Analysis of Foreshock Sequences in California and Implications for Earthquake Triggering

Transcription

1 Pure Appl. Geophys. Ó 25 Springer Bsel DOI.7/s Pure nd Applied Geophysics Anlysis of Foreshock Sequences in Cliforni nd Implictions for Erthquke Triggering XIAOWEI CHEN nd PETER M. SHEARER 2 Abstrct We nlyze foreshock ctivity in Cliforni nd compre observtions with simulted ctlogs bsed on brnching ftershock-triggering model. We first exmine foreshock occurrence ptterns for isolted M 5 erthqukes in southern Cliforni from 98 to 2 nd in northern Cliforni from 984 to 29. Among the 64 M 5 minshocks, excluding 3 swrms nd 3 doubles, 53 % of the rest re preceded by t lest one foreshock within 3 dys nd 5 km. Foreshock occurrence ppers correlted with minshock fulting type nd depth. Foreshock re is correlted with the mgnitude of the lrgest foreshock nd the number of foreshocks, however, it is not correlted with minshock mgnitude. We then exmine the occurrence pttern of ll seismicity clusters without minimum mgnitude requirement, nd the possibility tht they re foreshocks of lrger minshocks. Only bout 3 % of the smll clusters led to lrger cluster. About 66 % of the lrger clusters hve foreshock ctivities, nd the sptil distribution pttern is similr to M 5 minshocks, with lower occurrence rtes in the Trnsverse Rnge nd centrl Cliforni nd higher occurrence rtes in the Estern Cliforni Sher Zone nd the By Are. These results suggest tht foreshock occurrence is lrgely controlled by the regionl tectonic stress field nd fult zone properties. In specil cses, foreshock occurrence my be useful for short-term forecsting; however, foreshock properties re not relibly predictive of the mgnitude of the eventul minshock. Comprison with simulted ctlogs suggest tht the swrmy fetures nd foreshock occurrence rte in the observed ctlogs re not well reproduced from common sttisticl models of erthquke triggering.. Introduction MOGI (963) distinguished three min types of erthquke sequences: () minshocks with both foreshocks nd ftershocks; (2) minshocks nd ftershocks but no foreshocks; nd (3) erthquke swrms tht lck cler minshocks. There hve been studies of the triggering process involved in ech University of Oklhom, Normn, OK 739, USA. E-mil: xiowei.chen@ou.edu 2 University of Cliforni, Sn Diego, L Joll, CA 9293, USA. ctegory. Aftershocks re usully ssumed triggered by dynmic or sttic stress chnges imposed by the minshocks (e.g., TODA et l. 22), nd erthquke swrms re thought to result from underlying crustl trnsient processes (e.g., VIDALE nd SHEARER 26; CHEN et l. 22). Foreshocks re of gret interest becuse of their possible triggering role nd predictive vlue, but their reltionship to minshocks is still poorly understood. The successful evcution prior to the 975 M7.3 Hicheng erthquke is promising exmple for erthquke prediction; however, mny minshocks occur bruptly without foreshocks (e.g., the 24 Prkfield erthquke), or the foreshocks re only recognized retrospectively (e.g., the 992 Lnders erthquke) MIGNAN (24). Two models hve been suggested to explin foreshock occurrence: () rupture model, where foreshocks nd ftershocks cn be explined with common triggering model, s indicted by sttisticl tests of Cliforni seismicity FELZER et l. (24), therefore, the minshock is just n ccidentlly lrger ftershock; (2) pre-slip model, where foreshocks re triggered by qusi-sttic slip occurring within the minshock nucletion zone, nd foreshock properties re possibly predictive of minshock mgnitude (DODGE et l. 996). DODGE et l. (996) reported scling of foreshock re with minshock mgnitude, which is similr to the scling reltionship of the proposed nucletion phse of ELLSWORTH nd BER- OZA (995). However, FELZER et l. (24) found much stronger correltion between foreshock re nd the mgnitude of the lrgest foreshock, insted of the mgnitude of the minshock, suggesting tht foreshock re is not useful predictor of the eventul minshock size. Recent observtions hve found tht foreshocks my be driven by n independent slow-slip phse (not prt of the nucletion process), concurrently occurring within the fult zone (KATO

2 X. Chen nd P. M. Sherer Pure Appl. Geophys. et l. 22; CHEN nd SHEARER 23), or within wide region long the plte interfce for interplte erthqukes (BOUCHON et l. 23). The reltive loction nd time between foreshocks nd minshocks is of gret importnce in recognizing foreshock sequences. For the foreshock sequences in ABERCROMBIE nd MORI (996), ll but one continue to the lst dy before the minshock within 5 km of its hypocenter. In BOUCHON et l. (23), 7 % of interplte erthqukes hve foreshocks continuous to the lst dy, but within much lrger sptil extent (up to 5 km). For the three M7 minshocks in southern Cliforni, high-resolution erthquke ctlogs revel foreshock ctivities concentrted within hours of the minshock CHEN nd SHEARER (23) within.5 2 km of the minshock hypocenter. Some ocenic trnsform fults hve enhnced immedite foreshock ctivities within hours before minshocks within 5 km MCGUIRE (25). These observtions suggest tht, if foreshocks exist, they typiclly continue to immeditely before the minshock; thus, if sequence is identified s foreshock sequence, such s the 24 Chile erthquke (KATO nd NAKA- GAWA 24), the loction nd time of the eventul minshock my be predicted. Studies hve found foreshock occurrence is dependent on the regionl stress field, e.g., norml fulting versus reverse fulting ABERCROMBIE nd MORI (996), or intrplte erthqukes versus interplte erthqukes (BOUCHON et l. 23), suggesting tht the occurrence of foreshocks is not purely rndom, but my be influenced by the regionl stress field. In this regrd, retrospective serches of foreshock occurrence ptterns in vriety of tectonic settings will be useful for future prospective forecsts. Recently developed high-resolution ctlogs provide opportunities to review previously identified foreshock fetures, nd further probe the possible reltionships mong precursory seismicity, chrcteristics of erthquke clusters, nd minshock properties, which my be helpful in developing or improving erthquke forecsting models. In this study, we first retrospectively serch for foreshocks for minshocks (M 5) nd compre foreshock occurrence with minshock fulting type, loction, nd foreshock nd minshock mgnitudes, in order to see if there re ny ptterns in the pprent rndomness of foreshock occurrence, nd if there is ny reltionship between foreshock properties nd minshock prmeters. We then investigte the occurrence ptterns of smll clusters tht resemble swrm-like foreshock sequences but which do not lwys led to lrger events, nd perform comprisons with synthetic ctlogs bsed on n ETAS-like triggering model (epidemic-type-ftershock-sequence: brnching point process where the totl seismicity rte is summtion of ll triggered ftershocks from prior events, OGATA 999), in order to exmine to wht extent the sttisticl model cn explin the observed seismicity ptterns. 2. Foreshock Occurrence Pttern for M C 5 Erthqukes We serch for isolted minshocks with M 5 using two wveform relocted ctlogs in Cliforni (with reltive loction ccurcy typiclly less thn 2 m): () the HAUKSSON et l. (22) ctlog for southern Cliforni from 98 to 2, excluding events north of 35.5 nd south of 32. ; (2) the double-difference ctlog for northern Cliforni from 984 to 29, excluding events south of 35.5 nd north of 39.5 (dt source: columbi.edu/*felixw/ncaeqdd/) WALDHAUSER nd SCHAFF (28). The res excluded re beyond the coverge of the regionl network recording the events nd thus likely hve higher detection thresholds nd lrger loction errors. To reduce potentil ctlog incompleteness issues for smller erthqukes, we use events with M :5 throughout this study. We select minshocks tht re reltively isolted from other lrge events, i.e., events tht re not prt of ftershock sequences or immedite foreshocks of lrger events. Specificlly, we exclude: () smller events within dys nd 5 km fter M 5 events; (2) smller events within 2 dys fter M 6 events; (3) smller events immeditely before M 5 event within 2 dys nd 5 km. These requirements re not n ttempt to decluster the ctlog, but rther to ensure the minshocks tht we nlyze re lrgely independent from other lrge events (e.g., not within direct ftershock sequences or

