FORESHOCK PROBABILITIES IN THE WESTERN GREAT-BASIN EASTERN SIERRA NEVADA BY M. K. SAVAGE AND D. M. DEPOLO

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1 Bulletin of the Seismological Society of America, Vol. 83, No. 6, pp , December 1993 FORESHOCK PROBABILITIES IN THE WESTERN GREAT-BASIN EASTERN SIERRA NEVADA BY M. K. SAVAGE AND D. M. DEPOLO ABSTRACT We quantify foreshock occurrence probabilities by applying the empirical technique of Jones (1985) to the western Nevada and eastern California earthquake catalog compiled by the University of Nevada, Reno, from 1934 through The foreshock occurrence rates depend heavily on the parameters used to remove aftershocks from the catalog. It is necessary to separate the Mammoth/Mono region from the rest of the catalog to determine the parameters that most effectively remove the affershocks from the catalog. The probability that an M > 3.0 earthquake will be followed by an earthquake of larger magnitude within 5 days and 10 km is 10% in the Mammoth/Mono region and 6% in the Nevada region, and seems to be independent of the magnitude of the proposed foreshock. The probability that an earthquake will be followed by another one at least one magnitude unit larger is 1 to 2% in each region. These probabilities imply that the occurrence of an earthquake M > 4.0 increases the possibility of a damaging earthquake of M > 5.0 by several orders of magnitude above the low background probability. Most mainshocks occur within a few hours after a possible foreshock, and the probability that a mainshock will still occur decreases logarithmically with time after the proposed foreshock. These foreshock properties are similar to those in southern California and in other parts of the world, with the exception that the Mammoth / Mono region, a volcanic area, exhibits more swarm-like behavior than does the southern California or Nevada region. INTRODUCTION When a moderate earthquake is felt, one of the first things most people want to know is whether a larger one will soon follow. The U.S. Geological Survey and the California Earthquake Prediction Evaluation Council have recently employed time-dependent earthquake hazard evaluation (e.g., Reasenberg and Jones, 1989; Jones, 1990; Agnew and Jones, 1991) in order to inform emergency management personnel and the public of the possibility that a moderate earthquake could be a foreshock to a much more damaging earthquake. The University of Nevada, Reno, Seismological Laboratory (UNRSL) and the Nevada Division of Emergency management would like to be able to perform a similar service for the people in Nevada. However, the tectonic setting of the northern Basin and Range, an extensional region of diffuse seismicity that encompasses parts of eastern California as well as Nevada and much of Utah, is quite different from the strike-slip, plate-boundary setting in western California, in which most of the earthquakes occur along a single fault or a set of faults. Therefore the probability that a given earthquake in the Basin and Range will be a foreshock to a larger earthquake could be significantly different from the values determined using the California catalog (Jones, 1985). Indeed, it has been suggested that the Basin and Range has a higher incidence of foreshocks than does southern California (Doser, 1990). We present herein appropriate 1910

2 FORESHOCK IN GREAT-BASIN AND SIERRA NEVADA 1911 figures for the Nevada and eastern California region based on the UNRSL earthquake catalog. DATA The data set for our study consists of the UNRSL earthquake catalog from 1934 to Some of this catalog has been summarized by Jones (1975) and by Corbett (written communication, 1985). The years before 1961 were compiled by Slemmons et al. (1965) who augmented the Townley-Allen (1939) "Descriptive Catalog of Earthquakes of the Pacific Coast of the United States, " with several other sources including the United States Coast and Geodetic Survey Bulletins, the Seismological Society of America Bulletins, and earthquake catalogs compiled by the California State Division of Water Resources, the University of California Seismographic Station at Berkeley, and the California Institute of Technology Seismological Laboratory. Other sources for early data included a Wiechert smoked-paper recorder operated semicontinuously from 1916 to 1959 by UNRSL, which gave reliable S-P times and Richter magnitudes, and early newspapers archived in the University of Nevada, Reno, library and the University of California, Berkeley, Bancroft Library. Although the early catalog can never be considered complete, Slemmons et al. (1965) believed that the early catalog contains all known events with felt reports and those instrumentally determined events that have magnitudes of 4.0 or greater. Data from 1961 through 1963 were compiled by personnel at UNR, using locations from the University of California at Berkeley, supplemented by readings from a station operating in Reno, and two installed in Golconda and Tonopah in Data from 1964 through 1969 was provided by the U.S. Geological Survey, Denver in 1988, from the database used for a seismicity map of North America (Engdahl and Rinehart, 1988; 1991). Since 1970, locations have been determined by UNRSL personnel from stations operated by the UNRSL, and have been published in periodic bulletins (e.g., depolo et al., 1992). Two other catalogs that include Great Basin earthquakes are available: the Utah region (e.g., Smith and Arabasz, 1991; Arabasz et al., 1992) and the southern Great Basin in the region surrounding the Nevada Test Site (Gomberg, 1991; Rogers et al., 1987; Gawthrop and Carr, 1988). The Gawthrop and Carr (1988) catalog overlaps the UNRSL catalog for the time period 1931 to 1974 and uses some of the same sources (in particular, the Slemmons et al catalog is used as a base). A full analysis of Basin and Range hazard would include these catalogs; we have not included them in our analysis because the catalogs would need to be treated separately, as we have already had to do for the Mammoth/Mono region within the UNRSL catalog. Arabasz (personal comm., 1993) is performing such an analysis for the Utah catalog. Figure 1 shows sample station configurations at the beginning of the network (1970 to 1974) and at present. Although the number of stations in the network has increased, the locations have moved further west so that coverage is now concentrated more in the California/Nevada border region than it was 20 years ago. Since the Mammoth Lakes earthquakes in 1980 and the subsequent earthquake sequences, the UNRSL network has been concentrated in the Mammoth Lakes and Mono Lake region; consequently, the seismicity in the UNRSL catalog has been similarly concentrated. With the variable spatial coverage and completeness levels for this region and for regions outside it, it is necessary to separate the catalog to achieve stable results in the analysis.

3 1912 M.K. SAVAGE AND D. M, DEPOLO I I I I o~o m - o ~eo._it- (/) n- z ~o " = =- /L\~~ =11 ; = '=,'(-.='::" II! t i i e- ~ ~e g~r z,9 o~ I "~ ~ c"

4 . '-.~',..'. FORESHOCK IN GREAT-BASIN AND SIERRA NEVADA 1913 Clustered Cctalog Declusiered Catalog I ~ I I I I I.:...,..~ ~-" -,. i" I" ::.,..'...'"' 38.2 :i \. i i.,:i I, :~',... ~-., , 376 ' '~,':"'" "~ "~'~'c ~'''. 57.l...,,...~\~ ~ i..i I I I I II I I I I I I I lB Km Km (a) MognTtude (b) Mognltude..:..~.%: m Clustered C~talog ' ~ ' ~ 42 ::i, -i.....,:,... - ~,.,..i.,.'~..,... '.. :~ "~,~.'.': ). '..~....,..,,~:,. ; %'.'.':~.:~'~.:.,.,. ". "~, ; ~.'" ".3"k "'~.. ", ' "..' :::... l '". ".~ ~ '..A :",',.'. '.:; ' '. "".~,./ ". i,.,,~-~-~. ~,~i.;.~-'.,..'--.'. ' '1..., '.~.', ~ " / '.". "~: iii.....$7. t':r'~,...,,.=~.....~.2~ z.f " Declustered Cctolog o, 119, ,.. i i, 42 o.: i" ".i+.i..i '.. i "....t" 41 '..fi,." ". " " L~: :." "'~ ~. :..'....;~ :.' y~:..~;/...',..:.~, ~.....,,,..,-:"~,';!i... "' " "-"... '?, m "iii~i...:..:.,.,~..... ~'":".' '.:... '" S " "- "" " '"" "" '.~,}~:~~:~...~, ~:...~..,...,... ~... "..%,'.%:~ ~,'~'.'.';,IF.,.'..~':~_.~.,: ~. " ~ '~".'~..,, ",~ i..,. ~.:I":.~o" -' ~-'"' - "' ', ~ ("~: : ~. : :;',.~.y:,:~l"'.., ', ' :..'. ~ :'.'. '. 39 "~.,:,~.~:,.,T.'~.'.:~. ~.,,_.~.,!2;,'-:.." : "..... ~ $. :. " : - :.~..-:,o : " '~ "'*~'4,.~'...'...".'...: '" '~.'_4~:.'.' "'.. ;",.':.' '~",."i~~.,.[,...~'1~j,'.",,. Y.:.. -.;~:. :.--...".,'-~.. "/ ~"~. '" :- ".: " "- " ~ +36 o. i~ I ~.L"::~,..". '. ". " ~ 3~. lj. ". 0 ~ 100 Km o L ~ o Km Magnitude Magnitude (c) (d) FIG. 2. Events used in this study. (a) All events in Mammoth/Mono area. (b) Events in "declustered" catalog in the Mammoth/Mono area, using the parameters judged best at removing affershocks, with Q = 10, Tma x = 10 days. (c) All events outside Mammoth/Mono area. (d) Events in "deelustered" catalog, using Q 10, z,,axo = 20 days.

