Foreshock probabilities in New Zealand

Transcription

1 New Zealand Journal of Geology & Geophyscs, 2000, Vol. 43: 461^ /00/ $7.00/0 The Royal Socety of New Zealand Foreshock probabltes n New Zealand MARTHA K. SAVAGE STEPHAN H. RUPP* School of Earth Scences and School of Chemcal and Physcal Scences Vctora Unversty of Wellngton P.O. Box 600 Wellngton, New Zealand *Present address: Industral Research Ltd, P.O. Box 31310, Lower Hutt, New Zealand. Abstract An event that s not already part of an aftershock sequence s consdered a foreshock f t s followed by an equal or larger earthquake wthn 5 days and 30 km. The lkelhood that an apparently solated event (shallower than 40 km and greater than magntude 5.0) n New Zealand s a foreshock averages 4.5 ± 0.7%. If the manshock s requred to have a magntude at least one unt greater than the foreshock, the probablty drops to 0.8 ± 0.3%. Lttle dfference n foreshock probablty s notceable between two dfferent aftershock-removal wndows, between dfferent magntude ranges, or between dfferent tme perods. However, events deeper than 40 km yeld probabltes that depend on magntude and also on aftershock-removal parameters, suggestng that clusterng of deep earthquakes occurs va a dfferent process from that n shallow earthquakes. For shallow earthquakes, the results are consstent wth a model n whch foreshocks are manfestatons of the same process as aftershocks. Keywords foreshocks; sesmcty; deep earthquakes; shallow earthquakes; New Zealand; aftershock removal INTRODUCTION New Zealand s regularly shaken by moderate earthquakes (Fg. 1), and a queston arses as to whether a medum-szed event could be followed soon by a larger, more damagng one. If the probablty of such an occurrence s known to be hgh, smple measures could be taken by emergency nsttutons, and ndvduals mght take useful precautons. Earthquake predcton and the analyss of foreshocks and earthquake swarms have been topcs of major research. Smth (1981) found that 6 out of 8 magntude (M L ) c. 6 events n New Zealand were preceded by smaller earthquakes wthn 30 days before, and wthn 50 km of, the manshock. The rate s too hgh to be descrbed by chance. Further, he ndcated that many proposed foreshocks occur less than 24 h before the manshock. However, hs study G99041 Receved 30 August 1999; accepted 31 May 2000 could not determne the nverse queston of, gven an event, how lkely s t to be a foreshock of a bgger event? Evson & Rhoades (1993,1997) determned that swarms or clusters of swarms may precede manshocks by perods of several years to tens of years, and they are currently testng ther model relatve to a Posson model. However, ths swarm hypothess can not provde any nformaton on a short tmescale of weeks or days. Chong (1983) examned condtonal probabltes of foreshocks and aftershocks of New Zealand earthquakes, fndng strong clusterng, such that many earthquakes were preceded and followed by larger events closely n tme and dstance. He dd not remove aftershocks from the catalogue, however, so that many of the smaller events followed by larger events were part of other aftershock sequences. Jones (1985) nvestgated foreshocks n Southern Calforna. Her results showed that the probablty that a M L > 3 event s followed by a larger earthquake wthn 5 days and 10 km s c. 6%, f the event s not already part of an aftershock sequence. She also found that manshocks mostly occur wthn 24 h of the proposed foreshock. A smlar study by Savage & DePolo (1993) n the Great-Basn and Serra Nevada regon obtaned a 10% probablty for an M L > 3 event to be followed by a manshock n the volcanc Mammoth/Mono Lake regon, and 6% for the Nevada area, respectvely. These deas have been taken further. Agnew & Jones (1991) examned the condtonal probablty for earthquakes occurrng wthn gven fault zones. Console et al. (1993) consdered foreshocks occurrng after perods of quescence. The relatonshps between clusters of earthquakes and later ones as a functon of cluster locaton and sze are also examned (Ogata et al. 1995; Maeda 1996). Reasenberg & Jones (1989, 1994) suggested that foreshocks are smply extensons of aftershock occurrences, and they showed that foreshock rates can be determned from aftershock parameters. The assumpton of the smlarty of foreshocks and aftershocks s also bult nto the statstcal models of Ogata (e.g., 1983, 1989, 1992). Jones et al. (n press) formalsed the hypothess, and suggested that, except for thrust faultng, foreshock occurrence rates can be determned from aftershock parameters (.e., that foreshocks could be manshocks whose aftershocks happen to be bg). However, n thrustng earthquakes n Italy, fewer than the expected number of foreshocks occur (Jones et al. n press). Some of these deas have been adopted to produce real-tme hazard maps (e.g., Kagan & Jackson 1994). The tectonc regme of New Zealand contans strke-slp and normal events as well as thrustng events, and may therefore behave dfferently from Calforna and Italy. Ths paper follows the approach that Jones (1985) and Savage & DePolo (1993) appled n the western Unted States to New Zealand. The smple technque provdes a baselne wth whch to compare more sophstcated analyses of the occurrence of foreshocks.

