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Aftershock decay, productivity, and stress rates in Hawaii:

Indicators of temperature and stress from magma sources

Fred W. Klein,1 Tom Wright,2 and Jennifer Nakata3

Received 19 July 2005; revised 10 January 2006; accepted 11 April 2006; published 25 July 2006.

[1] We examined dozens of aftershock sequences in Hawaii in terms of Gutenberg-Richter and modified Omori law parameters. We studied p, the rate of aftershock decay;Ap, the aftershock productivity, defined as the observed divided by the expected numberof aftershocks; and c, the time delay when aftershock rates begin to fall. We found that forearthquakes shallower than 20 km, p values >1.2 are near active magma centers. Weassociate this high decay rate with higher temperatures and faster stress relaxation nearmagma reservoirs. Deep earthquakes near Kilauea’s inferred magma transport path show arange of p values, suggesting the absence of a large, deep magma reservoir. Aftershockproductivity is >4.0 for flank earthquakes known to be triggered by intrusions but isnormal (0.25 to 4.0) for isolated main shocks. We infer that continuing, post-main shockstress from the intrusion adds to the main shock’s stress step and causes higher Ap. HighAp in other zones suggests less obvious intrusions and pulsing magma pressure nearKilauea’s feeding conduit. We calculate stress rates and stress rate changes from pre-mainshock and aftershock rates. Stress rate increased after many intrusions but decreasedafter large M7–8 earthquakes. Stress rates are highest in the seismically active volcanoflanks and lowest in areas far from volcanic centers. We found sequences triggered byintrusions tend to have high Ap, high (>0.10 day) c values, a stress rate increase, andsometimes a peak in aftershock rate hours after the main shock. We interpret these valuesas indicating continuing intrusive stress after the main shock.

Citation: Klein, F. W., T. Wright, and J. Nakata (2006), Aftershock decay, productivity, and stress rates in Hawaii: Indicators of

temperature and stress from magma sources, J. Geophys. Res., 111, B07307, doi:10.1029/2005JB003949.

1. Introduction

1.1. Hawaiian Earthquakes

[2] A variety of patterns characterize aftershock sequen-ces around Hawaiian volcanoes. Some main shocks producedozens of aftershocks and others very few; some sequenceslast months or years, and others last a day or two. Ratherthan just counting aftershocks or measuring rates, we madea systematic study of aftershock sequence parameters. Weincluded apparently isolated sequences, sequences triggeredby intrusions, deep and shallow aftershocks, and sequencesfar from a volcanic center. We want to see if aftershocksequence parameters reveal the proximity of magma, andshow the effects of stresses from magma transport. Thispaper examines several aftershock parameters of potentialapplication to earthquakes anywhere in the world, andapplies the analysis to several questions about the workingsof Hawaiian volcanoes.

[3] Three active and two dormant volcanoes form theisland of Hawaii. The most active volcanoes, Kilauea andMauna Loa, grow with accumulating lava flows and withintrusions into their rift zones, the latter accommodated byseaward directed spreading on their south and west sides[e.g., Tilling and Dvorak, 1993]. The island of Hawaiiboasts a great variety of types of earthquake activity, mostof which is associated with Kilauea and Mauna Loa. Intenseswarms accompany eruptions and intrusions [e.g., Klein etal., 1987], long-period earthquakes reveal locations ofvolcano conduits [e.g., Koyanagi and Chouet, 1987; Wrightand Klein, 2006], large flank earthquakes up to M 7.9 oftenoccur by lateral slip of flank blocks on the decollementsurfaces at their base [e.g., Wyss, 1988; Klein et al., 2001],and upper mantle earthquakes deeper than 20 km occurprimarily near the Kilauea and Mauna Loa conduits [e.g.,Klein and Koyanagi, 1989; Wolfe et al., 2003]. Lessernumbers of crustal and upper mantle earthquakes occurboth onshore and offshore beneath the rest of the island.[4] Shallow swarms often accompany intrusions into

Kilauea’s rift zones as the summit deflates as magma drainsfrom the reservoir under the caldera. Some intrusions end ina rift eruption. Larger magma intrusions often compress theadjacent south flank and generate an earthquake response[Dvorak et al., 1986]. The south flank response may be anearthquake swarm without a dominating main shock, a mainshock–aftershock sequence, or a combination of the two.

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111, B07307, doi:10.1029/2005JB003949, 2006ClickHere

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1U.S. Geological Survey, Menlo Park, California, USA.2U.S. Geological Survey, Blaustein Department of Earth and Planetary

Sciences, Johns Hopkins University, Baltimore, Maryland, USA.3U.S. Geological Survey, Hawaiian Volcano Observatory, Hawaii

National Park, Hawaii, USA.

This paper is not subject to U.S. copyright.Published in 2006 by the American Geophysical Union.

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http://dx.doi.org/10.1029/2005JB003949

[5] Kisslinger [1996] presents an excellent summary ofthe analysis and physical interpretation of aftershocksequences. The modified Omori model of aftershock timedecay (rate � (t + c)�p [Utsu, 1961]) generally provides thebest fit to observed aftershock data before seismicity returnsto background levels, and has a minimum number of freeparameters [Kisslinger, 1996]. Kisslinger explores thestretched exponential, epidemic-type aftershock sequence,and full Dieterich models to the aftershock rate curve. Wechoose the simpler modified Omori model because it hasfewer parameters and because we do not need a formula thatfits individual secondary aftershock sequences or that mod-els rates as they return to a constant background level.

1.2. Physical Basis of p Value Variation

[6] Kisslinger [1996] provides a good overview of thephysical basis of variation in p value. There is evidence thatp value increases and that aftershocks decay faster in high-temperature areas. Mogi [1962, 1967] found higher p valueson the side of Japan next to the Japan Sea relative those onthe Pacific Ocean side, and associated these higher p valueswith higher crustal temperature and faster stress relaxation.Kisslinger and Jones [1991] found that higher p values inSouthern California are in areas of high heat flow: thehighest p values greater than 1.35 were in the geothermallyactive Salton Trough and Walker Pass. Creamer andKisslinger [1993] found that only fast aftershock decayoccurs in areas in Japan with estimated temperature morethan 400oC, and cooler areas can have a range of decayrates. Wiemer and Katsumata [1999] found that p value iscorrelated with areas of high slip in the four aftershockzones they studied. They hypothesize that areas with morefrictional heating produce higher p values. If steady statecreep is a mechanism of stress decay after the stress step ofa main shock, creep is empirically accelerated at highertemperatures [i.e., Jaeger and Cook, 1969, chapter 11].[7] Stress decay must also be considered along

with temperature when interpreting p values. Mikumo andMiyatake [1979, 1983] performed numerical experimentsand concluded that the p value is larger (faster decay) formore rapidly relaxing stress relaxation times. This is inagreement with Dieterich’s [1994, Figure 8] modeling offaster aftershock decay with higher rates of logarithmicstress decrease after the main shock.[8] Fault strength and stress heterogeneity are also im-

portant. Mikumo and Miyatake [1979] found that p is largerfor a more homogeneous distribution of fault strength. Utsu[1961] also found that p value is larger for a morehomogeneous distribution of shear strength on the fault,and for faster recovery of shear strength on the fault. Thiseffect of homogeneity does not seem to be the dominant onein Hawaii because the strength of faults near active volcaniccenters such as Kilauea and Mauna Loa is unlikely to behomogeneous given the common occurrence of intrusions,lava flows, and hydrothermal and magmatic fluids.Helmstetter and Shaw [2006] found that a heterogeneousdistribution of stress change can lower the p value from the1.0 value predicted for a uniform stress change, but did notindicate a way to increase p above 1.0 using Dieterich’s[1994] rate-and-state friction law.[9] There is no good evidence that p varies strongly with

depth. Davis and Frohlich [1991] found that p was lower

for a set of intermediate depth and deep earthquakes thanfor a set of shallow ridge and transform earthquakes.Nyffeneggar and Frohlich [2000] found the opposite depthbehavior: p was higher for two deep earthquakes than for aset of intermediate depth earthquakes, and that neitherdiffered significantly from shallow sequences.[10] We seek physical interpretations of the Omori decay

parameter p of Hawaiian sequences. We also use themodified Omori model to estimate aftershock productivity,and then interpret its variation. Finally, we suggest thatproperties of aftershock sequences may be used to revealaspects of stress rates and to identify the presence of magmain other volcanic systems.

2. Methodology

[11] We chose a model where aftershock rates followthe Gutenberg-Richter and modified Omori laws [e.g.,Reasenberg and Jones, 1989]:

R t;Mð Þ ¼ 10aþb Mm�Mð Þ tþ cð Þ�p ð1Þ

where R(t, M) is the aftershock rate at time t after the mainshock, for magnitude M and greater. Here, Mm is the mainshock magnitude, a is the rate parameter, b is the magnitudeparameter, c is the time delay parameter, and p is theaftershock decay parameter.[12] We use a practical definition of aftershocks. We use

earthquakes within one week of the main shock to definethe aftershock zone, and use this zone to select aftershocksand to determine the background earthquake rate. After-shocks end as the Omori decay curve reaches a backgroundlevel. We may thus have included a few background earth-quakes in the aftershock counts, but our results do notchange because the number of possible background eventsis small. Rate comparisons before and after main shockswere only done for larger and readily identifiable aftershockzones with lots of earthquakes.[13] We simplify the aftershock history by ignoring any

spatial variability of aftershocks and ignoring lobes of stresschange from the main shock. Most main shock focalmechanisms are unknown, and the number of aftershocksis generally too small to compare with calculated stresslobes.

2.1. Omori Parameters

[14] We determined the modified Omori parameters a, b,c and p using Reasenberg’s [1994] program aspar. Theprogram allows the user to choose the minimum magnitude,and beginning and ending times after the main shock. Theprogram determines the four parameters by a maximumlikelihood technique based on the method of Ogata [1983].Good parameter fitting requires a well-recorded sequencewith a magnitude range of about 3 or 4 between the mainshock magnitude and the completeness magnitude Mc. Wegenerally set the minimum magnitude Mmin for countingaftershocks to Mc so the linear Gutenberg-Richter relationpredicts the number of events we count. Because the mainshock initially obscures the seismograms, or because apower failure may prevent recording immediately after themain shock, aftershocks are only used after recording iscomplete down to Mc. Aftershocks are used before the rate

B07307 KLEIN ET AL.: AFTERSHOCKS IN HAWAII

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returns to the background rate, or until another main shockoccurs.[15] Our standard aftershock sequence (Figure 1, open

symbols) follows the Ms 7.2 Kalapana earthquake of29 November 1975, which is the largest earthquakerecorded by the modern Hawaii seismic network. Kalapanais a good standard event because its parameters are welldetermined and a majority of other sequences are in thesame south flank region. We tried using different standardevents other than the 1975 Kalapana earthquake, but foundthe general patterns of parameters, which depend on thechoice of a standard event, did not change. The 29 Novem-ber 1975 decay parameter p = 0.82 is typical of flankearthquakes in Hawaii. The upper curve (Figure 1) is forM � 2.6 aftershocks which are complete as judged bylinearity of the frequency-magnitude distribution. The ratecurve shown by the line was fit using aftershocks between0.25 and 100 days after the 29 November 1975 main shock.The first 4 hours of aftershocks are missing because ofseismograph failure. After 100 days, the earthquake rateexceeded that extrapolated from the initial aftershock decay

curve, and in this case approached a background level ofabout one earthquake per day.[16] We want to evaluate the number of aftershocks

following different main shocks. Once a, b, c and p aredetermined for our standard aftershock sequence, we canestimate the expected number of recorded aftershocks Ncalc

for any sequence by integrating equation (1) from theminimum magnitude Mmin to Mm and over the time periodof valid aftershock recording. The result uses only themagnitude spread DM = Mm � Mmin. When the numberof aftershocks is large, a log(rate) versus log(t) plot similarto Figure 1 is how we choose the time interval that showsnormal Omori decay. When the number of aftershocks issmall, we choose a standard interval from 0.05 to 5 daysfollowing the main shock for counting and calculatingaftershock numbers. We used Reasenberg’s [1994] programenas to do the integration and estimate the expected numberof aftershocks Ncalc.[17] An objective measure of aftershock productivity is a

quantity we will use to compare different main shocks. Wedefine aftershock productivity as Ap = Nobs/Ncalc, whereNobs is a count of aftershocks larger than Mc. Ap can thus bedetermined for many small sequences which have only afew recorded aftershocks.[18] Aftershock productivity Ap is sensitive to the main

shock’s magnitude. For example, underestimating the mainshock magnitude by 0.3 can cause Ap to increase twofold.Productivity values are also sensitive to variations in catalogcompleteness and magnitude irregularities. Because theratio Ap may have a large error, we plot only its logarithmand interpret only large variations in aftershock productiv-ity, and seek values from many sequences to form a pattern.

2.2. Stress Parameters

[19] Dieterich [1994] took a major step in practicalseismology when he related changes in earthquake rate tochanges in stress. He derived aftershock rates and obtainedthe modified Omori’s law from a constitutive law with rateand state-dependent fault properties. Dieterich models anaftershock sequence resulting from a shear stress step Dt.Unlike the descriptive Omori law, Dieterich physicallyrelates aftershock rates to stress parameters and includes areturn to background rates if the stressing rate continuesunchanged after the main shock. Dieterich [1994, equation[13]] expressed the earthquake rate increase above thebackground rate at the time of the main shock by a stressterm

R0=r ¼ e Dt=Asð Þ ð2Þ

R0 is the aftershock rate immediately after the main shock att = 0 but before the rate begins to decay. We use R0 forearthquakes of the background minimum magnitude Mc orgreater; r is the background rate. ‘‘A’’ is a faultconstitutive parameter, generally 0.005 to 0.012 [Dieterich,1994, p. 2604], Dt is the shear stress change and s is thenormal stress. This relation has been experimentally verified[e.g., Gross and Kisslinger, 1997]. We measure R0 graphi-cally from the aftershock rate curves like Figure 1 or 2a and2b. Both R0 and r must be referred to the same minimumcompleteness magnitude for counting earthquakes, but thecompleteness magnitudes before and after the main shock

Figure 1. Aftershock rate curves for two large earth-quakes. The M 7.2, 29 November 1975 Kalapana earth-quake (top curves, open symbols) is the largest earthquakerecorded by the modern seismic network. It is our‘‘standard’’ earthquake because the aftershock parameters(a, b, c, and p) describing the Kalapana aftershock rates areused to calculate the expected aftershock numbers for otherearthquakes. The south Hawaii M 5.2, 1 February 1994event is the best recorded deep (35 km) earthquake (solidsymbols). The lower 29 November 1975 curve estimatesaftershock rates with the same magnitude spread DM =Mm � Mmin = 3.9 (between the main shock and aftershockcutoff magnitudes) as the deep 1994 event. In other words,the lower curve is shifted downward by a factor of 0.22 tothe rate expected for M � 3.3 aftershocks using equation(3). Identical magnitude spreads facilitate comparisonbetween the aftershock rates of the two earthquakes.


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may not be the same; b0 is the slope of the aftershockfrequency-magnitude distribution whose rate we are adjust-ing. R0 (for a standard background completeness magnitudeMc) can be calculated from R0

0 (for the aftershock complete-ness magnitude M0

c) using

R0 ¼ R0010

�b0 Mc�Mc0ð Þ ð3Þ

If you equate the modified Omori law (equation (1)) withDieterich’s [1994, equation [13]] rate equation for t c,other stress terms can be derived from measurable seismicityrate parameters

As= _tr ¼ 10aþb Mm�Mcð Þ=r ¼ G ð4Þ

where _tr is the background or reference stressing rate. Weabbreviate the exponential expression of a, b, r andDMas theaftershock ‘‘gain’’ G, which has the units of days. G is ameasure of the sustained aftershock rate relative to the pre-main shock rate r. Equation (4) relates an empirical butmeasurable rate expression to a stress expression based onDieterich’s [1994] rate-state friction constitutive law. Equa-tion (4) allows inferences about stress rates to be made fromaftershock earthquake rates. The abbreviation and definitionof G is arbitrary but convenient. Dieterich [1994] assumeseither the applied stressing rate after the main shock is 0 (wedo not assume this), or the time forwhich a and b aremeasuredis before the aftershock rate begins to return to backgroundlevels (we do assume this).[20] The aftershock duration ta and aftershock gain G are

useful parameters because they show the stress rate changesof main shocks in different situations. We measure tadirectly from the aftershock decay curve as the time when

the aftershock rate stops decaying and reaches a constantbackground rate. Like G, ta can be related to stress rates. tais the fundamental relaxation time in Dieterich’s [1994,equations [12] and [14]] rate equation

ta ¼ As= _t ð5Þ

where _t is the stress rate after the main shock; _t thus has adirect effect on the level of postaftershock backgroundseismicity. Note that G and ta are different quantitiesdepending on stress rate before and after the main shock,respectively, that we will compare later in the paper.[21] A relation between stress decay and p value falls

beautifully from Dieterich’s [1994] rate equations: Dieter-ich’s Figure 8 noted that Omori aftershock decay withdifferent decay rates (p values) is consistent with differentrates of logarithmic time decay of stress after a main shock.

Figure 2a. Aftershock zones of three types of sequenceswith different decay rates and aftershock productivity. Eachsequence uses a different plotting symbol.

