VOL. 83,NO. B7
JOURNALOF GEOPHYSICAL
RESEARCH
JULY 10, 1978
Seismological
Aspects
oftheGuatemala
Earthquake
ofFebruary
4, 1976
HIROO KANAMORI AND GORDON S. STEWART
Seismological
Laboratory,
California
Institute
of Technology,
Pasadena,
California
91125
Detailed
analyses
of teleseismic
surface
waves
andbodywaves
fromtheGuatemala
earthquake
of
February
4, 1976,showthefollowing:
(1) Leftlateraldisplacement
alonga vertical
faultwitha strike
varying
fromN66øEtoN98øEisconsistent
withtheteleseismic
data.(2)Theseismic
moment
was2.6X
102?
dyncm.Thedirectivity
of thesurface
waveradiation
indicates
anasymmetric
(1:2.3)bilateral
faulting
witha totallength
of 250km.In modeling
thedisplacement
a rupture
velocity
of 3 km/swas
used,
andthefaultcurvature
wasincluded.
(3)If a faultwidthof 15kmisassumed,
theaverage
offset
is
estimated
tobeabout
2m.Thisvalue
isabout
twice
aslarge
astheaverage
surface
offset.
(4)Although
the
observed
directivity
suggests
a uniform
overall
displacement
along
thefault,thebodywave
analysis
suggests
thattheearthquake
consists
ofasmanyas10independent
events,
eachhaving
a seismic
moment
of 1.3-5.3X 1026
dyncmanda faultlength
ofabout10km.Thespatial
separation
ofthese
events
varies
from14to 40km.Thismultiple-shock
sequence
suggests
thattherupture
propagation
isjagged
and
partially
incoherent
withan average
velocity
of 2 km/s.(5) Theaverage
stress
dropestimated
from
surface
waves
isabout30bars,butthelocalstress
dropfortheindividual
events
maybesignificantly
higher
thanthis.(6)Thecomplex
multiple
event
isa manifestation
ofa heterogeneous
distribution
ofthe
mechanical
properties
along
thefault,which
maybecaused
byeither
asperities,
differences
instrength,
differences
inporepressure,
differences
inslipcharacteristics
(stable
sliding
versus
stick
slip),orcombinationsof these
factors.
(7) Thiscomplexity
hasimportant
bearing
onthestate
of stress
along
transform
faultsandisimportant
in assessing
theeffect
of largeearthquakes
alongothertransform
faultslikethe
San Andreas.
INTRODUCTION
The Guatemalaearthquake
of February4, 1976(0901:42.2
UT; 15.27øN,89.25øW;M8 = 7.5;rno= 5.8),notonlyisoneof
the mostdisastrous
earthquakes
in recenthistorybut alsois
uniquein variousaspects.
According
to the preliminary
reports of the U.S. GeologicalSurvey[Espinosa,
1976]and
Plafker[1976],thisearthquake
is oneof the largesteventsof
transform
faultmechanism,
characterized
bya verylongfault
with a relativelyshallowdepth.The surfacebreaksassociated
withthisearthquake
havebeenmapped
in detailbyPlafkeret
shocks.
Imamura[1937,p. 267]madea detailed
analysis
of
seismograms
of the 1923Kantoearthquake
to determine
the
location
andthesizeof theindividual
events
of themultipleshocksequence.
Wyss
andBrune[ 1967]analyzed
a largenumber of seismograms
of the 1964Alaskanearthquake
andlocated six individual events.From the time intervals between
theseevents
theyobtained
an average
rupturevelocity
of 3.5
km/s.Otherstudies
pertinent
to multipleshocks
includethose
of Miyamuraet al. [1964]and Trifunac
andBrune[1970].
These
studies
clarified
thedetails
ofcomplex
rupture
propagaal. [1976], and the distribution of aftershockshas been studied tion associated
withverylargeearthquakes.
In the present
by Personet al. [1976],Langeret al. [1976],andMatumotoand studywe matchthe observed
P waveformswith synthetic
Latham[1976].Teleseismic
data are verycompleteand have waveformsto investigate
thedetails
of therupturepropagabeenusedto studythe fault mechanism
of thisearthquake tionassociated
withtheGuatemala
earthquake.
[DeweyandJulian,1976;Kanamori
andStewart,1976b].This
BASIC SEISMOLOGICAL DATA
completenessof various kinds of data warrants a further seis-
mological
investigation
intothedetailsof thefaultingmecha- TheP wavefirst-motion
dataareshownin Figure1 andare
nism of this importantevent.This paperis primarilycon- listedin Appendix
TableA 1.xAll of thedatapointswereread
cerned with (1) a comparisonof the surfaceoffsetwith the
by the authorsfrom the WWSSN records.The resultis consis-
displacement
determined
fromseismological
data,(2) thevari- tentwiththatgivenbyDewey
andJulian[1976].
