lines are theoretical results for all the events, background events and triggered events, respectively. Fig. 4. Probability density functions for magnitudes of four types of events. The solid lines represent the corresponding theoretical results derived from the improved model. Fig. 4. Average numbers of children from the four type of events. The solid lines represent the corresponding theoretical results derived from the improved model.