GEOPHYSICAL RESEARCH LETTERS, VOL. 25, NO. 19, PAGES 3665-3668, OCTOBER 1, 1998
Slow rock fracture as eruption precursor at Soufriere Hills
volcano, Montserrat
ChristopherR.J. Kilbum
BenfieldGreigHazardResearch
Centre,
Department
of Geological
Sciences,
University
College
London,
London,
U.K.
BarryVoight
Department
of Geosciences,
Pennsylvania
StateUniversity,Pennsylvania
Abstract. Breakout of magmaticactivity at Soufflere Hills tips of existingflaws, promotingcrack growthand reducingthe
volcano,Montserrat,wasprecededby a tenfoldincreasein rateof bulk strengthof a rock.(Mineral precipitationfrom fluidscanalso
rock,butnormallyat timescales
greater
earthquake
occurrence.A new modelof subcriticalrock failure healcracksandstrengthen
showsthat this increaseis consistentwith the growth, possibly thanthosefor stress-induced
corrosionto takeplace.)
episodic,of the magmaconduitat a ratecontrolledby progressive Crackspropagateby breakinga rock'smolecularbonds. As
weakeningof the host countryrock. The preferredweakening the stretchedbondsrelax, they releaseelasticstrainenergyand
mechanismis stresscorrosion,by which circulatingjuvenile and this becomesavailable to drive further growth or to open new
hydrothermalfluids chemicallyattack the country rock and cracks[Marder and Fineberg,1996]. The new and growing
promotefailure at stressessmallerthan the rock's theoretical cracks increase the bulk volume of rock under stress and,
strength.The resultsilluminatethe potentialfor slow-cracking eventually,
theycoalesce
to forma majorfracture[Lockndret al.,
models to enhanceeruption forecastsusing the inverse-rate 1991; Main and Meredith, 1991].
As collectionsof cracksgrowtowardseachother,their local
techniquecombined
withtraditionalmonitoring
methods.
stressfieldsmayinteractto inhibitcoalescence
until the numberdensityof cracksexceeds
a criticalvalue[Mainet al., 1993]. The
bulk fractureresistanceof the host rock may thereforeincrease
Introduction
temporarily
until coalescence
begins. Shouldthis occuramong
Followingmore than three yearsof elevatedseismicityand small cracksaheadof a main fracture(in the so-called"damage
four monthsof strongphreaticeruptionsat the SoufriereHills zone"),then the main fracturemay show intermittentratesof
volcano[Younget al., 1997],a tenfoldincreasein the daily rates advance.The averagegrowthrateof the mainfracture,however,
of earthquakes
immediately
preceded
thebreakoutof andesitclava is expected
to increase
withtimebecause
the net rateof elasticin November1995(Figure1). Thisincrease
wasaccompanied
by strain-energy
releasevaries with the increasein total crack
accelerating
rates of grounddeformation[Jacksonet aL, this volume,whilethe net rateof energylossdependson the increase
issue]and was clearly relatedto propagationof a magmatic in total crackarea [Griffith, 1920]. Thusthe meangrowthrate
conduitthroughthe volcanicedifice. Conduitpropagation
results accelerates
until the deformingbulk stressis relaxed,or until the
from somecombinationof an increasein magmatically-inducedfractureis haltedby strongerrock.
stressand a weakeningof hostrock. Sincemagmaticstresses
are
often assumed to be the dominant factor at active volcanoes,
comparativelylittle attentionhas been directed toward the
influenceof rockweakening[Voight,1988;1989]. The computed
accelerationis here usedinsteadto highlightthe importanceof
slow rock fractureas a mechanismfor limiting the rate at which
an eruptionis approached.We reviewpertinentaspects
of timedependentsubcriticalrock fracture,considerits occurrencein
volcanicenvironments
and, appliedto SoufriereHills volcano,
evaluateitspotentialfor forecasting
eruptions.