5 1914 M. K. SAVAGE AND D. M. DEPOLO Figure 2 shows the locations of earthquakes used in this study and delineates the two regions that are studied. The catalog of earthquakes located outside the Mammoth Lakes/Mono Lake region contains most of the Nevada earthquakes, as well as some other earthquakes in eastern California. For simplicity, we refer to the catalogs as "Mammoth/Mono" and "Nevada" in further discussions. METHOD We follow the method of Jones (1985) to calculate foreshock probabilities from catalog data. This technique is based on the assumption that the foreshock process is stationary; i.e., that foreshocks are as likely to occur in the future as they have in the past. The probability p that an earthquake will be a foreshock is then equal to the percentage of times in the past that an earthquake of similar magnitude was followed soon after by a larger earthquake in close proximity. The standard deviation of the estimate with n data points (Bevington, 1969) is [p(1 - p)/n] 1/2. (1) The small number of earthquakes in our two catalogs yields large error bars (equation 1) when only earthquakes within a given 10th of a magnitude unit are considered. In addition, the early catalog that provides many of our larger events has many magnitudes reported to the nearest 0.5 units. Thus, to calculate foreshock percentages, we round the magnitudes to the nearest 0.5 units. The original magnitudes are used in all other applications, including the statistics of the resultant foreshock/mainshock pairs, as discussed below. Magnitude Completeness Levels We determine completeness thresholds of the catalog by the standard method of visual inspection of magnitude/frequency plots, defining the completeness level as the magnitude where the magnitude-frequency data begin to deviate from a linear relationship (Evernden, 1969). The slope of the magnitude/ frequency plots above the threshold defines the b-value of the catalog used. To be conservative, in our study we assume the catalog is complete to M = 5.0 before 1940 and to 4.0 since We are concerned that, if we included too many early events, the reporting method would bias our results toward higher foreshock probabilities. This is because people are more likely to remember and report feeling a moderate earthquake if it is soon followed by a larger event than if nothing else occurs. Table 1 includes the completeness thresholds and b-values, determined using the maximum likelihood method of Aki (1965) for the years studied. These completeness thresholds are determined for the catalog as a whole and vary considerably from region to region and from time to time due to changes in station coverage and lab personnel, and to increased seismic activity that affects the analysts' ability to keep up with earthquake locations. Although we attempt to be conservative in determining the thresholds, it is likely that the spatial variability has overestimated the thresholds in some of the regions (Gomberg, 1991). This may explain the generally low b-values determined on a yearly basis. When we include only earthquakes with M > 4.0, we find b-values of (1 standard deviation) and for the Mammoth/Mono and Nevada regions, respectively.

6 FORESHOCK IN GREAT-BASIN AND SIERRA NEVADA TABLE 1 CUTOFF MAGNITUDES AND B-VALUES WITH TIME IN NEVADA AND MAMMOTH/MONO 1915 Year Nevada M C Nevada b ( + 1 Cr ) Mammoth/Mono Mc Mammoth/Mono b ( ± 1~ ) _ ± _ ± _ _ ± ± ± _ ± _ _ _ _ _ ± ± ± _ ± _ ± 0.03 b-values were determined with the maximum likelihood method of Aki (1965). Magnitude cutoffs were determined as described in the text. The magnitude completeness thresholds for the Gawthrop and Carr (1988) catalog are higher than our levels because they are concerned with coverage throughout southern Nevada, whereas we are only considering coverage within our network. The b-value of 0.83 determined for the Gawthrop and Carr (1988) catalog as a whole is similar to the values in Table 1. The spatiallyvarying levels of magnitude completeness determined by Gomberg (1991) for the Southern Great Basin were based on a catalog made from the Southern Great Basin network, which is not part of the UNRSL catalog and thus cannot be compared directly to the completeness levels in Table 1. The variation in completeness has caused problems (treated in detail below) for declustering the catalog, but it should have less effect in the probability analysis as we present it because the foreshocks occur closely in space and time to the mainshocks. Thus, although magnitude completeness and perhaps even scales of magnitudes could change in time and space throughout the catalog (Habermann, 1987), the relative difference in magnitude between a foreshock and its mainshock should be more consistent across different regions and time periods. Declustering Methods As discussed in Jones (1985) and Reasenberg (1985), apparent foreshock probabilities will be raised by the presence of aftershocks in a catalog because the occurrence of smaller aftershocks followed by larger aftershocks would be misconstrued as foreshock-mainshock pairs. Therefore some method of removing aftershocks from a catalog is necessary. Jones (1985) used the method of Gardner and Knopoff (1974). This consists of defining an aftershock as an earthquake with a magnitude smaller than that of the mainshock, occurring within a simple space-time window of the mainshock. The size of the space-time window increases with increasing magnitude of the mainshock. Several other methods have been proposed to remove aftershocks or "decluster" catalogs.

7 1916 M. K. SAVAGE AND D. M. DEPOLO Savage (1972) first applied a declustering algorithm to the Nevada region to examine microearthquake clustering in selected regions. The emphasis on small earthquakes led to a restrictive definition of clusters as groups of events which occurred within 10 min and several hundred meters of other earthquakes. Davis and Frohlich (1991) compare the performance of several different clusterdefining techniques on a set of "synthetic" earthquake catalogs. The synthetic catalogs were generated to contain mainshocks and aftershocks in distributions that matched the appearance of those in two teleseismic and two regional earthquake catalogs. All techniques worked rather poorly on the regional catalogs; specifically, each algorithm failed to identify a significant fraction of synthetically generated "aftershocks." The techniques that best removed the aftershocks from the catalog were those that used some form of cluster-link scheme. In cluster-link methods, an earthquake is considered part of a cluster if it falls within some space-time criterion of any earthquake within the cluster, rather than considering only the largest event, as is done with the Gardner- Knopoff space-time window described above. The final size and shape of the cluster is then defined by the distribution of seismicity in the cluster itself. This makes it possible for very distant earthquakes to belong to the same cluster if there is a chain of intervening related earthquakes. This feature can cause problems if too large a space-time criterion is used because a single cluster can sometimes grow to include the entire catalog. Thus, in all the cluster-link techniques, parameters relating to the distance and time criterion need to be fine-tuned for each catalog. For the regional catalogs, Davis and Frohlich observed no significant difference between various cluster-link techniques. We chose to use Reasenberg's cluster-defining code (Reasenberg, 1985). For small earthquakes, the spatial distance (r) to look for a related earthquake is given by the formula r = Q(0.011)[10 ( '4M1)] + (0.011)[10( 4M2)], where Q is a scaling parameter, M1 is the magnitude of the event, and M2 is the magnitude of the largest event in the cluster associated with the event. This equation was determined assuming the circular-crack relations in Kanamori and Anderson (1975), a moment-magnitude relation (Bakun, 1984), and a stress drop of 30 bars (Reasenberg, 1985). A maximum value of 30 km (about one crustal thickness) is assumed for all events, and is in effect for events over magnitude 6.1 when a value of Q = 10 is used. If an event is part of a cluster, the look-ahead time, 7, used to determine if the next event is also part of the cluster, is given by the expression -ln(1 - P1)tl ~- = 102(AM - 1)/3, where AM is the magnitude difference between the largest event in the sequence and the minimum completeness threshold of the catalog, P1 is the degree of confidence desired to be sure of observing the next event, and t 1 is the time between the largest event and the last event in the sequence. This last equation, determined by Reasenberg (1985), is based on Omori's law for the rate of aftershock occurrence over time, with a decay rate of t (Mogi, 1962), and an empirical relation between maximum and minimum magnitudes within individual aftershock sequences. Parameters ~min and 'l'ma x are used to provide lower and upper bounds to the otherwise unbounded expression for 7. If the