Figure 2b. Aftershock rate curves for three main shocksillustrating different types of aftershock sequences. (1) TheM 6.7, 16 November 1983 earthquake in the Kaoiki seismiczone is a large flank earthquake with a typical 0.75 p value(open triangles, point down). (2) The 10 August 1981sequence followed an M 4.3 earthquake in Kilauea’s southflank, which was triggered by an intrusion into Kilauea’sadjacent southwest rift zone (open triangles, point up). The0.80 p value of this intrusion sequence is comparable toother flank earthquakes. (3) The aftershock decay rate (p =2.67) of the M 4.3, 24 January 1993 event near KilaueaCaldera (solid triangles), however, is much higher than theothers. The three curves are normalized to the samemagnitude spread DM = Mm � Mmin = 3.2 between themain shock and aftershock cutoff magnitudes to facilitaterate comparison. The caldera and intrusion aftershocksequences are considerably more productive than theaftershocks of the 16 November 1983 earthquake, whichhad no known immediate triggering event.


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Dieterich added a logarithmic term to the stress historyapplied to a region after the main shock’s stress step t0:

t tð Þ ¼ t0 þ u ln wtþ 1ð Þ ð6Þ

If u is 0 or positive (applied stress is constant or increaseswith the logarithm of time), aftershocks decay with p = 1.0[Dieterich, 1994]. Aftershocks decay with a range of pvalues above and below 1.0 for the case of a negative u(post-main shock stress decreases with the logarithm oftime). Empirically, Dieterich’s figure yields u �p/5 (fornegative u) after the characteristic time w�1, for Dieterich’schoice of A, s, and Dt. Thus the faster the stress decay afterthe main shock, the more rapid the aftershock decay.Dieterich thus provides a physical link between p value andstress decay.[22] The time parameter c in Omori’s law can also be

represented using Dieterich’s [1994, equations [15] and[16]] rate equation, where we define c0 as this estimate of c

c0 ¼ As= _trð Þe �Dt=Asð Þ ¼ 10aþb Mm�Mcð Þ=R0 ¼ Gr=R0 ð7Þ

Thus c0 can be estimated from the initial aftershock rate R0

and the aftershock frequency-magnitude relation. Dieterich[1994, equation [18]] refers to c0 as te, the time for the rate tomerge with the 1/t asymptote. Our quantity c, on the otherhand, is determined by fitting the aftershock rate curvedirectly. The c in the Omori relation is often difficult toestimate from the shape of the aftershock decay curvebecause it depends on measuring the changes in theaftershock rate immediately after the main shock. The c0

is also difficult to estimate because it depends on measuringthe rate R0 in the first hour or hours after the main shock.[23] Stress change Dt, background stress rate _tr, and c0

value are determined from aftershock rates and are allrelated. Dt/As depends on aftershock rate early in thesequence (equation (2)), and As/ _tr depends on sustainedrates (equation (4)). It is therefore sensible that Dt/As andAs/ _tr should be highly correlated. Transforming equation(7) implies there is a linear relationship if the Omori timedelay c0 is a constant

Dt=As ¼ ln As= _trð Þ � ln c0ð Þ ð8Þ

We will examine this relation for Hawaiian earthquakes inmore detail later.

2.3. Main Shock and Aftershock Selection

[24] We use aftershock sequences from 1960 to 2001selected from the catalog of the Hawaiian Volcano Obser-vatory (2002, October 1959 through 2001 Hawaiian earth-quake catalog, unpublished annual computer files availableat ftp computer sites, through the Council of the NationalSeismic System and other sources), supplemented with afew well-recorded 1868–1951 aftershock sequences fromthe historical catalog of Klein and Wright [2000]. Momentmagnitudes are only available for a very few Hawaiianearthquakes, and we rely mostly on local magnitudesdetermined with a Wood-Anderson seismometer, teleseis-mic surface wave magnitudes, or on scales calibratedagainst them.

[25] We included as large a selection of main shocks aswe could. All M � 4.8 earthquakes, and many smallerearthquakes that produced at least two aftershocks largerthan their completeness magnitude Mc, were examined aspotential main shocks. We excluded offshore events withpoor network coverage. We also excluded swarms at Loihisubmarine volcano, which has no aftershocks with Omoridecay. The lack of Omori decay suggests that stresses atLoihi are largely magmatic, with rapid variation and nogradual stress buildup that can cause isolated main shocks.Table 1 lists the essential parameters of all the main shockswe used.[26] Of special interest in our aftershock study are trig-

gered main shocks, namely those with an identifiablecausative event stressing the main shock area withinminutes, hours or days before the main shock. By thisdefinition, triggered main shocks include flank earthquakesadjacent to an active rift intrusion, and larger aftershocks,which may become ‘‘main shocks’’ if they have their ownsecondary aftershocks. Many earthquakes may be ‘‘trig-gered’’ by a sudden stress increase whose origin is un-known, and we will examine earthquakes where we did notclass them as triggered even though they behave likeearthquakes with a known triggering event. We searchedfor and found many triggered sequences but used them onlyif they had Omori time decay. The flank earthquakestriggered by large intrusions such as December 1974 andJune 1982 had several episodes of high swarm activity buthad Omori decay only at the end of the sequence when theintrusion had largely ended. Klein et al. [1987] has timeplots of the seismicity of these and other intrusions thatinclude Omori aftershock sequences.[27] We also studied aftershocks of the great M 7.9 Kau

earthquake of 2 April 1868 [Wyss, 1988] using the catalogof Klein and Wright [2000]. Including aftershocks of anearthquake this old is remarkable. An excellent diary ofHawaiian earthquakes felt at Hilo, with enough descriptionto determine intensities, exists for 1833–1917 [Wyss et al.,1992b]. We also determined the background seismicity ratebefore and after the Kau aftershock sequence. The medianmagnitude corresponding to maximum intensity V earth-quakes in this era is 5.3 [Klein and Wright, 2000]. Thecompleteness magnitude of the post-1840 seismicity isabout 5.2 because of linearity of the frequency-magnituderelation. Thus the record of intensity V (M 5.3) earthquakesfelt at Hilo is probably complete. The Kau earthquakeaftershock catalog has 239 M � 5.2 events in 19 years,after which rapid Omori decay ends and seismicity resumesa more constant rate. Because the 1868 rupture zoneincludes most of south Hawaii and coincides with thecontemporary active seismic zones, we assume that allintensity V or greater earthquakes felt in Hilo or southHawaii are within the Kau rupture zone.

3. Observations

3.1. Aftershock Decay Parameter p

[28] Our study compiled 40 aftershock p values of goodquality rated A, B or C (Table 1; details are in givenTable 2). C-rated sequences are included in plots becausetheir p values have the same geographic correlations as Aand B rated sequences and thus reinforce their behavior.


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Table 1. Essential Parameters of Hawaiian Main Shocksa

Date Time, LT

Latitude Longitude

Depth, km Location Mm Mmin p Value and Quality c Ap Notesbdeg min deg min

Shallow Earthquakes28 Mar 1868 1328 19 6.00 155 39.00 �10 Hilea 7.0I 5.2 0.84 ± 0.57 d- - (43) int 22 Apr 1868 1600 19 12.00 155 30.00 �10 Hilea 7.9I 5.2 0.77 ± 0.09 a (0.41) (6.1) int 2,325 Oct 1913 0057 19 21.00 155 1.00 �10 S. flank 5.8H �3 0.71 ± 0.17 b - -5 Jul 1914 1918 19 26.00 155 24.00 �10 Kaoiki 4.8N �2 0.77 ± 0.22 c - -5 Oct 1929 2122 19 43.00 156 5.00 �10 Hualalai 6.5S �3 1.95 ± 0.73 c- - -16 Jun 1940 2356 21 0.00 155 18.00 �10 Maui 6.0S �3.5 0.89 ± 0.12 b - -21 Feb 1942 0811 19 32.00 155 28.00 8.00 M.Loa 6.1H �3 0.89 ± 0.23 c - -27 Apr 1942 2143 19 32.00 155 28.00 5.00 M.Loa 6.1A �3 1.32 ± 0.29 c - -21 Aug 1951 0057 19 30.00 155 57.00 �10 Kona 6.9S 3.0 0.91 ± 0.05 a 0.02 0.9330 Mar 1954 0842 19 21.00 155 0.00 10.00 S. flank 6.4H 2.6 - - 0.1827 Jun 1962 1827 19 23.89 155 27.10 10.18 Kaoiki 6.1L 2.3 (0.9) (0.3) (2.2) 19 May 1969 1533 19 21.61 155 4.57 12.70 S. flank 4.2L 1.9 1.08 ± 0.36 D - 7.68 Oct 1969 1417 19 13.82 155 20.97 0.01 SW.flank 3.4L 1.9 1.93 ± 0.61 D - 114 int9 Nov 1969 1912 19 11.20 155 32.38 9.64 Hilea 4.5L 2.1 - - 1.4324 Nov 1969 0912 19 44.18 156 5.75 2.27 Hualalai 4.6L 2.6 - - 2.712 Apr 1970 0913 19 23.84 155 26.18 9.78 Kaoiki 4.3L 2.0 - - 6.421 Sep 1970 0126 19 19.93 155 12.18 10.82 S. flank 4.5L 1.9 1.05 ± 0.56 D - 2.730 Sep 1971 2128 19 16.11 155 20.74 0.95 SW.flank 4.2L 2.0 0.97 ± 0.24 B 0.05 17 int9 Dec 1971 0215 19 20.17 155 6.72 8.18 S. flank 4.3L 1.9 0.73 ± 0.25 D - 2.929 Dec 1971 0042 19 15.18 155 22.27 6.39 SW.flank 4.3L 1.9 1.09 ± 0.05 A 0.02 31 int29 Feb 1972 1208 19 21.60 156 20.48 6.43 Kona 5.0L 2.6 - - 1.1131 Mar 1972 1620 19 20.12 155 3.55 9.70 S. flank 4.5L 1.9 - - 1.155 Sep 1972 0131 19 19.69 155 12.35 10.14 S. flank 5.2L 1.9 - - 0.8423 Dec 1972 0904 19 34.83 155 57.09 15.97 Kona 5.1L 2.8 - - 1.4415 Apr 1973 0059 19 19.39 155 7.06 9.89 S. flank 4.5L 2.1 - - 2.912 Jan 1974 0604 19 19.83 155 7.25 8.87 S. flank 4.7L 2.0 0.62 ± 0.17 C - 2.119 Jun 1974 0505 19 22.78 155 25.32 10.36 Kaoiki 4.6L 1.9 0.95 ± 0.09 A 0.03 2720 Jun 1974 2050 19 19.70 155 12.60 9.50 S. flank 4.4L 1.8 - - (0.81) 227 Aug 1974 2149 19 19.59 155 12.31 10.28 S. flank 4.4L 1.8 - - 1.6330 Nov 1974 0354 19 26.28 155 25.17 6.09 Kaoiki 5.5L 2.0 0.95 ± 0.09 A 0.06 13.115 Dec 1974 2317 19 24.35 155 26.00 9.01 Kaoiki 4.5L 1.9 0.69 ± 0.07 A 0.01 35 aft25 Dec 1974 1813 19 13.87 155 18.11 9.72 S. flank 4.2L 1.4 0.78 ± 0.23 C - 0.5831 Dec 1974 1240 19 17.79 155 21.74 2.62 SW.flank 5.6L 2.0 (1.27 ± 0.05) 1.42 17 int4 Jan 1975 1532 19 14.79 155 22.31 5.58 SW.flank 4.8L 2.0 0.86 ± 0.10 A 0.01 19.5 int21 May 1975 2232 20 17.42 155 39.33 11.81 Kohala 4.7L 2.8 - - (0) 29 Jul 1975 0840 19 31.86 155 28.50 7.15 M.Loa 4.6L 2.0 1.28 ± 0.25 B 0.06 22 int10 Nov 1975 0126 19 21.26 155 1.58 9.79 S. flank 4.5L 2.1 - - 2.315 Nov 1975 1255 19 18.69 155 13.51 10.74 S. flank 4.5L 1.4 - - 3.829 Nov 1975 0447 19 20.34 155 0.26 9.14 S. flank 7.2S 2.6 0.82 ± 0.06 A (0.43) 0.84 329 Nov 1975 2015 19 25.16 155 22.37 11.75 Kaoiki 4.6L 2.5 0.49 ± 0.14 B 0.17 8.2 trig29 Jan 1976 1019 19 22.20 154 58.90 9.91 S. flank 4.5L 2.5 - - (0) aft20 Feb 1976 1951 20 23.16 156 3.36 6.93 Kohala 5.1L 2.9 - - (0) trig24 Feb 1976 0550 19 21.70 155 6.40 9.30 S. flank 4.3L 2.6 - - 24 aft2 Apr 1976 0814 19 20.36 155 6.34 9.91 S. flank 4.6L 2.4 - - 1.7 aft4 Jun 1976 2250 19 21.27 155 6.97 9.88 S. flank 4.3L 2.3 - - 8.7 aft18 Dec 1976 0401 19 19.75 155 6.89 9.70 S. flank 5.0L 2.0 0.95 ± 0.40 D - 1.9614 Jan 1977 1326 19 19.66 155 7.19 9.87 S. flank 4.8L 2.0 - - 1.213 Feb 1977 1520 19 20.75 155 4.44 9.93 S. flank 4.5L 2.1 - - 2.420 Apr 1977 1849 19 55.95 155 19.69 12.97 M.Kea 4.8L 2.4 0.82 ± 0.17 C - 1.545 Jun 1977 2342 19 21.61 155 4.88 9.52 S. flank 5.3L 2.1 - - 0.9419 Aug 1977 0819 19 19.73 155 7.09 10.22 S. flank 4.5L 2.0 - - (0.76) 215 Sep 1977 1850 19 20.33 155 3.59 9.42 S. flank 4.2L 2.0 0.80 ± 0.11 A 0.82 83 int23 Sep 1977 0208 19 20.96 155 2.70 8.60 S. flank 4.1L 2.0 - - 32 int23 Jun 1978 0147 19 19.08 155 15.46 10.37 S. flank 4.5L 2.1 - - 2.31 Jul 1978 0918 19 18.39 155 6.74 7.89 S. flank 4.5L 1.95 - - 2.911 Sep 1978 2016 19 19.87 155 6.52 9.60 S. flank 4.5L 2.0 - - 2.414 Dec 1978 0412 19 18.60 155 13.53 10.36 S. flank 4.4L 1.7 - - 1.8227 Dec 1978 0040 19 20.06 155 12.95 9.81 S. flank 4.4L 1.7 - - (1.32) 210 Mar 1979 0355 19 19.95 155 6.69 9.56 S. flank 4.7L 2.0 - - 2.121 Mar 1979 2047 20 1.66 155 48.18 13.57 Kohala 4.7L 2.0 0.88 ± 0.11 B 0.01 1.827 Mar 1979 2130 20 0.44 155 46.92 10.66 Kohala 5.1L 2.0 - - 0.6031 Jul 1979 0330 19 28.13 155 25.81 11.86 Kaoiki 4.5L 1.8 - - 1.3221 Sep 1979 2159 19 20.65 155 4.23 9.28 S. flank 5.7L 1.7 0.83 ± 0.06 A 0.01 2.227 Sep 1979 0535 19 19.66 155 7.25 9.96 S. flank 4.6L 1.95 - - 4.113 Dec 1979 1744 19 24.82 155 24.47 11.36 Kaoiki 4.3L 2.1 - - (0.72) 212 Mar 1980 0257 19 21.45 155 14.21 1.85 Koae 4.3L 1.7 - - 4.2 int11 Aug 1980 2042 19 19.91 155 6.23 10.09 S. flank 4.4L 2.0 - - 10 int1 Mar 1981 0701 19 21.46 155 2.05 9.20 S. flank 4.7L 2.0 - - 1.828 Jul 1981 1000 19 21.45 155 1.60 8.70 S. flank 4.4L 2.0 - - (0.57) 210 Aug 1981 0820 19 19.02 155 21.03 2.02 SW.flank 4.3L 1.8 0.80 ± 0.06 A 0.34 11.4 int22 Aug 1981 1205 20 11.25 156 25.05 9.43 Hual.OS 4.5L 2.9 - - (0) 2


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Table 1. (continued)