Subcritical
Fracturing at volcanoes
Conditionswithin and below volcanicedificesare particularly
conducive to stress corrosion: volcanic
rocks contain structural
flaws for crack propagation,they are strongly strained by
intrudingmagma,and they are subjectto severechemicalattack
from hot geothermalor magmaticfluids. Indeed,eruptionsare
commonlyprecededby self-acceleratingprocesses,including
earthquakefrequencyand rates of grounddeformation[Scarpa
and Tilling, 1996]. Such accelerationscan be describedby
[Voight, 1988]:
rock failure
(d2Oddt
2)= A (d•/dt) •
Rocks can weaken and crack at stresses much smaller than
(1)
whereA and a are constants,
and 1'2is the quantitywhoserate of
theirtheoreticalstrengths
[Atkinson,1984;Meredithet al., 1990].
changemeasures
the rate at which eruptionis beingapproached.
Underconventional
geologicconditions,
the dominantweakening
In this "failureforecastmethod"(FFM), the constants
A and a are
mechanism is considered to be stress corrosion, i.e. stressdeterminedempiricallyfrom observationaldata and, when they
enhancedchemicalreaction[Andersonand Grew, 1977;Atkinson,
are known,Equation(1) canbe integratedto yield an estimateof
1984].Circulating
fluids,'
notably
waterwhichcanreadilycorrode
the
timeto eruption.Appliedto severalpre-emptivesequences,
a
silicatematerials[Atkinson,1984], attackmolecularbondsat the
has been found to lie between 1 and 2 (typically closer to 2),
irrespectiveof the processwhich .(2 describes[Voight, 1988;
Corneliusand Voight,1995].
Copyright1998by theAmericanGeophysical
Union.
Fracturestudiesin the laboratorysuggestthat rates of crack
nucleationincreaseexponentially
with time [Locknetet al., 1991;
Papernumber98GL01609.
0094-8534/98/98GL-01609505.00
Main and Meredith, 1991], but that rates of crack extension
3665
3666
KILBURN AND VOIGHT: SLOW ROCK FRACTURE AS ERUPTION PRECURSOR
increaseexponentially
with the lengthof the crack[Main et al.,
1993]. Extrapolatinglaboratoryresultsto large-scale
failure,the
bulk rockstraine dueto a populationof fracturesis expected
to
changewith time as [McGuireandKilburn, 1997]
d•/dt= (d•/dt)0
ex(t-tø)
ea(e-eø)
(2)
where(de/dt)o
is thebulkstrainrateat time,to,,• is an empirical
(1) therateof fracturegrowthis accelerating,
and(2) fracturing
is
occurringat shorterdistancesfrom the monitoringequipment,
therebyincreasing
the proportionof small events(e.g., in a
damage
zone)whichcanbe recognised.
Of primaryinteresthere
is the increasein seismicity
dueto accelerated
fracturegrowth,
and so the effect of a changingsourcepositionmustbe filtered
out.
nucleation
constant
(1/time),
a = Bw2•L•kT(dimensionless),
L
Sincelargereventsaremostlikelyto be caused
by extension
of
is the characteristic diameter of the zone of strained rock when
a principalconduit,an obviousstrategyis to focusattentionon the
slowcrackingcommenced,
S is the remoteappliedstress(tensile frequencyof seismiceventslargerthana thresholdvalue. Ideally,
or compressive), Y is Young's modulus, k is Boltzmann's the thresholdvalue is chosenby selectiveanalysisof the total
constant, T is rock temperature (absolute), co is an atomic population;in practice, and especiallyduring a crisis, it is
stretchingdistancefor breaking bonds at crack tips, and B determinedby expediency.Even so, providedthe absoluterange
(dimensionless)
incorporates
Poisson'sratio for the hostrock, the and frequencydistributionof fracture sizes show only modest
coefficientof frictionalongthe crack,and termsdescribingthe variationswith time, the frequencyof eventsgreaterthan the
geometryof the array [Locknet, 1993; Main et al., 1993]; all thresholdshouldbe proportionalto the event-rateof the whole
componentsof a are assumedto be constant.
population. It is thus viable to seek evidencefor fracture
usinglarger-eventdata.