8 FORESHOCK IN GREAT-BASIN AND SIERRA NEVADA 1917 event is not yet part of a cluster, then is set equal to the parameter %. Thus, the distance link has a single parameter to vary, Q, while the time link involves parameters P1, Trnin, Tmax, and ~0- Another, less obvious parameter is the magnitude threshold above which events are included in the cluster analysis. Reasenberg (1985) pointed out that, despite including the AM term above, he needed to include events below the assumed magnitude threshold to provide enough earthquakes to associate clusters together properly. In contrast, if we include events below magnitude 2.0, the character of the "declustered" catalog changes markedly over time; and the later events tend to be grouped into a few large clusters. This is probably caused by the varying completeness at small magnitudes because when seismic activity is high or personnel are cut, location of the smaller events is often delayed or stopped. When we only include events over magnitude 2.5, however, we encounter the problem pointed out by Reasenberg (1985), namely that earthquake sequences tended to break up into separate clusters sooner than one would pick by eye. Thus, the decision of which magnitude level to include in the cluster is another parameter that can affect the distribution of earthquakes into clusters. We use all events over magnitude 2.0 to retrieve the "declustered" catalogs. These consist of all events not associated with another event (unclustered events) plus an "effective" event from each cluster. The "effective" event has a magnitude calculated from the summed moments of all the events in the cluster, and a location given by the weighted average location of each event in the cluster (Reasenberg, 1985). In these "declustered" catalogs, foreshocks could be included in a single cluster along with the mainshock and aftershocks, eliminating the very data we want. To remove aftershocks, and yet include foreshocks, we construct "de-aftershocked" catalogs consisting of the unclustered events and the increasing-magnitude events from each cluster. For example, if a cluster consisted of events with magnitudes 3.2, 3.8, 3.4, 4.6, and 4.2 the events retrieved would be 3.2, 3.8, and 4.6. Thus, more than one foreshock might be included in a sequence, increasing the likelihood of foreshocks compared with a technique that allowed only one foreshock in each cluster. We use this technique because it is similar to the method used by Jones (1985) in her determination of foreshock probabilities for southern California, and because a major focus of our study is to compare the probabilities within the two regions. Because of the difficulty of applying Reasenberg's (1985) technique, we use the simple space-time windows described in Gardner and Knopoff (1974) to check our results. An advantage to this technique is that it does not depend upon small earthquakes to help determine the distribution of a cluster; therefore, it should be independent of the completeness threshold of the catalog. In particular, variable spatial and temporal completeness thresholds do not affect the results. The disadvantages noted by Reasenberg (1985) and Davis and Frohlich (1991) are that it assumes a constant, rectangular, space-time window that is centered at the mainshock epicenter. This window will not be realistic for most earthquakes, especially because many mainshocks occur at one of the edges of the aftershock sequences. Thus, events may be excluded from the catalog that should be kept in, and others will be included that should not be. We calculate appropriate space-time windows as a function of magnitude by interpolating directly from Table 1 of Gardner and Knopoff (1974). Although these values were determined for southern California earthquakes, we did not

9 1918 M.K. SAVAGE AND D. M. DEPOLO change them, because visual inspection suggests the resultant, declustered catalogs are similar to those determined using the Reasenberg method. Determining Appropriate Declustering Parameters The major effect of any parameter adjustment is in the final time and distance link to be used to consider two earthquakes to be associated. To determine the correct parameters, space-time plots such as those in Figure 3 are computed for suites of parameters and for subsets of the catalog. They are examined to determine if the algorithm has adequately removed events that are parts of clusters and has not "glued together" events into a cluster that should not be part of the same cluster. A Q of 10 works fairly well in defining the distance link for both our catalogs, as it also did for Reasenberg (1985). Varying Q does not have a large effect; however, as expected, a smaller Q includes fewer events in each sequence. The appearance of the "declustered" catalogs is most dependent upon the time parameters, and varying ~'max has the largest effect. P1 of 0.9 works well, but variations in P1 do not substantially change the appearance of the declustered catalog. We observe little dependence on r 0 or train, and used % = Tmax/lO, and Tmin = Tmax/20. The value of rma x has a profound effect on each catalog. Using a value of Tma x that is too short leaves several "clusters" when a single cluster looks best by eye (we sometimes call this having "too little glue"); and a rma x that is too long allows unrelated events to become part of the same cluster ("too much glue"). Chains of events in differing distance ranges allow the cluster to grow in space as well as in time. This dependence of the results on Tma x suggests that the physical processes of interactions between earthquakes are still not well understood. When we separate the Mammoth/Mono area from the rest of the catalog, we achieve more stable results. The majority of the seismicity in the Mammoth/ Mono area has occurred since 1978, and the magnitude completeness threshold does not have a large variation since that time; therefore we are able to consider parameters independent of the completeness threshold. We examine a suite of max values for two sample periods, one from 1989 to 1990 and another from 1986 to 1987, which encompasses the Chalfant earthquake sequence. Figure 3 shows examples from the Mammoth/Mono catalog that have ~m~x too short (5 days; 3a), "just right" (10 days; 3b, c), and too long (40 days; 3d). As would be expected from the Davis and Frohlich (1991) analysis, none of the 7 o and Tma x values perform perfectly, as evidenced by the behavior that, even for the best max values, some of the clusters appear to be too broken up while others that a seismologist would consider to be separate clusters are merged together. The resultant "declustered" Mammoth/Mono catalog, using Q = 10, 7ma x = 10 days, is shown in Figure 2. For the Nevada catalog, it is necessary to vary the Tma x parameter depending on the magnitude completeness threshold at the time of the event; this was also found by Gross and Jones (1988) for the southern California earthquake catalog. We determine an empirical formula that recreates the ~m~x value that appears best for each time period. It is: r 0 = ~00(2.0 (Me 2.0)) and Tma x = ~'maxo(2.0(mc 2.0)) where M c is the magnitude completeness threshold, and %o and rma~0 are parameters that fit best when M c is 2.0. The earliest time period considered, 1934, with M c = 5.0, yields ~max = 8"rmaxO" We then vary rma~o to determine the most suitable end members. The character of this catalog does not depend very much on the value of %~0. The best values are Q = 10, rma~o = 20 days. The

10 FORESHOCK IN GREAT-BASIN AND SIERRA NEVADA Clustered Catalog Declustered Catalog West.... East ~West / ++* ++ + East 100 -, + +~ "o v * + + +Z' ~+ ~ +.I~ + $ ++ +.'~'~+c + * + ++z ++ + x # +*~t "~ I Magnitude (a) Clustered Catalog Declustered Catalog 100 West I I I East + ~++ * ~*Ft * + ~West I / / I East ~. :,+/ "~ 5O0 + + x+. + *+ ++~ ~ R Magnitude (b) FIG. 3. Sample space-time diagrams for the Mammoth/Mono area, before and after declustering, using different parameters. Top axis is epicentral distance along an E-W profile through the Mammoth region. Each diagram includes letters for events that are considered part of a cluster and plus signs for events that are not part of a cluster. The plot on the left contains all events in each cluster, whereas that on the right contains only the "effective" event from each cluster (see text). (a) The 1986 to 1987 period, using Q = 5, T~a ~ = 5 days. Note that the Chalfant aftershock sequence, denoted by the letters "N" at the east beginning about day 200, has stopped including earthquakes that a seismologist would consider to be part of the sequence, before about day 600. (b) The 1986 to 1987 period, using Q = 10, %,ax = 10 days. The Chalfant sequence, here denoted by the letter "I," continues to include earthquakes to the end of the plot. This is considered to be a more effective set of parameters than those in Figure 3a. (c) The 1989 to 1990 period, containing several small swarms, using the "best" parameters Q = 10, ~mex = 10 days. The swarms near distance 20 and between 100 and 400 days appear to have "too little glue," in the sense that a seismologist might include more events as part of the swarm, whereas the letters "S" and "Z" between 400 and 600 days appear to have included unrelated events in the same cluster. (d) The 1989 to 1990 period, using Q = 10, T, nax = 40 days. The swarms at distance 20 km between 100 and 400 days are included as one sequence, but the letters "G" starting at about 400 days are beginning to pull much of the later catalog into one sequence. We therefore consider these parameters to give "too much glue," and those in Figure 3c are considered more ideal.