2 462 New Zealand Journal of Geology and Geophyscs, 2000, Vol E 165'E 170'E E 180" 175"W 16S - E E 175'E 180" 175"W 30 - S sesmcty ' '. ' aftershocks removed 3O'S 35"S r; Vv IP?" > 40'S J 40'S f 45'S *3BP # 45"S 50'S..^S SO'S Fg. 1 Sesmcty n New Zealand. Left: All earthquakes consdered n the catalogue. Rght: Catalogue after aftershocks were removed. Dashed box shows restrcted area used to compare the effect of ncludng only the better locatons. Lne shows secton along whch Fg. 2 s projected. DATA AND METHOD For calculatng the foreshock probabltes, we use the New Zealand earthquake catalogue from the Insttute of Geologcal & Nuclear Scences, Wellngton, from 1951 through November We use local magntude M (Inst. Geol. & Nucl. Sc. Scence Report 1991). Detals are gven n Rupp (1995). Durng the 1960s and early 1970s the number of recordng statons ncreased sgnfcantly n New Zealand. Due to ths ncrease n recordng statons wth more sophstcated equpment, the number of regstered earthquakes has ncreased also. A magntude cut-off threshold (Me) s found from manual examnaton of the magntude/frequency plot for consecutve tme perods. The threshold s determned by the pont where the lnear relatonshp between log (AO and magntude M starts to cease. A^s here defned as the number of earthquakes greater than the correspondent magntude. Above the threshold, the data are consdered to be complete. We use M c = 4.8 for , and 3.8 for 1981-present); the same cut-off s used for all depths (see plots n Rupp 1995). In calculatng the foreshock probabltes, aftershocks must be removed fully from the earthquake catalogue. An earthquake s often followed by a seres of aftershocks wth smaller magntudes. The algorthm that s appled to fnd foreshock/manshock pars would recognse any aftershock followed by a larger aftershock as a foreshock/manshock event. Ths, of course, would gve a hgher value for the probabltes than one would get wth all aftershocks properly removed. For example, f there s a local earthquake seres wth ncreasng tme order and magntudes of 4.8, 4.0, 4.4, 4.0, and 5.5, the events 4.0, 4.4, 4.0 should be dentfed as aftershocks related to the frst event and consequently be removed from further consderaton. The 5.5 event would later be nterpreted as a manshock followng the 4.8 foreshock. Ths removal algorthm results n a catalogue that s useful for calculatng the rate of foreshocks, but wll not be useful for determnng how many foreshocks precede a manshock. We use the Gardner & Knopoff (1974) method to fnd aftershocks n an earthquake catalogue. It was found to be more stable than other methods for removng aftershocks from the Nevada earthquake catalogue, where completeness levels vared wth space and tme (Savage & depolo 1993). For each event, we look for earthquakes wthn a magntude-dependent space-tme wndow (Table 1). Earthquakes wth magntude smaller than the orgnal event occurrng durng the wndow are deemed to be aftershocks, are gven a sequence number and letter n the man catalogue, and are Table 1 Tme and dstance wndows used to remove aftershocks from the catalogue. M L Dstance (km) Tme (days)

3 Savage & Rupp Foreshock probabltes n NZ 463 All events depth<40km 1990 Aftershock-free catalogue depth<40km A Y v W Q + * + + z * + X u + S R + * All events depth>120 km Aftershock-free catalogue depth >120 km z *;» f ^ x 120 " Fg. 2 The 1990 orgnal (left) and aftershock-free {rght) catalogues plotted as a space-tme dagram, along projecton gven n Fg. 1. Top: Depths <40 km. Bottom: Depths >120 km. Events that are not related to any aftersocks are represented by a (+). All earthquakes belongng to an aftershock sequence are ndcated wth a letter; the sze represents the magntude. Dfferent sequences can have the same letter, snce there are only 26 characters n the alphabet, but they can be dstngushed by ther tme and space separaton. An example of an aftershock seres s ndcated by the letters N and O (top). These represent the magntude 5.8 Tennyson earthquake of 1990 February 10 and ts magntude 4.2 foreshock. The space-tme wndow used for aftershock assocaton for the Tennyson earthquake s shown by the long rectangle. In the aftershock-free