Date Time, LT

Latitude Longitude


10 Nov 1981 0302 19 20.37 155 12.71 10.17 S. flank 4.5L 1.8 1.00 ± 0.27 C - 2.721 Jan 1982 1152 19 13.61 155 35.57 10.14 Hilea 5.6L 1.8 1.06 ± 0.04 A 0.03 2.511 Apr 1982 1604 19 19.71 155 6.69 9.24 S. flank 4.5L 1.8 - - 0.6114 May 1982 0626 19 59.90 155 51.78 18.69 Kohala 4.8L 2.7 - - (1.07) 218 May 1982 1736 19 57.37 156 25.57 0.87 Hual.OS 4.8L 2.9 - - (0) 224 Jun 1982 2059 19 16.86 155 21.65 7.13 SW.flank 3.0L 1.8 1.33 ± 0.39 C - (433) int 212 Aug 1982 0043 19 24.89 155 16.08 16.20 K.caldera 4.3L 1.9 0.82 ± 0.18 B 0.02 2.98 Mar 1983 0641 19 11.89 155 35.64 11.49 Hilea 4.6L 2.2 - - 1.4220 Mar 1983 1718 19 21.51 155 3.04 6.95 S. flank 4.9L 1.8 - - 1.820 Mar 1983 2302 19 21.88 155 25.08 11.12 Kaoiki 4.0L 1.8 - - 2.927 Apr 1983 2334 19 19.74 155 7.59 8.35 S. flank 4.3L 1.8 - - 1.813 May 1983 0030 19 10.12 155 34.83 9.34 Hilea 4.4L 2.0 - - (0.38) 29 Sep 1983 0630 19 19.79 155 7.32 8.96 S. flank 5.7L 1.8 - - 0.5516 Nov 1983 0613 19 25.76 155 27.12 10.97 Kaoiki 6.7S 2.1 0.75 ± 0.02 A (0.17) 1.00 321 Feb 1985 1948 19 19.61 155 12.66 9.37 S. flank 4.8L 1.7 0.54 ± 0.11 B 0.01 1.87 Jul 1985 0200 19 9.97 155 35.66 10.28 Hilea 4.5L 1.8 1.57 ± 0.37 C - 2.112 Dec 1985 0901 20 34.97 155 45.11 23.64 Kohala 5.0L 2.6 - - (0) 26 Apr 1986 2237 19 12.18 155 36.86 8.42 Hilea 4.4L 1.8 - - 0.769 Jul 1986 0228 19 31.74 155 56.03 12.59 Kona 4.4L 2.1 - - 2.163 Feb 1987 1622 20 4.42 156 25.25 0.05 Hual.OS 5.2L 2.7 1.02 ± 0.07 B 0.02 1225 Nov 1987 1849 20 20.60 156 14.35 17.20 Maui 4.4L 2.6 - - (1.39) 219 Feb 1988 1847 19 21.46 155 1.67 8.70 S. flank 4.2L 1.9 - - 2.21 Mar 1988 2241 19 19.60 155 12.50 10.13 S. flank 4.9L 1.8 - - 0.3924 Mar 1988 1429 19 57.00 156 23.91 2.00 Hual.OS 5.0L 2.2 1.21 ± 0.45 D - 2.427 Mar 1988 1733 19 56.56 156 24.18 2.29 Hual.OS 5.1L 3.0 0.93 ± 0.07 B 0.02 221 Apr 1988 1848 19 54.92 156 22.99 31.46 Hual.OS 4.9L 2.7 - - 5.611 May 1988 1314 19 47.04 155 31.30 23.03 M.Kea 4.3L 1.9 0.92 ±0.24 D- - 1.83 Jul 1988 1938 19 12.81 155 27.31 9.47 Hilea 5.4L 1.8 0.65 ± 0.08 B 0.01 0.3513 Aug 1988 1620 20 12.18 156 29.66 7.72 Hual.OS 4.5L 3.0 - - (0) 225 Jun 1989 1727 19 21.53 155 5.01 9.30 S. flank 6.2L 2.0 - - 1.4327 Dec 1989 2313 19 19.60 155 12.41 9.42 S. flank 5.3L 1.6 0.62 ±0.54 D- - 0.411 Aug 1990 1937 19 49.55 155 37.29 18.36 M.Kea 4.7L 2.1 0.80 ± 0.08 B 0.01 2.38 Aug 1990 1606 19 20.02 155 6.76 9.21 S. flank 4.8L 1.8 - - 0.8124 Jan 1993 2214 19 25.34 155 19.20 6.01 K.caldera 4.3D 1.1 2.67 ± 0.49 A 0.31 12.326 Jan 1993 0524 19 13.47 155 29.73 9.43 Hilea 4.8D 1.4 1.35 ± 0.17 B 0.03 0.398 Jun 1993 0257 19 20.61 155 12.88 9.85 S. flank 5.3D 1.3 - - 0.2819 Mar 1995 2229 20 3.13 156 34.52 0.41 Hual.OS 4.3D 3.0 - - (0) 211 May 1995 0349 20 4.05 155 20.97 5.96 M.Kea 4.8D 1.8 - - 0.2321 Jan 1996 1109 19 50.83 155 31.37 20.71 M.Kea 4.4D 1.6 1.27 ± 0.31 C - 2.218 Jul 1996 0739 19 53.61 155 35.02 14.70 M.Kea 4.2D 1.6 - - (0.38) 223 Nov 1996 1639 19 19.90 155 12.34 10.50 S. flank 4.3D 1.5 - - 1.4630 Jun 1997 0547 19 21.13 155 4.02 9.16 S. flank 5.5D 1.5 0.96 ± 0.19 B 0.01 0.3814 Aug 1997 1554 19 20.03 155 6.90 8.93 S. flank 5.0D 1.3 1.14 ± 0.45 D - 0.5527 Sep 1998 2156 19 26.28 155 13.59 0.80 K.caldera 4.6U 1.8 1.44 ± 0.39 C - 1.4628 Sep 1998 2039 19 20.78 155 7.59 9.52 S. flank 4.8U 1.3 0.86 ± 0.27 B 0.03 1.0622 Nov 1998 0554 20 24.43 156 4.17 27.71 Kohala 4.5U 2.2 - - (0.72) 216 Apr 1999 1456 19 15.34 155 29.38 9.37 Hilea 5.6U 1.1 0.96 ± 0.07 A 0.01 0.7126 May 1999 0601 19 25.21 155 19.50 7.64 K.caldera 4.3U 1.5 1.33 ± 0.20 B 0.02 3.93 Jun 1999 0141 19 58.56 155 33.18 27.67 M.Kea 4.4U 1.8 - - 016 Aug 1999 1405 19 16.85 155 30.12 8.97 Hilea 4.4U 1.8 - - 0.741 Apr 2000 2018 19 20.73 155 12.50 9.46 S. flank 5.0U 1.0 - - 0.2625 Apr 2001 1737 19 25.44 155 18.28 6.34 K.caldera 4.4U 1.0 - - 0.60

Earthquakes Known to Be Deeper Than 20 km23 Jul 1961 0528 19 23.60 155 17.95 23.78 D.Kilauea 4.4L 2.6 - - 2325 Aug 1961 0845 19 49.84 155 5.20 43.53 M.Kea 4.6L 3.2 - - (0) 211 May 1971 1600 18 57.14 155 33.00 37.08 D.SW.rift 4.7L 2.4 - - 1.815 Aug 1971 1536 19 21.95 155 16.70 34.04 D.Kilauea 4.9L 2.3 - - 1.122 Apr 1973 2107 20 1.33 154 35.66 33.72 offshore 5.0L 3.5 - - (0) 226 Apr 1973 1026 19 51.92 155 9.17 38.71 M.Kea 6.2S 2.4 1.11 ± 0.14 A 0.29 0.719 Oct 1973 0153 19 20.24 155 16.07 32.50 D.Kilauea 4.8L 2.3 - - 4.713 Dec 1973 0425 19 22.44 155 17.54 34.84 D.Kilauea 4.8L 2.3 - - 1.525 Dec 1974 0747 19 20.86 155 16.84 32.30 D.Kilauea 4.8L 2.0 0.97 ± 0.27 C - 2.16 Nov 1975 0205 19 20.56 155 18.83 31.90 D.Kilauea 4.6L 2.0 0.94 ± 0.19 B - 2.27 Sep 1977 1351 19 22.37 155 19.34 31.42 D.M.Loa 4.6L 2.1 - - 2.131 Aug 1978 1307 18 59.97 155 28.97 35.25 D.SW.rift 4.5L 2.2 - - 2.16 Mar 1979 0507 19 31.23 155 16.20 27.53 D.Kilauea 4.8L 2.1 - - 0.4419 Jan 1980 1528 19 18.67 155 32.41 26.84 D.SW.rift 4.5L 2.2 - - 012 Jan 1981 0418 19 21.33 155 18.28 31.19 D.Kilauea 4.9L 2.1 - - 1.515 Mar 1981 2017 19 22.42 155 14.03 31.57 D.Kilauea 4.4L 2.1 - - 4.37 Feb 1983 1602 19 21.44 155 14.46 28.08 D.Kilauea 4.3L 2.1 - - 2.6


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D-rated p values are not plotted or interpreted. The older1868–1959 catalog requires special treatment. Lowercaseratings a–d are for older sequences with larger magnitudeerrors. We only use the two a-rated p values from the M 7.9,2 April 1868 Kau earthquake, and the M 6.9, 21 August1951 Kona earthquake in this study.[29] Two important Hawaiian aftershock sequences have

contrasting decay curves: the 1 February 1994 deep (35 km)M 5.2 earthquake (solid symbols, Figure 1) decays faster thanthe 29 November 1975 reference earthquake located beneathKilauea’s south flank (open symbols). We must use the samemagnitude spread DM = Mm � Mc to compare the twoaftershock curves. The magnitude spread of the 1994 se-quence is DM = 5.2 � 1.3 = 3.9. Rather than decimating the1975 aftershocks with an Mmin = 3.3 cutoff to get the samemagnitude spread, we shift theM� 2.6 curve downward by afactor of 0.22 to the rate expected for M � 3.3 aftershocksusing equation (3) (open symbols, lower curve, Figure 1).The deep 1 February 1994 earthquake thus has a higher initialaftershock rate in the first day, but a faster decay rate.[30] Examples of three aftershock sequences with con-

trasting p values are in Figures 2a and 2b. The M 6.7, 16November 1983 earthquake in the Kaoiki seismic zone, likethe M 7.2 November 1975 earthquake (Figure 1), is anexample of a large flank earthquake with a well-recordedaftershock sequence. The 10 August 1981 sequence followsan M 4.3 earthquake in Kilauea’s south flank that wastriggered by an intrusion into Kilauea’s adjacent southwest

rift zone. The p value of this intrusion sequence (0.80) iscomparable to other isolated flank earthquakes. The after-shock decay rate of the M 4.3, 24 January 1993 event nearKilauea caldera, however, is much higher. Its 2.67 ± 0.49p value is the highest we found.[31] Earthquake sequences of different types have similar

p values. Three earthquake classes, shallow (less than 20 kmdepth), deep, and those triggered by an intrusion or aprimary main shock, all have similar peaked p distributionswith p mostly in the range 0.7 to 1.1. The p distributions ofthese three classes have means of 1.03 ± 0.39, 1.05 ± 0.19and 0.83 ± 0.24 (all 1s errors) respectively. Thus there is noapparent p value dependence on whether the main shockwas triggered, and no dependence on depth.

3.2. Aftershock Productivity

[32] We estimate the productivity (relative to the standardevent) of 130 Hawaiian aftershock sequences with theparameter Ap = Nobs/Ncalc (Table 1). Table 3 lists detailedparameters used in the calculation. For example, we counted72 aftershocks of the 1 February 1994 earthquake from0.0125 to 125 days after the main shock (Figure 1)compared to an expected number of 54, for a productivityof Ap = 1.3. Note that a productivity calculation of thestandard 29 November 1975 earthquake will not alwaysyield exactly 1.0. The productivity calculation uses theparameters a, b, c and p of the standard event, plus themagnitude spread and time window of each sequence, and


Date Time, LT

Latitude Longitude


30 Jun 1985 1112 19 22.39 155 17.87 26.89 D.Kilauea 4.5L 2.1 - - 022 Apr 1986 1843 19 17.89 155 16.24 32.14 D.Kilauea 4.4L 2.2 - - 3.519 Sep 1986 0444 19 20.20 155 21.10 30.82 D.Kilauea 4.2L 1.9 - - 4.317 Jul 1988 1725 19 15.46 155 16.18 31.52 D.Kilauea 4.3L 1.8 - - 0.958 May 1991 0821 19 20.49 156 13.30 30.50 Kona OS 5.5L 2.7 - - 0.491 Feb 1994 0001 19 15.39 155 17.99 34.73 D.Kilauea 5.2S 1.3 1.39 ± 0.12 A 0.12 1.321 Jun 1998 0221 19 12.65 155 20.64 46.48 D.Kilauea 4.2U 1.9 - - 1.417 Feb 2000 1419 19 20.21 155 16.76 35.29 D.Kilauea 4.5U 1.4 0.84 ± 0.15 C - 0.65

aDate and time are Hawaii Standard Time as quoted from original sources and computer files. Depth is depth below the epicentral ground surface.Earthquakes in northern Hawaii with depths between 20 and 30 km are grouped with the ‘‘shallow’’ earthquakes because their depth distribution and timebehavior suggest they are not distinguishable from earthquakes shallower than 20 km. Location is earthquake source region determined by Klein andWright [2000] or by computer location. Abbreviations are D.Kilauea, deep Kilauea caldera; D.M.Loa, deep Mauna Loa volcano; D.SW.rift, deep zoneunder Kilauea’s SW rift zone; Hilea, Hilea seismic zone in Mauna Loa’s south flank; Hualalai, Hualalai volcano area; Hual.OS, Hualalai offshore (west riftzone); K.caldera, Kilauea caldera; Kaoiki, Kaoiki seismic zone in Mauna Loa’s SW flank; Koae, Koae fault zone immediately south of Kilauea caldera;Kohala, Kohala volcano; Kona, Kona coast (west coast of Hawaii); Maui, Maui island region; M.Kea, Mauna Kea volcano; M.Loa, Mauna Loa volcanocaldera or rift zones; S. flank, south flank of Kilauea; SW.flank, west part of south flank of Kilauea. Mm is main shock magnitude. The magnitude is chosenas the best type available from either Klein and Wright [2000] or the modern HVO catalog. The codes are I, intensity areas from isoseismal map; H,Honolulu seismogram amplitude reading; N, nomogram based size class from HVO Bosch-Omori; S, surface wave amplitude; A, average of 2 or moretypes; L, local from Hilo Wood Anderson; D, coda duration; U, local based on amplitudes from analog stations with approximate Wood-Andersonresponse. Mmin is minimum (completeness) magnitude of aftershock sequence. The p value is the decay parameter of aftershock rate expression. The letter(A, B, C etc.) is a quality rating of the p value based on the calculated error in the p value and the number N of aftershocks. Quality letters in lowercaseindicate that p values meet the same criteria but are based on the early catalog with larger magnitude and completeness uncertainty: A, p(error)/p < 0.3 andN > 100; B, p(error)/p < 0.3 and N > 20; C, p(error)/p < 0.3 and N > 8; D, p(error)/p < 0.6 and N > 8 D quality sequences are judged too poor to plot orinterpret. C is time delay parameter of aftershock rate expression derived from fitting the rate curve; c is usually not well determined. When c values are inparentheses, the early aftershock recording is incomplete and the c value is very poor. Ap is aftershock productivity defined as NOBS/NCALC, where NCALC

is the expected number of aftershocks calculated from the a, b, c, and p. Parameters of the ‘‘standard’’ 29 November 1975 sequence.bNotes are int, preceded by a rift intrusion; aft, an aftershock sequence following an aftershock; trig: triggered by the 29 November 1975 main

shock. (1) Before 1968, earthquakes were recorded at HVO on smoked paper. It was common practice to manually advance the pen carriage everyrevolution of the drum to prevent trace overlap during times of intense seismicity [see Koyanagi et al., 1966, Figure 4]. This was done in the firstday or so of the aftershock sequence and resulted in more complete recording and catalog completeness in the first hours than in the following days.Thus the catalog of located earthquakes does not determine a good p value. The tabulated p value is from Koyanagi et al. [1966], who used agraphical fit to a log-log plot of aftershock numbers from 1 to 70 days after the main shock. They also determined the c value from a linear plot ofM � 0.5 aftershocks. (2) The aftershock productivity ratio is not plotted or interpreted because there was not a large enough main shock (as theleading event in an Omori decay period during a swarm) for a meaningful ratio; the observed number of aftershocks (0-1) was too small for ameaningful ratio; or the 1868 earthquake aftershocks in the early days of the sequence have imprecise magnitude estimates and catalog completeness.(3) First few hours of aftershocks not recorded, c value probably incorrect.