11 1920 M. K. SAVAGE AND D. M. DEPOLO 0 I West Clustered Catalog ~+ l+ ~. I East 0 I West Declustered Catalog ,, East *+~ * + + +~,:;+ + +, ~+ * ~+ 100 k= 200-3oo 400 5OO + +++~i+++, ~+, + u L++~++ ++ sl~i, u ++ TT+, + ++~++~ : + + e+ + +.~.~ o ~ ~ *++, ~P * + R ++ T (3 +,+~+ ++*+u + +;.+~ ~< J+ NM~ o~ ~ ,++ T* :.?/+~ : Clustered Catalog ?West I ~t~ ' =" -~.~.~ East J, Magnitude (c) Declustered Catalog. ~l,~. 2,+ ;~East, Owsst 20 l ~ :t + ** ~ + + J* i + +~ p:; + +%+ ~ ~ i= 5O0 +~. +~ + + ~:t.,~ ~ ~'~a *+ +. "h ~ :~-+ *+ + + "+ ~'~+~'+ A ++ V ~H + * ~++$ *C ~. Z*+* + M + E + *+ + ~ ~ I 4-+ K + H + G P *:++ 28O ,< 500 ~= =.a ~d.," ~': Z # /* % B 6O0 70O. + +-} Magnitude (d) FIG. 3. (continued) "declustered" catalog using these values is presented in Figure 2. An end member with "too little glue" is Q = 10, Tma~O = 10 days, and one with "too much glue" is Q = 10, TmaxO = 80 days. A second method to determine how well the aftershocks are removed is to calculate the percentage of earthquakes in the "declustered" catalog (i.e., the catalog that includes all unclustered events and one event for each cluster) that are followed by other earthquakes. We assume that, if the aftershocks were perfectly removed, then the catalog would appear random (Poissonian); and there would be only a small number of earthquakes that occur close to other events in space and time. We consider events larger than magnitude 3 that are followed by other events of any magnitude greater than 3 within 10 km and 5 days. In the original Mammoth/Mono area catalog, the probability of an event being followed by another event (either smaller or larger) under such criteria is

12 FORESHOCK IN GREAT-BASIN AND SIERRA NEVADA % (1287 of 1895 events) whereas in the "best" decluster catalog, the probability decreases to % (37 of 524 events). For the Nevada catalog, using the same window of 10 km and 5 days, the probabilities are % (508 of 1994), decreasing to % (99 of 1451 events) for the "best" declustered catalog. Thus, in the Mammoth/Mono area, the majority of events are parts of clusters (only 28% of the events are left after declustering); and we have removed most of the aftershocks. The 7% figure probably represents clusters that are broken into too many groups and indicates that, although the majority of the aftershocks have been removed, there has been some failure. This is also evident in maps of the original and "declustered" catalogs (Fig. 2). Time-Space Distribution of De-Aftershocked Catalog As discussed by Jones (1985), a precise definition of a foreshock should include an optimum space-time window in which a possible mainshock could occur. It should be large enough so that most of the foreshock-mainshock sequences will be included but small enough so that resulting probabilities are above the background level. This space-time window is probably related in a loose sense to the windows used in defining the clusters, but it is determined separately and should not be confused with the others. To determine the optimum space-time windows for foreshock probability calculations, we follow Jones (1985) in examining the "de-aftershocked" catalogs. For each event, we count the numbers of earthquakes of larger magnitude that follow within distance intervals of I km and time intervals of i day. These numbers are then summed for the entire catalog to calculate a matrix K(i,j), where i,j ranges from 1 to 30 and K(i,j) represents the total number of nonaftershocks that were followed by an event of larger magnitude in the range i - 1 to i and the time interval j- 1 to j. These are displayed in Figures 4a and 5a as a histogram of counts as a function of day by summing over distance via ~i= 30 1 K(i, j) and in 4b and 5b as a histogram of counts as a function of distance by summing over time via E~ 1 K(i, j). As the distance interval increases, the area in the annulus surrounding the proposed foreshock increases linearly. Therefore if events occur randomly, the number of events increases linearly with increasing distance from the proposed foreshock. So we also consider the distribution in terms of the number of events per unit area. These are shown in Figures 4c and 5c as E~ l(k(i, j)/2 i - 1) and in part 4d and 5d as El= 3o 1( K ( i, ])/ " 2i - 1). For the Mammoth/Mono area, a window of 10 km and 5 days is considered optimum (Fig. 4) whereas, for the Nevada area, a window of 15 km and 10 days is more appropriate (Fig. 5). The 5-day, 1O-km window for the Mammoth/Mono region is similar to that used for southern California by Jones (1985). The larger space window for the Nevada catalog may be explained as follows: poorer station coverage in the Nevada catalog may increase the distance window because poor locations suggest that events are farther apart than they really are. However, poor timing would not cause differences of 5 days in the time windows. Another explanation could be that the decay in number of events as a function of distance and time from a foreshock or mainshock allows the Nevada catalog, with larger numbers of events (1955 events in the de-aftershocked "Nevada" catalog compared to 772 events in the Mammoth/Mono catalog) and a lower background seismicity, to have a signal above the background level at further distances and times. This is most likely the case because, as we will see below, the decay of hazard with time

13 1922 M. K. SAVAGE AND D. M. DEPOLO Mammoth/Mono O E o o a 20 0 i i i i o s lo is 30 Day 20 bo O' ~) Distance (km) 40 -; ~,0 ~ o "-~ 10 0 C o o Day Distance (km) FIG. 4. Histograms for the Mammoth/Mono catalog. (a) Number of earthquakes larger than the original earthquake recorded within a 30-km radius circle as a function of the number of days since the original earthquake. (b) Number of earthquakes larger than the original earthquake recorded within 30 days as a function of the distance from the original earthquake. (c) and (d) are the same as (a) and (b) except that the number of earthquakes has been replaced by the number per unit area multiplied by a constant factor of ~ (see text for equations used). is similar for the two catalogs. For the Nevada catalog, the wider date and time windows pull in few events; so the probabilities calculated using 10 days and 15 km are only somewhat larger (less than 1% difference) that those calculated using 5 days and 10 km. For an earthquake hazard warning, the decay in hazard with time (equations 10 to 12, below), compared to the background seismicity, would be a better indicator of when to cut off an alert than the somewhat arbitrary 5- and 10-day windows used in the calculations. We also calculate probabilities from the catalogs declustered by the Gardner- Knopoff method for each of Mammoth/Mono and Nevada and for the combined catalogs using the same 5-day, 10-km window that was used for the Mammoth/ Mono and southern California catalogs. It is therefore a better catalog to use for direct comparisons between different regions.