catalogue, only the two events are left. Crosses wthn the rectangle represent earthquakes that are outsde the wndow but whose projectons are wthn the wndow. Deep earthquakes are numerous but not as strongly clustered as the shallow events. The aftershock removal programme s evdently removng a large proporton of background actvty. removed from the aftershock-free catalogue (Fg. 2). The wndow s modfed from those publshed by Gardner & Knopoff (1974) to take nto account the New Zealand envronment, usng aftershock areas and tme duratons determned by Gbowcz (1973) and Evson & Rhodes (1993) for swarms, multplets, and manshock/aftershock sequences of New Zealand earthquakes (Rupp & Savage 1995). We plotted a graph of swarm and aftershock dstrbuton rad as a functon of magntude (not shown here), and used as our dstance wndow the lne that acted as the envelope below whch all the ponts fell. Usng a doubled wndow, correspondng to the dameter nstead of the radus, yelded smlar results, but more events were consdered aftershocks, so that fewer events were left for analyss, and the error bars were larger (Rupp & Savage 1995). The tme wndow follows Gardner & Knopoff (1974), but wth extended tme ntervals for magntude 7 and hgher events. An envelope above the tme for background sesmcty to drop to less than one event per 10 days s the tme lmt for the wndow, and s gven n Table 1. Ths envelope s conservatve and may force out some events that are not true aftershocks. In partcular, f n some areas the average tme between events s greater than the wndow (e.g., 42 days for MA), then the model may msbehave (see, e.g., secton on deep earthquakes below). To remove aftershocks of events pror to the start of our catalogue, we run the aftershock removal programme through the catalogue from 1920 through 1994, and cut events before 1951 for the foreshock probablty study. The aftershock removal programme starts on the frst earthquake of the catalogue and contnues n chronologcal order of the regstered events. The result of ths algorthm s an aftershock-free catalogue. It contans two classes of events: those that are not assocated wth any other earthquakes, and the equal or ncreasng magntude earthquakes n a seres of closely located events. Thus, ths method s not able to gve vald nformaton about the dstrbuton of aftershocks wthn a cluster tself. Fgure 2

4 464 New Zealand Journal of Geology and Geophyscs, 2000, Vol. 43 shows the 1990 catalogue before and after the removal of aftershocks on a tme-dstance plot. Table 2 gves the number of events n catalogues for three depth ntervals, before and after aftershock removal. A second space-tme wndow represents a dstance n space and tme for each event of the aftershock-free catalogue n whch a greater or equal event s consdered to be a manshock. Its sze s defned separately from the one used to fnd aftershocks. We choose the same 5 day wndow used by Jones (1985). We follow Console et al. (1993) n usng a space wndow of 30 km, because of more dffuse sesmcty and poorer locaton accuracy n our catalogue compared to that n southern Calforna, where Jones (1985) used a space wndow of 10 km. Another choce would have been to use a dstance wndow that depends on magntude, but to keep our results comparable to prevous work, we keep a constant nterval. Subducton-related earthquakes may have a dfferent cause than the shallow earthquakes for whch most smlar studes have been carred out. Therefore, we sort both the orgnal and the aftershock-free catalogue nto three dfferent depth ranges: 0^0, , and >120 km. In general, a foreshock s an earthquake of smaller or equal magntude precedng the manshock wthn a defned dstance and tme nterval. Because magntude calculatons are not precse, however, there wll always be an uncertanty as to the true magntude of an event, and therefore how to classfy a par of events. For example, f an earthquake of magntude 4.2 s followed by an earthquake of magntude 4.1, our aftershock removal program wll consder t to be a manshock/aftershock sequence, but f the frst earthquakes' magntude were 4.0, t would be consdered a foreshock/ manshock par. In addton, earthquakes n the early part of the