3 Anlysis of Foreshock Sequences in Cliforni when the ctlog is temporrily influenced by the occurrence of lrge event). Tests without pplying such criteri resulted in severl lrge minshocks tht re cler ftershocks of previous lrger events (two re within the ftershock zone of M6 erthquke nd one is within long-lsting swrm in the Long Vlley volcnic region), in which their foreshocks cnnot be distinguished from ftershocks of the erlier event. In totl, 7 minshocks in the two ctlogs meet our criteri. Visul exmintion found five of these events re prt of long-durtion continuous sequences, nd re excluded from the finl list. The M6.6 event on the Superstition Hills fult in 987 occurred 2 h following the M6.2 Elmore Rnch erthquke (noted with * in Tble ) nd is excluded from the finl list, becuse its precursory seismicity is dominted by seismicity following the first event. Among the 64 minshocks, 3 re within erthquke swrms in Nevd nd the Slton Trough, nd 3 re erthquke doublets (two events of similr mgnitude occurring lmost instntneously, listed with ** in Tble ). For the remining 58 minshocks, we exmine the precursory ctivity within 5 km nd dys before the minchock. The sctter plot of dys before the minshock nd distnce to the minshock suggests tht most of the precursory ctivity is concentrted within 5 km of the minshock hypocenters (Fig. ). For most of the minshocks tht hve precursory ctivity within 5 km, the cumultive number of foreshocks stedily grows until up to 3 dys before the minshocks, n incresed rte of foreshocks occurs within pproximtely 2 dys before, nd significntly enhnced ctivity occurs within 2 dys before the minshocks (see Fig. 2). To check if the pprent ccelertion behvior is dominted by few lrger sequences, we normlize event occurrence time by the durtion of the precursory sequence (see Tble 2 for clcultion of durtion), then clculte the cumultive density function (CDF) for ech sequence, nd verge ll sequences to get n verged CDF for ll minshocks. Individul sequences hve considerble sctter, however, the verged CDF suggests enhnced precursory ctivities within the lst 2 % of the totl precursor durtion (see Fig. 3), where the seismicity rte is significntly bove the stedy bckground rte. Bsed on the brod sptil temporl behvior of the precursory ctivities, we define foreshocks in this study s immedite precursory ctivity within 3 dys nd 5 km of the minshock. Becuse foreshocks cn only be identified in reltion to their sptil nd temporl proximity to minshocks, there is no perfect method to seprte foreshocks from bckground ctivity, just s there is no wy to uniquely discriminte very lte ftershocks from bckground ctivity. We believe our 3-dy nd 5-km cutoff is resonble nd prcticl choice (see sctter plot in Fig. ) to ensure tht the vst mjority of our foreshocks re indeed foreshocks nd not bckground ctivity. Using lrger sptil nd/or temporl window might yield more foreshocks, but t the cost of including mny bckground events. We use fixed selection window regrdless of minshock mgnitude to void bising ny comprisons between foreshock nd minshock properties. We find tht 27 of the 58 minshocks (excluding the 3 swrms nd 3 doublets) hve no foreshocks within 3 dys nd 5 km. Among the 3 minshocks with foreshocks, 4 minshocks hve swrm-like foreshocks (with more thn 3 events, so we re ble to estimte foreshock re in the following section, nd the foreshocks do not strt with the lrgest foreshock). Some specil cses re included (noted with * in Tble ): () the 986 Mt. Lewis sequence hs swrm with 4 events tht occurred 7 dys before the minshock, which re included in the foreshocks; (2) for the 986 Chlfnt erthquke, M5.9 event occurred dy before the M6.4 event, nd the former is ssumed to be the minshock, with 4 foreshocks. Thus, from the 64 minshocks exmined here, excluding 3 swrms nd 3 doublets, 53 % hve t lest one foreshock (58 % if including the swrms nd doublets). A list of foreshocks is in Tble nd mp view of the minshock loctions is shown in Fig. 4. Our observed 53 % rte of foreshock occurrence is consistent with previous work. ABERCROMBIE nd MORI (996) found 44 % rte of M 2 foreshocks prior to M 5 events in the western United Sttes. However, s noted by REASENBERG (999), one expects the rte of foreshock occurrence to increse for lower foreshock mgnitude cutoffs compred to the minshock, so studies re best compred by dividing the