Seismiceventratecanbe relatedto bulkstrain-rate
by settinge propagation
Pre-emptiveseismicdata at SoufriereHills (Figure 1) were
= N•L, whereN is the numberof recordedeventsand (pis the
length extensionper fracturingevent averagedfor the whole obtained from an array of short-period vertical-component
with triggereddata obtainedfrom the PC-SEIS
population(including both the openingand the extensionof seismometers,
acquisitionprogram[Aspinallet al., this issue]. The triggering
fractures).With this substitution,
Equation(2) yields
algorithm countsthe number of events during each 10-minute
dN/dt= (dN/dt)0
ex(t-tø)
e•-•ø)
(3)
period by comparing successive2.5-second average signal
where 2,= a•L, and (pis assumedconstant.The referenceevent amplitudes,with thresholdsset on ratio of comparedamplitudes,
rate (dN/dOo describesthe host rock's resistanceto fracture, andon absoluteamplitudevalue [Murray et al., 1996].
smallervaluesbeinglinkedwith greaterresistance.Derivedfrom
On an inverse-ratediagram(Figure2a), the datashowa broad
reaction-ratetheory, 2' measuresthe fractionof fluid molecules inverse relation between rate of triggered events and time.
with energysufficientto corrodecountryrock. As 2'increases,
the Initially the trendis crudely-defined,
but alter 11-12Novemberit
energyavailablefor crackingincreasesand,hence,alsothe rate of appearslinearand converges
uponthe observeddateof eruption
crack acceleration. Notice that (dN/dOoand 2' need not vary (aboutNovember15). The early fluctuationsmay reflect data
together:once fracturinghas started,the rate at which dN/dt uncertaintyor truly intermittentrates of fracturegrowth. The
changes(measuredby y) can be the samein rockswith different main sourcesof uncertaintyin measuredevent rates are (1)
resistance,
althoughthe actualeventrateat anygiventime will be variationin the proportionof active cracksthat trigger detected
events,(2) clusteringwith time of detectedevent-rates,and (3)
smallerin rockswith greaterresistance
(smaller(dN/dt)o).
variabilityin the physicalpropertiesdetermining•, in Equation
DifferentiatingEquation(3) with respectto time leadsto
d2N/dt
2= • dN/dt+ ¾(dN/dt)
2
(4) (5); instrumentalerroris expectedto be negligiblein comparison.
Althoughlack of data preventstheseuncertainties
from being
(using, for convenience,initial values to define the reference measureddirectly,first-orderestimatescan be madeby analogy
parameters).Equation(4) shows,as expected,that at low event with laboratorydataandfrom standarderrorpropagation.
rates(and strainrates),fracturingis drivenby the appearanceof
Laboratorymeasurements
of slow cracking(for which errors
newcracks,
such
thatd2N/dt
2• AdN/dt
(a-->1,A--->•in( 1)), while on 2' are assumedinsignificant)show typical scattersof a few
at large event rates, fracturing becomeslimited by the rate of percent[e.g.,Meredithet al., 1990];accordingly,
or,thecombined
crackextension,
forwhichd2N/dt
2• y(dN/dt)
2(a-•2, A-->2').The errordueto (1) and(2) above,is setat 5-10%. For uncertainties
limits to Equation (4) are identical to those reportedfor pre- in event rate due to variationsin g, standarderror propagation
eruptiveepisodesusingFFM Equation(1), providinga physical
interpretationof the FFM approachin terms of subcriticalrock
1400
fracture.
ERU[•.•_•......
Equation (3) indicatesthat the final stagesof deformation
beforecatastrophicfailure (when dN/dt is very large) shouldbe
well-described
by d2N/dt
2 • g(dN/dt)
2 which gives,after
1200
•
1000
•
800
so that a plot of inverseeventrate againsttime yieldsa negative
linear trend. The time at failure (as dN/dt-->oo)can then be
•
600
estimated from the intersection
'•
400
integration,
(dN/dt)
4 = (dN/dt)04
- ¾(t- to)
(5)
between this trend line and the
timeaxis((dN/dO
4 = 0). Thelinearnature
of thetrendgreatly
helps failure forecasting[Voight, 1988] and forms an important
partin our analysisof eventsat SoufriereHills.