catalogue wll have less accurate magntudes than later events due to fewer statons beng avalable. Furthermore, we do not have enough events to acheve statstcal valdty f we consder earthquakes n only 0.1 unt ntervals. Thus, we follow Savage & depolo (1993) and round our magntudes to the nearest 0.5 unt to make the foreshock/ manshock probablty calculatons. We also follow Jones (1985) and Savage & depolo (1993) by treatng the earthquakes n three categores: (1) those "foreshocks" wth equal or greater magntude events followng, whch wll nclude swarms and probably also some msdentfed manshock/aftershock pars wth close magntude dfferences between the manshock and aftershock; (2) those wth rounded magntudes separated by more than 0.5 unts; and (3) those wth a full magntude between the proposed foreshock and manshock. The condtonal probablty that a manshock wll occur, gven that an earthquake has already occurred, s obtaned from the data of the earthquake catalogue. It s assumed that the probabltes have not changed sgnfcantly snce The probablty s then smply the frequency of occurrence of foreshock/manshockpars n the catalogue (Jones 1985). Table 2 Number of events n the catalogue. Catalogue Intal/Aftershocks M>3.8 M>4.& Depth 0-40 km Depth km Depth > 120 km 5538/ / / / / /1053 removed M> /103 16/16 127/104 If the probabltes change wth tme, we wll be calculatng the average probablty over the tme. Each half unt n the rounded catalogue s examned to see how many tmes t occurred (N), and how many tmes t was followed by an event wth equal or larger rounded magntude (n). We defne the probablty by the smple bnomal model: the probablty of occurrence p s gven by/? = (n/n) and as long as N > 0, the standard devaton (o)s gven byct = [p(l-p)/n] 1/2 (e.g., Bevngton 1969). Smlar procedures are followed for probabltes for cases (2) and (3) above. For evaluatng the probabltes, the normal background actvty must be consdered. Probabltes are calculated n two ways. One estmate s calculated on the bass of aftershock-free data from 1987 to 1994, durng whch perod unform procedures were followed to locate earthquakes. Consder the number of events (M = 796) wth rounded magntude above 4.0, and the area (A = 8.3 x m 2 ) for whch the catalogue s approxmately complete. D s the number of days n the catalogue (D = 2891). Then the background probablty (BG) of a magntude 4.0 or greater event occurrng n any gven crcle of radus r = 30 km and 5 days s: BG = (SMnr^yDA = 0.47%. Smlar calculatons are performed for larger magntudes. Ths method has the advantage of beng smple, but assumes a unform dstrbuton of sesmcty n space, whch s obvously not true (Fg. 1). As an alternatve method of calculatng the background probablty that uses a more realstc spatal dstrbuton, we also evaluate the probabltes by the followng procedure: we use the locatons and magntudes from the catalogue, but randomly re-order the earthquake occurrence tmes. Then the probabltes are calculated from the catalogue wth randomsed tmes, usng the same programs and parameters used for the true catalogue. We do ths for fve realsatons of the random catalogue and report the averages and ranges here (see Table 4). RESULTS The aftershock removal programme removes a substantal fracton of the catalogue for all depth ranges (Fg. 1, Table 2). The wndow leaves only 45% of the catalogue for shallow and deep events, and 60% of the catalogue for ntermedate-depth earthquakes. Proportonally fewer larger events have been removed than smaller events. For example, for events above magntude 5.8, >80% of the earthquakes reman at all depth ntervals. Ths bases the ^-values for the catalogue wth aftershocks removed from the standard Gutenberg-Rchter law. For shallow earthquakes, the probablty of a manshock occurrng, gven that a moderate earthquake has already occurred, yelds slghtly hgher values at magntudes <5 than those >5; however, the error bars are consstent wth the probabltes beng constant wth foreshock magntude (Fg. 3; Table 3). Because of ths dfference, and the larger numbers of smaller events, the averages (last three rows n Table 3) vary slghtly dependng on the averagng method. Includng all earthquakes wth rounded magntude 4.0 or hgher, there s a 5.3 ± 0.5% probablty of an event beng followed by an equal or larger event wthn 5 days and 30 km, 2.1 ± 0.3% probablty of beng followed by an event magntude 0.5 or more hgher, and 0.6 ± 0.2% probablty of an event one or more magntude unts hgher. These numbers drop to 4.5 ± 0.7%, 1.5 ± 0.4%, and 0.8 ± 0.53%,