14 FORESHOCK IN GREAT-BASIN AND SIERRA NEVADA 1923 Nevacla c O (D ~0!i a o 80 0, Day Distance (km) ~, '~ 40.,.-. t- o (-) 2o 60 ~. 40 ~. 20 ~, C 0 " ~!i~: Day Distance (km) FIG. 5. Same as Figure 4, for the "Nevada" catalog of events outside the Mammoth/Mono region. Foreshock Probabilities RESULTS AND DISCUSSION To see how much the choice of parameters affects the probability calculations, we include two end-members; one with Q = 5, rma x = 5 days, which we consider to have "too little glue," and one with Q = 10, rma x = 40 days, which we consider to have "too much glue" (Fig. 3; Table 2). The number of clusters identified in each group varies considerably and one might therefore expect the calculated probabilities to vary. If too many clusters are "glued together," then important groups of events might not be counted in the statistics. If clusters are broken up too much then, as in the case of catalogs in which aftershocks are not removed, we might get foreshock occurrence rates that are too high because we could be including aftershocks that are followed by still larger aftershocks. Figure 6 shows the percentages of earthquakes followed by larger events for the different de-aftershocked catalogs, calculated from the Nevada and Mammoth//Mono catalogs using the optimum declustering parameters from the

15 1924 M.K. SAVAGE AND D. M. DEPOLO TABLE 2 AVERAGE PROBABILITY THAT AN EARTHQUAKE WILL BE FOLLOWED BY A LARGER EVENT Method PM > F(-- + l~r )(%) PM >_ F+ o.5(-+ 1~)(%) PM > F+ 1.0(--+ la )(%) Nevada, R I 10.9 ± ± ± 0.4 Nevada, R c 5.4 _ ± _+ 0.4 Nevada, G-K 6.3 ± ± ± 0.5 Mammoth/Mono, R~ 17.2 ± ± ± 0.6 Mammoth/Mono, R C 9.5 ± ± ± 0.6 Mammoth/Mono, G-K 11.3 _ ± ± 1.5 Combined, G-K 7.1 ± ± ± 0.3 Best Guess, Mammoth/Mono Best Guess, Nevada R t is initial estimate using the best-fitting parameters from Reasenberg's declustering algorithm. R C is Rr corrected for possible misidentification of aftershocks. This is a lower bound for the probability. G-K represents Gardner-Knopoff aftershock removal as described in text. Probabilities (P) and standard deviations (a) for mainshock magnitudes larger than foreshocks by 0.0, 0.5, and 1.0 units are given. Reasenberg method, as well as the end-member parameters that seem to break up too many clusters or to pull too many clusters into one. Three types of foreshocks are considered: those followed by mainshocks of equal or greater magnitude, those followed by mainshocks 0.5 or more units above the foreshocks, and those followed by mainshocks 1.0 or more units above the foreshock. Each of the last two cases is a subset of the first case. We feel that this approach to reporting our results is better for our catalog than the somewhat more easily assimilated presentation of the probability that an event of a given magnitude will be followed by an M = 4.0 or M = 5.0 event, which was used by Jones (1985). This is because of the variable methods used over time for reporting magnitudes. Habermann (1987) has shown that such changes can have large effects on seismicity. Thus, the, percentage of magnitude 4.0 events might change over time as a result of changing magnitude definitions, or even of changing station locations. However, the difference in magnitude between foreshocks and mainshocks will change less over time because changes in magnitude definition and station locations are less likely in the 5-day periods examined here than they are in the 58-y interval we have studied. Considering the Mammoth/Mono catalog for the percentage of events that were followed by mainshocks of equal or greater magnitude, there is a large difference between the catalogs that were de-aftershocked with the three sets of parameters (Fig. 6a). The error bars (one standard deviation) from each set of calculations do not overlap at the lower magnitudes; and the values tend to decrease when the declustering parameters effectively "add more glue" by increasing ~ma~ or Q, or both. In addition, there is an apparent decrease in probability of mainshock occurrence with increasing magnitude of a potential foreshock. The probabilities are also somewhat larger than those in the "Nevada" catalog. Considering mainshocks that are 0.5 or 1.0 units higher than the foreshock yields more stable results (Figs. 6b, c, e, f), both within the different declustering parameters and between the Mammoth/Mono area catalog and the Nevada catalog. In all cases, the error bars are quite large for earthquakes above magnitude 4 to 4.5 (Fig. 6). This is because few events are available to use in the analysis. We

16 FORESHOCK IN GREAT-BASIN AND SIERRA NEVADA 1925 ( o +o [ ~ o $ o AI I ] I o g o E E ( ( cs + ~ ~ N 0 ^l c I i if..~ lf ]l~ I i ( [ (lua~jad) /~l!l!q~qo~ a "~ooqsajo3 i ~ ~. AI "~ ~ ~.~,~ /,~l!ql~qojd "~oqsa,~o3 ~ ~,..a,-= ' ~ u~

17 1926 M. K. SAVAGE AND D. M. DEPOLO [- 25 Combined Catalog J Nevada Mammoth/Mono o E ,0 01 I T v '1" ~ I I -- T I a) Magnitude b) Magnitude ) Magnitude FIG. 7. Foreshock probabilities for the Mammoth/Mono, Nevada, and combined catalogs, using the Gardner-Knopoff de-aftershock method. Squares represent the probability that an event will be followed by a larger event, circles that an event M = 0.5 units higher will soon follow, and triangles that an event 1.0 unit higher will soon follow. (a) Complete catalog; (b) Nevada catalog; (c) Mammoth/Mono catalog. plot only those values for which 10 or more earthquakes are observed within the given magnitude range. For the Mammoth/Mono region, this is magnitude 5; and for the larger Nevada catalog, it is magnitude 6. This criterion results in leaving out a point at M = 5.5 in the Mammoth/Mono catalog, at which two of six earthquakes with rounded magnitudes equal to 5.5 are followed by other events of equal or greater magnitude. The results from the Gardner-Knopoff de-aftershocking technique are shown in Figure 7 for the Nevada and Mammoth/Mono catalogs and for the combined catalog. Averages for each of these methods are shown in Table 2. More events are removed from the catalog using this technique, leaving only 254 events in the Mammoth/Mono catalog and 1273 events in the Nevada catalog. This results in larger error bars. The dependence on magnitude appears smaller for these probability calculations and suggests that the technique may be more robust. Unfortunately, the choice of declustering parameters strongly affects the foreshock probabilities for the Mammoth/Mono area catalog, especially for the occurrence of mainshocks equal or greater than the foreshock magnitude. The apparent decrease in foreshock probability with increasing magnitude up to about magnitude 4.5 for each of the methods may indicate that aftershocks are still not completely removed because there is an even stronger dependence of foreshock probability on magnitude when the aftershocks have not been removed at all. To estimate how much of the apparent variation of probability with magnitude is caused by misidentified aftershocks contaminating the data, we calculate foreshock probabilities on the "declustered" catalog, which includes only one event from each cluster. Thus, foreshocks that are identified within the same cluster as a mainshock are not included in the probabilities. Instead, events that are true foreshocks but are missed in the cluster-link scheme, as well as aftershocks that are mistakenly broken into more than one cluster and are followed by a larger aftershock in another "cluster," are included; the results from this analysis can be considered an upper bound on the errors in probabili-

18 FORESHOCK IN GREAT-BASIN AND SIERRA NEVADA Corrected Nevada M Corrected ammoth/monc Z 0 ~ 15 ~ 10 u_ a!z a) Magnitude b) Magnitude FIG. 8. "Corrected" probabilities for the Mammoth/Mono and Nevada catalogs, calculated by subtracting the probabilities from the "declustered" catalog from those of the "best" curves in Figure 6. These values represent a lower bound on the foreshock probabilities. Symbols are as in Figure 7. (a) Nevada; (b) Mammoth/Mono. ties due to the misidentification of aftershocks within the declustering technique. Figure 8 shows the results of subtracting the foreshock probabilities calculated using the declustered catalog from those calculated using the de-aftershocked catalog and represents a low estimate of the probability that an earthquake will be followed by a larger event. It is equivalent to calculating the foreshock probabilities using the clusters alone. There is less difference between the results using different ~ parameters, and we show only the "best" parameters. Probabilities are more stable as a function of event magnitude. The plots in Figure 6 for the "best" parameters probably represent a somewhat high estimate of foreshock probability whereas those in Figure 8 represent a low estimate of foreshock probability. The values for the Gardner-Knopoff declustering technique are intermediate (Fig. 7). Combining this with the results of Jones (1985) for the much larger southern California catalog, in which foreshock probability is independent of earthquake magnitude, we consider an average value or a range of values to be more meaningful than a value picked from the plot. Table 2 shows the average values for each method, calculated with a weighted mean in which the weights are based on the standard deviation of each point. The averages for the weighted means are somewhat smaller than one would pick by eye because the measurements with smaller probabilities will also have smaller standard deviations (see equation 1) and therefore will be weighted more heavily than the other values. In Nevada, the average probability that a mainshock with magnitude equal or higher than a given proposed foreshock will occur within 15 km and 10 days is