200
ß
ß
0
3
Application to Soufriere Hills, November 1995
As a magmaticconduitpropagatestowardsthe surface,the
ratesof detectedrock crackingare expectedto increasebecause
5
7
9
11
13
15
17
19
Time, November 1995 (days)
Figure 1. Accelerationin daily seismiceventratebeforeeruption
on 15 November1995. Filled trianglesas in Figure2a.
KILBURN AND VOIGHT: SLOW ROCK FRACTURE AS ERUPTION PRECURSOR
3667
0.05
0.05
.............
I......
0.04
ERUPTION[
'
'!iii
•'•0.04[
•'
0.04',•.
•o•l
.03
• 0.02
............
•0.01
•,,,,•
.
5
9
11
13
15
17
19
Time, November 1995 (days)
21
0.02
0.01
.
0 00
ß
3
ERUPTION
I
,,
9
11
13
15
17
19
21
0.00
I
Time, November 1995 (days)
3
5
7
9
11
13
15
17
19
21
Time, November 1995 (days)
Figure2. Inverse
seismic
eventrateswithtime. (a) Treated
asa singlepopulation,
a simplelineartrendis clearonlyafter11
November.
Fillederrorbars,or=n= 0.05;dashed
errorbars,cr= n = 0.1. Thenarrow
solidlineis a linearregression
forthewhole
data.Backward
extrapolation
(dashed)
ofregression
line(bold)forlastfourdatapoints
(filledtriangles)
runsclose
tofiveearlier
points
andsuggests
thepossibility
oftwodistinct
trends
(seec). (3)Simulated
inverse
event
using
nonlinear
FFManalysis
andextrapolating
from12November.
Thepreferred
valueof a is 1.88,yielding
failureon 19-20November
(solidline). Theeruption
window
is 14
November13December
(broken
lines).(c)Treated
astwopopulations,
thedatafallonnear-parallel
inverse-rate
trends,
perhaps
due
toepisodic
growth
ofthemagmatic
conduit
(filledtriangles,
population
1;opentriangles,
population
2).
[Barlow, 1989] yields a fractionalerror on inverseevent rate of
displacement
indicatesa greaterresistance
to fracturegrowthfor
tptx/8,
where
n (assigned
a single
valuefor simplicity)
is the population2 events. The simplestinterpretationis that the
fractionalerroron component
termsfor 2'(exceptfor k, whichis populations
are produced
by the intermittent
advanceof a single
beinginducedeitherby alternating
constant).
Figure
2ashows
example
variations
intotalerrorfor2' fracturesystem,intermittency
or by temporary
= 0.0024d4 (seebelow)andcr= n andsetat 5 and10%. The layersof rockwith differentfractureresistance,
in effectiveresistance
withina damagezone.
largererrorbars(or= n = 0.1) yield total uncertainties
on inverse increases
event rate from 13% to almost 400% as event rate increases.