5 Savage & Rupp Foreshock probabltes n NZ ] Depth km 1 T r- Mm>=Mf Mm>=Mf+0.5 Mm>=Mf Depth < 40 km before fr- T T r r _ ( ) > ( r Depth < 40 km after 1980 I, 1 T 1 T T" t Depth < 40 km restrcted area Foreshock magntude * e Foreshock magntude Fg. 3 Foreshock probabltes as a functon of magntude for the three depth ntervals examned. Crcles: Probablty that a foreshock wll be followed by an equal or larger event. Crosses: Probablty that a foreshock wll be followed by an event at least 0.5 magntude unts hgher. Stars: Probablty that a foreshock wll be followed by an event one magntude unt larger. Labelled panels show depth nterval used. Left panels nclude all events n the catalogue. The top two rght panels separate the catalogue nto events occurrng before and after 1980, whle bottom rght panel shows results for events occurrng wthn the restrcted box shown n Fg

6 466 New Zealand Journal of Geology and Geophyscs, 2000, Vol. 43 Table 3 Condtonal probabltes (P) n percent for a manshock of magntude Mm to follow a foreshock of magntude A^f wthn 5 days and 30 km. P, n, N, and standard devatons, defned n the text, are gven n three categores. These are manshocks greater than the foreshock by 0.0, 0.5, and 1.0 unts. "Avg" s the mean of all the results for ndvdual magntude wndows, whle "M>5.0" and "all" represent averages calculated by usng the same formulas as for the ndvdual magntude ranges. All three averagng methods yeld smlar results. There are more events wth magntude >5.0 than 4.5 because of the magntude 5.0 cut-off used from 1951 through Mf (M L ) Avg M>5 All N P(Mm>Mf) n P(%) ± ± ± ±0.5 P(Mm>Mf+0.50) n ± ± ± ± ± ± ±0.3 n P(Mm>Mf+\) 0.8 ±0.3 0±0 0.6 ± ±0 0.6 ± ± ± 0.2 respectvely, for potental foreshocks of magntude 5.0 or greater (Table 3). Further tests were made to see f the varaton n completeness wth tme was affectng the data, and f areas of poorer coverage were gvng dfferent values (Fg. 3). To examne the tme dependence, we calculate probabltes usng the shallow catalogue separated nto two tme perods, and (Fg. 3). Wthn the error bars, there s lttle dfference between the two tme wndows. To examne the effect of coverage, we used a subset of the catalogue that manly ncluded events onshore (Fg. 1,3). Agan, there s lttle dfference between these values and the other subsets. The probabltes are smlar for all shallow catalogue subsets, except that the error bars are ncreased due to the smaller number of events. Therefore, we report only the results for the full catalogue n Table 3. Deeper earthquakes, however, show unexpectedly large (6%) probabltes at low magntude, and strong dependence on magntude (Fg. 3). DISCUSSION Shallow earthquakes The smlarty of probabltes for shallow events at most magntudes, and for all subsets of the catalogue, suggests that the most accurate probabltes wll come from usng the largest catalogue (.e., the entre tme and dstance range avalable). However, there s a possblty that the somewhat hgher probabltes for magntudes 4 and 4.5 events wll bas the results because of the larger numbers of events n those ranges. Thus, for the rest of the dscusson, we use the ndvdual probablty calculatons for magntudes 4 and 4.5, and the combned probablty (lne M > 5 n Table 3) for events wth magntudes 5 and above. Thus, f a magntude 5 or greater earthquake s recorded that s not already assocated wth an aftershock sequence, there s a 4.5 ± 0.7% probablty of an equal or larger event wthn 5 days and 30 km, % probablty of an event of magntude 0.5 or more hgher, and 0.8 ± 0.3% probablty of an event one or more magntude unts hgher. Deep earthquakes The apparent strong dependence of foreshock probablty on magntude for deep events may be caused by dfferent clusterng characterstcs for deep events. A strong decrease of foreshock probablty for ncreasng magntude