Thedipangles
ation of the displacement
alongthe fault, and (3) the com- andthestrikedirections
areshownin thefigure.Thestrikeof
plexityof the rupturepropagationalongthe fault.Thesefeatureswill providea keyto the understanding
of thenatureof
the northeasttrendingnodal plane and the senseof dis-
placement
alongit agree
withthoseoftheM otaguafaultatthe
plate motion alongtransformfaults,as well asthe mechanical earthquake epicenter.
propertiesof earthquakefaulting.The resultswill be usefulfor
The distribution
of aftershocks
shownin Figure1 is taken
predicting
thenatureof faultingin othermajortransformfault fromLangeret al. [1976].The horizontalandverticalextentof
earthquakes,suchasthe 1906San Franciscoand the 1857Fort the aftershock zone and the location of the main shock with
Tejon typeearthquakes
alongthe SanAndreasfault.
respect
to theaftershock
zonewereusedto constrain
partially
In this study, long-periodsurfacewaveswere usedto con- the geometryof the fault plane.
strain the overall sourceparameterssuchas the seismicmoFigure2 shows
surface
waves
G3(Lovewaves)
andR3(Ray-
mentandthedirectivity,
andbodywaveswereusedto study leighwaves)
whichwererecorded
bytheWWSSNlong-period
thedetailsof thefaulting.Thefar-fieldbodywavesrecorded seismographs
andequalized
to a propagation
distance
of 360ø
on the World-Wide Standard SeismographNetwork + 90ø. The methodof equalization
is that described
byKana(WWSSN)long-period
seismograms
areverycomplex,
anindication
thattheGuatemala
earthquake
isa multiple
event.It
is widelyknownthat mostlargeearthquakes
aremultiple
Thispaperisnotsubject
to U.S.copyright.
Published
in 1978b•
the AmericanGeophysicalUnion.
Papernumber8B0225.
xAppendixTable A I is availablewith entirearticleon microfiche.
Orderfrom AmericanGeophysical
Union, 1909K Street,N. W.,
Washington,
D.C. 20006.Document
J78-004;
5;1.00.
Payment
must
accompany order.
3427
3428
KANAMORI
ANDSTEWART:
MECHANISM
OF 1976GUATEMALA
EARTHQUAKE
91ø W
N
(a)
(b)
90 ø
89 ø
'
ßA!tershocks
.C?'•
,•'
88 ø
16ON
i5ø
j/x
•_.•
•Oamanl
....... • •'• • ^g,•
•
J'•;tøemaa
'
14ø
o-
.o
•o
20 N •
40
Fig. 1. (a) TheP wavefirst-motion
datafortheGuatemala
earthquake,
indicating
leftlateralstrikeslipmotiononthe
preferred
faultstrikingN66øE.A stereographic
projection
of thelowerfocalhemisphere
isshown.
(b) A mapof themain
shockand aftershock
locations.
The observed
displacements
alongthe Motaguafaultareplottedinsidethecircles(values
arein meters)[afterLangeretal., 1976;Plafker,1976].(c) A plotofthenumberof aftershocks
asa functionof depth[after
Langer et al., 1976].
mori[1970].Short-period
surface
waveshavebeenremoved
by
easternand the westernbranchesbeing 75 and 175 km long,
usinga filter describedby KanamoriandStewart[ 1976a]with a
short-periodcutoff at 40 s. Both Love and Rayleigh waves
indicatea four-lobedradiationpatternwhich is consistentwith
the fault geometrydeterminedby the P wave data shownin
Figure 1. The theoreticalradiation patternsof Love and Rayleigh wavesfor a shallowstrike slip fault are shownby Kanamori and Stewart [1976a]. These are the fundamental
seismologicaldata setsto be usedin the following analysis.
respectively
(b is the dip angle,4 is the averagestrikeof the
M otaguafaultmeasured
clockwise
fromnorth,andX istheslip
angle).Signconventions
are givenby Kanamoriand Stewart
[1976a].The syntheticseismograms
for thisgeometrywith a
rupturevelocityof 3 km/s werecomputed,andthe amplitude
variationis shownin Figure3. The fit in the easternazimuthis
significantly
improved.We trieda rupturevelocityof 2 km/s;
SURFACE WAVE ANALYSIS
as shownin Figure 3, the asymmetryof the radiationpattern
of the syntheticseismogram
becomestoo largeto matchthe
data. However, in view of the scatter of the data a rupture
velocityof 2.5 km/s is still acceptable.
In orderto investigate
Since short-period(T < 40 s) surfacewavesare severely furtherdetailsof the rupturepropagation,the directivityfuncaffectedduringpropagationby structuralheterogeneities,
only tionswerecomputedfor a suiteof modelsandcomparedwith
long-periodsignalswereusedin the presentanalysisto deter- those for several stations. For G waves, three stations, AFI,
AAE, and CTA, were chosenbecausethey are nearly in the
to
As is shownin Figure2, sincethe overallradiationpatternis directionof the fault strike(½r= 66ø) andaremostsensitive
consistentwith the geometrydeterminedfrom P waves,we the directivityof the source.Sincethesestationsare nearlyin
first computedsyntheticsurfacewavesfor a point double- the sameazimuth(© = 8.7ø for AFI, 2.7ø for AAE, and 10.2ø
couplesourcecorresponding
to the P wavemechanism.