4 X. Chen nd P. M. Sherer Pure Appl. Geophys. Tble List of foreshocks with M 5 included in this study Time Loction Depth Mg N fore Focl mechnism Fult type Plne diff 98/9/4 5:5: , (5.) , 69 (3.9, 8 ).2 (.) /7/8 9:2: , (.) , -77 (294.37, 56 ) -.3 (.27) /7/3 3:47: , (5.) , -67 (26.37, 6 ) -.4 (.82) // 4:42: , (.) , 83 (27.3, 98 ).92 (.9).7 988/6/ 23:6: , (N/A) , 76 (N/A).4 (N/A) N/A 988/2/3 :38: , (N/A) , 69 (N/A).2 (N/A) N/A 99/6/28 4:43: , (.) , 74 (93.43, 3 ).82 (.56) /2/3 7:54: , (N/A) 5.32 N/A (N/A). (N/A) N/A 993/5/28 4:47: , (N/A) , 7 (N/A) O. (N/A) N/A 994//7 2:3: , (8.) , 6 (278.42, 65 ).82 (.72) 3. 2/2/8 23:36: , (.) 5.7 N/A (4.59, -49 ) N/A (-.34) N/A 24/9/29 22:54: , (3.5) , 73 (293.7, -69 ).8 (-.2).3 28/2/9 7:2: , (2.9) , -75 (226.79, 3 ) -.6 (.3) /7/29 8:42: , (4.7) , 46 (44.55, 29 ).38 (.32) /2/6 4:8: , (7.3) , -57 (253.83, 6 ) -.26 (.7) //23 5:4: , (N/A) , l (N/A). (N/A) N/A 984/4/24 2:5: , (8.) , (333.76, 79 ). (.) /2/2 8:39: , (N/A) , (N/A). (N/A) N/A 988/6/27 8:43: , (N/A) , 3 (N/A).33 (N/A) N/A 988/9/9 2:56: , (N/A) , - (N/A) -. (N/A) N/A 989/8/8 8:3: , (N/A) , 3 (N/A).33 (N/A) N/A 989//8 :4: , (9.) , 3 (235.4, 29 ).56 (.32) /9/7 2:: , (N/A) , 5 (N/A).56 (N/A) N/A 993/5/7 23:2:49:5 37.7, (7.) , 2 (2.3, -93 ).22 (-.97) //27 2:7: , (.) 5. N/A (244.7, -3 ) N/A (-.3) N/A 23/2/22 9:5: , (7.6) , 8 (296.32, 88 ).89 (.98) /9/28 7:5: , (8.8) , -7 (32.72, -78 ) -. (-.2) /2/6 5:53: , (N/A) , 48 (N/A).36 (N/A) N/A 987/2/7 3:45: , (5.) , 98 (22.7, 2 ).9 (.2) /4/26 :37: , (N/A) , -4 (N/A) -.43 (N/A) N/A 2//3 7:56: , (N/A) , 72 (N/A).9 (N/A) N/A 22/2/22 9:32: , (7.) N/A (9.66, -4 ) N/A (-.4) N/A 25/6/2 5:4: , (4.2) , 72 (35.53, -79 ).9 (-.) /5/24 4:2: , (N/A) , (N/A) N/A (N/A) N/A 29/9/9 22:55: , (3.) , 75 (25.7, -72 ).83 (-.9) /2/3 8:48: , (9.) , -92 (328.82, -78 ) -.98 (-.2) //23 8:8: , (N/A) , 3 (N/A).33 (N/A) N/A 986//26 9:2: , (7.) , - (66.9, 8 ) -. (.) /2/4 7:26: , (3.) , 9 (3.46, 38 ). (.42) /6/3 :45: , (9.) , - (325.76, -75 ) -. (.6) //24 6:5: , (2.) , (56.59, - ). (-.) //7 4:32: , (N/A) , -7 (N/A) -. (N/A) N/A 27//3 3:4: , (.) , (324.8, 76 ). (.4).8 994/9/2 2:23: , (4.) , -4 (42.74, -3 ) -.44 (-.4) //24 :54: , (5.) 6.2 6* 28.86, 7 (35.9, 8 ). (.) /2/28 23:43: , (.) , 67 (37.73, 69 ).4 (.2) /4/23 4:5: , (.) , 7 (8.87, - ). (-.) /6/28 :57: , (5.) , -77 (34.7, -72 ) -.3 (-.9) //27 6:: , (N/A) , 67 (N/A).4 (N/A) N/A 997/3/8 5:24: , (N/A) , -63 (N/A) -.9 (N/A) N/A 999//6 9:46: , (.) , 59 (336.8, 74 ).23 (.7) /4/4 22:4: , (6.) , 65 (223.84, -2 ).7 (-.2) /8/4 2:: , (5.) , 4 (38., 5 ).44 (.83) /3/3 :55: , (6.) 5.7 5* 355.8, -8 (353.79, -7 ). (-.).6 986/7/2 4:29: , (8.) 5.9 4* 25.85, - (223.54, -35 ) -. (-.39) /4/8/ 3:53: , (N/A) , 4 (N/A).44 (N/A) N/A 997//2 8:5: , (5.) N/A (238.63, 5 ) N/A (.7) N/A

5 Anlysis of Foreshock Sequences in Cliforni Tble continued Time Loction Depth Mg N fore Focl mechnism Fult type Plne diff 998/8/2 4:: , (8.8) , - (48.85, - ) -. (-.). 98/4/26 2:9: , (6.) , -5 (249.45, -8 ) -.32 (-.9) /9/2 :27: , (9.8) , -6 (335.76, -67 ) -.82 (-.4) /4/26 6:4: , (.4) N/A (328.86, 8 ) N/A (.) N/A 2/7/7 2:7: , (N/A) 5.2 4** 8.9, (N/A). (N/A) N/A 24/9/8 23:2: , (5.) ** 65.9, - (33.76, -7 ) -. (-.) //3 :5: , (2.5) 5. 52** N/A (24.56, -36 ) N/A (-.4) N/A CMT solutions re in prentheses Events with * re specil cses nd events with ** indicte erthquke doublets (see text for detils) Events with high degree of disgreement between CMT solutions nd the regionl moment tensor ctlog time (dys) dys 2 dys 5 km distnce (km) Figure Sctter plot of ll events within 5 km nd dys before ech minshock (excludes the 3 swrms nd 3 doublets). Dots with the sme color belong to the sme foreshock minshock sequence pprent foreshock rte by the differentil mgnitude. In our cse, we obtin foreshock rte density of 5 % per mgnitude unit. For comprison, ABERCROMBIE nd MORI (996) obtined 5 % per mgnitude unit, nd REASENBERG (999) obtined 3 % per mgnitude unit from globl study of M 6 events. 2.. Reltionship Between Foreshock Properties nd Minshock Prmeters Next, we exmine if there is ny reltionship between foreshock properties nd minshock source () Culmultive number of foreshocks (b) Culmultive number of foreshocks Time (dys before minshock) Time (dys before minshock) Figure 2 Cumultive number of foreshocks within 5 km before ech minshock. Verticl dshed line mrks 5 dys before minshock. b Closeup of the lst 5 dys before the minshocks. The colors correspond to individul minshock sequences in Fig.