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Table 2. Time Parameters of Aftershock Sequencesa

Date Where Depth Mm Mmin N p a b c t1 t2 Notesb

Shallow (z < 20 km)28 Mar 1868 Hilea �10? 7.0 5.0 25 0.84 ± 0.57 d- - - - 0.04 5 19 int2 Apr 1868 Hilea �10? 7.9 5.2 239 0.77 ± 0.09 a �3.51 1.11 (0.41) 0.16 7000 19 int25 Oct 1913 S. flank �10? 5.8 �3 47 0.71 ± 0.17 b - - - 1.0 200 205 Jul 1914 Kaoiki �10? 4.8 �2 18 0.77 ± 0.22 c - - - 0.1 31 205 Oct 1929 Hualalai �10? 6.5 �3 37 1.95 ± 0.73 c- - - - 8 1000 20, 2316 Jun 1940 Maui �10? 6.0 �3.5 27 0.89 ± 0.12 b - - - 0.01 140 20, 2121 Feb 1942 M. Loa �10? 6.1 �3 16 0.89 ± 0.23 c - - - 0.01 20 20, 2227 Apr 1942 M. Loa �10? 6.1 �3 13 1.32 ± 0.29 c - - - 0.01 50 20, 2221 Aug 1951 Kona �10? 6.9 3.0 116 0.91 ± 0.05 a �2.84 1.02 0.02 0.016 250 2027 Jun 1962 Kaoiki 10.2 6.1 2.3 53 0.9 - 0.98 0.3 1 70 19 May 1969 S. flank 12.7 4.3 1.9 18 1.08 ± 0.36 D - - - 0.016 98 Oct 1969 SW flank 1–9 3.4 1.9 45 1.93 ± 0.61 D - - - 0.10 31 18 int21 Sep 1970 S. flank 10.8 4.5 1.9 9 1.05 ± 0.56 D - - - 0.01 830 Sep 1971 SW flank 1.0 4.2 2.0 25 0.97 ± 0.24 B �2.58 1.54 0.05 0.02 33 15 int9 Dec 1971 S. flank 8.2 4.3 1.9 17 0.73 ± 0.25 D - - - 0.016 3529 Dec 1971 SW flank 6.5 4.5 1.9 128 1.09 ± 0.05 A �1.14 0.98 0.02 0.016 700 16 int12 Jan 1974 S. flank 8.0 4.7 2.0 17 0.62 ± 0.17 C - - - 0.01 1619 Jun 1974 Kaoiki 10.4 4.6 1.9 140 0.95 ± 0.09 A �2.32 1.39 0.03 0.01 1730 Nov 1974 Kaoiki 6.1 5.5 2.0 300 0.95 ± 0.09 A �1.74 1.03 0.06 0.016 815 Dec 1974 Kaoiki 9.0 4.5 1.9 156 0.69 ± 0.07 A �1.22 1.03 0.01 0.01 14 2 aft25 Dec 1974 So Coast 9.7 4.4 1.4 10 0.78 ± 0.23 C - - - 0.06 630 331 Dec 1974 SW flank 2.6 5.6 2.0 880 (1.27 ± 0.05) �0.69 0.91 1.42 0.01 250 4 int4 Jan 1975 SW flank 5.6 4.8 2.0 108 0.86 ± 0.10 A �1.11 0.90 0.01 0.01 8.5 2,4 int9 Jul 1975 M. Loa 7.2 4.6 2.0 84 1.28 ± 0.25 B �1.25 1.09 0.71 0.06 35 11 int29 Nov 1975 Kalapana 9.2 7.2 2.6 401 0.82 ± 0.06 A �2.42 0.93 (0.43) 0.25 10029 Nov 1975 Kaoiki 11.8 4.6 2.5 46 0.49 ± 0.14 B �1.99 1.06 0.17 0.10 280 10 trig18 Dec 1976 S. flank 9.7 5.0 2.0 16 0.95 ± 0.40 D - - - 0.05 16 aft20 Apr 1977 M. Kea 13.0 4.9 2.4 13 0.82 ± 0.17 C - - - 0.014 25015 Sep 1977 S. flank 9.4 4.2 2.0 259 0.80 ± 0.11 A �0.94 1.19 0.82 0.02 70 12 int21 Mar 1979 Kohala 13.6 4.7 2.0 23 0.88 ± 0.11 B �1.43 0.66 0.01 0.01 250 1321 Sep 1979 S. flank 9.3 5.7 1.7 214 0.83 ± 0.06 A �2.28 0.97 0.01 0.01 1810 Aug 1981 SW flank 2–9 4.3 1.8 229 0.80 ± 0.06 A �1.18 1.01 0.34 0.016 310 14 int10 Nov 1981 S. flank 10.2 4.5 1.8 16 1.00 ± 0.27 C - - - 0.01 821 Jan 1982 Hilea 10.2 5.6 1.8 192 1.06 ± 0.04 A �1.40 0.75 0.03 0.03 660 524 Jun 1982 SW flank 7.1 3.0 1.8 417 0.52 ± 0.05 A �0.37 1.53 0.39 0.013 130 17 int12 Aug 1982 Caldera 16.2 4.3 1.9 9 1.33 ± 0.39 C - - - 0.01 1820 Mar 1983 S. flank 7.0 4.9 1.8 27 0.82 ± 0.18 B �4.10 1.55 0.02 0.016 1816 Nov 1983 Kaoiki 11.0 6.7 2.1 947 0.75 ± 0.02 A �3.85 1.26 (0.17) 0.16 35521 Feb 1985 S. flank 9.4 4.8 1.7 56 0.54 ± 0.11 B �2.64 1.10 0.01 0.01 317 Jul 1985 Hilea 10.3 4.5 1.8 13 1.57 ± 0.37 C - - - 0.016 353 Feb 1987 Offshore 0.1 5.2 2.7 50 1.02 ± 0.07 B �1.75 1.01 0.02 0.016 630 624 Mar 1988 Offshore 2.0 5.0 2.2 12 1.21 ± 0.45 D - - - 0.01 3.1 6,727 Mar 1988 Offshore 2.3 5.1 3.0 58 0.93 ± 0.07 B �1.24 0.95 0.02 0.016 550 611 May 1988 M. Kea 23.0 4.3 1.9 7 0.92 ±0.24 D- - - - 0.01 140 83 Jul 1988 Hilea 9.5 5.4 1.8 54 0.65 ± 0.08 B �3.28 1.02 0.01 0.01 50025 Jun 1989 S. flank 9.3 6.2 2.0 154 1.09 ± 0.10 A �3.64 1.24 0.06 0.016 15.827 Dec 1989 S. flank 9.4 5.3 1.6 53 0.62 ±0.54 D- - - - 1.0 31 91 Aug 1990 M. Kea 18.4 4.7 2.1 34 0.80 ± 0.08 B �2.58 1.14 0.01 0.01 70024 Jan 1993 Caldera 6.0 4.3 1.1 160 2.67 ± 0.49 A �1.17 0.88 0.31 0.01 7.926 Jan 1993 Hilea 9.4 5.3 1.4 36 1.35 ± 0.17 B �2.75 1.02 0.03 0.01 4021 Jan 1996 M. Kea 20.7 4.4 1.6 16 1.27 ± 0.31 C - - - 0.01 830 Jun 1997 S. flank 9.2 5.5 1.5 32 0.96 ± 0.19 B �4.22 1.26 0.01 0.01 814 Aug 1997 S. flank 8.9 5.0 1.3 16 1.14 ± 0.45 D - - - 0.016 527 Sep 1998 Caldera 0.8 4.6 1.8 8 1.44 ± 0.39 C - - - 0.01 8028 Sep 1998 S. flank 9.5 4.8 1.3 28 0.86 ± 0.27 B �3.17 1.15 0.03 0.01 916 Apr 1999 Hilea 9.4 5.6 1.1 163 0.96 ± 0.07 A �1.12 0.57 0.01 0.01 1826 May 1999 Caldera 7.6 4.3 1.5 26 1.33 ± 0.20 B �1.55 0.74 0.02 0.01 35

Deep (z > 20 km)26 Apr 1973 Honomu 38.7 6.2 2.4 65 1.11 ± 0.14 A �2.57 1.00 0.29 0.28 17825 Dec 1974 Kilauea 32.3 4.8 2.0 13 0.97 ± 0.27 C - - - 0.01 166 Nov 1975 Kilauea 31.9 4.55 1.7 20 0.94 ± 0.19 B - - - 0.027 701 Feb 1994 S Hawaii 34.7 5.2 1.3 93 1.39 ± 0.12 A �3.10 1.08 0.12 0.013 8917 Feb 2000 Kilauea 35.3 4.5 1.4 15 0.84 ± 0.15 C - - - 0.014 300

aDepth is in km below the local ground surface; Mm is main shock magnitude; Mmin is minimum (completeness) magnitude of aftershock sequence; N isnumber of aftershocks larger than or equal to Mmin and between t1 and t2 used to fit the four parameters; p, a, b, and c are parameters of aftershock rateexpression; and c is usually not well determined (early aftershock recording is incomplete when c values are in parentheses). The letter (A, B, C etc.) is aquality rating of the p value: A, p(error)/p < 0.3 and N > 100; B, p(error)/p < 0.3 and N > 20; C, p(error)/p < 0.3 and N > 8; D, p(error)/p < 0.6 and N > 8 Dquality sequences are too poor to plot or interpret (quality letters in lowercase indicate the p and N values meet the same criteria, but are based on the earlycatalog with more uncertainty); t1 is start time of aftershocks used for fitting parameters, days after main shock; t2 is end time of aftershocks used for fittingparameters, days after main shock.


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bNotes are int, preceded by a rift intrusion; aft: an aftershock sequence following an aftershock; and trig, triggered by the 29 November 1975 main shock. (1)Before 1968, earthquakes were recorded at HVO on smoked paper. It was common practice to manually advance the pen carriage every revolution of the drum toprevent trace overlap during times of intense seismicity [see Koyanagi et al., 1966, Figure 4]. This was done in the first day or so of the aftershock sequence andresulted in more complete recording and catalog completeness in the first hours than in the following days. Thus the catalog of located earthquakes does notdetermine a good P value. The tabulated P value is fromKoyanagi et al. [1966], who used a graphical fit to a log-log plot of aftershock numbers from 1 to 70 daysafter the main shock. They also determined the c value from a linear plot of M� 0.5 aftershocks, and the b value from a least squares fit of a frequency-magnitudediagram.We determined b = 1.09 from amaximum likelihood fit of the location catalog. (2) An aftershock of an earlier main shock, which had its own aftershocks.Some aftershocks may be used to fit parameters of both the main and secondary aftershock sequences. The end cutoff time to fit both the main and secondarysequences is the point at which the exponential Omori decay visually deviates from a straight line, whether from a new aftershock sequence, onset of backgroundactivity, or resumption of dominance of the primary aftershock sequence. (3) Double main shock of 4.2 and 4.4. (4) This is a ‘‘triggered’’ main shock in Kilauea’ssouth flank adjacent to an intrusion in the SWrift zone.Mechanically, the rift was expanding frommagma intruded from the summit reservoir and stressing the flankfor about a day following themain shock.The first dayof the sequence shows anearly constant earthquake ratewithout any timedecay in rate typical of an aftershocksequence.The curve thus has both constant anddecaying portions. This entire sequencewasused in fitting the rate curve,which corrupts the Pvalue. The stress fromthe rift on the aftershock zone in the flank probably stopped about 2 days after theM5.6main shockwhen the summit tilt bottomed out, indicating that no additionalmagma was being fed into the rift zone. The early part of the sequence thus can be viewed as a superposition of an aftershock sequence of the M5.6 event and anintrusive swarm. Large aftershocks with their own aftershocks occurred on 2 January 1975, 0327 LT (M5.0), 3 January 1975, 0732 LT (M5.1) and 4 January 1975,1532 LT (M4.8). The time after the first two earthquakeswas not long enough to record enough aftershocks to fit an individual rate curve before the next large eventstruck, but the last event (4 January 1975, 1532 LT) yielded a long aftershock sequence and a P value that represents the Omori decay rate of the whole sequence.(5) Double main shock of 5.6 and 5.6. (6) Offshore event more than 60 km outside the seismic network, thus depth is poorly determined. (7) Aftershock sequencetruncated by another main shock. (8) Even though this event has one less aftershock than necessary for quality category D, it is included because it is in an area ofsparse seismicity and helps resolve which of two other nearby P values best represents this volcanically inactive area. (9) Sequence is missing its first day ofaftershocks and is in an area of high background seismicity. The time range is thus shortened at the beginning and end, and the P value is thus unusable. (10) ThisKaoiki event occurred at 2015 LT outside the Kalapana aftershock zone on Kilauea’s south flank and was ‘‘triggered’’ by the 04:47 main shock. (11) Thissequence accompanied and followed the intrusion into Mauna Loa’s NE rift zone following the summit eruption that occurred entirely on 5 July 1975. The largestevents in the sequence wereM4.7 at 1447 LTon 7 July 1975 andM4.6 at 0840 LTon 9 July 1975, near the end of the sequence and the event chosen as the ‘‘mainshock’’ for the parameter fit. The P value thus represents the Omori decay after the intrusion. (12) This is not an aftershock sequence, but a south flank sequence ofearthquakes triggered by an east rift zone intrusion and eruption. There is no obvious main shock. The sequence began on 13 September 1977. The two largestearthquakeswereM4.2 (15 September, 1850 LT) andM4.2 (23 September, 0208 LT). The sequencewas nearly over at the time of the 23 September event, and the15September eventwas chosen the ‘‘main shock’’ time. The slight delay of the decline in earthquake rate (C= 0.82 days) probably results from continuing intrusionand persistence of the swarm at the time of the 15 September earthquake. (13) There were two large events in this sequence asM4.7 (21March 1979, 2047 LT) andM5.2 (27 March 1979, 2130 LT). The larger, second event fits the aftershock decay of the first event, which is the sequence listed in the table. The second eventproduced a few aftershocks but only enough to suggest a similar aftershock decay to the first event, and not enough to independently determine aftershock sequenceparameters. (14) These earthquakes in the south flank were triggered by a SWR intrusion. It is similar to the 31 December 1974 intrusion sequence, but seismicitydecays soon after an intense beginning, like a normal aftershock sequence. The largest events occurred early in the sequence on 10 August 1981 (M4.3 at 0820 LTandM4.7at 0940LT) butwere probably too small for the sequence to beentirely causedby them.The beginning of the sequence ismeasured from the firstM4event.(15) The sequence accompanied and followed an eruption/intrusion into Kilauea’s SW rift zone. The south flank response to the stress increase was this swarm,which culminatedwith anM4.2 event on 30September 1971, 2128LT6days after the swarmbegan. The intrusion had stoppedwhen thisM4.2 event happened andseismicity declined (from the high level of the previous 6 days)with a typical aftershock decay. (16) This sequencewas also apparently the south flank response to anintrusion, though no summit collapse or eruption occurred. It may have reflected magma movement in the SWR following the September 1971 eruption. It had11M4.0or larger events during its duration from23 to29December, and theM4.4 (0042LT)andM4.5 (0138LT)events on28December1971were the last of them.After this time, the sequence decreased in time with a typical Omori power law decay. Test fits of the sequence with the Omori function starting after earlier largeearthquakes showed level seismicity during the swarm (with a C value of several days) followed by a decay, but the determined P values were corrupted withinclusion of the swarm. (17) This sequence is the flank response to an intrusion intoKilauea’s SWrift zone, which occurred during 22–27 June 1982. Therewas nolarge ‘‘main shock’’: the largest flank earthquakewasM3.4 near the beginning of the sequence.We chose theM3.0 event of 24 June 1982, 2059 LT to represent the‘‘main shock’’ because the intensityof the swarmdeclined after this time.This is also the timewhen the summit collapse and tilt ended their sharpdrop, signaling thatthemagma supply to the intrusion ended.This couldbetter be described as a swarmendingwith gradually declining seismicity, rather than amain shock–aftershocksequence. (18) This sequence is the flank response to an intrusion into Kilauea’s SWrift zone, which occurred during 7–11 October 1969. The largest event of thesequencewas onlyM3.4 on 8October 1969, 1417LT in themiddle of the sequence. The sequence is reasonablywell recorded and shows a clearOmori decay in thelast days of the sequence. The P value is higher that other intrusions in this area but unfortunately is not very precise. (19) The 28March 1869 (M7.0) earthquakecould be considered a foreshock of the greatKau earthquake of 2April 1868 (M7.9). These flank earthquakeswere apparently triggered by the intrusion/eruption inMaunaLoa’s SWrift zone. The counted aftershocks are for any earthquakes strongly felt (intensityVor greater, roughly corresponding toM5.3 or larger) anywhereon the island.Wedid not require that the earthquake location be precisely knownbecause the rupture zone encompassedmuchof the south side of the island, becausefew epicenters are well-located, and because aftershocks dominated seismicity for decades. The parameters for the 28 March 1868 event are not well determinedbecause of the short interval before the great earthquake, but it is included because the P value is consistent with the M7.9 event. All magnitudes are based onmaximum intensities, or on isoseismal areas for the larger earthquakes. The imprecise magnitudes and incomplete reporting are adequate for tabulating aftershockswith time. The aftershock record for the month following theM7.9 earthquake is somewhat erratic, but the P value is very well determined by aftershocks between1 month and 19.4years (1887) after themain shock. The error in thePvalue is lower than that stated,which is only basedon the first 1000days of aftershocks. (20)Asequence from the early catalog based on manual processing of two or three stations. The completeness, location certainty, and magnitudes are much less reliablethan in the catalog from the 1970s and later. H. Wood served as HVO’s seismologist during 1913–1916 and was more meticulous than the staff was in later yearsabout cataloging earthquakes andmeasuring their distances and amplitudes. Some sequences are included if they are from an unusual and infrequently active placewhere earthquakes were easy to distinguish from typical seismicity and where uncertainties may be less important. It is known that the sample of earthquakesassigned to a given region is incomplete, but the aftershock decay rate will be valid if the catalog omissions are random. This is true if the probability of any eventbeing left out or misclassified is independent of time. P values from the early catalog are evaluated using the same quality criteria as the later catalog, but qualityletters are shown in lowercase to indicate some additional uncertainty. Except for the 1929Hualalai and 1951Kona sequences, these early sequences are not plottedon themap figuresbecause their exact location is uncertain andmay interferewith interpretationofmodern sequences. (21)The sequence is fromanoffshore seismiczone about 60 km due east of Maui. A second M6.0 earthquake occurred 14 July 1940 and is counted as an aftershock because it did not generate appreciableaftershocks of its own. (22) The locations of these sequences were classed as Mauna Loa NE rift area, but it is not known if they were on the rift or on an adjacentflank. The low P value of the 21 February 1942 event suggests it is a flank event. This M6.1 event preceded the NE rift eruption by 2 months. The M6.1 event of27April 1942 occurredwithin and near the end of the preeruptive swarm and preceded the eruption by 7 hours. The close time associationwith the intrusive swarmand eruption and the high P value suggest that the M6.1, 27 April 1942 earthquake was located closer to or within the rift zone than the 21 February 1942 event.(23) This Hualalai sequence probably represents an intrusive swarm beginning on 18 September 1929, but it certainly involved response on its flanks because thelargest events were M 6.2 on 25 September 1929 andM 6.5 on 5 October 1929. The sequence is a swarm with a gradual onset. The last part of the sequence (after5 October 1929) exhibits Omori decay. The decay is difficult to measure quantitatively because in the 10 days after 5 October 1929, only the largest earthquakeswere measured, but later earthquakes were measured to smaller magnitudes. This means that the effective sensitivity of the catalog increased with time as theseismicity decreased, such that the number of earthquakes in any few days was approximately the same. This probably seemed appropriate to HVO at the timebefore earthquake physics and even the magnitude scale were invented. Therefore the fit of aftershock decay begins 9 days after the largest M6.5 earthquake.