The for CTA, where© is the anglebetweenthe fault strikeandthe
mine the seismic moment Mo.
point sourcehad the sameepicenter
as the mainshockanda
depthof 16km.Themethodof synthesis,
thevelocity,andthe
Q structureare described
by Kanamori[1970]and Kanamori
andCipar [1974].The samefilteraswasusedfor the observed
recordswasappliedto the syntheticrecordssothat theycould
be compareddirectly.The maximumtraceamplitudes
of the
observedand syntheticrecordsare comparedin Figure 3 as
functionsof azimuth.Althoughthe overallagreementis satisfactory,the observedamplitudesare clearlytoo smallin the
azimuthalrangeof 0ø-90ø, indicatinga rupturepropagation
toward the west. This direction of propagationis consistent
greatcirclepassing
throughtheepicenter
andthestation),the
directivityfunctionwascomputedfor © = 10ø.The resultsare
shownin Figure4. Althoughthe scatteris considerable,
it is
evidentthat the combinations(150, 50, 2.5) and (175, 75, 3.0)
givea satisfactory
fit to the datawherethe first,second,and
third numbersin parentheses
denotethe fault lengthsof the
westernand easternsegments
andthe rupturevelocity,respec-
tively. When a rupturevelocityof 2 km/s is used,the fit
becomesworse than that for these two cases.For Rayleigh
waveswe chosestationsBUL' and KIP. Thesestationsare in
the directionof the maximumof the radiation pattern, yet they
have© = 38.5ø and 40.8ø, respectively,
and are still sensitive
zone.A seismicmomentof 2 X 10•7dyn cm givesa reasonably to the sourcedirectivity.The directivity functionswere comwith the location of the main shock relative to the aftershock
goodfit. The preliminaryanalysismadeby DeweyandJulian putedfor © = 41ø and comparedwith the data in Figure4.
(175,75, 3.0)gavea satisfactory
fit. A
[1976]usinga pointsourceandestimated
spectralamplitudes Againthe combination
of G wavesat 100-speriodgavea value,2.6 X 10•7 dyn cm, rupturevelocityof 2 km/s didnotgivea goodfit. It is imporwhichis in reasonablygoodagreementwith thisvalue,despite tant to note that the dislocation was assumed to be uniform
along the fault strike in thesemodels.The fact that these
their simplifiedmethod.
asymmetric
radiationpattern
The slightasymmetryof the observedradiationpatterncan modelscanexplainthe observed
be explained
in termsof thedirectivity[Ben-Menahem,
1961].
To a firstapproximation
the faultgeometryshownin Figure1
can be modeledby an asymmetricbilateralfault with b = 90ø,
4 = 75ø, andX = 5ø extending
overa distanceof 250 km, the
(Figure3) and the directivities
(Figure4) indicatesthat the
fault displacement,
averagedoverthe lengthof the fault, is
relativelyuniform,althoughsmall-scale
irregularities
arevery
likely to exist.
KANAMORI
ANDSTEWART:
MECHANISM
OF 1976GUATEMALA
EARTHQUAKE
In order to supplementthe WWSSN data a seismogram
from an ultra-long-periodinstrumentat the Seismological
Laboratory,CaliforniaInstituteof Technology,
wasused.This
instrument(PAS, number33) hasa peakresponse
at 150s and
is adequate
for recording
verylongperiodsurface
waves.Figure
5 showsthe observedand syntheticRs at Pasadena.No filtering hasbeenapplied.The syntheticseismogram
wascomputed
for the fault geometryshownat the bottom of Figure 2. The
agreementof the wave forms is very good. A seismicmoment
of 2.3 X 11Y
? dyn cm was found which is in good agreement
As shown in Figure 1, the Motagua fault is not straight but
is slightly convextoward the south. For the sake of completeness,synthetic seismogramswere computed for the geometry
shown at the bottom of Figure 2. In this calculationthe fault
wasbroken up into four segments,syntheticseismograms
were
computed for each segmentby the standard method, and then
the resultsfor eachsegmentwere addedwith delaysappropriate for a rupture velocityof 3 km/s. The resultsare shownin
Figure 2, and the azimuthalvariation of the amplitudeis compared with the observedone in Figure 3. The differencebetweenthe straight and the curvedfault model is very small and
is probably unresolvableby the presentdata. However, it is
important that a realisticfault geometrycan explain the overall radiation patterns of surfacewavesand the amplitude ratio
of Rayleigh to Love wavesvery we!!. By matching the amplitude a seismicmoment of 2.6 X 11Y
?dyn cm was obtainedfrom
both Love and Rayleigh waves.