6 X. Chen nd P. M. Sherer Pure Appl. Geophys. Tble 2 Definition of prmeters, the superscript letter re prmeters nlyzed in this study T i T X i Time of ech event Time of the first event 3D loctions of ech event M ðiþ :5MðiÞþ9: t i ðt P i T Þ=menðT i T ; i ¼...NÞ t N i t i M ðiþ= P N i M ðiþ P l N 3 i ðt i tþ 3 M ðiþ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d ðt i tþ 2 m ðiþ C j i P N i r Centroid loction¼ medinðx k ; k ¼ i...jþ Rdius ¼ medinðx i C N ; i ¼...NÞ t dur Durtion ¼ medinðjt i T j; i ¼...NÞ t mx t i ; fmðiþ ¼mxðMÞg l Dr qusi d s M fmx N fore M mx F re Swrm-type Aftershock-type l 3 =d P N 7 MðiÞ i 6r 3 ðc N=2 CN=2 N Þ=r Mximum mgnitude of foreshocks Number of foreshocks Mgnitude of minshock Are of foreshocks t mx :2 t mx \:2 prmeters. We first compre foreshock occurrence with focl mechnism. We obtin focl mechnism solutions from: () the YHS (by YANG, HAUKSSON nd SHEARER 22) ctlog for southern Cliforni, reclculted using the HASH method (in HARDEBECK nd SHEARER 23) with dt from the Southern Cliforni erthquke center (YANG et l. 22); (2) the northern Cliforni moment tensor ctlog [Northern Cliforni Erthquke Ctlog nd Phse Dt]; nd (3) Globl Centroid-Moment-Tensor (CMT) solutions when vilble. We compute fulting type bsed on rke ngle ( is norml fult, is strike slip fult, is reverse fult): k=9 if jkj9; f ¼ ðþ ð8 jkjþ ðk=jkjþ=9 if jkj [ 9: For 8 minshocks, there is high degree of mismtch ([4 between fult plne orienttions nd df ¼ jf regionl f cmt j [ :4 between the globl CMT solution nd the regionl network solution (see Tble ; Fig. 4). The mismtch my be due to reduced zimuthl sttion coverge for events outside the Culmultive number of foreshocks Time (normlized) Figure 3 Cumultive density functions (CDF) with origin time normlized by durtion of ech precursory period, (see text nd Tble 2 for detils). Ech grey line corresponds to individul minshock, the thin blck line is n pproximtion of constnt bckground rte. The blck dshed line is the verged CDF of ll the individul grey lines, note the cler devition from the constnt rte within the lst 2 % of the precursory period regionl network (e.g., events off-shore nd events in Mexico), or complexity in the erthquke rupture process (e.g., the rupture initited with sub-event with different focl mechnism). Becuse the regionl networks do not provide unique solutions for mny events, we use CMT solutions when vilble. We first exmine foreshock occurrence in fulting type bins from to. From Fig. 5, there is higher foreshock occurrence rte for minshocks with diltionl components (f \) nd reverse-fulting minshocks tend to hve lower foreshock occurrence rtes. Although some minshocks hve lrger degree of mismtch between the regionl nd CMT solutions, these events do not ffect the overll trend of decresing foreshock occurrence for reversefulting events. There is only one pure normlfulting minshock, which hs no foreshock. However, with the regionl focl mechnism ctlog, ll the norml-fulting erthqukes re preceded by t lest one foreshock. Our result is most relible for fulting types from.4 to.5, where n increse in the compressionl component decreses foreshock occurrence for strike slip fults. We lso compre foreshock occurrence with minshock depth from the two regionl ctlogs. In Fig. 5, for shllower events (mostly 5 km), the mjority of minshocks hve

7 Anlysis of Foreshock Sequences in Cliforni Hywrd Fult 38 LV 37 SF By Clvers Fult Coso Sn Andres Fult Grlock fult Sn Andres Fult TR ECSZ No foreshocks foreshocks Swrms Doublets Lrge mismtch with globl CMT solution Slton Se Figure 4 Mp view of M 5 minshocks. Events with lrge mismtch with CMT solutions correspond to events with red colors in Tble ). Focl mechnisms re from CMT solutions when vilble. Regions in the mp: TR Trnsverse Rnge, LV Long Vlley foreshocks, nd the occurrence rte decreses with depth. We test the sttisticl significnce of the pttern with the Student s t test (ABERCROMBIE nd MORI 996). For this, we divide foreshock occurrence rte into severl groups in fulting type nd depth: for fulting type, we use.5 (f),.5 (f2), nd.5 (f3); for depth, we use 5 nd 5 25 km. For fulting type, group f is different from f2 nd f3 t 97 % confidence level, while f2 nd f3 re similr; for depth, the shllow group is different from the deeper group t 98 % confidence level. We lso exmine the reltionship between fulting type nd depth (see Fig. 6). The shllowest events spred evenly between f ¼ :5 nd f ¼ :5. For events deeper thn 5 km, there is no cler dependence between fulting type nd depth, nd fulting type dependence of foreshock occurrence is cler. Thus, the most relible trends re dependence on fulting type for :5 f nd higher foreshock occurrence rte t shllow depth. We compre foreshock properties with minshock mgnitude by exmining: () the rdius of foreshock rupture re for the 4 swrm-like foreshock sequences; (2) the number of foreshocks; (3) the mgnitude of the lrgest foreshock; nd (4) foreshock durtion (see Tble 2 for definitions). For the three