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Table 3. Aftershock Productivitya

Date Where Depth Mm Mmin DM t1 t2 NOBS NCALC AP = NOBS/NCALC Notesb

Earthquakes Shallower Than 25 km28 Mar 1868 Hilea �10? 7.0 5.2 1.8 0.08 3.2 16 0.37 43c int2 Apr 1868 Hilea �10? 7.9 5.2 2.7 0.32 5 17 2.8 6.1c

21 Aug 1951 Kona �10? 6.9 3.0 3.9 0.05 5 40 43 0.9330 Mar 1954 S. flank �10? 6.45 2.6 3.85 0.05 5 7 39 0.18c 1527 Jun 1962 Kaoiki 10.2 6.1 2.3 3.8 0.032 1.26 37 17 2.29 May 1969 S. flank 12.7 4.3 1.9 2.4 0.05 5 13 1.7 7.6 13 int?8 Oct 1969 SW flank 1–9 3.4 1.9 1.5 0.13 5 33 0.29 114c 1 int9 Nov 1969 Hilea 9.7 4.5 2.1 2.4 0.05 8 3 2.1 1.4324 Nov 1969 Hualalai 2.3 4.6 2.6 2.0 0.013 5 2 0.74 2.712 Apr 1970 Kaoiki 9.8 4.3 2.0 2.3 0.08 5 9 1.4 6.421 Sep 1970 S. flank 10.8 4.5 1.9 2.6 0.05 5 7 2.6 2.730 Sep 1971 SW flank 1.0 4.2 2.0 2.2 0.05 5 19 1.12 17 5 int9 Dec 1971 S. flank 8.2 4.3 1.9 2.4 0.05 5 5 1.7 2.929 Dec 1971 SW flank 6.5 4.5 1.9 2.6 0.05 5 65 2.1 31 6 int29 Feb 1972 Kona 6.4 5.0 2.6 2.4 0.013 5 2 1.8 1.1131 Mar 1972 S. flank 9.7 4.5 1.9 2.6 0.05 5 3 2.6 1.155 Sep 1972 S. flank 10.2 5.2 1.9 3.3 0.05 5 10 11.9 0.8423 Dec 1972 Kona 16.0 5.1 2.8 2.3 0.05 5 2 1.39 1.4415 Apr 1973 S. flank 9.9 4.5 2.1 2.4 0.032 5 5 1.7 2.912 Jan 1974 S. flank 8.0 4.7 2.0 2.7 0.05 5 7 3.3 2.119 Jun 1974 Kaoiki 10.4 4.6 1.9 2.7 0.05 5 89 3.3 2720 Jun 1974 S. flank 9.5 4.4 1.8 2.6 0.05 1.26 1 1.23 0.81c

27 Aug 1974 S. flank 10.3 4.4 1.8 2.6 0.05 1.26 2 1.23 1.6330 Nov 1974 Kaoiki 6.1 5.5 2.0 3.5 0.05 5 236 18 13.115 Dec 1974 Kaoiki 9.0 4.5 1.9 2.6 0.05 5 90 2.6 35 aft25 Dec 1974 So Coast 9.7 4.4 1.35 3.05 0.05 8 5 8.6 0.5831 Dec 1974 SW flank 2.6 5.6 2.0 3.6 0.05 2.0 232 14.0 17 7 int4 Jan 1975 SW flank 5.6 4.8 2.0 2.8 0.05 5 80 4.1 19.5 7 int21 May 1975 Kohala 11.8 4.7 2.8 1.9 0.05 5 0 0.58 0c

9 Jul 1975 M. Loa 7.2 4.6 2.0 2.6 0.05 5 56 2.6 22 8 int10 Nov 1975 S. flank 9.8 4.5 2.1 2.4 0.05 5 4 1.72 2.315 Nov 1975 S. flank 10.9 4.5 1.4 3.1 0.05 5 26 6.9 3.829 Nov 1975 Kalapana 9.2 7.2 2.6 4.6 0.31 8 176 209 0.8429 Nov 1975 Kaoiki 11.8 4.6 2.5 2.1 0.13 5 7 0.85 8.2 trig29 Jan 1976 S. flank 9.9 4.5 2.5 2.0 0.05 5 0 0.72 0c aft20 Feb 1976 Kohala 6.9 5.1 2.9 2.2 0.05 5 0 1.11 0c

24 Feb 1976 S. flank 9.3 4.3 2.6 1.7 0.05 5 9 0.30 24 14 aft2 Apr 1976 S. flank 9.9 4.6 2.4 2.2 0.01 5 2 1.15 1.7 aft4 Jun 1976 S. flank 9.9 4.3 2.3 2.0 0.032 2.0 4 0.46 8.7 14 aft18 Dec 1976 S. flank 9.7 5.0 2.0 3.0 0.05 5 11 5.6 1.9614 Jan 1977 S. flank 9.9 4.8 2.0 2.8 0.05 3.2 4 3.3 1.213 Feb 1977 S. flank 9.9 4.5 2.1 2.4 0.05 5 4 1.7 2.420 Apr 1977 M. Kea 13.0 4.9 2.4 2.5 0.05 8 4 2.6 1.545 Jun 1977 S. flank 9.5 5.3 2.1 3.2 0.5 5 9 9.6 0.9419 Aug 1977 S. flank 7.1 4.5 2.0 2.5 0.05 2.0 1 1.32 0.76c

15 Sep 1977 S. flank 9.4 4.2 2.0 2.2 0.05 5 93 1.12 83 9 int23 Sep 1977 S. flank 8.6 4.1 2.0 2.1 0.08 5 28 0.88 32 9 int23 Jun 1978 S. flank 10.4 4.5 2.1 2.4 0.013 5 4 1.76 2.31 Jul 1978 S. flank 7.9 4.5 1.95 2.55 0.05 5 7 2.4 2.911 Sep 1978 S. flank 9.6 4.5 2.0 2.5 0.05 3.2 4 1.7 2.414 Dec 1978 S. flank 10.4 4.4 1.7 2.7 0.05 0.8 2 1.10 1.8227 Dec 1978 S. flank 9.8 4.4 1.7 2.7 0.05 0.5 1 0.76 1.32c

10 Mar 1979 S. flank 9.6 4.7 2.0 2.7 0.05 5 7 3.3 2.121 Mar 1979 Kohala 13.6 4.7 2.0 2.7 0.05 8 7 4.0 1.8 227 Mar 1979 Kohala 10.7 5.1 2.0 3.1 0.32 8 5 8.4 0.60 231 Jul 1979 Kaoiki 11.9 4.5 1.8 2.7 0.05 1.26 2 1.52 1.3221 Sep 1979 S. flank 9.3 5.7 1.7 4.0 0.05 5 118 53 2.227 Sep 1979 S. flank 10.0 4.6 1.95 2.65 0.05 5 12 2.9 4.1 313 Dec 1979 Kaoiki 11.4 4.4 2.1 2.3 0.05 5 1 1.39 0.72c

12 Mar 1980 Koae 1.9 4.3 1.7 2.6 0.05 5 11 2.6 4.2 4 int11 Aug 1980 S. flank 10.1 4.4 2.0 2.4 0.05 5 17 1.7 10 12 int1 Mar 1981 S. flank 9.2 4.7 2.0 2.7 0.05 5 6 3.3 1.828 Jul 1981 S. flank 8.7 4.4 2.0 2.4 0.013 5 1 1.76 0.57c

10 Aug 1981 SW flank 2–9 4.7 1.8 2.9 0.05 5 57 5.0 11.4 10 int22 Aug 1981 Offshore 9.4d 4.5 2.9 1.6 0.05 5 0 0.30 0c

10 Nov 1981 S. flank 10.2 4.5 1.8 2.7 0.05 5 9 3.3 2.721 Jan 1982 Hilea 10.2 5.6 1.8 3.8 0.05 5 87 35 2.511 Apr 1982 S. flank 9.2 4.5 1.8 2.7 0.05 5 2 3.3 0.6114 May 1982 Kohala 18.7 4.8 2.7 2.1 0.006 5 1 0.93 1.07c

18 May 1982 Offshore 0–10d 4.8 2.9 1.9 0.05 5 0 0.58 0c

24 Jun 1982 SW flank 7.1 3.0 1.8 1.2 0.05 5 52 0.12 433c 11 int12 Aug 1982 Caldera 16.2 4.3 1.9 2.4 0.05 5 6 2.1 2.9


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Date Where Depth Mm Mmin DM t1 t2 NOBS NCALC AP = NOBS/NCALC Notesb

8 Mar 1983 Hilea 11.5 4.6 2.2 2.4 0.05 8 3 2.12 1.4220 Mar 1983 S. flank 7.0 4.9 1.8 3.1 0.05 5 14 7.7 1.820 Mar 1983 Kaoiki 11.1 4.0 1.8 2.2 0.05 8 4 1.4 2.927 Apr 1983 S. flank 8.3 4.3 1.8 2.5 0.05 3.2 3 1.7 1.813 May 1983 Hilea 9.3 4.5 2.0 2.5 0.05 8 1 2.6 0.38c

9 Sep 1983 S. flank 9.0 5.7 1.8 3.9 0.05 1.26 11 20 0.5516 Nov 1983 Kaoiki 11.0 6.7 2.1 4.6 0.20 8 220 219 1.0021 Feb 1985 S. flank 9.4 4.8 1.7 3.1 0.05 5 17 9.6 1.87 Jul 1985 Hilea 10.3 4.5 1.8 2.7 0.032 5 7 3.3 2.112 Dec 1985 Kohala 23.6 5.0 2.6 2.4 0.05 5 0 1.7 0c

6 Apr 1986 Hilea 8.4 4.4 1.8 2.6 0.05 5 2 2.64 0.769 Jul 1986 Kona 12.6 4.4 2.1 2.3 0.05 5 3 1.39 2.163 Feb 1987 Offshore 0–10d 5.2 2.7 2.5 0.05 5 26 2.1 1225 Nov 1987 Offshore 17.2d 4.5 2.6 1.9 0.05 8 1 0.72 1.39c

19 Feb 1988 S. flank 8.7 4.2 1.9 2.3 0.05 5 3 1.39 2.21 Mar 1988 S. flank 10.1 4.9 1.8 3.1 0.08 5 3 7.6 0.3924 Mar 1988 Offshore 2.0d 5.0 2.2 2.8 0.032 3.2 8 3.3 2.427 Mar 1988 Offshore 2.3d 5.1 3.0 2.1 0.05 5 20 0.90 221 Apr 1988 Offshore 31.5d 4.9 2.7 2.2 0.05 3.2 5 0.90 5.611 May 1988 M. Kea 23.0 4.3 1.9 2.4 0.05 5 3 1.7 1.83 Jul 1988 Hilea 9.5 5.4 1.8 3.6 0.05 5 8 23 0.3513 Aug 1988 Offshore 7.7d 4.5 3.0 1.5 0.05 5 0 0.24 0c

25 Jun 1989 S. flank 9.3 6.2 2.0 4.2 0.05 5 117 82 1.4327 Dec 1989 S. flank 9.4 5.3 1.6 3.7 0.05 3.2 9 22 0.411 Aug 1990 M. Kea 18.4 4.7 2.1 2.6 0.05 5 6 2.6 2.38 Aug 1990 S. flank 9.2 4.8 1.8 3.0 0.05 5 5 6.2 0.8124 Jan 1993 Caldera 6.0 4.3 1.1 3.2 0.05 5 118 9.6 12.326 Jan 1993 Hilea 9.4 5.3 1.4 3.9 0.05 5 17 43 0.398 Jun 1993 S. flank 9.7 4.8 1.3 3.5 0.05 5 5 18 0.2819 Mar 1995 Offshore 34.5d 4.3 3.0 1.3 0.05 5 0 0.15 0c

11 May 1995 M. Kea 6.0 4.8 1.8 3.0 0.05 32 3 12.9 0.2321 Jan 1996 M. Kea 20.7 4.4 1.6 2.8 0.05 5 9 4.1 2.218 Jul 1996 M. Kea 14.7 4.2 1.6 2.6 0.05 5 1 2.6 0.38c

23 Nov 1996 S. flank 10.5 4.3 1.5 2.8 0.05 5 6 4.1 1.4630 Jun 1997 S. flank 9.2 5.5 1.5 4.0 0.05 5 20 53 0.3814 Aug 1997 S. flank 8.9 5.0 1.3 3.7 0.05 3.2 12 22 0.5527 Sep 1998 Caldera 0.8 4.6 1.8 2.8 0.05 5 6 4.1 1.4628 Sep 1998 S. flank 9.5 4.8 1.3 3.5 0.05 5 19 18 1.0622 Nov 1998 offshore 27.7d 4.5 2.2 2.3 0.05 5 1 1.39 0.72c

16 Apr 1999 Hilea 9.4 5.6 1.1 4.5 0.05 5 110 155 0.7126 May 1999 Caldera 7.6 4.3 1.5 2.8 0.05 5 16 4.1 3.93 Jun 1999 M. Kea 27.7 4.4 1.8 2.6 0.05 5 0 2.64 016 Aug 1999 Hilea 9.0 4.4 1.8 2.6 0.008 5 2 2.72 0.741 Apr 2000 S. flank 9.5 5.0 1.0 4.0 0.032 0.8 5 19 0.2625 Apr 2001 Caldera 6.3 4.4 1.0 3.4 0.05 5 9 15 0.60

Earthquakes Deeper Than 25 km23 Jul 1961 Kilauea 26.2 4.4 2.6 1.8 0.05 5 11 0.47 2325 Aug 1961 Honomu 43.5 4.6 3.2 1.4 0.05 5 0 0.19 0c

11 May 1971 South Point 37.1 4.7 2.4 2.3 0.05 7.9 3e 1.7 1.815 Aug 1971 Kilauea 34.0 4.9 2.3 2.6 0.02 31 6 5.5 1.14 22 1973 NE offshore 33.7 5.0 3.5 1.5 0.05 5 0 0.24 0c

4 26 1973 Honomu 38.7 6.2 2.4 3.8 0.31 20 40 56 0.719 Oct 1973 Kilauea 32.5 4.85 2.3 2.55 0.0125 31 23 4.9 4.713 Dec 1973 Kilauea 34.8 4.8 2.3 2.5 0.031 7.9 4 2.6 1.525 Dec 1974 Kilauea 32.3 4.8 2.0 2.8 0.0079 12.6 13 6.1 2.16 Nov 1975 Kilauea 31.9 4.55 2.0 2.55 0.031 31 11 4.9 2.27 Sep 1977 Kilauea 31.4 4.6 2.1 2.5 0.05 21 8 3.8 2.131 Aug 1978 South Point 35.3 4.4 2.2 2.3 0.0125 5 3 1.4 2.16 Mar 1979 north of Kilauea 27.5 4.8 2.1 2.7 0.0079 31 3 6.8 0.4419 Jan 1980 west of Kilauea 26.8 4.5 2.2 2.3 0.05 5 0 1.4 0c

12 Jan 1981 Kilauea 31.2 4.9 2.1 2.8 0.0079 12.5 9 6.1 1.515 Mar 1981 Kilauea 31.6 4.4 2.1 2.3 0.0125 5 6 1.4 4.37 Feb 1983 Kilauea 28.1 4.3 2.1 2.2 0.02 5 3 1.14 2.630 Jun 1985 Kilauea 26.9 4.5 2.1 2.4 0.05 5 0 1.7 0c

4 22 1986 Kilauea 32.1 4.4 2.2 2.2 0.0079 5 4 1.15 3.519 Sep 1986 Kilauea 30.8 4.2 1.9 2.3 0.0125 5 6 1.4 4.317 Jul 1988 Kilauea 31.5 4.3 1.8 2.5 0.05 5 2 2.1 0.958 May 1991 offshore Kona 30.5 5.5 2.7 2.8 0.05 5 2 4.1 0.491 Feb 1994 south Hawaii 34.7 5.2 1.3 3.9 0.0125 7.9 72 54 1.321 Jun 1998 Kilauea 46.5 4.2 1.9 2.3 0.05 12.6 3 2.1 1.417 Feb 2000 Kilauea 35.3 4.5 1.4 3.1 0.0125 20 9 13.8 0.65


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will vary depending on the parameter choices. We found thatAp calculated from sequences with 2 to 4 aftershocks largerthan Mc followed the same patterns as productivities fromlarger sequences, and thus are meaningful. It is important toevaluate Ap values based on small numbers of aftershockswhen, for example, a large magnitude event produces only 2or 3 aftershocks and is therefore unusual. We only interpretAp as an approximate number, and statistical uncertainty ofindividual numbers is acceptable in our study.[33] The decay curves of Figure 2b show very different

aftershock productivities. The three curves are normalized tothe same magnitude spread DM = Mm � Mmin = 3.2 tofacilitate comparison, by shifting the rate curves usingequation (3). The productivity of the 16 November 1983flank earthquake is normal with Ap = 1.00, meaning itproduced exactly the number of aftershocks predicted bythe parameters of our standard earthquake. The higherrelative rates of the intrusion-triggered 10 August 1981earthquake and the 24 January 1993 event correspond tohigher productivities of 11.4 and 12.3, respectively. HigherAp is typical of intrusion-triggered sequences (Table 4).[34] The measured post-main shock rate R0 in earthquakes

per day provides a second estimate of aftershock productivity.