19 1928 M. K. SAVAGE AND D. M. DEPOLO between 5% and 11%. A reasonably conservative estimate would be 6%, which is equal to the value determined by the Gardner-Knopoff method for the entire catalog for 10 km and 5 days, and is also equal to the value reported by Jones (1985) for southern California. The probability of an event 0.5 magnitude or more higher than a moderate earthquake is between 3% and 6%, with 3% as a conservative estimate. This compares to about 5% of magnitude 3.5 and 4.5 events followed by M = 4.0 and 5.0 events, respectively, for southern California (Jones, 1985). The probability of a mainshock 1.0 magnitude unit or more larger than a moderate earthquake is 1 to 3%, with 2% as a conservative estimate, comparable to about 2.5% of magnitude 3.0 or 4.0 events followed by 4.0 or 5.0 mainshocks in southern California (Jones, 1985). Thus, the probability that an event in the Nevada region of magnitude less than or equal to 4.5 will be followed by a larger event is about equal to the probabilities for earthquakes of the same size in southern California. The likelihood that events of magnitude 0.5 or 1.0 higher than a random event wilt soon follow is somewhat smaller in Nevada than in southern California. This is seen in both the average values reported above and in Table 2, and in the relation between mainshock/foreshock magnitude difference discussed below (Fig. 10; equations 4, 5, 10 to 12). Although there may be a tendency for increased probabilities for larger earthquakes, the sample of such earthquakes is too small to given confidence to those results; and the most conservative hypothesis is that the values do not change much with magnitude. The probability that a given, moderate earthquake in the Mammoth/ Mono region will be followed by a larger event is about 10%, somewhat higher than for either Nevada or southern California. Using the student "t" test (Burington and May, 1953), we find that the differences between the Nevada and Mammoth/Mono catalogs using the "corrected" Reasenberg de-aftershocked catalogs or the Gardner-Knopoff de-aftershocked catalogs are significant at the 90% confidence level. The differences are smaller and are not statistically significant when probabilities of mainshocks 0.5 or 1.0 higher than the foreshocks are considered. Again, this is consistent with the plots in Figure 10 and with equations 4 and 5, which show a somewhat steeper decay of magnitude difference with increasing foreshock magnitude between the Mammoth/Mono region and the Nevada or southern California regions. At larger magnitudes, the differences between the two regions become smaller because of the differences in slope of the magnitude difference plots. Reasonable estimates of foreshock probability for the Mammoth/Mono region are then 10% for events to be followed by larger events, decreasing to 5% and 2% for events to be followed by mainshocks more than 0.5 and 1.0 larger than the proposed foreshock. These latter values are similar to the values in southern California. If we use the same (smaller) distance and time windows for the Nevada region as for the Mammoth/Mono region, the foreshock probabilities for the Nevada region would decrease, enhancing rather than decreasing the differences between the two probability calculations. The similarity of the Nevada foreshock probabilities to those in southern California seems to contradict the "inverse" observation that western Cordilleran earthquakes are preceded 65% of the time by foreshocks (Doser, 1990) while those in southern California are preceded only 35% of the time by foreshocks (Jones, 1984). The differences can be explained by the different windows used to define foreshocks in the above two studies. When we apply the same criteria

20 FORESHOCK IN GREAT-BASIN AND SIERRA NEVADA 1929 to each study, we find that 70% of earthquakes in southern California and 65% of earthquakes in the Western Cordillera are preceded by earthquakes within 2 mo and 40 km, whereas 35% of earthquakes in southern California and 37% of earthquakes in the western Cordillera are preceded by foreshocks within 1 day. Magnitude Distribution The magnitude distribution of the foreshocks is similar to that in Jones (1985). Figure 9 shows the cumulative number of events N at or above a given magnitude M for the declustered catalog and for the foreshocks in the Nevada and Mammoth/Mono catalogs, along with the best linear fits. For all events in the de-aftershocked catalogs, we find from a least-squares fit, with error bars of one standard deviation, that: loglo(n) = ( )M loglo(n) = ( )M loglo(n) = ( )M (Nevada) (Mammoth/Mono) (Southern California; Jones, 1985). (2) For all events that are foreshocks to larger events: loglo(n) = ( )M loglo(n) = ( )M loglo(n) = (0.83 _+ 0.10)M (Nevada) (Mammoth/Mono) (Southern California; Jones, 1985). (3) The somewhat smaller magnitude coefficients (b-values) for the Nevada and Mammoth/Mono de-aftershocked catalogs compared to the Southern California catalog suggest that proportionately more small events are excluded from our catalogs, using the Reasenberg technique, than were excluded from the catalog used by Jones (1985). However, the differences are just barely significant. Likewise, the differences between foreshocks and de-aftershocked events (equations 2, 3) are not significant; and the values are similar to those determined using the entire UNRSL catalog (Table 1). These compare with higher b-values of 1.4 ± 0.1 for earthquakes larger than M L = 1.6 in the southern Great Basin (Gomberg, 1991) and suggest variation between the northern and southern Great Basin. Figure 10 shows the distribution of events as a function of differences in magnitude between foreshock/mainshock pairs, determined from the catalogs that were de-aftershocked using the best parameters from the Reasenberg technique. As observed by Jones (1985) for the southern California earthquake catalog, the distribution looks somewhat like standard magnitude/frequency relations, with slopes of and ± 0.02 for the Mammoth/ Mono and Nevada areas, respectively. This compares to the slope of ± 0.10 reported by Jones (1985) for southern California. As noted above, there may be some contamination from misidentified aftershocks. Therefore, we also calculated the distribution using the same type of "correction" scheme as above, i.e., calculating the number of events in the "de-aftershocked" catalog with a given magnitude difference between foreshocks and mainshocks, and subtracting the corresponding number of events in the "declustered" catalog. In this case, the b-value is and for Mammoth/Mono and

21 1930 M. K. SAVAGE AND D. M. DEPOLO Mammoth/Mono 3 I i i - i! All Nonaftershocks ~ ~ i,q -- Foreshocks M < Main 2.5 i ~, ~ i-- "~ -- Foreshocks M < Main ~ - ~... ~ O'reshOckS M < Main + 1"0 Z V 0 _J 1.5 -F---~-~-... o....i ~ %.~." i, i 1 ~ ~ i... x.x~-~<-x... ~-~----o4o~... i... L Magnitude (a) Nevada I I I I I ~ i i O All Nonaftershocks 3 ~-'--'--'-i... [] --Fore shocks M < Main _ ~-~ ",,v,~ -~, -- ~ -- Foreshocks U < Main ~_... ~I~C):: - -X- -- Foreshocks M < Main i i i i g 2 S... i o: Magnitude (b) FIG. 9. Cumulative number of events with magnitude greater than or equal to a given magnitude. Circles: all nonaftershocks; squares: foreshocks followed by equal or larger events; diamonds: foreshocks followed by events at least 0.5 units larger; crosses: foreshocks followed by events at least 1.0 magnitude units larger. (a) Mammoth/Mono catalog. (b) Nevada catalog. i 6