8 X. Chen nd P. M. Sherer Pure Appl. Geophys. () 25 foreshocks no foreshocks 25 no foreshocks foreshocks depth (km) (b).5.5 Norml Strike-slip fulting type foreshocks no foreshocks depth (km) Figure 5 Histogrm of fulting types for 27 minshocks without foreshocks nd 37 minshocks with foreshocks. Fulting types from to to correspond to norml fulting strike slip reverse fulting, respectively. b Histogrm of the depth distribution for 27 minshocks without foreshocks nd 37 minshocks with foreshocks. Note the prevlence of foreshock occurrence t shllow depth nd for trnstentionl fults (f, for definition of f, refer to Eq. ). We perform Student s t test to exmine the sttisticl significnce of the pttern (ABERCROMBIE nd MORI 996). For fulting types, the group of.5 to is different from to t 97 % confident level, nd the shllow group ( 5) is different from the rest t 98 % confident level M [ 7 minshocks (the 992 Lnders, the 999 Hector Mine nd the 2 El Myor-Cucph erthqukes), we hve shown tht none of these properties re correlted with minshock mgnitude (CHEN nd SHEARER 23). For ech of the 4 minshocks, we visully check seismicity within ech minshock rupture zone using n interctive tool, to ensure good selection of foreshocks from the utomtic serch process described bove. We.5.5 focl type Figure 6 Sctter plot of depth versus fulting type for ech minshock. Blck dots re minshocks with foreshocks, blck strs re minshocks without foreshocks. The verticl lines corresponds to the three groups tht we test ginst for fulting types. The horizontl line mrks the depth groups tht we test ginst. For events deeper thn 5 km, there is no cler reltionship between fulting type nd depth, nd the most prominent feture is fulting type dependence of foreshock occurrence lso compre two different methods to estimte foreshock re, specificlly: () we clculte re bsed on the rdius ssuming circulr re; (2) we compute the convex polygon tht includes ll foreshocks. Both methods yield similr results, where minshock mgnitude is correlted with the number of foreshocks, but not foreshock re, while foreshock re is correlted with the number of foreshocks nd the mgnitude of the lrgest foreshock (see Tble 3). The lck of correltion of foreshock re with minshock mgnitude, but with foreshock number nd mgnitude, suggests foreshock processes re controlled by interctions within foreshocks themselves, rther thn being n indictor of minshock mgnitude. Most of the foreshocks do not strt with their lrgest event, suggesting the swrmy nture of foreshock sequences. The fct tht minshock mgnitude is correlted with the number of foreshocks suggests tht swrms with mny events increse the probbility of lrge erthqukes, such s the 975 Hicheng sequence, the 992 Lnders nd the 999 Hector Mine erthqukes. Overll, observtions of foreshock dependence on fulting type nd depth re consistent with the results in ABERCROMBIE nd MORI (996); however, our result

9 Anlysis of Foreshock Sequences in Cliforni Tble 3 Correltion between foreshock properties nd minshock prmeters M mx F re (convex) cc ¼ :46; p ¼ : M mx F re (rdius) cc ¼ :32; p ¼ :28 M mx N fore cc ¼ :62; p ¼ :2 M mx M f mx cc ¼ :7; p ¼ :86 M mx t dur cc ¼ :; p ¼ :75 M f mx F re (convex) cc ¼ :56; p ¼ :5 M f mx F re (rdius) cc ¼ :6; p ¼ :3 N fore M f mx cc ¼ :; p ¼ :73 N fore F re (convex) cc ¼ :69; p ¼ : N fore F re (rdius) cc ¼ :58; p ¼ :4 (cc is correltion coefficient, nd p is the sttisticl significnce of correltion, p :5 is generlly considered s significntly bove rndom chnce) Significnt correltion Rdius (m) 3 Chlfnt 2 Uplnd Mt Lewis Joshu Tree El Myor-Cucph Lnders Hector Mine Moment (N-m) Figure 7 Foreshock rdius versus minshock moment plotted on Figure 6 from DODGE et l. (996). Red dots re 4 minshocks in this study, boxes indicte nmed events in the ctlog. Blck dots re source rdii estimted in BEROZA nd ELLSWORTH (996), stright lines re best-liner fit nd r boundries. Note the scttered red dots bove the r limit. The p vlue of the correltion for the red dots is.28, indicting no sttisticl significnce (see Tble 3) is more relible for strike slip fults nd shllow depths, becuse we hve used improved ctlogs, exmined more events nd obtin consistent results with both regionl nd CMT ctlogs. It is interesting to compre our foreshock rdius estimtes with results in DODGE et l. (996) (see Fig. 7). In generl, for the events in common, our rdius is consistent with previous mesurements; however, bout hlf of the points re bove the r boundries of nucletion rdius estimted from the slow onset of minshock wveforms (ELLSWORTH nd BEROZA 995). There is no correltion between foreshock durtion nd minshock depth (cc ¼ :5; p ¼ :62), which is inconsistent with previous observtions (JONES 984; ABERCROMBIE nd MORI 996). There is some degree of sptil seprtion between different types of minshocks: within the Trnsverse Rnge region in Los Angeles county nd centrl Cliforni, most minshocks do not hve foreshocks; in contrst, in the Sn Frncisco By re nd Estern Cliforni Sher Zone (ECSZ), t the intersection of different fults, the occurrence rte of foreshocks is reltively high (see Fig. 4) Precursory Seismicity The rupture re of M5.8 erthquke is bout 5 km, ssuming stress drop of 2 MP (the verge stress drop for southern Cliforni from SHEARER et l. (26), clculted from SHEARER (29), with r ¼ð 7M 6Dr Þ=3. According to SHEARER nd LIN (29), the rdius of the Mogi-doughnut (enhnced precursory seismicity) roughly grees with the expected rupture rdius for trget minshocks. Due to the smll number of M5 erthqukes in the ctlog, such behvior is not relibly resolved for lrger events in their study. For the 64 M 5 minshocks, we exmine the verged precursory seismicity for: () 27 minshocks without foreshocks; (2) 3 minshocks with foreshocks; (3) 3 erthquke swrms; nd (4) 3 erthquke doublets. For ech group, we clculte seismicity density for ech time nd distnce bin bsed n on: D ¼ Nðt 2 t Þð4=3Þpðr 3 Þ, where n is the totl number 2 r3 of precursory events in the spce/time bin, nd N is the number of trget events in ech group. We use spce-time bins, evenly spced in log distnce bins between. nd km, nd in log time bins from. to dys. From Fig. 8, within dy prior to the minshock, the low seismicity zone extends beyond the 5 km criteri, consistent with the empiricl scling of Mogi doughnut behvior. Due to the limited number of vilble minshocks, we do not ttempt to perform sttisticl nlysis to test the relibility of the Mogi zone reltive to smller event bins from SHEARER nd LIN (29). Foreshock ctivity is confined within the Mogi zone, nd well