was seen for shallow earthquakes when aftershocks were not removed before the calculaton, and when smaller wndows were used n the aftershock removal routne. Savage & depolo (1993) found a smlar behavour when they examned results usng the Reasenberg (1985) declusterng method. We follow them n suggestng that, when aftershocks are not removed, the observed dependence of probablty on magntude s consstent wth the Gutenberg-Rchter relaton. Further support for ths suggeston comes from the same trend beng apparent n the tme-randomsed catalogue (Table 4). Deep events n New Zealand have long been noted as yeldng dfferent clusterng than shallow events (e.g., Vere-Jones et al. 1964). The apparently hgher probablty of manshocks after moderate events (Fg. 3) may be another manfestaton of ths phenomenon. Stock (pers. comm. 1999) found that the dstrbuton of deep events s more unform n tme than for shallow events. The large number of events consdered as aftershocks (Table 2) may therefore be a consequence of ths more unform dstrbuton. Perhaps deep earthquakes occur often enough and close enough together, that the wndows used to determne f an event s an aftershock are large enough to allow the deep earthquakes to be consdered as aftershocks, even though they represent a more contnuous energy release. The shallow catalogue exhbts clusterng, wth a large number of events occurrng close together n tme and space and gradually decreasng n frequency over tme (Fg. 2). In contrast, the deep catalogue s more evenly dstrbuted to start wth. The aftershock removal programme has removed some of ths dstrbuted sesmcty by the use of large tme wndows (Table 1). Table 4 Condtonal probabltes (%) calculated as n Table 3, but for the average of fve realsatons of the catalogue wth randomsed tmes. Parentheses gve lower and upper ranges for the realsatons. No earthquakes of magntude 5.5 or hgher were followed by equal or larger events wthn the requred tme ntervals n the catalogues wth randomsed tmes. Mf P(Mm>Mf) P{Mm>Mf+0.50) P(Mm>Mf+\) ( ) ( ) (0-0.57) 0.39 ( ) 0.21 ( ) 0.11 (0-0.19) 0.17( ) 0.18(0-0.35) 0.038(0-0.19)

7 Savage & Rupp Foreshock probabltes n NZ 467 Comparson to other studes Chong (1983) examned the New Zealand earthquake catalogue from 1964 through 1982, and found that earthquakes between magntude 4.0 and 5.0 were followed by earthquakes wthn 5 days and 9 km 2000 tmes more often than expected from a Posson process. However, these results nclude aftershocks and are therefore not drectly comparable to our results. For shallow earthquakes, a smlar lack of dependence on magntude, but slghtly hgher probabltes, was found n the western Unted States. Wth the same technques n Nevada, probabltes averagng 6.3 ± 0.8% were found for manshocks followng moderate earthquakes wthn 15 km and 10 days (Savage & depolo 1993). 6 ± 0.5% of events were followed by equal or larger earthquakes wthn 10 km and 5 days n southern Calforna (Jones 1985). For magntude 0.5 unts hgher, the respectve comparsons are 3.1 ± 0.6% for Nevada and 5% n Calforna. For 1.0 unts hgher they are 2.1 ± 0.5% for Nevada and 2.5% for Calforna. Stll hgher probabltes of 10% for events followed by equal or larger earthquakes were found n the geothermal Mammoth/Mono regon of eastern Calforna (Savage & depolo 1993). Especally consderng the larger dstance wndow used here, the somewhat smaller probabltes n New Zealand suggest that there are not as many foreshocks as n the western Unted States. These smaller values are smlar to those found n Italy (DLucco et al. 1997). Hgher foreshock occurrence rates of 15% or greater are reported for Japan (e.g., Maeda 1996), but the results are dffcult to compare because they have used dfferent aftershock removal technques and dfferent methods for defnng foreshocks. Reasenberg (1999) found, worldwde, that 7.5% of magntude 5 events are followed by magntude 5 or larger events wthn 7 days and 75 km, and 2.3% are followed by magntude 6 or larger. These numbers are also somewhat larger than the results n New Zealand, but are agan for a wder tme and dstance wndow than ths study. The hgher probabltes found n the Savage & depolo (1993) study for