•3
with that obtained from the WWSSN data. This agreement
suggests
that the sourcespectrumis flat at periodsof 100-300
s. In the discussionwe will use the moment of 2.6 X l0 s?dyn
cm obtained from the WWSSN
The resultsobtainedabovecan be interpretedin termsof the
stressdrop Aa. The verticalextent w of the fault cannotbe
(15-100,
x1500)
G3
(15-I00,X1500)
12hI0m 12h20m
360ø
' '•
$NC
•._--,-../vv•C
0p4
/•x/
XKIP
270ø
••• '•/'•TRN'
• ••
••
ADE•
CUA*
COP
DAG
-
NUR
_30
ø
....
SAC
• •TOL
ATU-
-
• --
-- 60ø
CUA
q •AAI:
270ø
•90
ø
TRN
KEV
•
MAT
-1 •
4
PMC/
SHILI
•
SHEI
_
300ø•DAV
•-••½•½
12hI0m 12h20m
330ø•C0L
d
NUR 30 o
--XlV\l[l_[/_\l..\
data.
averagedislocation
(displacement
discontinuity)
/J and the
12h40
m 12h5c)
m 13boo
m 12h40m 12h50m 13boom
330
ø_
3429
_
TRN*/
PMC• -
.•- PMC*_
TRN 90ø
CTA -I
-
AFI-I
o
8UL
240ø
AAE*.__I
.....CUA*•
120
ø
L..../,m•
V - MUN
TOL*••
RIV /
o
180o
•
210ø
d
_.•••"U"* • • c•COL* 150ø,soo
•
•
•
•
• •
•
•
•
•
•180 o
4.5 4.4 4.3
i
U, km/sec
300
i
t
_1
t
I
I
t
I
•
TI
-1 4.5 44
4.3
,-,soo
42
4l
U, km/sec
•$ (Mo=1027dyne-cm)
Synthetic
--
_
330 ø
4.1
ANP*-]
LP.B
--1150o
COL*
12h05
m 12hl5
rn 12h25
rn 12h05
rn 12hl5
m 12h25
m
*
*,
'
12h45
m 12h55
m 13h05
m 12h45
m 12h55
m 13h05
m
t
4.2
sec
•3 (Mo
--1027
dyne-cm)
Synthetic
360 ø
COP.•
NUR*•
I
I
I
I
-- 0 o
Oo
360 ø
30 ø
330 ø
30 ø
60 ø
300 ø
- 60 ø
-
_
300 ø
_
-
_
_
_
270 ø
_90
ø
. !30 ø
270 ø
-
_
240 ø
120 ø
210 ø
- lcm
-
_
_
180 ø
3.8
3.7
3.6
3.5
3.8
3.7
3.6
150 o
210 .....
180 o
180 o
3.5
120 ø
240 ø
-150
180 ø
4.6 4.5 4.4
U, km/sec
ø
4.3 4.2
4.6 4.5 4.4
43
42
U, km/sec
,
Epicenter
-• ./•"•
•
o
o
o
':(•'ss,
i ••••mbposite
fault
Fig. 2. Azimuthalplotsof equalizedseismograms
for RaandGaandsynthetic
seismograms
computedfor thecomposite
faultgeometryshown.A seismic
momentof 11Y
?dyncrnwasusedin the synthesis.
In the observed
patterns,oneasterisk
indicatesthat R4andG• datawereequalizedto RaandGadistances.
Two asterisks
indicatethat R• andG• wereequalizedto
R• and Gadistances.
The amplitudescaleis for thetraceamplitudeon the WWSSN long-periodinstrument(15-100) with a
magnification of 1500.
3430
KANAMORI
ANDSTEWART:
MECHANISM
OF1976GUATEMALA
EARTHQUAKE
km
v= 3 0 km/sec
trum and provideimportantinformationregardingthe details
of the rupture process.Unfortunately, for the Guatemala
earthquake,both P and S waveswere off scaleat moststa-
Biloterol 175-75 km
v =20km/sec
tions. P waves were on scale at some stations near a node of
....... Point
source8=90%q•f=75
ø, X=5ø
Mo=2
6 x1027
dyne-cm
B•loterol
175-75
Composde
R3....,,
the radiationpattern,but useof thesestationsfor waveform
,,"-",
"7.'•,,•,
analyses
is not desirable.Figure6 showswaveformsof P
-•>:•'•
wavesat sevenstationswhich are considerablyremovedfrom
the radiation nodes.Except LPB, all stationslie in a narrow
E 0
azimuthalrange from 19.6ø to 41.1ø. Thus this data set is
•
•
•0 •
,--,
' •,
/'%
/
90 ø
/--,,
•
,• ,
180ø
270•
ß
somewhat limited in terms of azimuthal coverage,but it is
evident that the wave forms at these stations exhibit a very
,
remarkablecomplexity.Sincethe distancesto thesestations
arelargerthan68ø (exceptLPB), thiscomplexityis unlikelyto
be dueto later phases.At thesedistances,
the only laterphase
560 ø
Azimuth, degree
that arrives within 2 min after the onset of the P wave is the
Fig.3. Equalized
station
peak-to-peak
amplitudes
œor
observed
R• PcP phase,but, for a verticalstrikeslip fault, PcP is always
andG3dataplottedasa œunction
of'azimuth(solidcircles).