10 X. Chen nd P. M. Sherer Pure Appl. Geophys. () 3 2 (b) time (dys) time (dys) distnce (km) distnce (km) 7 (c) 3 2 (d) time (dys) time (dys) distnce (km) distnce (km) 7 Figure 8 Precursory seismicity within dys nd km prior to trget minshocks with M [ 5. Four minshock types re included: minshocks with no foreshocks; b minshocks with foreshocks; c erthquke swrms; d erthquke doublets. Horizontl blck lines correspond to T ¼ 2 dys, verticl blck lines correspond to D ¼ 5 km. The color scle shows log of seismicity rte in ech distnce-time bin seprted from bckground seismicity. The high event density per time/distnce bin suggests tht foreshocks re highly loclized within future minshock rupture zones (lso see Fig. ). 3. Seismicity Clusters tht Resemble Foreshock Sequences So fr, our nlysis hs been limited to M 5 trget events, nd ny foreshock ctivities within 5 km nd 3 dys. However, there re other importnt questions relted to precursory ctivities, such s: () how re foreshock sequences different from rndom smll clusters? (2) How often do smll clusters led to lrger clusters tht might include lrger event? To ddress this, we remove the mgnitude requirement, nd serch for smll compct clusters tht resemble the observed foreshock sequences. Specificlly, we serch for smll clusters tht hve t lest N events within 5 km nd 2 dys, nd fewer thn 5 events in the previous 7 dys within 5 km. The 2-dy requirement is bsed on the observtion tht enhnced ctivities typiclly occur within 2 dys before minshocks (see Fig. 2), the number requirement is to ensure the reltive independence of

11 Anlysis of Foreshock Sequences in Cliforni () (b) (c).2.8 (ftershock type) (swrm type) 2 3 t mx (d).2.5 d s μ Δσ qusi Figure 9 Distribution of different prmeters for: ftershock-type (t mx :2) (solid line) nd swrm-type (t mx :2) (dshed line) sequences from combined observtions in southern nd northern Cliforni. d Correspond to the four prmeters discussed in the text: t mx, d s, l, Dr qusi the smll cluster, nd minimize the number of rndom scttered clusters. We pply the sme criteri s before to temporrily remove immedite ftershock sequences from the ctlog for consistency. Next, we check whether these clusters grow into lrger clusters. To define lrger cluster, we require: () N cluster 5 within 28 dys nd 5 km following the smll cluster; (2) N outside :2N cluster within 28 dys between 5 nd km. The ltter requirement is to ensure the cluster is sptilly isolted from bckground seismicity; however, it does not ffect the reltive distribution of different types of clusters. To chrcterize the cluster type, we compute four prmeters s described in CHEN et l. (22) nd listed in Tble 2: () t mx, the reltive timing of the lrgest event in the cluster with respect to the men dely time; (2) the skew (l) of moment relese history; (3) the distnce seprtion of the first nd second hlf of the cluster normlized by the rdius of the cluster (d s ); nd (4) Dr qusi ¼ 7P n Mi 6r, the effective stress drop. The prmeter d s is proxy 3 to mesure the sptil migrtion of seismicity clusters, nd Dr qusi is prmeter to mesure the effectiveness of moment relese compred with the rupture re. The observtions in CHEN et l. (22) suggested clusters with t mx :2 re more prone to sptil migrtion controlled by externl seismic trnsients. We use this empiricl reltionship, nd define ftershock-type clusters s those with t mx :2, nd swrm-type clusters s those with t mx :2. Foreshocks re ny erthqukes occurring before the lrgest erthquke (minshock) in the cluster, nd ll swrm-type clusters hve foreshocks by definition. For the southern Cliforni ctlog, we identify 3 smll clusters, of which 87 grow into lrger clusters, nd 27 strt with their minshock. Smll clusters re less common in northern Cliforni, where we identify 84 smll clusters, 56 of which grow into lrger clusters, nd 2 strt with their minshock. From Fig. 9, the CDF of the four prmeters re consistent with CHEN et l. (22):

12 X. Chen nd P. M. Sherer Pure Appl. Geophys. ftershock-type clusters hve lower d s, higher l nd higher Dr qusi. Overll, in totl 495 smll clusters re identified, of which 3 % eventully grow into lrger cluster. Among the lrger clusters, 66 % hve precursory ctivities. If we only focus on ftershock-type lrger clusters (see Tble 2), there re 39 % with precursory ctivities. For southern Cliforni, we observe similr reltionship to M 5 minshocks between precursory occurrence nd smll minshock fulting type (foreshock occurrence rte is higher for fultingtype \), which is consistent with CHEN et l. (22), however, the correltion is not so cler for northern Cliforni. For smller events, the focl mechnism is likely poorly determined compred () (b) Northern Cliforni Southern Cliforni Figure Depth distribution of ll clusters with t lest one foreshock nd without foreshocks. Northern Cliforni, b Southern Cliforni. The mjority of minshocks shllower thn 8 hve foreshocks, while ll minshocks deeper thn km hve no foreshocks with M 5 events, nd the reduced correltion my be due to uncertinties in the fult plne solutions (s shown in Tble, there is sometimes lrge mismtch for M 5 events). The southern Cliforni YHS ctlog is improved compred to the routine ctlog solutions, nd likely is more ccurte (YANG et l. 22). For both ctlogs, we observe prevlence of precursory ctivities t shllow depth nd lck of precursory ctivities t deeper depth (Fig. ). The overll sptil distribution is similr for M 5 minshocks (see Figs. 4, ). For exmple, the Trnsverse Rnges nd centrl Cliforni re still dominted by minshocks without foreshocks. The By Are, the ECSZ, the Slton Trough nd the Long Vlley region re dominted by minshocks with foreshocks. Considering the geologicl fetures of these regions, this suggests tht foreshocks tend to occur within extensionl step overs, high het flow regions, nd complex fult zones, while lck of foreshocks is expected t thrust fult zones nd reltively simple plnr fult zones. The consistency between foreshocks for M 5 minshocks nd generl clustering types suggests tht loclized fult zone properties control precursory ctivities. We next investigte whether foreshock properties re predictive of minshock prmeters. We find tht:. Neither foreshock re nor the number of foreshocks is correlted with minshock mgnitude; none of the other foreshock properties correlte with minshock prmeters. 2. Foreshock re is well correlted with the number of foreshocks: correltion coefficient (cc) ¼ :8; p ¼ 5 (see Tble 4). 3. If we consider swrms (t mx :2) s foreshock minshock sequences, then for clusters with M mx 4:5, foreshock re is correlted with the mximum mgnitude of foreshocks (M f mx ) with cc ¼ :55; p ¼ :5, however, for clusters with 2 M mx 4:5, there is no correltion between foreshock re nd M f mx (see Tble 4). 4. The mgnitude difference (d m ) between M mx nd M f mx is dependent on M mx : for M mx 4:5, d m is pproximtely uniformly distributed between.5 nd 2, nd the medin vlue is.47; for 2 M mx 4:5, d m is skewed towrds lower vlues, nd is mostly below (Fig. 2).