To compare different aftershock sequences, we calculate R0S,the aftershock rate corrected to a standard magnitude spreadMmin =Mm� 4.0 (Table 5), and compareR0S toAp=Nobs/Ncalc.Recall that Ap requires only 2 or 3 aftershocks to estimate, butR0S requires enough aftershocks in the first few hours after themain shock to measure the rate and can only be determined forlarger sequences. We found log(Ap) = 0.840 log(R0S) � 1.927are linearly proportional with a correlation coefficient of 0.77.

4. Interpretation of Aftershock Decay Rate

4.1. Geographic Distribution of p Values ofShallow Earthquakes

[35] A map view of shallow main shocks (Figure 3)shows that the highest p values (triangles) are generally

Notes to Table 3:

aComparison of the observed number of aftershocks NOBS with those expected from the parameters of 29 November 1975 sequence NCALC. Depth is inkm below the local ground surface; Mm is main shock magnitude; Mmin is minimum (completeness) magnitude of aftershock sequence; dM is magnitudespread Mm–Mmin; t1 is start time (days after main shock) of aftershock counts; t2 is end time (days after main shock) of aftershock counts; NOBS is observednumber of aftershocks M �Mmin; NCALC is number of aftershocks M �Mmin calculated from parameters of 1 February 1994 sequence.

bNotes are as follows ‘‘int’’ means the sequence was triggered by a rift zone intrusion (it might be either a main shock-aftershock sequence, or a swarmwith an Omori (1/t) time decay; see the notes 1–15); ‘‘aft’’ is an aftershock with its own aftershocks; and ‘‘trig’’ is a triggered event outside the 29November 1975 aftershock zone. (1) Flank response from an intrusion. There was no main shock, but the M 3.4 event was the largest and near the middletime of the intense part of the swarm. (2) These two earthquakes (M 4.7 and M 5.1, 6 days later) are in the same sequence. The second event did not havemany immediate aftershocks and could be considered an aftershock of the first event because the whole sequence looks like an Omori decay from the firstevent. The second and larger event is also listed as a main shock, which should have generated more aftershocks than the first event did. (3) This is anaftershock of the 21 September 1979 event, which generated aftershocks of its own. (4) This is the largest event within and at the end of an intrusive swarm.It is preceded by 1.2 days of swarm activity but is followed by an Omori aftershock-like decay. (5) This is the largest event within and near the end of anintrusive swarm. It is preceded by 6 days of swarm activity but is followed by an Omori aftershock-like decay. (6) The ‘‘main shock’’ for this sequence isthe last of several M 4 earthquakes during this south flank response to an intrusion. This earthquake is followed by an Omori decay. (7) This sequence is thesouth flank response to a SW Rift intrusion. The M 5.6 event on 31 December 1974 was close to the beginning of the sequence, and the M 4.8 event on4 January 1975 was near the end. The latter event was followed by an Omori decay. Both were followed by many more events than one would expectfrom isolated main shocks. (8) This sequence accompanied and followed the intrusion into Mauna Loa’s NE rift zone following the summit eruptionthat occurred entirely on 5 July 1975. This M 4.6 earthquake at 0840 LT on 9 July 1975 is near the end of the sequence and is followed by an Omoridecay after the intrusion. (9) This sequence was triggered by an east rift zone intrusion and eruption. The sequence began on 13 September 1977. Thetwo largest earthquakes were M 4.2 (15 September) and M 4.1 (23 September). The sequence was nearly over at the time of the 23 September event.Both events were followed by Omori decay, and both were tested as ‘‘main shocks’’ for aftershock productivity. (10) These earthquakes in the southflank were triggered by a SWR intrusion. It is similar to the 31 December 1974 intrusion sequence, but seismicity decays soon after an intensebeginning, like a normal aftershock sequence. The largest events occurred early in the sequence on 10 August 1981 (M 4.3 at 0820 LT and M 4.7 at0940 LT) but were probably too small for the sequence to be entirely caused by them. The beginning of the sequence is measured from the first M 4.3 event, butaftershock numbers were calculated for an M 4.7 event. (11) There was no large ‘‘main shock’’ during this 22–27 June 1982 intrusion: the largest flankearthquake was M 3.4 near the beginning of the sequence. We chose the M 3.0 event of 24 June 1982, 2059 LT to represent the ‘‘main shock’’ because theintensity of the swarm declined after this time. This could better be described as a swarm ending with gradually declining seismicity rather than a main shock–aftershock sequence. Because there is no event with a large magnitude to serve as a ‘‘main shock,’’ it is impossible to calculate howmany ‘‘aftershocks’’ shouldbe expected from the sequence. (12)This 11August 1980 sequence is a small intrusion into the east rift zone not previously published. Intrusionswith noticeableand typical rift seismicty took place on 30 July and 27August 1980. This intrusion did not have any accompanying shallow rift seismicity, but there was a smallsummit deflation indicated by a drop in tilt. The high aftershock productivity also indicates an intrusion took place. (13) This 9 May 1969 event is unusuallyproductive of aftershocks for south flankmain shocks in this area. Thismain shock preceded theMaunaUlu eruption by 15 days andmay have been triggered bya small intrusion ormagmamovementwithin the rift preceding the eruption. No shallow rift seismicity ormeasurable summit deflation accompanied this 9May1969 event. Another preeruptive sequence in the south flank during 20–23 May 1969 probably indicated magma movement or flank instability [Klein et al.,1987, p. 1070]. (14) This is an aftershock of the M7.2, 29 November 1975 event, which generated a prolific number of aftershocks of its own. (15) Theaftershock set for this early earthquake is probably not complete, and it is omitted from the plots.

cRatio not plotted because (1) there was not a large enough main shock (as the leading event in an Omori decay period during a swarm) for a meaningfulratio, (2) the observed number of aftershocks (0–1) was too small for a meaningful ratio, or (3) the 1868 earthquake aftershocks in the early days haveimprecise magnitude estimates and catalog completeness. No aftershocks were located. Even though the ratio is strictly 0, the number of expectedaftershocks is also small, and the ratio is really undefined.

dThe depths of offshore earthquakes are poorly determined.eThe last two aftershocks did not have determined magnitudes, but the threshold for obtaining a location at this time was about 2.4. They are counted

even though they do not strictly exceed the cutoff magnitude of 2.4.

Table 4. Productivities Ap = Nobs/Ncalc of Four Earthquake

Classes

Main Shock ClassNumber ofSequences

Mean oflog(Ap)

Geometric Meanof Ap

South flank 39 0.12 ± 0.32 1.32Kaoiki 7 0.61 ± 0.49 4.08Kilauea deep 16 0.36 ± 0.35 2.26Intrusions and aftershocks 18 1.29 ± 0.53 19.6


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near the active volcanic centers. The rapid aftershock decayof all four sequences near Kilauea caldera probably resultsfrom high temperatures (and rapid stress relaxation) near theshallow (3–7 km depth) magma reservoir below the caldera.The active south flanks of Kilauea andMauna Loa, includingthe Kaoiki zone, have normal p values, predominantlybetween 0.8 and 1.0 (Figure 3). These flank areas consistof subaerial flows and clastic deposits [e.g., Swanson et al.,1976], are distant from known primary magma systems, andthus are areas of lower subsurface temperature. The scatteredmain shocks in the north part of the island between volcaniccenters also have normal p values. Unfortunately, we cannotrelate p value to temperature directly because island-widemaps of subsurface temperature and heat flow do not exist. Aphysical model relating temperature to stress decay is beyondthe scope of this paper.

[36] The high p value sequences at Hualalai and MaunaKea volcanoes are probably related to the continuedpresence of magma beneath these two volcanoes. Thesevolcanoes are in their post shield-building alkalic stagewhere eruptions continue but are infrequent [Porter et al.,1977; Peterson and Moore, 1987]. The two offshore mainshocks near the submarine extension of Hualalai’s NW riftzone have normal p values, indicative of a flank zone,rather than a hot magma center. Hualalai experienced anintense earthquake sequence in September–October 1929.A two-week swarm preceded the largest M6.5 earthquake,which was followed by an Omori decay with a high p =1.95. The 1929 sequence thus has both swarm and mainshock–aftershock characteristics, and could equally beinterpreted as either accompanying subsurface magmamovement [Moore et al., 1987] or a large tectonic

Table 5. Aftershock Rates and Implied Stress Parameters of Hawaiian Main Shocksa

Date

Background Aftershocks Only Comparative Rate Stress Parameters

NotesbMmin

r,eq/d Mmin

0R0

0,eq/d b0

R0,eq/d R0/r

MC

for R0S

R0S,eq/d

NOBS/NCALC

ta,days Dt/As

As/ _tr = G,days

Dt/ _tr,years

c0,days

2 Apr 1868 5.2 0.0042 5.2 �5.6 1.11 �5.6 1330 3.9 155 - 5000 7.20 73 1.4 0.055 Int 321 Aug 1951 2.5 0.05 3.0 200 1.02 650 13,000 2.9 250 0.93 - 9.47 890 23 0.068 429 Dec 1971 2.0 0.078 1.9 320 0.98 250 3200 0.4 10,000 31 32 8.07 260 5.7 0.082 Int 119 Jun 1974 2.0 0.66 1.9 500 1.39 400 600 0.6 10,000 27 10 6.41 30 0.53 0.04930 Nov 1974 2.0 1.41 2.0 410 1.03 410 290 1.5 1340 13.1 - 5.67 52 0.81 0.17915 Dec 1974 2.0 3.07 1.9 417 1.03 329 107 0.5 11,500 35 - 4.67 7.4 0.095 0.0874 Jan 1975 2.0 0.040 2.0 302 0.90 302 7600 0.8 3600 19.5 - 8.94 650 16 0.085 Int9 Jul 1975 2.2 0.018 2.0 41 1.09 25 1380 0.6 1380 22 15 7.23 2127 42 0.930 Int29 Nov 1975 2.6 0.21 2.6 71 0.93 71 340 3.2 20 0.84 3030 5.82 340 5.4 1.01529 Nov 1975 2.0 0.70 2.6 9 1.06 39 56 0.6 1200 8.2 �100 4.03 8.3 0.09 0.149 215 Sep 1977 2.1 1.068 2.0 43 1.19 33 30.6 0.2 6000 83 63 3.42 34 0.32 1.097 Int21 Mar 1979 2.4 0.0086 2.0 65 0.66 35 4000 0.7 470 1.8 �1300 8.31 140 3.2 0.03521 Sep 1979 2.0 1.99 1.7 590 0.97 300 152 1.7 590 2.2 32 5.02 10 0.14 0.06810 Aug 1981 2.0 0.043 1.8 47 1.01 29 670 0.3 1500 11.4 - 6.51 323 5.8 0.763 Int21 Jan 1982 2.2 0.036 1.8 710 0.75 356 9900 1.6 1000 2.5 1000+ 9.20 390 9.8 0.04024 Jun 1982 1.8 0.73 1.8 34 1.53 34 47 �1.0 650,000 430 270 3.85 40 0.42 0.859 Int20 Mar 1983 1.8 0.83 1.8 92 1.55 92 111 0.9 2300 1.8 10 4.71 6.1 0.08 0.0559 Sept 1983 1.8 2.01 1.8 100 1.32 100 50 1.7 135 0.55 1.5 3.91 2.5 0.03 0.05116 Nov 1983 2.1 0.36 2.1 �220 1.26 �220 610 2.7 �39 1.00 400 6.42 250 4.4 0.40121 Feb 1985 1.7 1.28 1.7 95 1.10 95 74 0.9 720 1.8 20 4.31 4.6 0.054 0.0623 Feb 1987 2.7 0.0008 2.7 180 1.01 180 225,000 1.2 6000 12 >420 12.32 7500 250 0.03327 Mar 1988 3.0 0.0016 3.0 140 0.95 140 88,000 1.1 9000 22 550 11.38 3500 109 0.0413 Jul 1988 2.1 0.024 1.8 25 1.02 12 500 1.4 64 0.35 580 6.21 50 0.85 0.10225 Jun 1989 1.9 0.41 2.0 450 1.24 600 1500 2.2 250 1.43 �80 7.28 120 2.4 0.0821 Aug 1990 2.4 0.022 2.1 46 1.14 21 950 0.7 1800 2.3 400 6.86 50 0.94 0.0528 Aug 1990 1.8 0.44 1.8 95 1.53 95 216 0.8 3200 0.81 5 5.38 3.1 0.045 0.01424 Jan 1993 1.1 0.24 1.1 880 0.88 880 3700 0.3 4500 12.3 9 8.22 180 4.1 0.05026 Jan 1993 1.8 0.055 1.4 340 1.02 130 2400 1.3 430 0.39 12 7.77 120 2.6 0.05030 Jun 1997 1.5 0.35 1.5 650 1.26 650 1860 1.5 650 0.38 8.5 7.53 19 0.39 0.01016 Apr 1999 1.1 0.16 1.1 660 0.57 660 4100 1.6 340 0.71 20 8.32 170 3.9 0.04226 May 1999 2.1 0.036 1.5 300 0.74 110 3000 0.3 2300 3.9 10 8.02 33 0.73 0.01126 Apr 1973 2.4 0.0070 2.4 �100 1.00 �100 14,000 2.2 �160 1.8 980 9.57 2430 64 0.1701 Feb 1994 1.8 0.020 1.3 250 1.08 72 3600 1.1 410 1.2 60 8.19 645 14 0.179

aMmin is the minimum completeness magnitude of the background seismicity before the main shock; r is the background earthquake rate before the mainshock; Mmin

0 is the minimum completeness magnitude of the aftershocks; R00 is aftershock rate immediately after the main shock for earthquakes greater

than the aftershock minimum magnitude M0min; b

0 is Gutenberg-Richter b value of the aftershock sequence; R0 is aftershock rate immediately after the mainshock for earthquakes greater than the background minimum magnitude Mmin; R0/r is earthquake rate immediately after main shock relative to backgroundrate, both referred to same completeness magnitude; MC for R0S is the main shock magnitude minus 4.0 (completeness magnitude for normalized rate); R0S

is normalized aftershock rate immediately after the main shock for earthquakes greater than the aftershock minimum magnitude MC; R0S is highlycorrelated with the aftershock productivity AP; NOBS/NCALC is the aftershock productivity AP defined as the ratio of the observed to calculated number ofaftershocks above the completeness magnitude Mmin; ta is aftershock duration when the rate returns to background and some values were difficult toestimate because the sequence did not return to background; Dt is change in shear stress due to the main shock; _tr is background shear stress rate before themain shock; A is fault constitutive parameter, generally 0.005 to 0.012; s is normal stress; c0is estimate of time delay parameter c derived from earthquakerates in equation (5).

bNotes are int, indicates a main shock following a rift zone intrusion. (1) Background rate r is measured long after the sequence because a swarmpreceded the aftershocks. (2) A triggered event of the 29 November 1975 Kalapana event in the Kaoiki zone, and not in the Kalapana aftershockzone. (3) Rates are for the entire south side of Hawaii island, most of which is in the inferred rupture zone. Background rates are equal and are from 1840–1868and 1877–1918. (4) The background rate is from 1962 to 1986 because the catalog from the 1940s and 1950s is poor in completeness and location quality.


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earthquake under Hualalai’s south flank [Wyss andKoyanagi,1992].[37] The Hilea seismic zone (Figure 3) is anomalous

because it is a flank area located away from known magmacenters, but has two high p values. There is no surfaceevidence for a magma system or high temperature in theHilea area, but a high-velocity structure discovered byseismic tomography in this area has been interpreted byPark et al. [2005] as an intrusive complex or buried riftzone from an older volcano. This complex could be a sourceof heat causing high p values. In any case, the wide range ofHilea p values suggest this is a heterogeneous area, perhapswith variable temperature and intermixed zones of rapid andslow stress relaxation.

4.2. The p Values of Deep Earthquakes

[38] The p values of four out of five deep earthquakessuggest cool temperatures (Figure 4). The four main shocksjust south of the caldera are within Kilauea’s seismicallydefined magma conduit. Three of these Kilauea sequenceshave normal p values between 0.8 and 1.0. If the hypothesisthat p values smaller than about 1.2 indicate cooler temper-atures is correct, then these three deep sequences indicate thatthe rock near the deeper magma conduit is cooler than theregion surrounding the shallow (3–7 km depth) magmareservoir.[39] The lack of universally high p values at depth below

Kilauea also implies a lack of significant deep (30–40 km)magma storage, consistent with the lack of other observa-tional evidence for a deep magma storage zone beneathKilauea. Seismic tomography indicates a broad, elongatedlow-velocity region below Hawaii but no concentration oflow velocities below Kilauea [Tilmann et al., 2001]. Surfacedeformation does not show inflation of a 30–40 km deep

magma body, but the deformation network is not optimallyconfigured to test this. Thus it is probable that magma inKilauea’s conduit at 30–40 km depth passes through theconduit without residing there, and does not heat the sur-rounding region as much as magma heats the shallowreservoir at 3–7 km depth.[40] The M 5.2, 1 February 1994 earthquake places im-

portant constraints on deep magma pathways. Its aftershocksextend north from a point 5 km south of themain shock to justbelow Kilauea caldera in a nearly horizontal zone [Wolfe etal., 2003]. Wright and Klein [2006] interpret this aftershockzone as a part of Kilauea’s conduit system because it is withinthe seismically defined conduit and connects a zone of long-period (magmatic) earthquakes below and to the south of the1 February 1994 rupture zone to another LP zone located 5–17 km directly below Kilauea caldera. The high p value (p =1.39, Figures 1 and 4) of the 1 February 1994 aftershockssuggests the aftershock zone is associated with higher tem-peratures within the magma conduit.[41] Unfortunately, there are not enough deep aftershock

sequences to define regions of high and low p values (and byinference regions of high and low temperature). However, theexistence of a range of p values (0.9–1.4) below Kilaueaindicates some heterogeneity of warm and cool regionswithin the conduit. This heterogeneity is compatible withmany small, episodically active magma conduits within thelarger conduit region defined by deep earthquakes.