Curves nearlynodal.Thus mostof the complexities
are considered
to
represent
thevarious
œault
models
usedin thisstudy.
be due to the source.From thesefiguresit appearsthat the
radiation from the source lasted about 2 min. Since the dis-
tanceto LPB is only38ø andthePP phasearrivesabout1 min
directlydetermined
fromthepresentdata,butthedistribution after P, only the first minuteof that recordis shown.
of the aftershocksindicates that w •- 15 km (Figure 1). By
Althoughthe azimuthalcoverageof the data is somewhat
usingthefaultlengthL = 250km suggested
by theextentof limited, these recordscontain extremely important informathe surfacebreak, the asymmetry,and the directivitywe have tion regardingtheruptureprocess.
In thefollowinganattempt
1• = Mo/#Lw= 2 m andAa = 2#/JDrw= 30bars,where# = is madeto interpretthesecomplexrecordsin termsof multiple
3.5 X 10• dyn/cm2 is used.
events.Inspectionof theserecordssuggests
that at leastseven
Sincethe wavelengthof the surfacewavesusedin the pres- major pulsesare distinguishable
duringthe 2-mintime interent analysisis longerthan about300 kin, thesewavesare not val. Each pulsecorresponds
to an individualevent of the
significantly
affectedby structuralheterogeneity
alongthe multiple-shock
sequence.
Sincesucha sequence
involves
a very
propagation
pathandgivea reliable
gross
average
of/• and large numberof parameters,e.g., sourcegeometryof each
Aa overthe entirelengthof the fault. Althougha depthof 16 event,spatialand temporalseparationof the multipleevents,
km was used in the above analysis,the amplitudeof these strength(the seismic
moment),fault length,and risetimeof
long-period
surfacewavesis not sensitive
to a changein the each event, etc., it is extremelydifficult to determineall of
sourcedepthfrom 0 to 16 km, in particular,for a vertical theseparameters.
Hencewe usedthe followingprocedure.
strike slip mechanism.
We first took station NUR and tried to match the first part
of the P waverecordwith a syntheticwaveform computedfor
BODY WAVE ANALYSIS
a point sourcewhosetime functionis adjustedso that it
Althoughthesurface
waveanalyses
described
aboveprovide
reliablegrossfaultparameters,
theyareinadequate
to resolve
the detailsof the ruptureprocess.
On theotherhand,seismic
bodywavesrepresent
the short-period
endof thesourcespec-
matchesthe overall wave form of the first pulseof the P wave
record.A symmetrictrapezoidalsourcetime functionwith a
risetime(andfall-offtime) of 4 s and a totalwidthof 9 s was
chosen(Figure6). Althoughthe detailsof thistimefunction
Frequency, mHz
5
I0
6
8
I0
150-50
2.5===175-75
175-75
25
', I''''
' '3.0-•
'/ 175;75
' 20
' ©:41
' o OIBUL•-•
200-100
2.5
----/
225-25
2.5_1
,:oo1
I • ....125-75
2.5
I ,
R3•
-
•F•
o:.•,.
250 200
, ,
I•
I00
:
70
150
Symmetric
•
120
IO0
Period, sec
Fi•,4. Observed
andcomputed
dircctivity
For(½)Love
waves
and(•) Rayleigh
waves,
Thepreferred
model
Forboth
datasetsisthe17S-7½-3.0
combination
(lo•-dashdFo•bothsets);
e isthea•lc bctwcc•
theFault
strikeandtherupture
direction.Hatchinssindicatethe ran•c oFtheobserved
data.
KANAMORI
ANDSTEWART:
MECHANISM
OF1976GUATEMALA
EARTHQUAKE
from the available data. We therefore assumedthat the time
function and the mechanism of the second event are identical
to those of the first event. In view of the results of the surface
Pasadena Ultralong Period (No:.33)
1[--Iih33
m
R2
P-P=035
cm
Ohs --
wave analyses,which indicatea relativelyuniform left lateral
slip overthe entirelengthof the fault, the assumption
of the
identicalmechanism
is probablyjustifiedeventhoughthe fault
Syn...............