13 Anlysis of Foreshock Sequences in Cliforni Figure Mp view of seismicity bursts in Cliforni. Red dots ftershock-type clusters with t lest one foreshocks; green dots ftershock-type clusters without ny foreshocks; ornge dots swrm-type clusters (hve foreshocks by definition); grey dots smll rndom clusters tht do not grow into lrge clusters Tble 4 Correltion between foreshock re F re, minshock mgnitude M mx, mgnitude of lrgest foreshock M f mx nd number of foreshocks (N fore ) from combined result of southern nd northern Cliforni Type 2 M mx 4:5 M mx 4:5 F re nd M mx cc ¼ :9; p ¼ :5 cc ¼ :7; p ¼ :43 F re nd M f mx cc ¼ :23; p ¼ :83 cc ¼ :55; p ¼ :5 F re nd N fore cc ¼ :74; p ¼ 2:9e cc ¼ :8; p ¼ :4e 6

14 X. Chen nd P. M. Sherer Pure Appl. Geophys ll types (2 M mx 4.5).2 ll types (M mx >4.5). ftershock type (2 M mx 4.5) ftershock type (M mx > 4.5) mgnitude difference d = m m m mx fmx Figure 2 Mgnitude difference between the minshocks nd their lrgest foreshock for combined observtions from southern Cliforni nd northern Cliforni. Blck lines re for ll cluster types (include both ftershock-type nd swrm-type), grey lines only include ftershock-type clusters. Dsh lines 2 M mx 4:5, solid lines M mx 4:5 Overll, results in this section confirm the reltionship between foreshock prmeters nd M 5 minshocks in the previous section. However, we lso find tht the correltion between foreshock re nd foreshock mgnitude, nd the mgnitude difference distribution, re different for clusters with 2 M mx 4:5 nd M mx 4:5, which my suggest different triggering processes for different sized erthqukes. Next, we exmine whether or not these observtions re consistent with synthetic ctlogs generted bsed on empiricl sttisticl reltionships. 4. Comprison with Synthetic Ctlogs Erthquke-to-erthquke triggering models relte the probbility of erthqukes to the pst history of nerby erthqukes using Omori s lw for ftershocks nd other empiricl reltionships nd hve been extensively described by number of uthors (e.g., OGATA999; HELMSTETTER et l. 23, 25; FELZER et l. 24). To investigte which fetures of our observtions re consistent with triggering models, we crete synthetic ctlogs bsed on the selfsimilr triggering model described by SHEARER (22) tht is similr to the ETAS model (epidemic-typeftershock-sequence) (OGATA 999). In the models, ech prent event independently triggers its own ftershock chin of dughter events. The number of direct ftershocks N sl for n event with mgnitude m follows productivity lw, nd event probbliity follows power-lw decy in with time nd distnce: N sl ¼ Q ðm m Þ Nðr; tþ ¼N sl ðt þ cþ p r q ; ð2þ where m is the minimum mgnitude erthquke, Q is the ftershock productivity, describes ftershock genertion efficiency, N(r, t) is the ftershock rte s function of distnce nd dely time from the triggering event, c nd p re Omori s lw prmeters, nd q is the distnce decy constnt. The mgnitude of bckground events, or triggered events, is rndom vrible drwn from the Gutenberg Richter (G R) distribution: NðmÞ ¼ bm ; ð3þ where is relted to the totl number of erthqukes, nd b (the b vlue) describes the reltive numbers of lrger events compred with smller events. In prctice, for computer simultions, m r (individul mgnitude drwn from G R distribution) is computed s: m r ¼ m log x r ; ð4þ where x r is rndom vrible drwn from the uniform distribution between ðm m 2 Þ nd. For the model here, we use m ¼ :5 nd m 2 ¼ 7:, which correspond to the mgnitude of completeness nd lrgest erthquke in the ctlog. Recent studies suggest tht ¼ b ¼ (used in this study) produces self-similr behvior, for which the incresed triggering cused by lrger mgnitude events is compensted by their decresed numbers in the G R reltion (SHEARER 22). For the selfsimilr triggering cse, the brnching rtio tht describes the verge number of first genertion ftershocks to the number of bckground events is n ¼ Qb lnðþðm 2 m Þ ð5þ nd n ¼ :39 for the cse of m ¼ :5 nd m 2 ¼ 7: in order to stisfy Båth s lw (BATH 965), i.e., tht the mgnitude difference between the minshock nd the lrgest ftershock is, on verge,.2.

15 Anlysis of Foreshock Sequences in Cliforni () ll clusters (b) ftershock type Socl (M mx 2) Socl (M mx >4.5) Sim- (M mx 2) Sim- (M mx 4.5) M M (c) 2 observtion (d) 2 observtion foreshock rte for ll clusters foreshock rte for ftershock type clusters Figure 3 Top mgnitude difference between minshock nd lrgest foreshock. All cluster types (both ftershock-type nd swrm-type); b only ftershock-type clusters. In both nd b, solid lines M mx 4:5; dshed lines ll M mx (M mx 2). Grey synthetic ctlogs, blck observtions. Error brs re 5 nd 95 % percentiles from synthetic ctlogs, line styles mtch corresponding dt types. In, the distribution tht includes smll minshocks (M mx 4:5) is clerly bove the 95 % limit from synthetic ctlogs, thus is significntly different from synthetic ctlogs. In b, the long verticl dshed lines indicte tht the distribution of d m from synthetic ctlogs is considerbly vribly due to the smll number of clusters; the grey solid line is not pplicble due to smll number of clusters from synthetic ctlogs. Bottom foreshock occurrence rte from observtions nd synthetic ctlogs. c Foreshock occurrence rte for ll clusters, including swrm-type clusters; d foreshock occurrence rte only considering ftershock-type clusters. Verticl lines re observtions (66 % for ll clusters, nd 39 % for only ftershock-type clusters, these re the results from generl cluster serch, nd differs from the 53 % for only M 5 minshocks), note the observed foreshock occurrence rte for with nd without swrm-type clusters is significntly higher thn in synthetic ctlogs For the sptil temporl decy, we use c ¼ : dys, p ¼ nd q ¼ :. The p nd c vlues re consistent with SHEARER (22b), the q vlue is slightly lower thn the.37 used in SHEAR- ER (22b), but does not strongly ffect the results. We generte synthetic ctlogs using the declustered southern Cliforni ctlog with ll events M :5. The declustering process follows REASENBERG (985), where ech ftershock sequence is replced by single equivlent event (the minshock), nd the residul ctlog pproximtes Poisson process. We generte synthetic ctlogs using the declustered ctlog s prent erthqukes (bckground seismicity), nd generte triggered ftershocks using the bove reltionships. The synthetic ctlogs re then processed the sme wy s we did for the rel ctlogs. On verge, only 2 % of the M 5 minshocks in the synthetic ctlogs hve foreshocks, nd the probbility of observing 53 % foreshock occurrence rte mong our 7 minshocks is only 3 % (bsed on Gussin distribution of the occurrence rte from the synthetic ctlogs). Next, we exmine