5. Interpretation of Aftershock Productivity

5.1. Enhanced Aftershock Productivity AfterEarthquakes Triggered by Intrusions

[42] The most productive aftershock sequences are trig-gered by intrusions, or aftershocks of an aftershock of an

Figure 3. Map of p values of shallow main shocks. The earthquakes are typically are 8–12 km depth.Pluses are volcanic summits not otherwise outlined. The p values are of A, B, and C quality (see text). Thesymbols are keyed to ranges of p value. The four youngest volcanic centers have the fastest aftershock decayrates and highest p values (p > 1.20), probably because of higher temperatures and faster stress relaxation.


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earlier, primary main shock. The secondary main shock–aftershock sequence can be viewed as triggered by theprimary, isolated main shock. Of the triggered south flankaftershock sequences (Figure 5), four follow large, primaryaftershocks of the 29 November 1975 Kalapana earthquakeand 11 follow intrusions in one of the two rift zones. In theKaoiki, one is a secondary aftershock sequence of the 30November 1974 main shock, and the other was triggered bythe 1975 Kalapana earthquake. The Mauna Loa sequencewas triggered by the July 1975 summit eruption and NE Riftintrusion.[43] High Ap is not a characteristic of a geographic

region, but depends on the stress state at the time. Thecentral south flank from 155� 10 to 80 produces bothtriggered (Figure 5) and isolated (Figure 6) main shocks,but the triggered aftershock sequences are consistently moreproductive.[44] The high Ap of triggered main shocks is probably

caused by the intrusion or primary main shock adding to thestress step produced by the triggered main shock. Theearthquake rate is a nonlinear function of applied stressand time [Dieterich, 1994] such that two stresses addedtogether produce much greater seismicity than the totalearthquake rates from each stress acting alone. Isolatedmain shocks produce a stress step that results in Omoriaftershock decay [Dieterich, 1994]. Triggered main shocks,on the other hand, add their large stress step to thecontinuing stress induced by adjacent intrusions. If theintrusion is still in progress when the main shock occurs,the continuing intrusion stress may add to the main shock’sincremental stress. We view aftershocks as caused by thestress step of their main shock, but at rates modulated byrapid increases in external stress caused by the triggeringintrusion.

[45] The quantitative time history of stress in thesouth flank can be derived from observed earthquake rates[Dieterich et al., 2000]. They found the stress rate increasedafter the 1977 and 1983 intrusions, for example, andquantitatively agreed with geodetic stress models of theintrusions. Thus earthquakes were a ‘‘stress meter.’’ Themain shock stress steps and intrusion stresses derived fromaftershock rates could, in some future study, be modeled tosee the stress differences between normal and triggeredmain shocks in the south flank.[46] Another way to view the high Ap rate of secondary

aftershocks (aftershocks of aftershocks) is that secondaryaftershocks add to the count of primary aftershocks. Thisview supports our enhanced post-main shock stress inter-pretation because the stresses of the two main shocks areadded just as the aftershock counts are added. The epidem-ic-type aftershock sequence [Ogata, 1988] models second-ary aftershocks in this way, which can account for 30–50%of total recorded aftershocks [Felzer et al., 2003].

5.2. Aftershock Productivity in the Hilea andKaoiki Zones

[47] On the basis of the behavior of the south flank, wesuspect that high Ap > 4.0 sequences (triangles on the maps)are triggered, for example by an otherwise unknown mag-matic intrusion. A map of Ap might thus show whereintrusion stresses are important (Figure 7). Main shocks inthe Hilea zone on the south flank of Mauna Loa havenormal Ap (0.25 to 4.0), and are not known to be triggeredevents. Aftershock sequences on the north and west sides ofthe island are also normal productivity. The two sequenceson the north side of Mauna Kea (stars, Figure 7) are locatedfar from active volcanoes and are very low productivitysequences (Ap < 0.25).

Figure 4. Map of p values of deep main shocks. The earthquakes are deeper than 20 km and typicallyare 30–40 km depth. The p values are of A, B, and C quality (see text). Kilauea’s deep conduit has arange of p values, suggesting temperatures are mixed and there is no persistent or large deep magmastorage reservoir.


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[48] Magmatic stresses are probably important in theKaoiki seismic zone, even though the role of volcanicstresses may not have been recognized. The three highAp > 4.0 sequences in the Kaoiki, 12 April 1970 (Ap = 6.4),19 June 1974 (Ap = 27), and 30 November 1974 (Ap = 13)were not immediately preceded by known rift intrusions.What was happening near the Kaoiki at these times?The July 1975 Mauna Loa eruption was anticipated after25 years of quiescence because it was preceded by16 months of greatly increased seismicity and summitexpansion [Lockwood et al., 1987; Decker et al., 1995].Two of the Kaoiki’s high Ap sequences were within this16-month inflation period. Mauna Loa inflation can en-hance coulomb stress and enhance earthquakes in much ofthe Kaoiki [Walter and Amelung, 2004]. In addition,Kilauea was also in an inflated state during 1974 andhad the highest summit tilt observed during 1956–1985[Decker, 1987, Figure 42.5]. There was also high calderaseismicity in 1974 related to inflation. Thus it is verypossible that the two high-productivity 1974 Kaoiki se-quences were triggered by the nearby and inflating MaunaLoa and Kilauea summit reservoirs, and had their after-shock sequences enhanced by elevated stress.[49] Two other Kaoiki main shocks were probably trig-

gered. During the four months before the Ap = 6.4, 12 April1970 main shock, tilt indicated that Kilauea was inflatingrapidly and four inflationary earthquake swarms occurredunder the caldera [Klein et al., 1987]. This inflation prob-ably stressed the Kaoiki in a manner similar to an intrusionto raise the Ap of this 1970 event. The 15 December 1974Kaoiki earthquake (Ap = 35, Figure 5) appears to be an

aftershock of the 30 November 1974 event. It could haveexperienced stress enhancement by two inflating volcanoesplus the earlier, primary main shock.[50] The Kaoiki seismic zone is a complicated place

because there are time-dependent stresses imposed bycalderas and rift zones on two sides, and because thereare both normal and high Ap sequences. Quantitativemodels incorporating stresses estimated from inflating cal-deras and rift zone intrusions [e.g., Wyss et al., 1992a] andfrom seismicity [Dieterich et al., 2000] may eventuallyestimate the time history of Kaoiki stresses to which Ap

can be compared.

5.3. Aftershock Productivity Near theOffshore Hualalai NW Rift Zone

[51] High Ap values in an area about which little is knownmay provide insights into the causes of the area’s seismicity.The offshore area 40 km northwest of Hualalai has persis-tent earthquake activity, which culminated with four largeaftershock sequences starting on 3 February 1987, 24 and27 March, and 1 April 1988. The high productivity of 3 ofthe 4 sequences (Figure 7) suggests that these are triggeredby magma intrusions in Hualalai’s NW rift zone. The rift isbathymetrically difficult to trace west of the rift mapped byMoore and Chadwick [1995] (dashed line, Figure 7), butflat-topped volcanic cones [Clague et al., 2000] indicatethat the rift continues at least to the longitude of the high Ap

aftershock sequences. The southern earthquake clustercoincides with a steep, south facing bathymetric scarp[Moore and Chadwick, 1995; Mark and Moore, 1987].Thus it is tempting to associate the earthquakes with active

Figure 5. Map of main shocks triggered by rift zone intrusions and of aftershocks (‘‘triggered’’ by theirprimary main shocks) that have their own secondary aftershocks. The symbols are keyed to ranges of thelog of the aftershock productivity ratio Ap = Nobs/Ncalc. Nearly all triggered sequences are highlyproductive, perhaps as a result of post-main shock stress from the intrusion adding to the stress step fromthe main shock to enhance aftershock rates.


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normal faults on the flank of a volcanic rift zone, analogousto the subaerial normal faults of Kilauea’s south flank. Themeasurable p values of two of these sequences are normal(Figure 3) and thus we do not associate them with a high-temperature volcanic center. We infer that the high produc-tivity of aftershock sequences near the submarine HualalaiNW rift zone means it is magmatically active. If we acceptthat Hualalai’s NW rift is active, then we must conclude thatall high productivity (Ap > 4) aftershock sequences inHawaii are in flanks adjacent to active rifts or calderas.

5.4. Aftershock Productivity of Deep Earthquakes

[52] The highest productivities of deep (>20 km) earth-quakes are near Kilauea’s magma conduit, suggestingtriggering by magmatic stresses. Unfortunately, deep mainshocks are not well distributed geographically (Figure 8).Kilauea’s conduit as defined by seismicity is nearly verticaland narrow from 0 to 20 km depth under the caldera, butenlarges and dips southward below 20 km depth [Klein etal., 1987]. Significantly, all three of the sequences that arewell north and west of Kilauea have below normal Ap andare not associated with magma centers. The two Ap > 1.0offshore main shocks at about 19� latitude (Figure 8) arewithin a deeper part of Hawaii’s magma conduit character-ized by deep (50 km) seismicity, long-period earthquakesand harmonic tremor [Koyanagi and Chouet, 1987; Wrightand Klein, 2006]. Thus each of the deep sequences with Ap >1.0 is associated with a magma conduit, and like shallowHawaiian earthquakes, there is a good correlation between Ap

and magma conduit proximity.[53] We suggest that pulses of magmatic stress trigger

most deep conduit earthquakes. The high Ap (>1.0) of deep

earthquakes is probably accomplished by intrusion-likestress from the magma conduit after the main shock’s stressstep. Therefore we hypothesize that deep earthquakes nearKilauea’s magma conduit are triggered by stress pulses frompressurized magma conduits, analogous to shallow flankearthquakes triggered by intrusions.

6. Interpretation of Aftershock Rates, Duration,Stress Rate, and Stress Change

6.1. Aftershock Duration and Stress Rate Change

[54] Earthquake rates of aftershock sequences permitstress rate estimates that have implications for the types ofstresses acting on Hawaiian earthquakes. Table 5 listsvarious rate and stress-related parameters for the aftershocksequences with measurable background and aftershockrates. Figure 9 affords comparison of the post-main shockstress rate _t with the pre-main shock stress rate _tr. Weassume the normal stress s is relatively little changed at thetime of the main shock. We also assume that the aftershockzone we have chosen to measure a, b, r and ta receivedsignificant rupture in the main shock, and thus that the mainshock stress change influenced the seismicity rate in theaftershock zone. The equality line _tr = _t in Figure 9separates the main shocks into ones that were accompaniedby an apparent increase in the stress rate (above the middleline) from those that decreased the stress rate (below themiddle line).[55] The two largest earthquakes (stars, Figure 9) have the

longest aftershock sequences, and produced a large apparentstress rate decrease ( _t � _tr). One would expect large M > 7earthquakes to relieve regional stress rates. Intuitively, a

Figure 6. Map of main shocks at Kilauea’s caldera and south flank, keyed to their aftershockproductivity. The main shocks, unlike those in Figure 5, have no identified triggering event. The symbolsare keyed to ranges of the log of the productivity ratio Ap = Nobs/Ncalc. Kilauea’s south flank has normalproductivity sequences with Ap � 4.0.


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Figure 7. Map of aftershock productivity on and near Hawaii island. The main shocks, unlike those inFigure 5, have no identified triggering event. The symbols are keyed to ranges of the productivityratio Ap = Nobs/Ncalc. Most of the island has normal productivity (Ap < 4.0) sequences. Some of thehigh productivity sequences (triangles, Ap > 4.0) in the Kaoiki and off the west coast may haveaftershock rates enhanced by unrecognized magmatic inflation and intrusion. Dashed lines show theaxis of the rift zone of the extinct submarine Mahukona volcano [Clague and Moore, 1991] and theNW rift of Hualalai [Moore and Chadwick, 1995].

Figure 8. Map of aftershock productivity of deep (>20 km) main shocks under Hawaii. The symbolsare keyed to ranges of the productivity ratio Ap = Nobs/Ncalc. The symbol intervals of Ap are the same asFigures 5–7. The sequences with higher Ap > 1.0 (triangles and circles) are related to Kilauea’s magmaconduit and to the conduit 60 km south of Mauna Loa. As with the high Ap of intrusion-related shallowaftershock sequences, we infer that stresses near the active magma conduit pulse and continue after thestress step from the main shock.


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large main shock means there will be a larger stress releaseand a lower earthquake rate after the aftershock sequenceends than the rate before the earthquake. A longer after-shock duration ta is required to reach the lower backgroundrate.[56] The main shocks with a large stress rate increase

(above the _t = 5 _tr line in Figure 9) are mostly triggered byintrusions. Intrusion-triggered main shocks (open symbols,Figure 9) do not follow a consistent pattern, but most areaccompanied by a stress rate increase.[57] Most Kilauea south flank (SF) main shocks we

studied see a drop in stress rate. The six moderate (M4 or5) SF earthquakes in Table 5 that were not directly causedby an intrusion plot in the lower left corner of Figure 9(solid squares). This is because the background earthquakerate in the SF is high, and thus the aftershock duration ta andaftershock gain G are small. The apparent stress rate appearsto have been reduced for four of the six moderate SF mainshocks. Dieterich et al. [2004] examined the coulomb stresschange surrounding these and other SF main shocks in greatspatial detail using a revolutionary method of quantifying

seismicity rate changes. They mapped the areas of stressrate change surrounding the SF main shocks, but mappingstresses in this way requires high seismicity to measurerates. We use a simpler procedure: we examine earthquakerates in the larger Omori-type aftershock sequences to seethe average stress rate changes in the whole aftershock zone.Both studies use earthquake rates and show a net stressrate decrease surrounding most of these moderate SFearthquakes.

6.2. Background Stress Rate and Main ShockStress Change

[58] We found that main shocks with the lowest back-ground stress rate have the largest stress change. The relationbetween Dt/As and ln(As/ _tr) (equation (8)) can be seengraphically in Figure 10. In other words, regions with a lowstress rate tend to fail with a large stress change and withaftershock rates very large compared to the backgroundseismicity rate. We believe this relation between backgroundstress rate and stress change is not a unique property ofHawaiian earthquakes, but is a consequence of an approxi-

Figure 9. Two measures of an aftershock sequence can be related to the shear stress rate before ( _tr) andafter ( _t) the main shock using results of Dieterich’s [1994] constitutive law applied to earthquake rates.The aftershock duration to the time the earthquake rate returns to its background level ta is As/ _t. Theaftershock ‘‘gain’’ above the background rate r, defined as G = 10a+b(Mm � Mc)/r, is As/ _tr. These twoparameters are uncorrelated for Hawaiian earthquakes but show the situations where the stress rateincreased (above the middle diagonal line) or decreased (below the middle diagonal line) at the time ofthe main shock. Earthquakes with a large stress rate decrease include the largest M > 7 earthquakes(stars). Sequences resulting from a known (open diamonds) or suspected (open squares) rift intrusion arelabeled INT. Solid squares are moderate (M 4 or 5) south flank sequences. Abbreviations are caldera,Kilauea caldera; HLE, Hilea; HO, Hualalai offshore; KIL, Kilauea; MLO, Mauna Loa; and SF, Kilaueasouth flank. Sequences with a large stress rate increase tend to be triggered by an intrusion or locatedadjacent to an active rift zone or caldera, which is probably the source of continuing stress.


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mately constant time delay c0 (equation (8)) and equivalentlyof a strong proportionality between the two measures ofaftershock rate 10a+b(Mm�Mc) and R0 (equation (7)).[59] The background stress-rate inferred from aftershock

rates has a strong geographical dependence, as seen in amap of ln(As/ _tr) = ln(G) (Figure 11). The areas withhighest stress rates (triangles) are in the Kaoiki zone andin the south flank adjacent to the most active parts of thecentral east rift zone. These are also very seismically activeareas as judged both by high background seismicity andoccurrence of large earthquakes [e.g., Klein et al., 2001].The central south flank has the highest consistent stressrates on Kilauea, and is currently the zone of the highestdeformation on the island [e.g., Owen et al., 2000]. Themain shocks in areas with the lowest stress rate (diamonds)are mostly in western Hawaii and under the Hamakuacoastline, far from the tectonically active south side of theisland. Relative aftershock rates provide a new, alternativeway to estimate stress rates that supplements other seismicand geodetic methods.

[60] We interpret these high stress rates as a NW trendingactive zone under Hawaii including the south side of theisland. The background stress rates for the two main shocksunder Kohala and Mauna Kea (circles, Figure 11) indicatethat north central Hawaii is locally still being stressed atrates comparable to the active south side of the island.Tilmann et al. [2001] found a broad, �5% seismic low-velocity zone running SE-NW under the center of Hawaiiisland at depths of 30–90 km. Thus the main shocks inareas of higher stress rate (Kilauea, Kaoiki, Hilea and northcentral Hawaii) are underlain by lower seismic velocities,have presumed higher temperatures, are still mobile and arebeing stressed. In contrast, the NE and west coasts, includ-ing offshore Hualalai, are underlain by higher velocities andpresumed lower temperatures, and appear to have lowbackground stress rates.