,......"',..'",
/'"',•.,',"'",.
i i i i
"'
300 sec
3431
Mo=
2.3x1027
dyne.cm
trace has somedegreeof curvature.Sincethe rise time and the
Fig. 5. Observed
and synthetic
Rayleighwaves(R2)at Pasadena pulsewidth are determinedby the initial tectonicstress,stress
(ultra-long-period
instrument,
number
33).Notetheagreement
ofthe drop,and dimensionof the individualevent,theyare likelyto
phase.
vary considerablyfrom event to event.
The aboveprocedurewasrepeatedfor the later eventsuntil
the 2-minrecordof theP wavewassatisfactorily
matched.The
are not resolvable
by our data, it canexplainthe firstpart of
theseismogram
satisfactorily.
Thepointsource
wasplacedat a later eventswere placedat the samelocation as the first event.
of the eventswas
depthof 5 km in a homogeneous
half space.In the synthesis This first approximationto thetime sequence
the surfacereflections
pP and sP wereincluded(Figure6). then adjustedto fit the observationsbetter by the methodof
This typeof modelinghas beensuccessfully
appliedto the leastsquares.Let S(t) and s(t) be the observedP wave and the
determination
of source
parameters
of relatively
simple
events syntheticwavelet for the individual event ('sum' shown in
Figure 6), respectively.We soughtto minimize the function
[Langston, 1976]. The seismicmoment of this first event was
estimatedto be 1.6 X 11Y
6 dyn cm. Then we subtractedthe
N
synthetic
tracefromtheobserved
oneandrepeated
theproce(t) - • mts(t- tt)
durefor the secondevent.Althoughthe time functionandthe
mechanism
of the secondeventmay be differentfromthoseof whererni and ti are the momentand the onsettime,respecthe first event,it is extremelydifficultto resolvesuchdetails tively, of the ith event and N is the total number of events.The
i=1
Multiple-Event Analysis
•
Source
time
function
NUR(A=88
Iø)
--,j',._-+---• +
:• )
sec
ß't4 --
p
0bs
pp
sum
- ½.
{•S(t)
m,s(t-ti)]•-•
I,.II Ill
t 1.6x1026
dyne-cm
minimum
I=•
LPB (6=379 ø )
COP
(A=83
97
ø)
0bs
I
! m•n
I
PP
0bs
'
Syn
!•
Source
IJ,I,III
I026dyne-cm
z,.•x
TimeSeriesII
J
KEV (A:84.5 ø)
KTG (A:68.2 ø)
Obs
,, l, ,
Obs.
•,, I I , J
Syn
I
dyne-cm
Syn
z.x,o
KdF (A=87.5ø)
STU (A=84.2 ø)
0bs
Syn.
0bs
•
Syn
•.1,
I
I
T 1.8xlO26
T2.2x•O
26
•1• •111
I __T3.0x•026
Fig.6. Observed
andsynthetic
P wavesfor individual
WWSSNstations
obtained
fromthemultiple-shock
analysis.
For
eachstationthe sourcetime seriesis obtainedby usingthe mechanism
givenin Figure la and the sourcetime function
shownhere.Thesurface
reflections
pP andsP areincluded
in thesourcetimefunction.Theresulting
series
isgivenforeach
stationalongwith the momentfor the firstevent.The heightof the verticalbar is proportionalto the momentof the
individualevent; A is the epicentraldistance.
3432
KANAMORI
ANDSTEWART:
MECHANISM
OF 1976GUATEMALA
EARTHQUAKE
2.11.3
A quiet interval of about 10 s betweenthe secondand
Moment
(10
26dyne-cm.)TOTALevent.
the third eventand a 15-sintervalbetweenthe eighthand the
3.3 2.9 5.3
4.6 4.1 3.3x1027 nintheventarecommonto all thestations.Somecomplication
is observedaround the fourth and fifth events, where some
I(XlO
26
dyne cm)
1
2.5
T
I
2.1
T
2.2
T
/'
2/,½,
1.6
1.6
3.0
7) suggests
an averagerupture velocityof about 2 km/s, which
t
T
i
insignificant.
It is interestingto note that Plafker [1976]found very large
surfacebreaks, with a maximum of 3.4 m, near the western end
of the fault, about 150km to the westof the epicenter(Figure
1). The large events,8 and 9, probably correspondto these
largedisplacements.
If one assumes
that the eightheventwas
150km to the west of the initial epicenter,the time separation
of about 72 s betweenthe first and the eighthevent(seeFigure
T
•
easternand the westernbranchesof the fault interactwith each
other, resultingin complexwave forms.The averagemoment
of each eventis shownat the top of Figure 7. The sum of the
momentsis 3.3 X 11Y
?dyn cm, whichis slightlylargerthan that
obtained from surface waves. However, in view of the various
errorsinvolvedin the body waveanalysis,this differenceis
i
i
stationsindicatea negativepulse.The causeof thiscomplication is unclear,but one possibilityis that the arrivalsfrom the
T
is somewhat smaller than that obtained from the surface wave
directivity,viz., 3 km/s. As is shownin Figure 3, a smooth
rupture
propagationwith a rupturevelocityof 2 km/s results
i
•T
6O
in a stronger asymmetry than the observeddata indicate.