volcanc areas rase the queston of whether the ncluson of swarms from the Taupo Volcanc Zone could be affectng our results (e.g., Sherburn 1992). In that case, the average probabltes n the rest of New Zealand mght be smaller than we report. Comparson to aftershock occurrence rates Several nvestgators (Reasenberg & Jones 1989, 1994; Ogata 1992; Reasenberg 1999) suggest that foreshock occurrence probabltes should be gven by extrapolatng the aftershock occurrence probabltes to larger "aftershocks". We can test ths n New Zealand. Eberhart-Phllps (1998) presented aftershock sequence parameters based on the Reasenberg (1985) declusterng analyss for 17 manshocks wth magntude Mm > 5.5. The expected rate of aftershocks of magntude M or larger, at tme t (n days) followng a manshock Mm wll be: R(t,M) = 10 [fl + * ( - Mm - M) \t + C)~P Here a, b, c, and/? are parameters that are ft separately for each sequence Eberhart-Phllps determned averages of a = -1.66, b = 1.03, c = 0.03, and/? = We use these parameters together wth the expresson for probablty gven by Reasenberg & Jones (1989, 1994): P = 1 - exp[-lr(t,m)dt]. The probabltes depend only on the dfference n magntude between the two events, and for Mm = M, the probablty s 10.7%. For Mm-M = -0.5 (an "aftershock" wth magntude 0.5 hgher than the "manshock"), the probablty s 3.4%, and for Mm-M = -1.0, the probablty s 1.1%. These values are larger than our averages of 4.5, 1.5, and 0.8%, for probabltes of an event beng followed by another event wth magntude equal or greater, 0.5 unts or greater, and 1.0 unts or greater than the frst event, respectvely. The range of foreshock probabltes allowed by the aftershock statstcs s extremely large. Usng the parameters publshed for each of the 17 earthquake sequences (Eberhart- Phllps 1998), the range of probabltes s from , , and % for the three categores of foreshocks. Thus, our results are consstent wth models n whch foreshocks are a manfestaton of the same process as aftershocks, but the huge range allowed makes such consstency less meanngful. Warnng the publc Less than 1 n 20 earthquakes wll be followed by larger events, whch seems rather small. Yet, these numbers are qute large when compared to the background probablty that an event would occur n any gven 30 km radus crcle n 5 days. Table 5 shows the rato of the condtonal probablty to the background probablty, sometmes called the probablty gan. Usng the background probabltes calculated from the assumpton of unform spatal dstrbuton, the probablty of a larger event occurrng s c. 10 tmes the background probablty for magntude 4.0 foreshocks, rsng to c. 90 tmes background for magntude 5.0 events. If one compares the aftershocks nstead to the background probabltes determned from the randomsed catalogue, smaller probablty gans are determned. The probabltes from the randomsed catalogue decrease wth ncreasng magntude (Table 4). No magntude 5.5 or hgher events were followed by equal or larger events wthn 30 km and 5 days n any of the fve realsatons. If we use these values as background rates, rather than the unform background values determned above, the lkelhood of a bgger event, gven a magntude 4.0 has occurred, s seven tmes the background probablty. The lkelhood of a magntude 5 event beng followed by another magntude 5 or 6 s c. 20 tmes the background. The rato becomes hgher stll at hgher magntudes, but s undefned n our study snce the random catalogues gave no events wthn the crtera. Table 5 Probablty (n percent) of an event of magntude greater than or equal to the magntude Mm occurrng wthn a crcle of 30 km radus n tme nterval of 5 days followng an event of the gven magntude Mf. ForA/f>4.5, probabltes from lne M>5 n Table 3 are used. Column BG stands for the background probablty of any shallow event not already assocated wth a manshock occurrng gven the sesmcty rate durng and assumng a unform spatal dstrbuton of earthquakes. Numbers n parentheses are the factors by whch the probablty s greater than the background, usng BG before the colon, and the average probablty from Table 4 after the colon. Mm BG (%) Mf= 4.0 Mf= 5.0 Mf= (15:5) (13:7) 4.5 (87:20) 0.8 (100:21) 4.5 (550: «.)