22 FORESHOCK IN GREAT-BASIN AND SIERRA NEVADA 1931 Mainshock/Foreshock Magnitude Distribution I o IogiN) Nevada [] -log(n) Mammoth 2... ~--i... i... i... [... i slope ; i... i... i M - M m f FIG. 10. The cumulative number of foreshock-mainshock pairs with a difference in magnitude at or above each level of magnitude difference as a function of difference in magnitude. Squares: Mammoth/Mono area catalog. Circles: Nevada catalog. -.g Nevada, somewhat closer to the southern California values. Following Jones (1985), we use the above slopes in the difference of mainshock/foreshock magnitudes to find that, after an earthquake of magnitude My, the probability that it will be followed by a mainshock of magnitude M m or higher within 15 km and 10 days in the Nevada region is P = 0.11*Io-OS5(Mm-Mr); P = O.06*10-72(M~-Mr ). (4R) (4C) Where we have used the straight values from the de-aftershocked catalog in equation 4R and the "corrected" values in equation 4C and, using the same convention, the probability for 10 km and 5 days in Mammoth/Mono is: P = 0.17"10-96(Mm Mr), P = 0.10"10 - 'sg(im-mr). (5R) The steeper decay in the Mammoth/Mono region may be caused by the many swarms in this volcanic region, which contain many events of similar magnitude. This is consistent with the observation of Doser (1990) that the difference in magnitude between mainshocks and their largest aftershocks decreases with increasing heat flow. Decay in Earthquake Hazard with Time The probability that an earthquake will be followed by a larger event decreases rapidly with time after the event (Fig. 11). This distribution is very similar to (5C)

23 1932 M.K. SAVAGE AND D. M. DEPOLO Mammoth/Mono 200 I I I o o N main > fore o \ \ --~-N main > fore om 150 ~ ' = e- N main > fore I--... i!!!!i, li i o E "3 z t Hr+l (a) Nevada o o N main > fore... ~... H.9.o []- N main > fore LY o 200-~... I...- ~- N main > fore O ~" Hr+l (b) FIG. 11. The number of mainshocks still to occur as a function of time since the foreshock. Upper curve in each plot is for earthquakes with equal or larger mainshocks, next lower is for earthquakes followed by mainshocks of magnitude at least 0.5 larger, and the bottom curve is for foreshocks followed by mainshocks of magnitude at least 1.0 larger. (a) Mammoth/Mono area catalog. (b) Nevada catalog.

24 FORESHOCK IN GREAT-BASIN AND SIERRA NEVADA 1933 that described in Jones (1985), in which 26% of mainshocks occur within 1 h of the foreshock in the southern California catalog. The corresponding figures for the Nevada and Mammoth/Mono catalogs are 20% for each catalog, using the straight de-aftershocked catalogs. The best fits to the decay shown in Figure 11 for the Nevada catalog is as follows: N M = og10(t + 1), i.e., N M = NM0[ ogl0(t + 1)] (R = 0.98; Nevada catalog). (6) Here N M is the number of mainshocks still to come at time t + 1, in hours since the foreshock, and R is the correlation coefficient, NMO is a constant designed to make comparisons easier between different catalogs. In this case it is also almost equal to the number of foreshock/mainshock pairs (291) separated by 1 h or less. For the Mammoth/Mono catalog, a quadratic function had a higher R than any other functions tested, but it did not fit the first hours' results well. The logarithmic fit yields: N M = og]0(t + 1), i.e., N M = NM0[ og10(t + 1)] (R = 0.93; Mammoth/Mono). (7) In this case NMO = 215 and is 1.2 times the 176 events that occurred within the first hour after a foreshock. We can approximate equations (6) and (7) by a simple form: N M = NMO[1 - ln(t + 1)]. (8) Here, In is the natural logarithm, and we have used the relation lnl0(t) 0.43 In(t). The decay in the rate of mainshock occurrence (PR) per hour is given by the derivative of equation (8), and is simply PR = PRo(--1/(t + 1)). (9) This t 1 decay is very similar to the t - 9 reported by Jones (1985) for southern California and similar to the Omori decay law for aftershocks (Mogi, 1962; Utsu, 1971). The smaller numbers of events in our catalog make it difficult to fit the rates directly as apparently was done by Jones (1985). As suggested by Jones (1985), the similarities between foreshock and aftershock decay rates suggest they are manifestations of the same process. Similar logarithmic decays in time between mainshocks and foreshocks, and mainshocks and aftershocks, occur for the worldwide catalog of earthquakes over M = 7.4 since 1904 and over M = 6.9 since 1970 (Tsapanos et al., 1988). The time difference between the largest foreshock and mainshock, and between the largest aftershocks and the mainshocks, fit a form of N(T)= c -k log Tp The values published for c and k for the mainshocks and aftershocks yield k/c very close to 0.43 (0.46 and 0.43 for the 1904 to 1980 and 1970 to 1983 catalogs, respectively). The coefficients for the foreshock/mainshock time differences are somewhat more variable, yielding k/c of 0.31 and 0.46 for the periods 1904 to 1980 and 1970 to 1983, respectively (Tsapanos et al., 1988). The closeness of all these coefficients to the natural logarithm is another example of the decay rates being similar to the

25 1934 M. K. SAVAGE AND D. M. DEPOLO Omori decay law. These decay rates were not significantly changed if we used corrections similar to those described above for the foreshock probabilities and distribution of events at given magnitude differences. This is probably caused by the similarity in decay rates between foreshocks and aftershocks. Incorporating the decay of hazard with time from equations (6) and (7) into equations (4) and (5), and using the same conventions as above, we get the following probabilities Ps that a mainshock is still to occur after a given time t: Ps(Mm, t) = O.11*Io-O85(M~-Mr)[ lOglo(t + 1)], Ps(Mm, t) = O.06*10-0"72(Mm-ir)[ lOgl0(t 1)], Ps(Mm, t) = 0.17"10-96(M'~ Mw)[ oglo(t + 1)] (Nevada) (10R) (Nevada Corrected) (10C) (Mammoth/Mono). (llr) Ps(Mm, t) = 0.095"10 0"89(Mm-Mf)[ oglo(t + 1)] (Mammoth/Mono Corrected). (11C) We have plotted equations 10C and 11C for Figure 12 for M m = Mf and for M m -Mf = 1.0. Note that these curves give slightly different values at zero time than the values in Table 2 for probability that an event will occur in the 10 Probability that Mainshock will Occur v o Probability of Mm >= Mf- Nevada I [] Probability of Mm >= Mf--Mammoth I I--<> Probability of Mm >= Mf Nevada I... ~ t y of Mm >= Mf Mammoth.Q O n : ~ ) ~ ( Number of Hours after Proposed Foreshock FIG. 12. Probability that a mainshock will still occur as a function of hours after a proposed foreshock, calculated according to equations 10C and 11C.

26 FORESHOCK IN GREAT-BASIN AND SIERRA NEVADA 1935 next few days. This is because there is a slightly different averaging procedure being used in each case. In the table, we have calculated probabilities with "binned" magnitudes at 0.5-unit intervals, then averaged the rates over values for given magnitudes of proposed foreshocks. The b-values were calculated for true magnitude differences between foreshocks and mainshocks, and will be weighted more heavily to the smaller foreshocks, which are more numerous. To get the probability of occurrence in any hour, we follow Jones (1985), by using the rate of decay given in equation (9) and the fact that 20% of the mainshocks occur in the first hour after the foreshock, yielding the probability that a mainshock will occur in the first hour as for Nevada and for Mammoth/Mono. Again using the same convention for labeling, the probability that a mainshock of magnitude M m will occur within the hour t after a given earthquake of magnitude Mf the becomes: P(M m, t) = 0.022"10 085(Mm-Mf)[(t + 1) 1.0] (Nevada) (12R) P(M m, t) = O.O12*lO-0"72(Mm-Mr)[(t + 1) -1' ] (Nevada) (12C) P(Mm, t) = O.034*lO-0"96(M'n-Mr)[(t + 1) -1 ] (Mammoth/Mono) (13R) P(Mm, t) = O.019*lo-OSg(M'-Mr)[(t + 1) 1.0] (Mammoth/Mono). (13C) Thus, the risk of a larger event following moderate events in Nevada is similar to that in southern California, and that in the Mammoth/Mono region is somewhat higher than in southern California. In the 226,000-km square region of western Nevada and northeastern California covered by our Nevada catalog, the background probability of earthquake occurrence in any given 15-km radius circle in any 10 days, calculated from the "declustered" catalog from 1934 to 1991, is: 0.07% for M = 4.0, 0.011% for M = 5.0, and % for M = 6.0 (Table 3). If a magnitude 5.0 earthquake occurs, however, the empirical chances of another M = 5.0 or higher event increase to 6%, or over 500 times the background rate, and the chances of an M = 6.0 or higher event increase to 2%, or over 1200 times the background level (Table 3). The background seismicity rates in the 18,700-km square Mammoth/Mono area have increased since TABLE 3 EARTHQUAKE OCCURRENCE RATES IN NEVADA, 1934 TO 1991 (AFTERSHOCKS NOT INCLUDED) M N N/t (1/yr) Usual Probability (%) Risk increase M = 4.0 Risk increase M x x x X x M represents event magnitude. N represents the total number of events (that were not aftershocks of a larger event) in the catalog at or above that magnitude. N/t is the average number of events per year at that magnitude or above, and Usual Probability is the background probability that an event of that magnitude or larger will occur within any given 15-kin radius circle and 10-day interval. Risk increase represents the increase in likelihood for an event at the given magnitude level or higher to occur, following another event of magnitude 4.0 or 5.0.