16 X. Chen nd P. M. Sherer Pure Appl. Geophys. () (b) (c) Socl ftershock type Socl swrm type ETAS ftershock type ETAS swrm type t mx (d) d s μ Δσ qusi Figure 4 Comprison of distributions of different prmeters between observtions nd synthetic ctlogs for southern Cliforni. In ll figures: solid lines ftershock-type, dshed lines swrm-type. Grey synthetic ctlogs, blck observtions. Verticl error brs correspond to the 5 nd 95 % percentiles from synthetic ctlogs. d Correspond to the four prmeters discussed in text: t mx, d s, l, Dr qusi. In ll cses, the dshed line (for swrm-type) is significntly outside the vribility limit from synthetic ctlogs, while the blck line is sometimes within model limits except the prmeter l tht describes the moment relese time history seismicity clusters in the synthetic ctlogs, s defined nd described for the dt in the previous section. We compre the CDF distribution of the four prmeters of CHEN et l. (22) with observtions from the southern Cliforni YHS ctlog, i.e., the timing of the lrgest event t mx, the skew l of moment relese history, the normlized distnce between the first nd second hlves of the cluster d s, nd the effective stress drop Dr qusi. The results re shown in Figs. 4 nd 3, nd my be summrized s follows:. Smll rndom clusters re common in synthetic ctlogs, nd bout 7 % of smll clusters do not grow into lrge clusters, which is consistent with observtions. 2. The synthetic ctlogs re dominted by ftershock-type clusters, nd the probbility of getting the observed foreshock occurrence rte is less thn 5 % (bsed on Gussin distribution of the foreshock occurrence rte from synthetic ctlogs), suggesting tht the synthetic ctlogs nd observtions re sttisticlly different in terms of foreshock occurrence (see Fig. 3c, d). 3. The mgnitude difference (d m ) between foreshocks nd minshocks for clusters with M mx 4:5 re overll consistent with observtions within the model vribility (see Fig. 3), nd the distribution of ftershock-type clusters is considerbly vrible due to the smll number of clusters. The distribution of d m for ll clusters with M mx 2 is sttisticlly different from the synthetic ctlogs, suggesting tht the smller events my not follow the sme triggering processes s lrger events (see Fig. 3, b). 4. For the two prmeters tht describe the sptil evolution of rupture re (d s nd Dr qusi ), the distributions for swrm-type nd ftershock-type

17 Anlysis of Foreshock Sequences in Cliforni clusters re indistinguishble in the synthetic ctlog, while observtions find swrm-type clusters hve higher d s nd lower Dr qusi. This suggests tht the grdul sptil expnsion observed for swrmy clusters is not produced from triggering models with pure power-lw sptil temporl decy (see Fig. 4b, d). 5. The skew of moment relese history grees with the temporl distribution of mgnitude. The synthetic ctlogs hve different distributions between swrm-type nd ftershock-type clusters, which is consistent with observtions. The exct forms of the CDFs differ from observtions, perhps due to regionl diversities of triggering prmeters (see Fig. 4c) % of the synthetic ctlogs (8 out of ctlogs) hve t lest 3 clusters with more thn 3 foreshocks (the minimum number to estimte foreshock re) nd find strong correltion between F re nd N fore, suggesting tht the observed correltion could be reproduced from simultion by rndom chnce. The correltion between F re nd M f mx is less sttisticlly significnt. These results depend to some extent on the prmeter choices for our triggering model. One could increse the clustering nd the number of foreshocks in the synthetic ctlogs by incresing the ftershock productivity Q. However, s discussed in SHEARER (22, b) this would result in ctlogs tht violte Bth s lw, nd, t lrger vlues of Q, runwy explosions of seismicity. In ny cse, even if the number of clusters nd foreshocks in the synthetic ctlogs could be incresed, the synthetic clusters would not show the sptil evolution nd temporl skewness distributions of our observed clusters. Overll, comprisons between synthetic ctlogs nd observtions in southern Cliforni suggests tht the swrmy fetures in the rel ctlog re not well reproduced from ETAS-like simultions. The foreshock occurrence rte is too low to be consistent with observtions, nd the distributions of the mgnitude difference between minshocks nd foreshocks is sttisticlly different from observtions for smll minshocks. This is consistent with results documented by SHEARER (22b) for M 2.5 to 5.5 minshocks in southern Cliforni, in which the foreshock-to-ftershock rtio is observed to be too lrge to be consistent with Båth s lw, nd suggests tht the observed foreshock rte cnnot be explined entirely with erthquke-to-erthquke triggering models with expected rtes of ftershock productivity. 5. Discussion nd Conclusions Our nlysis pproch is similr to the VIDALE nd SHEARER (26) study of erthquke bursts, which considers the reltive independence of the clusters from other minshocks. Although this pproch my miss some events due to the selection criteri, the erthqukes selected should represent bckground ctivity tht is lrgely free of stress chnges nd other trnsient effects from lrger events. Our foreshock sttistics re generlly consistent with previous observtions (e.g., ABERCROMBIE nd MORI 996) nd indicte tht foreshock occurrence rtes: () depend on fulting type, minshocks in trnstension setting tend to hve more foreshocks compred with minshocks in trnspression regime; (2) depend on minshock depth, shllow minshocks tend to hve more foreshocks. We observe this behvior for both retrospective serches of foreshocks of M 5 erthqukes, nd prospective serches of rndom clusters. The dependence of clustering type on focl mechnism ws lso noted in our study focusing on crustl bursts (CHEN et l. 22); however, the depth dependence ws not explored in tht study, s the mjority of bursts occur t shllow depth. The observed fulting type nd depth dependence is consistent with theories relted to stress loding during erthquke cycle, where the loding style depends on the regionl stress field (SIBSON 993). For pure norml fults, loding-wekening mechnism, where the sher strength reduces with stress loding, is expected; while for reverse fults, loding-strengthening mechnism is expected. For strike slip fults, depending on the ctul stress vlues, both mechnisms re possible, in which the style chnges progressively from loding-wekening to loding-strengthening s fulting type chnges from trnstension to trnspression sttus. If the men