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on the White Wolf fault, and over 100 bars for small earthq.uakes in the .... For magnitudes less than teen analyzed shocks are very close to vertical. 6 no reliable ...
JOURNALOF GEOPHYSICAL RESEARCH

VOL. 73, NO. 14, JULY 15, 1968

SeismicMoment, Stress,and SourceDimensions for Earthquakesin the California-NevadaRegion MAX WYss AND JAMES N. BRUNE

SeismologicalLaboratory, Cali/ornia Institute o• Technology Pasadena, California 911(}5 The source mechanism of earthquakes in the California-Nevada region was studied using surfacewave analyses,surfacedisplacementobservationsin the sourceregion, magnitude determinations, and accurate epicenter locations. Fourier analyses of surface waves from thirteen earthquakesin the Parkfield region have yielded the following relationship between seismic moment, Mo and Richter magnitude, M•,: log Mo -- 1.4 M•, nu 17.0,where 3 < M•, < 6. The following relation between the surface wave envelopeparameter AR and seismicmoment was obtained: log Mo -- log ARsoonu 20.1. This relation was usedto estimate the seismicmoment of 259 additional earthquakesin the westernUnited States.The combineddata yield the following relationship between moment and local magnitude: log Mo -- 1.7 M•, nu 15.1, where 3 < M•, < 6. These data together with the Gutenberg-Richter energy-magnitude formula suggest that the averagestressmultiplied by the seismicefficiencyis about 7 barsfor small earthquakes at Parkfield and in the Imperial Valley, about30 barsfor smallearthquakesnear WheelerRidge on the White Wolf fault, and over 100 bars for small earthq.uakes in the Arizona-Nevadaand Laguna Salada (Bain California) regions.Field observationsof displacementassociatedwith

eightParkfieldshocks,alongwith estimatesof fault area,indicatethat fault dimensions similar to the valuesfound earlier for the Imperial earthquakeare the rule rather than the exception for small earthquakesalongthe San Andreasfault. Stressdropsappearto be about 10% of the averagestressmultiplied by the seismicefficiency.The revisedcurvefor the momentversus

magnitudefurtheremphasizes that smallearthquakes are not importantin strainreleaseand indicatethat the zoneof shearmay be about 6 km in vertical extent for the Imperial Valley and even less for oceanic transform faults.

INTRODUCTION

Recent developmentshave greatly improved our understandingof the mechanismof shallow earthquakesin the California-Nevada region. Many of these earthquakesare strike slip and are relatedtectonicallyto the San Andreasfault system.In this paper seismicmomentsof these earthquakeswith local magnitudesbetween 3 and 6 have been obtained in two ways. First,

spectral densitiesof the surface waves were obtained for thirteen earthquakesfrom the San Andreas fault system which covered the mentioned magnitude interval about evenly. The momentswere computedby meansof the theoretical results of Ben-Menahem and Harkrider

[1964] and Andersonand Harkrider [1968]. To estimate the seismic moment for a large number of earthquakeswithout the time-con-

• Contribution 1513, Division of Geological Sciences, California Institute of Technology, Pasadena, California.

sumingand costly processof digitizingand Fourier-analyzingthe surface waves, the parameterAR, as definedby Brune et al. [1963], was used to estimate seismic moment for another 259 shocks from the western United States recorded at Pasadena.

For the eight Parkfield shocks for which spectral densities were determined by Fourier analyses,field observationsallowed an estimate of the average relative displacement accompanying them. These observations were obtained in the courseof the extensivestudy of the Parkfield 1966 earthquake sequence. In four casesthe relative displacementswere recorded on strain meters straddling the surface fault trace; in three other casesrepeatedmeasurements of the displacementof the white line on Highway 46 near Cholame were used; in another case the displacement was determined by small-scalegeodetic measurements.The details of these investigationsare describedby Smith and Wyss [1968]. Accurate determinations of the epicentersof these eight shocks

4681

4682

WYSS AND

BRUNE

0 I00200 2500 40

""'--' '"• "•'

Fig. 1. Map of Californiashowingthe San Andreasand relatedfaults.Earthquakesfrom the regionsnear Hollister, Parkfield, and Brawley were used for the surface wave Fourier analysisin the presentstudy. were

also available.