27 1936 M. K. SAVAGE AND D. M. DEPOLO 1978; but, if we ignore that increase, the average background probability for the 58 years covered by our catalog is 0.042% for an event of M = 4.0 or higher occurring in any given circle of 10-km radius in any given 5-day period, decreasing to % for M = 5.0, and % for M = 6.0. Following an M = 5.0 event, then, the probability of another M = 5.0 event within 10 km and 5 days increases to 10% (1600 times as large as background), and the probability of M = 6.0 or larger event increases to 2% (1200 times as large as background). These large increases in risk still represent a rather small risk of a large event, but are sufficient that a warning to emergency planners and to the public is appropriate. Particularly in Nevada, much of the populace has come from California and assumes that they have left "earthquake country" behind them. It would be reasonable to remind them that after a moderate earthquake, they are at the same risk for a larger earthquake that they would have been if they had felt the same earthquake in southern California. CONCLUSIONS The UNRSL catalog is not homogeneous either in space or time, and the calculation of the percentage of moderate earthquakes that are followed by larger events is dependent on the parameters and method used to remove aftershocks from the earthquake catalog. The effect is most severe in the Mammoth/Mono region and is less severe when considering mainshocks at least 0.5 units greater in magnitude than the proposed foreshocks. The simple space-time window of the Gardner-Knopoff method is easiest to apply to an inhomogeneous catalog, and the results for foreshock probabilities are close to the best estimates from the Reasenberg method. Therefore, the Gardner-Knopoff method may be the best technique for removing aftershocks from a catalog when the object is simply to calculate foreshock probabilities, especially with catalogs that have variable quality station coverage in different regions and time periods. Estimates of the probability that a moderate event will soon be followed by a larger event range from 5% to 11% for events in the Nevada region and from 9.5% to 17% for events in the Mammoth/Mono region. The differences between the two regions is significant at the 90% confidence level and may be related to the swarm-like nature of sequences in high heat-flow regimes. Apparent decreases in probability with increasing magnitude for several of the aftershock-removal parameters are probably caused by misidentification of aftershocks, and therefore the lower estimates are probably more accurate. Figures of 6% for Nevada and 10% for the Mammoth/Mono region are considered to be conservative estimates, suitable for reporting probabilities to emergency management personnel and to the general public. Estimates of the probability that a moderate event will soon be followed by an event at least 0.5 or 1.0 units larger range from 3% to 7%, and from 1.5% to 3%, respectively. Differences between these values for the Nevada and Mammoth/Mono regions are not statistically significant, and these values are similar to those in southern California. These probabilities represent a large increase compared to the background probability of occurrence of events in any similar time and space window. It would be reasonable to remind the general populace that after a moderate event in Nevada, they are at the same risk for a larger earthquake that they would have been if they had felt the same earthquake in southern California.

28 FORESHOCK IN GREAT-BASIN AND SIERRA NEVADA 1937 As in southern California, the decay of hazard with time is fit well by a power-law decay of t- 1.0, similar to that of the decay of aftershock hazard with time; and the differences between foreshock and mainshock magnitudes are similar to standard b-value relationships between all earthquakes. Incorporating the decay of hazard with time and the differences in foreshock/ mainshock magnitudes, at a time t hours after a given earthquake of magnitude Mf has occurred,' we get the following probability that a mainshock of magnitude M~ is still to come, from the "corrected" values above: Ps(Mm, t) = O.06*lO-0"72(M~-Mw)[ ogl0(t + 1)] (Nevada), Ps(Mm, t) = O.095*lO-0"89(Mm-Mw)[1 -- ln(t + 1)] (Mammoth/Mono). ACKNOWLEDGMENTS P. Reasenberg supplied declustering computer codes and advice at many stages of the study. K. Smith provided an early version of the foreshock probability calculation code. L. Jones, C. Jones, J. Louie, J. Anderson, J. Brune, and J. Carr also provided helpful advice. D. vonseggern and an anonymous reviewer provided useful reviews. This work has been funded by USGS grants G1973 and A0618, and FEMA grant NV EP104 EPSA. REFERENCES Aki, K. (1965). Maximum-likelihood estimate of b in the formula log N = a - bm and its confidence limits, Bull. Earthquake Res. Inst., Tokyo Univ. 43, Agnew, D. C. and L. M. Jones (1991). Prediction probabilities from foreshocks, J. Geophys. Res. 96, 11,959-11,971. Arabasz, W. J., J. C. Pechmann, and E. D. Brown (1992). Observational seismology and the evaluation of earthquake hazards and risk in the Wasatch Front area, Utah, U.S. Geol. Surv. Profess. Pap., 1500-D, D1-D36. Bakun, W. H. (1984). Seismic moments, local magnitudes, and coda-duration magnitudes for earthquakes in central California, Bull. Seism. Soc. Am. 74, Bevington, P. R. (1969). Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, New York. Burington, R. S. and D. C. May (1953). Handbook of Probability and Statistics with Tables, Handbook Publishers, Inc. depolo, D. M., W. A. Peppin, A. A. Aburto, and M. K. Savage (1992). University of Nevada, Reno Seismological Laboratory Bulletin: Seismicity in the Western Great Basin May 10, 1984 to December 31, 1989 Univ. of Nevada Report. Davis, S. D. and C. Frohlich (1991). Single-link cluster analysis, synthetic earthquake catalogues, and aftershock identification, Geophys. J. Int. 104, Doser, D. I. (1990). Foreshocks and aftershocks of Large (M >= 5.5) earthquakes within the western Cordillera of the United States, Bull. Seism. Soc. Am. 80, Engdahl, E. R. and W. A. Rinehart (1988). Seismicity Map of North America Geological Soc. America, Centennial Special Map CSM-4 scale 1 : 5,000,000. Engdahl, E. R. and W. A. Rinehart (1991). Seismicity map of North America project, in: Neotectonics of North America, D. B. Slemmons, E. R. Engdah], M. D. Zoback, D. D. Blackwell (Editors), Geological Society of America, Boulder, Colorado, Evernden, J. F. (1969). Precision of epicenters obtained by small numbers of worldwide stations, Bull. Seism. Soc. Am. 59, Gardner, J. and L. Knopoff (1974). Is the sequence of earthquakes in southern California, with aftershocks removed, Poissonian? Bull. Seism. Soc. Am. 64, Gawthrop, W. H. and W. J. Carr (1988). Location refinement of earthquakes in the southwestern Great Basin, , and seismotectonic characteristics of some of the important events, U.S. Geol. Surv. Open-File Rept., , 64 pp. Gomberg, J. (1991). Seismicity and threshold in the Great Basin, J. Geophys. Res. 96, 16,401-16,414. Gross, S. J. and L. M. Jones (1988). Characteristics of earthquake clusters in southern California, (abstract) Seism. Res. Lett. 58, 21. Habermann, R. E. (1987). Man-made changes of seismicity rates, Bull. Seism. Soc. Am., 77,

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