90 sec
However, if the rupture propagationis jagged and partially
Fig. 7. A comparisonof the sourcetime sequences
for the seven
incoherent
as is demonstratedby the P wave analysis,the
stationsusedin this study.The hatchedzonesdenoterangesof arrival
i
I
1.8
times;½sis the stationazimuth.The valuesgivenat the top are the
seismicmomentsof the individualeventsof the multiple-shockse-
effectof rupturepropagationwouldbecomelesspronounced
than that for smooth propagation [Haskell, 1966]. Thus the
valueof 3 km/s obtainedfrom the surfacewaveanalysisunder
the assumptionof smoothpropagationshouldnot be given
resultof this inversionis shownin Figure 6. The sourcetime too much significance.We prefer the result obtained from the
sequences
(e.g., plot of mt as a functionof tt) are shownunder P wave analysis:the rupture propagationis jagged with an
the individual syntheticrecords.It is encouragingthat a very averagevelocity of 2 km/s.
good match between observedand syntheticrecords is obThe resultsof the body wave analysiscan be summarizedas
tained by a superpositionof eventshavingpositivern•.Only follows:The entirerupturesequence
canbe represented
by the
one of the nine events was of reversedpolarity. This result sequentialoccurrenceof approximately10 distinctevents,the
suggeststhat the assumptionof identicalmechanismis reason- seismicmomentsof which varied by a factor of about 4, with
able.
time separationsvarying from 7 to 20 s. Since the average
The above method was applied to other signalsshown in
rupturevelocityis about 2 km/s, thisvariationof time separaFigure 6, and the resultingsyntheticrecordsand the source tion corresponds
roughlyto a spatialseparationof 14-40 km.
time sequences
are shown.In all casesa very good agreement The trapezoidaltime functionusedto modelthe point sources
is obtained with a positive rn• for most events. If all of the hasan effectivepulsewidth of about5 s, whichcorresponds
to
multiple eventshad the samemechanismand occurredat the a source dimension of about 10 km. However, as we mentioned before, the details of the time function cannot be resamelocation,the sourcetime sequenceshouldbe identicalfor
all the stations.Actually, as shown in Figure 6, the derived solved,so that this dimensionshould be considereda very
source time sequencesare similar from station to station, crude measureof the sizeof the individualevents.It is probalthoughthere are somedifferences.
Theseirregularities
are able that the sourcedimensionsalsovariedconsiderablyfrom
due to the followingcauses.First, the variouseventsprobably event to event.
were distributedalong the fault, sothat the differencebetween
This complexmultiple eventmay be envisagedin termsof
the arrival times of the signalsvariesfrom station to station, the heterogeneous
mechanicalpropertiesalongthe fault plane.
dependingon the azimuth and, to a lesserextent, the distance. This heterogeneity
may be causedeitherby asperities,differSecond, noise in the records can cause errors in the measured
encesin strength,differencesin pore pressure,differencesin
arrival timesof the events.Third, a slightchangein the mecha- slip characteristics
(stableslidingversusstickslip), or combinism also resultsin errors. For a verticalstrike slip event all nations of these factors.
teleseismicP rays leavethe sourcein a nearly nodal direction,
CONCLUSIONS AND DISCUSSIONS
so that a slight changein the mechanismcan causea significant change in the wave form, and the determination of the
The seismicmomentof the 1976Guatemalaearthquakeis
arrival timesis thus affected.In view of thesecomplexeffects estimatedfrom long-periodsurfacewavesto be2.6 X 102?
dyn
we must allow somerangesof arrival times in identifyingthe cm, whichsuggests
an averagedisplacement
of 2 m and a stress
individual events.Figure 7 comparesthe time sequences
for drop of 30 bars if the vert,ical width of the fault is taken as 15
the seven stations. Allowing for ranges of arrival times as km on the basisof the aftershockdistribution.It is possible
shownby hatchedbelts,we can probablyidentify events1, 2, that the actualfault planeextendsdeeperthan the aftershock
3, 6, 7, 8, and 9 as marked on the figure.It may be notedthat zone, but it is unlikely that a fault plane that is completely
the eighthandninth eventsare2-2.5 timeslargerthanthe first incapableof generatingaftershockscan generate100- to 200-s
quence.
KANAMORI
AND
STEWART:
MECHANISM
OF1976
GUATEMALA
EARTHQUAKE
3433
surfacewavesvery efficiently.On this basiswe considerthat
the above estimate,2 m, of displacementrepresentsthe actual
averageover the depth rangeof 15 km. On the other hand,
Plafker et al. [1976] and Plafker [1976] reported that the
averagesurfacedisplacementmeasuredimmediatelyafter the
earthquakeis about 1m with a maximumvalueof 3.4 m at one
locality. This value is about half the average displacement
derived from surface waves. It is possiblethat the surface
layersare partially decoupledfrom the layersat depthso that
the surface displacementrepresentsa fraction of the fault
displacementat depth. In this case we might expect postseismiccreepalong the fault over a prolongedperiodof time.