A damage-zone
controlis attractivebecauseit is an integral
part
of
the
fracturing
process,and doesnot dependon variations
Nevertheless,
a singleline cannotbe locatedthroughall theerror
bars(eventhe bestsolutions
omit2 of the 14 errorbars);for n < in external conditions. The alternativeinterpretationwould
0.1, thisconditioncanbe achievedonlywhencr> 0.2. Although requirea bimodalstructurefor SouMereHills. Even for fracture
the layersof differentstrength
musthave
large,component
errorsof 20% or morecannotyet be discounted. growthoverkilometers,
---100m or less,andsomaybe too thin to be resolved
Two evaluations
thusremainfor Figure2a, according
to whether thicknesses
surveys. However,if a damage-zone
or nottheearlyfluctuations
canbe attributed
to datauncertainty. by standardgeophysical
control
was
important,
then
the population2 eventsmight be
Treatingthe data as a singletrend with large scatter,linear
frompopulationI by a greateroccurrence
of smaller
regression
(Figure2a) givesan eruptiondateof 16 November,but distinguished
onlya modest
correlation
coefficient
(r2 = 0.79). A nonlineareventsas the damagezonesform. Suchanalysesawait future
regressionanalysisused in FFM forecasting[Corneliusand study. The key point is that the inverseevent-ratedata,whether
Voight, 1995] yields a = 1.88 (i.e., very close to the linear treatedas one or two populations,suggestthat subcriticalrock
inverse-rate
trend, a = 2) and preferrederuptiondatesof 19-20 fractureis a feasiblemechanismfor limiting the rate of conduit
November(Figure 2b). Both analysesgive preferrederuption propagationbeforean eruption.
dateswithindaysof the actualevent(15 November),supporting
Forecastingvolcaniceruptions
the associationof acceleratingeventrate with propagationof a
magmaticconduit.
A tantalizing
featureof the inverse-rate
methodis itspotential
sometypesof eruption[Voight,1988;
Relaxingthe single-trendassumption,Figure 2a showsthat as a tool for forecasting
half of the ten "scattered"data points(before 12 November)lie Corneliusand Voight, 1995, 1996]. As for SouMere Hills, a
alonga linearextrapolation
of theregression
line(r2 = 0.94)for commonproblemhasbeenambiguityin detectingan inverse-rate
noisydata [Corneliusand Voight,1995].
the lastfour pre-emptiveeventrates. The remainingdataappear trendfrom apparently
herethatevena singlefracturesystem
mightgenerate
to define a secondlinear trend and, if two trends are assumed Recognition
advanceoffersnewinsight
(Figure2c), linearregression
yields,for dN/dt in eventsper day parallelinversetrendsdueto episodic
to analysingsomeinverse-rate
data. In additionto seekinga
andt in days,
single
mean
trend
by
statistical
methods
[Corneliusand Voight,
(dN/dt)
-•= 0.037- 0.0024t
(6)
1995], parallel linear trendsmight also be consideredusing
for the trend that includes the last four pre-emptive data pattern-recognition
techniques. Applied to the Montserrat
(population
1;r2= 0.99for9 points),
and
seismicitydata, which fortunately(and perhapsdeceptively)
appearto be simple,evenjudgmentby eye might have raised
(dN/dt)
4 = 0.045- 0.0021t
(7) suspicions
of two trendsby November9. Extrapolating
the two
forthesecond
trend(population
2; r2= 0.87for5 points);
in both
trends from this date would have revealed 15-21 November as a
cases,to = 0 corresponds
to 01 November. Stronglinear trends
are implied,againsupporting
an interpretation
in termsof conduit
propagation,especially as the population I trend correctly
indicates15Novemberasthepreferreddateof eruption.
As expectedfor a commondeformingsource,the two trends
potentialeruptionwindow (smallerthan the window from FFM
analysisonthe wholedataset;Figure2b).
Previousexperiencehas shownthat forecastersshouldnever
rely on a singledata set, but shoulduse all appropriate
supplementary
evidence.
FFM analysis
(analogous
to Figure2b)
share
virtually
thesamegradient
(7•, 0.0024d'l). Theirrelative on November12 for line-length
displacements
of CastlePeak
3668
KILBURN
AND VOIGHT: SLOW ROCK FRACTURE AS ERUPTION PRECURSOR
measurement(SSAM) analyses with the Materials Failure
dome [Jacksonet al., this issue] suggestsan eruptionabout
ForecastMethod (FFM), June 1991 explosiveeruptionat
November 16, within an eruption window 13-27 November.