The

distance

from

the

Imperial earthquake of March 4, 1966. The fault length was about 35 km for the Parkfield earthquakeand about 10 km for the Imperial served can be considered a minimum value for earthquake. The results for the Parkfield and the fault length of that particular event. Based Imperial earthquakesindicated that previous on these field observations and the surface suppositionsabout fault length versus magniwave analyses,it has been possibleto estimate tude and stressdrop versusmagnitude [Press, roughlythe fault offset,fault dimensions, stress 1967] would have to be modified. They also drop, and averagestress. indicatedthat a singlescalinglaw, suchas that Basic to the understandingof the mechanics proposed by Aki [1967], could not be valid of faulting is the dislocationtheory of Maru- for all regionsof the earth. Tsuboi [1956] and epicenter to the locality where the surface displacement associatedwith a shock was ob-

yama [1963]. Dislocations are related to stress

Bdth and Duda [1964] showedthat Benio#'s [1951a, b, 1955] earlier assumptionthat earthquake volume was independentof magnitude combined these theoretical studies to interwas not valid. For large earthquakes(M > 6) pret earthquakemechanismin a study of the Bath and Duda found that earthquakevolume Niigata earthquakeand later in a study of the was approximately proporti.onalto magnitude Parkfield earthquake [Aki, 1967]. In the 1967 and the stressprior to earthquakeswas apstudy Aki proposeda scalinglaw for seismic proximatelyindependent of magnitudein agreespectrumwith a decreasein amplitudepropor- ment with Tsuboi'shypotheses. Chinnew [1964] tional to 1/.o?at frequencies higherthan some pointedout that the stressdropsfor mostlarge characteristicfrequencydependenton magni- earthquakeswere about 100 bars and sugtude. gestedthat this indicatedthe limiting strength The stressdrop was found by Aki to be 125 of the earth's crust was about 100 bars. The bars for the Niigata earthquake and 0.6 bar low stress drops found for the Parkfield and for the Parkfield earthquake.Brune and Allen Imperial shockssuggested that the stressdrop [1967] found a stressdrop of 1.1 bars for the for these earthquakeswas only a fraction of drop by the resultsof Starr [1928], Knopo# [1958], and Keylis-Borok [1959]. Aki [1966]

SEISMIC

MOMENT,

STRESS, AND SOURCE DIMENSIONS

the total stress, as in the stick-slip faulting mechanismof Brace and B•terlee [1966]. Burridqe and Knopo# [1964] gave equationsrelating the energy releaseto the ratio of the stressdrop to the initial stress.Earlier, Orowar• [1960] had shownthat, if the final stressafter rupture was equal to the frictional stressduring rupture, studiesof the energy of seismic wave radiationdid not determinethe pre-stress. Kinq and Knopo# [1968a] correlated the product of fault length and the square of displacement versus magnitude and found that for earthquakesthe fractionalstressdrop decreased with decreasingmagnitude; i.e., for small magnitudesthis stressdrop was a small fraction of the pre-stress. Bt•rridqe and Knopo# [1967] and Kinq and Knopo# [1968b] used a model of earthquake strain releaseconsistingof massesand springs in series.Many of the featuresof earthquakes occurrencewere explained by this model. The resultsfor fault length,fault displacement, and stress drop found in the present study for earthquakesalong the San Andreasfault are in approximateagreementwith the resultsfrom the Parkfield and Imperial earthquakesand with the fractional stress-dropcurves suggestedby King and Knopo# [1968a].

4683

fault region with the exception of one shock from the southernGulf of California. The epicenterswere obtainedfrom J. Eaton (personal communication),McEvill•t ei al. [1967], and t•ichter et al. [1967]. When the magnitudeassignedby the latter two sourcesdiffered, the averagewas taken. For the surfacewave analysis Press-Ewingseismogramsfrom the Pasadena station were used. In Table 1 the origin time, depth, and magnitude of these shocks are given. Considerationsof the uncertainties in the magnitudedeterminations,instrumental corrections,local geologicconditions,etc., suggests that in this experiment an uncertainty of a factor of 2 in relatingmomentto magnitude might be expected. In the future this uncertainty can be further reducedby use of more stationscloseto the source.The presentstudy has the advantagethat the station used (Pasadena) is also the station originally used to define the various magnitude scales. The equivalent double-coupleseismic moment, as definedin the dislocationtheory of faulting [Maruyarna,1963], was obtainedfrom surfacewave spectraldensityobservedat Pasadena.The procedureis essentiallythat.usedby Aki [1966]. The far-field displacementfor a

doublecoupleas given by Ben-Menahemand Harkrider [1964] was used to obtain moment