8 468 New Zealand Journal of Geology and Geophyscs, 2000, Vol. 43 Thus, t seems approprate to warn the publc about the possblty of more damagng events after magntude 5.0 or larger earthquakes. Warnngs for a proposed foreshock would be best taken from the probabltes for events 0.5 and hgher or 1.0 and hgher; probabltes of smlarmagntude events are probably best descrbed by the aftershock occurrence rates gven above n the comparson wth Eberhart-Phllps's results (probablty of 11%). Dependng on how background probabltes are calculated, f an earthquake of magntude 5.0 occurs, there s between 20 and 100 tmes greater lkelhood of a more damagng earthquake than the background probablty. Snce magntude 5.0 events themselves may cause some damage, we feel that t s approprate to warn the publc after such an event. We feel t s wrong to reassure them that there s no hgher rsk. On the other hand, we feel the publc mght msunderstand and be unduly alarmed f such fgures as "100 tmes the background probablty" are used. In addton, there s the possblty of regonal varaton n foreshock rates that could affect dfferent areas n dfferent ways; moreover, ntal earthquake locatons n many areas can be more than 30 km from the fnal locatons. Thus, we advocate answerng concerned ctzens' questons straghtforwardly, such as the followng statement: "We can't say for sure whether or not another damagng earthquake wll occur. But we do know that on average n New Zealand, for every 10 earthquakes lke ths one, one wll be followed soon by an earthquake about the same sze, but only one n 65 wll be followed soon by an earthquake that s substantally bgger (a magntude 0.5 unts hgher). The lkelhood of bgger earthquakes wll decrease wth tme, and wll be back to normal wthn a few days. We consder ths a good wake-up call to remnd people to check that ther earthquake preparedness measures are up-to-date." CONCLUSIONS Applyng the Gardner & Knopoff (1974) method of removng aftershocks, usng tme and space wndows modfed for the New Zealand earthquake dstrbuton, an average of 4.5 ± 0.4% of magntude 5+ earthquakes that were not prevously part of an aftershock sequence are followed by an equal or larger earthquake. Ths percentage drops to 1.5 ± 0.4% f the larger earthquake has a magntude 0.5 unts or greater than the foreshock, and to 0.8 ± 0.3% for earthquakes one or more unts greater. The percentages may ncrease slghtly wth smaller foreshock magntudes. The percentages can be drectly translated nto probabltes. These probabltes are consstent wth aftershock statstcs, and wth the model that foreshocks and aftershocks are manfestatons of the same process. When a magntude 5.0 or greater event occurs, the probablty that another 5.0 or greater event wll occur soon s tmes hgher than the normal background probablty. Magntude 5.0 earthquakes are also at the threshold for whch damage can become mportant. Thus, we suggest that, at ths level, t may be useful to warn the publc and emergency management agences about the possblty of a damagng event occurrng. Because of the smlarty between foreshocks and aftershocks, the tme dependence of the warnng could be found from Eberhart-Phllps's (1998) publshed aftershock occurrence decay rates. ACKNOWLEDGMENTS Dscussons wth Euan Smth, John Taber, Frank Evson, and Davd Vere-Jones were nvaluable n ths study. A. Merrfeld randomsed the tmes for the catalogues used to calculate background probabltes. D. Vere-Jones and E. Smth revewed the paper. Ths study has been partally supported by a subcontract to the Foundaton for Research, Scence and Technology grant number 98-GNS for the Insttute of Geologcal & Nuclear Scences. Warwck Smth provded the New Zealand earthquake catalogue for the Insttute of Geologcal & Nuclear Scences, Wellngton. Fgures were drafted usng the GMT package of Wessel & Smth (1995). REFERENCES Agnew, D. C; Jones, L. M. 1991: Predcton probabltes from foreshocks. Journal of Geophyscal Research 96: Bevngton, P. R. 1969: Data reducton and error analyss for the physcal scences. New York, McGraw-Hll. Chong, F. S. 1983: Tme-space-magntude nterdependence of upper crustal earthquakes n the man sesmc regon of New Zealand. New Zealand Journal of Geology and Geophyscs 26: Console, R.; Murru, M.; Alessandrn, B. 1993: Foreshock statstcs and ther possble relatonshp to earthquake predcton n the Italan regon. 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