6.3. Shape of Aftershock Rate Curves

[61] Aftershock rate curves suggest that stress continuesto increase after some main shocks following intrusions.Dieterich [1994, Figure 8] calculated synthetic aftershockrate curves where the post-main shock stress t increaseslogarithmically with time. His results indicate a peak ofaftershocks within hours after the main shock before ratesdecline according to the Omori law.[62] We looked for and found a rate hump in the best

recorded aftershock rate curves that followed intrusions.We selected M 4 or M 5 main shocks that did not obscuretheir immediate aftershocks, had an excellent fit to themodified Omori curve, and sought sequences where carefulmanual reading allowed as complete cataloging as possible.Figure 12 shows rate curves of three normal isolated sequen-ces (solid lines) and two intrusion sequences (dashed lines).Rates after the isolated main shocks consistently decline, butintrusion-triggered aftershocks increase to a peak about twohours after the main shock before declining. Dieterich’s[1994, Figure 8] calculated rate curves also peak around2 hours after the main shock, suggesting his choice ofparameters A = 0.01, s = 20 MPa, Dt = 0.5 MPa, w = 10 s,and u 0.2 in his equation (6) are appropriate for southHawaii. The rate humps were not caused by superposedaftershock sequences from a second large main shock.[63] Clearly, stress that is strong enough to cause

hundreds of earthquakes was newly applied by these two1971 and 1975 intrusions to the volcano flank, and was notjust a stress step resulting from a single main shock. Theaftershock rate hump following intrusion-triggered mainshocks strongly suggests that stress continued to increase,perhaps logarithmically, after the main shock.

7. Aftershock c (Time Delay) Values

[64] The parameter c (or c0) is the time delay after themain shock when aftershocks begin to decay at the powerlaw rate. The c values are determined by fitting aftershockdecay curves (Table 2), and c0 values are estimated fromrates during the Omori aftershock decay (equation (7)).Figure 10 shows that a line of constant c0 = 0.055 days istypical for Hawaii, and that values of c0 � 1 and c0 � 0.01occur for some aftershock sequences. Similarly, c values aretypically 0.01–0.04 with maximum c values of 0.82 and1.42 for two intrusions (Table 1). Recall that a high c (or c0)

Figure 10. Main shock stress change Dt and backgroundstress rate _tr can each be estimated from background rate r,aftershock rate R0, and aftershock gain G. The plot showsthese quantities are highly correlated, as predicted by therelation Dt/As = ln(As/ _tr) � ln(c0). The c0 is approximatelythe time delay before aftershocks begin to decay at a powerlaw rate. The value c0 0.055 day is typical for Hawaii andis comparable to c values measured from aftershock decaycurves; c0 1.0 day can sometimes found for sequencestriggered by intrusions. Inset: aftershock rate curvescalculated with the modified Omori law. The two curveshave the same sustained rate (the same G value) butdifferent c values. The c = 1.0 curve (typical of someintrusion-triggered sequences) has a lower initial aftershockrate R0 and thus a lower main shock stress change Dt.


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value means the rate R0 (and thus Dt/As) is lower than forsimilar (same G value) decay curves with a small c value(Figure 10 inset, also equation (7)).[65] The c values tend to be higher following an intrusion,

and lower c values are typical of normal isolated mainshocks. A plot of c versus c0 shows the distribution of eachand compares the two values (Figure 13). For most sequen-ces (and all isolated shallow sequences), c � 0.05 days andc0 � 0.10 days. Also, all c values larger than 0.10 days areeither deep or associated with intrusions or suspectedintrusions.[66] Caution must be used interpreting c values, which are

not precise numbers. High c values are often observed inglobal earthquake catalogs, and in local catalogs of computer-detected earthquakes as a result of missing smaller eventsin the high signal level immediately after the main shock[e.g., Kagan, 2004]. The Hawaiian aftershock catalogssurely have some missed events, but should be relativelycomplete above the cutoff magnitude Mc. This catalogcompleteness for Hawaii is because the main shocks duringintrusions are rarely larger than magnitude 5, because theHawaii network is dense, and because event selection duringthe 1970s and 80s was done by manually striving for a large,complete catalog from Develocorder records. Figure 13shows that for most of the sequences with c > 0.1 day, c0

increases with c. The discrepancies between c and c0 sug-gests that both estimates have errors, but both measure theshape of the aftershock decay curve. In most cases, c0 > c.This may result from undercounting aftershocks immediatelyafter the main shock, yielding a too-small R0 and too-largec0 (equation (7)), while c may be more accurate from fittingthe rate curve over a period of several hours.

Figure 11. A stress-rate map of ln(G) = ln(As/ _tr), where G is the aftershock ‘‘gain’’ and _tr is thebackground, pre-main shock stress rate. The highest stress rates (triangles) occur in the active Kaoikiseismic zone and the central south flank adjacent to the most active part of the east rift zone. The loweststress rates (diamonds) are in the west and NW parts of the island, far from the active south side of theisland. Stress rates are also high for two sequences near the central volcanic axis running NW underHawaii, suggesting that the center of Hawaii is still mobile and being stressed.

Figure 12. Rate curves of five well-recorded aftershocksequences with nearly complete catalogs starting withinminutes after the main shock. The main shocks are M 4 orM 5 from the 1970s, and only aftershocks above thecompleteness magnitudes (Table 2) are plotted. The threesolid lines are main shocks not preceded by a triggeringevent, and the dashed lines are two aftershock sequencesfollowing intrusions. The intrusion-triggered sequenceshave noticeable peaks about 2 hours after the main shock.The peaked earthquake rates after the intrusions apparentlyresult from a stress rate increase after the main shock.


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[67] Intuitively, c could be high, and the Omori decline ofaftershock rates delayed, if the stress rate is high for sometime after the main shock: in this case the aftershock ratedoes not subside as quickly because the main shock’s stressis supplemented by additional external stress [Dieterich,1994, Figure 8]. This interpretation of continuing stress fitsour observations of high c values and high aftershockproductivity after intrusions.

8. Discussion

8.1. Intrusion-Triggered Main Shocks andPost-Main Shock Stress History

[68] We found several characteristics of Hawaiian after-shock sequences that often are different if the main shockwas triggered by an earlier event, such as a magmaticintrusion or an earlier primary main shock. We infer thatthese characteristics of the aftershock rate curve result fromcontinuing stress external to the main shock.[69] Nearly all aftershock sequences triggered by an

intrusion, or which are secondary aftershocks (aftershocksof aftershocks), have high aftershock productivity Ap.Peaked aftershock rate curves provide direct evidence of apost-main shock stress increase after some intrusions. A highc value (prolonged aftershock rates early in the sequence) isanother characteristic of many intrusion-triggered aftershocksequences. We also found that most main shocks triggered bymagma movement are accompanied by a large increase instress rate. We infer that the magma conduits that triggeredthe initial main shock impose the increased stress rate, and

that continuing stress after the main shock causes thesemultiple effects in the aftershock rate.[70] We suspect that many main shock-aftershock sequen-

ces triggered by intrusions have relatively less stress re-leased in the main shock and more stress released byaftershocks than isolated sequences in the same area. Notethat higher c values, as observed for triggered sequences,correspond to lower main shock stress changes Dt, as seenfrom equation (8) and Figure 10 for the same aftershockgain G. Aftershock sequences triggered by intrusions havehigher productivity (and presumably higher stress release)relative to isolated main shocks of the same magnitude.These factors argue that stress release is proportionallyshifted from the main shock to aftershocks if the mainshock is triggered by an intrusion.

8.2. Prospecting for Magma and Other Sourcesof Rapid Stress Change

[71] Kilauea rift intrusions are well cataloged where theycorrelate with high south flank aftershock activity. We canthus infer that high productivity in other areas implies therewas probably an unseen triggering event such as volcanoinflation or an intrusion in a nearby rift. We inferred thatmagma movement triggered several high Ap sequences(triangles, Figure 7). We also inferred that pulses of magmain Kilauea’s feeding conduit from the mantle triggered thehigh Ap sequences at depth underneath Kilauea (Figure 8).[72] The p values (as a surrogate for temperature) and Ap

(as an indicator of magmatic stress) should be used togetherin magma prospecting. High p values indicate rapid stress

Figure 13. Observed c values measured from aftershock decay curves versus c0 values predicted fromaftershock rates. The c value is essentially the time delay (in days) after the main shock when aftershocksbegin to decay at the power law rate. The squares are Omori aftershock sequences triggered by intrusionsor secondary aftershocks. Larger c values (c > 0.10) require either magma involvement or a depth morethan 20 km. If aftershocks followed a perfect modified Omori decay law R(t,M) = 10a+b(Mm � M) (t + c)�p,and Dieterich’s [1994, equation [16]] rate equation was always followed, then c would equal c0. The c andc0 are correlated, but the discrepancy means that earthquake rates are often difficult to measure.


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relaxation, higher temperature and proximity to a volcaniccenter; high productivity and large c values indicate con-tinuing post-main shock stress as from a nearby intrusion ina conduit or rift zone. These measurements are both relatedto volcanism but with different physical causes.[73] The p values and Ap could thus be used at poorly

monitored volcanoes to get a sense of their potentialvolcanic activity. p value and Ap can be determined fromthe time history of aftershock sequences and need a catalogof earthquake occurrences and magnitudes, but do not needprecise earthquake locations requiring a dense seismographnetwork. Ap can be determined from just a few aftershockslarger than the completeness magnitude, whereas a good pdetermination requires a well-recorded aftershock sequence.[74] Hill et al. [1995] modeled and related the Long

Valley caldera earthquakes triggered by the 1992 Landersearthquake to possible changes in magma pressure mimick-ing the effects of an intrusion. The triggered Long Valleysequence displayed a modified Omori decay curve with p =1.25 [Hill et al., 1995]. While the ‘‘main shock’’ was not alocal earthquake, the triggered earthquakes were within thecaldera’s south moat adjacent to the resurgent dome wherevolcanic swarms occur. The Long Valley sequence also hada c value of 0.76 day. We associate large (>0.30 day)Hawaiian c values with sequences triggered by intrusions.It is tempting to group the high Long Valley p value withthe high p > 1.20 values characteristic of hot Hawaiianvolcanic centers, and to group the high Long Valley c valuewith Hawaiian intrusions. A survey of Long Valley andother volcano aftershocks should be done to use p values toseek thermal areas, and Ap and c values can be related tovolcanic behavior.

8.3. Swarms

[75] Swarms are a characteristic type of earthquake se-quence with stress implications. Earthquake swarms do nothave a dominating main shock and aftershock sequence[e.g., Mogi, 1963]. Swarms are often characteristic ofvolcanic areas [e.g., McNutt, 2002] and of induced seismic-ity [e.g., McGarr et al., 2002]. Fluids under pressures largerthan the least principal stress, as necessary for dike em-placement, can produce swarms [e.g., Hill, 1977]. For mostvolcanic and triggered earthquakes, the stress is imposed bya local source whose rate varies more rapidly than tectonicloading. Toda et al. [2002] established a connection be-tween stressing rate and the seismicity of the 2000 Izuislands swarm. Toda et al. [2002, p. 58] stated, ‘‘anysustained increase in stressing rate – whether due to anintrusion, extrusion or creep event – should produce suchseismological behavior’’ [such as earthquake swarms].[76] The behavior of aftershocks in Hawaii may refine

models of swarms. The association of intrusion triggeredaftershock sequences with swarms is strong because manyof the aftershock sequences we studied are the terminatingphase of swarms. Many Hawaiian aftershock sequencesdisplay evidence of external stress changes that associatethem with known or invisible intrusions.[77] This study found a new type of earthquake sequence,

aftershocks with enhanced productivity, to add to thesequence types noted by Mogi [1963] ranging from swarmsto main shock–aftershock sequences. We suggest thatcontinuing and variable stress, as from an intrusion, may

be the distinguishing characteristic of earthquake swarms;and that aftershock sequences with normal productivity andsmall c values may be characteristic of only a stress stepcaused by the main shock. This suggests a progression ofsequences, depending on the amount and time history ofexternal stress involved, from aftershock sequences withnormal decay and productivity (small external stresschange), to those with enhanced productivity, to thoseembedded within swarms, to swarms without main shocks(high and variable external stress).

9. Summary and Conclusions

[78] We scrutinized several parameters of aftershocksequences on the Island of Hawaii. We considered bothisolated main shocks with no apparent triggering event, andflank main shocks triggered by a rift intrusion or primarymain shock.[79] The p value is the decay exponent in the modified

Omori rate relationship R(t)� (t + c)�p. The highest Hawaiianp values (p > 1.20) are found near volcanic centers where thetemperature is highest. Deep p values near Kilauea’s conduitcommonly are smaller than 1.00, and suggest the lack ofpervasive high temperature and lack of significant deep (30–40 km) magma storage. A high 1.39 p value of the deepKilauea 1 February 1994 earthquake suggests it is associatedwith higher temperatures within the magma conduit.[80] We conclude that high p values are indicators of high

temperature and accelerated stress relaxation, where thestress steps from main shocks decay faster than in thecooler rocks on the volcano flanks. Values of p larger than1.00 are consistent with faster logarithmic stress decreaseafter the main shock [Dieterich, 1994].[81] We found high aftershock productivity for triggered

earthquakes and magma intrusions, and associate high Ap

with post-main shock stress increases. Aftershock produc-tivity Ap is larger than 4.0 for flank earthquakes triggered byintrusions, but is normal (0.25 to 4.0) for isolated mainshocks in the same areas.[82] A region of high Ap can identify previously unrec-

ognized magmatic stress. We used high Ap sequences in theKaoiki seismic zone and near Hualalai’s offshore rift zone toinfer that inflationary or intrusive stresses are acting there.We were able to show that Ap is a useful parameterinterpreting magmatic stresses because so much is knownfrom years of monitoring Hawaiian volcanism. Each of theseismic zones with high Ap sequences also has normal Ap

sequences in the same area because magmatic stress varieswith time. p values (as a surrogate for temperature) and Ap

(as an indicator of magmatic stress) should be used togetherin magma prospecting. Ap can be determined from just afew aftershocks larger than the completeness magnitude,whereas p determination requires a well-recorded aftershocksequence.[83] Among deep (>20 km) earthquakes, the highest pro-

ductivities are near Kilauea’s magma conduit. Analogy withthe association of intrusions with high Ap on Kilauea’s riftssuggests that pulses of magmatic stress, rather than constantmagma flow, triggers most deep conduit earthquakes.[84] Background rates, aftershock rates and aftershock

duration identify sequences where stress rate increased ordecreased at the time of the main shock. Stress rate


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increased after many intrusions and after many main shocksnear active rift zones. Stress rates decreased after largeM7–8 earthquakes because they were large enough torelieve regional stress rates.[85] We found main shocks with the highest stress de-

crease have the lowest background (pre-main shock) stressrates. This relation can be seen from Dt/As = ln(As/ _tr) �ln(c0). The inverse correlation of _tr and Dt is a consequenceof an approximately constant time delay c0, and is probablynot unique to Hawaiian earthquakes. The c0 typically isabout 0.055 day, but can be close to 1.0 day for someintrusion-triggered main shocks.[86] Background stress rates are highest in the seismically

active volcano flanks on the south side of the island, andlowest in the coastal areas far from volcanic centers. Stressrates are also high for two sequences near the centralvolcanic axis running NW under Hawaii. This patternsuggests the broad, �5% seismic low-velocity zone runningSE-NW under the center of Hawaii is still mobile and beingstressed.[87] Some intrusions are followed by an increasing after-

shock rate, which peaks about 2 hours after the main shock.This rate hump is predicted if stress increases logarithmi-cally after the main shock [Dieterich, 1994].[88] The c value (the time delay after the main shock

when aftershocks begin to decay at the power law rate)reveals cases of magma involvement in stress release inHawaii. We infer that high c values and continuing highaftershock rates result from continuing stress from magmainvolvement imposed on the rupture zone after the initialstress step of the main shock.[89] The p values, aftershock productivity, and c values

can be used for magma prospecting in other areas. TheLong Valley caldera earthquakes triggered by the 1992Landers earthquake had a large c value of 0.76 days anda large p value of 1.25 [Hill et al., 1995], suggesting thatan extended stress history as from an increase in magmapressure, and high temperatures played a role in thistriggered sequence.[90] Aftershocks of triggered main shocks (such as after

an intrusion, or aftershocks of aftershocks) have thesecharacteristics: (1) high aftershock productivity (almostalways); (2) increasing stress rate near the time of the mainshock (often); (3) a hump in aftershock rates a couple of hoursafter themain shock (when it can bemeasured); (4) high c andc0 value (often); and (5) a low main shock stress changerelative to the background stress rate (often). Thus severallines of evidence suggest the aftershock rate does not imme-diately subside after triggered main shocks, because addi-tional stress is applied to the aftershock zone after the stressstep of the main shock.

[91] Acknowledgments. The earthquake catalog on which this studyis based is the result of hard work by the staff of the Hawaiian VolcanoObservatory for many decades. Bob Koyanagi in particular directed theseismic network during an era of frequent intrusions and was dedicated toaccurately cataloging as many earthquakes as possible. We thank SteveKirby and Jim Dieterich for thoughtful discussions and Ross Stein, SueHough, Sandy Steacy, Susanna Gross, and Shinji Toda for reviews of themanuscript.

ReferencesClague, D. A., and J. G. Moore (1991), Geology and petrology of Mahu-kona volcano, Hawaii, Bull. Volcanol., 53, 159–172.

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Planetary Sciences, Johns Hopkins University, Baltimore, MD 21218,USA.


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