In fact, Bucknam et al. [1976] and G. Plafker (personal communication, 1977) found a significantincreasein the surface
offset (as much as 37% of the initial break) during the period
from February to October, 1976. Although the total displacementis still smaller than the seismicdisplacement,the
creep is still continuing, so that it is possiblethat the surface
break will eventuallycatch up with the displacementat depth.
Scholz et al. [1969] suggestthat for the 1966 Parkfield earthquake, near-surfaceafterslipabove4-km depthcan explainthe
discrepancybetweensurfaceslip observedimmediatelyafter
the earthquakeand seismicestimatesof the averagecoseismic
slip.
On the other hand, we cannotcompletelyexcludethe possibility that the fault plane responsiblefor surfacewave radiation is significantlylarger than that inferred from the aftershock zone. If this is the case, then both the average
displacement
and the stressdrop wouldhavevalueslowerthan
ground motion which resultsfrom earthquakesof this type.
Haskell [1966] and Aki [1967] showed that irregular fault
motion significantlyenhancesthe high-frequencyend of the
seismicspectrum.
The rate of the instantaneousplate motion of the Caribbean
plate with respectto the North American plate in Guatemala
is estimated to be about 2 cm/yr [Molnar and Sykes, 1969;
Jordan, 1975]. Historical recordssuggestthat the repeat time
of major earthquakeson the central and western Motagua
fault is about 200 years [Spenceand Person, 1976]. These
results suggesta coseismicdisplacementof about 4 m if the
strain is releasedtotally in earthquakes.The discrepancybetweenthis value and the averagedisplacement,2 m, in the 1976
Guatemala earthquakeobtainedby the presentstudyindicates
the following possibilities:(1) half the displacementon the
Motagua fault takes placein creep,(2) the repeattime fluctuatesconsiderably,(3) the rate of plate motion haschanged,(4)
part of the plate motion is taken up by displacementsalong
other faults, and (5) the estimateof the rate of plate motion is
those estimated for the vertical width
California
of 15 km discussed
in error.
Acknowledgments. We would like to thank the personnelof all the
WWSSN stationswho were kind enoughto sendus seismograms.We
also thank George Plafker for usefuldiscussions
and A. F. Espinosa
for an advancecopy of U.S. Geological Survey ProfessionalPaper
1002(1976). This researchwas supportedby a grant from the National
Academy of Sciences,through WDC-A for seismology;the Division
of Earth Sciences,by National ScienceFoundation grant (EAR7614262); and by' U.S. Geological Survey contracts 14-08-0001-15893
and 14-08-0001-16776.Contribution 2901, Division of Geological and
Planetary Sciences,California Institute of Technology, Pasadena,
91125.
earlier.
The asymmetryof the radiation pattern (Figures2 and 3)
and the directivity (Figure 4) suggestthat the displacementis
relativelyuniform alongthe entirelengthof the fault, although
short-rangeirregularitiesare possible.A rupture velocityof 3
km/s is suggestedif the displacementis assumedto be uniform.
TeleseismicP waves exhibit a complexity suggestingthat
this earthquakeconsistsof about 10 distinctevents.The duration of the sequence,about 2 min, probablycorresponds
to the
time for the entire fault to break. Analysis of the P wave forms
suggeststhat the fault broke in a relativelycoherentmanner
over distancesof only 10 km or so. The spatial separationof
the individual eventsis 14-40 km, suggestingthat either stress,
frictional characteristics,or slidingcharacteristicson the fault
planevary with comparablespatialscalealongthe fault plane.
This result is in striking contrastwith that obtained for large
earthquakesalongtheGibbsfracturezone(transformfault) of
the Mid-Atlantic ridge. Kanamori and Stewart [1976a] found
that the rupturepropagationin theseearthquakesis relatively
coherentover much longer distances,40 km or so. This differenceprobablyreflectsthe differencein the ageof the faultsand
the structurebetweenthe two transformfaults and providesan
important piece of information regarding the mechanical
propertiesof varioustypesof plate boundaries.Although the
averagestressdrop wasrelativelylow, about 30 bars,the local
stressdrop for the individual eventsmay have been significantly higher than this, perhapsby a factor of 2 or 3. Hanks
[1974] suggestedthat the 1971 San Fernando earthquakewas
characterizedby a high stressdrop event in the beginning.
Burdick and Mellman [1976] reported a relatively high stress
drop, 96 bars, over a circularrupturezone of radius8 km for
the 1968 Borrego Mountain, California, earthquake.
The complexity of the rupture processas revealedby the
present analysishas a very important effect on the strong
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EARTHQUAKE
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