Considered together, eruption windows from different
MountPinatubo,in Fire and Mud: Eruptionsand Laharsof
MountPinatubo,Philippines,editedby C.G. Newhall andR.S.
measurementscould provide information useful for hazard
Punongbayan,
pp. 249-268,PhilippineInst.Volc. Seismology,
management
decisions.The Montserratdatathusfurthersupport
QuezonCity, & Univ. Wash.Press,Seattle,1996.
the useof inverse-rateforecastsat leastfor vent openingbefore
of ruptureand flow in solids,
the emplacement
of andesitic-dacitic
lava domes[Corneliusand Griffith, A.A., The phenomenon
Phil. Trans.R. Soc.London,Set. A., 221, 163-197, 1920.
Voight,1995, 1996].
Jackson,P., et al., Deformationmonitoringat SoufflereHills
Volcano,Montserrat,Geophys.Res.Lett., thisissue.
Conclusions
Lockner,D., Room temperaturecreep in saturatedgranite,J.
The pre-eruptiveincreasein seismicevent rate at Soufflere
Geophys.Res.98, 475-487, 1993.
Hills in November1995 is consistent
with growthof the fracture Lockner,D.A., J.D. Byedee,V. Kuksenko,A. Ponomarev,and A.
systemalong which magma reachedthe surface. The rate of
Sidorin,Quasi-static
fault growthandshearfractureenergyin
granite,Nature 350, 39-42, 1991.
growthwasconstrained
by weakeningof countryrock aroundthe
tips of propagatingfracttires. The preferred weakening Main, I.G., and P.G. Meredith, Stresscorrosionconstitutivelaws
as a possiblemechanismof intermediate-term
and short-term
mechanismis stresscorrosion,driven by the stressenhanced
chemicalattackof hydrothermalandjuvenile fluids. Alternations
seismiceventratesand b-values,Geophys.J. Int. 107, 363372, 1991.
in daily seismiceventrate suggestthat propagation
wasepisodic.
Recognition of episodic fracture advance can simplify Main, I.G., P.R. Sammonds,
andP.G. Meredith,Applicationof a
interpretation
of lineartrendsbetweeninverse(seismic)eventrate
modifiedGriffithcriterionto the evolutionof fractaldamage
and time, encouragingthe view that such trendsmay usefully
duringcompressional
rock failure,Geophys.J. Int. 115, 367380, 1993.
contributeto eruptionforecasts,especiallywhen consistent
with
changesin associated
precursors
(e.g., grounddeformation).The Marder,M., and J. Fineberg,How thingsbreak,PhysicsToday
September1996, 24-29, 1996.
fracturecontrolalsohighlightsthe forecastingpotentialof other
seismologicaldata, such as informationon the size-frequency McGuire,W.J., and C.R.J.Kilburn,Forecasting
volcanicevents:
somecontemporary
issues,Geol. Rundsch.86, 439-445, 1997.
distributionof seismiceventsand high resolutionmonitoringof
foci migration.
Meredith,P.G., Main, I.G., andC. Jones,Temporalvariationsin
seismicityduring quasi-staticand dynamic rock failure,
Acknowledgements.The dataevaluatedherewere collectedby the
Tectonophysics
175, 249-268, 1990.
MontserratVolcanoObservatory,andthe helpof A. Miller is particularly
Murray, T.L., Ewert, J.W., Lockhart,A.B., and LaHusen,R.G.,
appreciated.Supportis acknowledged
fromthe BritishGeologicalSurvey,
The integrated
mobilevolcano-monitoring
systemusedby the
NSF grantsEAR 93-16739,96-14622 and96-28413(BV), andCEC grant
VolcanoDisasterAssistance
Program(VDAP), in Monitoring
EN4-CT97-0527 (CRJK). We thankI•R. Corneliusfor FFM data
and Mitigationof VolcanoHazards,editedby R. Scarpaand
processing
andFig. 2b, andA. Borgia,P.G. Meredith,P. Sammonds,
S.
R.I. Tilling, pp. 315-362,Springer-Verlag,
Berlin, 1996.
Day andan anonymous
reviewerfor their comments.
Scarpa,R., andR.I. Tilling (Eds.),Monitoringand Mitigationof
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