MOM•.NT V•Rsus MAaNIT•JD• CURVe, from spectral density. 3< M < 6 Thefaultplane solution fortheParkfield Seismic momentas a functionof magnitude earthquakes was givenby McEvilly ei al. wasfirst estimated by Brune[1968]in order [1967]; that for the Gulf of Californiaearthto calculateratesof slip alongmajor fault quakewasgivenby Sykes[1968].Shocks 4 zones.The moments of a numberof large and11 of Table1 wereassumed to haveorigearthquakes wereestimated from fieldobser- inatedon the SanJacintoandImperialfaults, vations[BruneandAllen,1966].A theoretical respectively, andthe approximate direction of curvebasedontheamplitudes of 100-sec man- the faultplanefor shock3 wasobtained from tle waves[BruneandKing,1967]wasfitted the CIT southern California array.The thirthroughthesedata.For magnitudes lessthan teenanalyzed shocks arevery closeto vertical 6 noreliabledatawereavailable for long-period strike-slipfaults.All the shocksare shallow. waves,andasa firstapproximation it wasas- For verticalstrike-slipfaults at a shallow sumedthat the localearthquake magnitudedepthBen-Menahem and Harkrider's exprescorresponded to the surfacewavemagnitude.sionfor Lovewavessimplifies to' Seismic moments for only two earthquakes

below magnitude 6 (Parkfield andImperial) Mo= (rCLT)•/2(•row/AL cos 20) (1) wereavailable at thattime.We hereestablishwhere r isthedistance, C•.istheLovewavephase moreaccurately the portionof the moment-velocity, •0 is the spectral density, 0 is the magnitudecurve for ML < 6. Surfacewaves azimuth from the strike of the fault to the

from thirteenearthquakes in the magnitudestation, AL is theexcitation function defined by rangefrom3.2 to 5.5 wereFourier-analyzed. Harkrider [1964], andw = 2r/T is theangular All of themwerelocatedin the SanAndreas frequency. For A L(t) the valuesfor a tectonic

4684

WYSS AND BRUNE

model given by Andersonand Harkrider [1968] were used, The surface waves of shock 8 recorded at

X

XXXXXX

X

Pasadena by 30-90 Press-Ewing instruments are shown in Figure 2. After resolving into transverse and longitudinal components, the Love waveswere Fourier-analyzed.Three values for moment were obtained for each shock,using three spectral density values around the peak density (T • 20 sec). The average moments for these three determinations are given in Table 1 and are plotted as solid circlesin Figure 3. Shocks3 and 4 lie somewhat below the fitted line. Their hypocenterswere deeper than the hypocentersof the other shocks,and it is not certain

that

their

motion

was strike

slip. The double circled point at magnitude 6

(Figure 3) was obtained from the Gutenberg definition of surface wave magnitude M, [Richter, 1955]. Accordingto the definition, a magnitude 6 earthquake produces a far field

displacement of 100• at a distanceof 22ø for surface waves of 20-sec period. From this amplitude the moment was calculated.This point thus representsthe average of the numerous observationson which the surface wave magnitude was based. As pointed out by Richter [1958, p. 347], the scalewas adjusted to agree with the local magnitude M•. for magnitude values of 6 to 7.

The logarithms of the moments of these thirteen earthquakes closely define the following moment-versus-magnituderelation:

log Mo-

1.4Ms •- 17.0 3 • Ms • 6 (2)

12h :59' u D N S E W •

I rnin.!-.•

Fig. 2. Shock 8, M -- 3.7, Parkfield, recorded by three componentlong-period Press-Ewingseismographsat Pasadena.

SEISMIC

MOMENT,

3O

I

STRESS, AND SOURCE DIMENSIONS

4685

=

I A I

(5)

Combining(3), (4), and (5) givesthe magnitude

X20/

as a function of moment.

28

1

M = • [log Mo+ log(5c)-- (logtz + a)](O) Thus b is the slope of the log moment versus magnitudecurve if c is not a function of magnitude. The observedvalue of the slope of Mo versusmagnitudeis 1.4 and thus is closeto the value of b = 1.5 for the Gutenberg-Richter relation, suggesting that c is not critically dependenton magnitudein the small range of magnitudesconsideredhere. From the Gutenberg-Richterenergyrelation

26

22

log Es = 1.5M -•- 11.8

(7)

Letting t• = 3 X 10•, we can solve equation 6 for the product of the average stress and efficiency,5c. For the nine Parkfield shocksin

20

4

6

8

ML

I

MS

Table I the result is

•c = 7.3 4- 1.8 bar

Magnitude

Fig. 3. Log of seismic moment as a function of magnitude for shocks along the San Andreas fault. After Brune [1967], modified for ML • 6. The solid circles represent the shocks listed in Table 1. Moments derived from the parameter AR

are represented by opencircles,andmomentsestimated from field evidence are representedby open triangles. The slope of the straight line below M _-- 6 is 1.4.

The slope of this line indicates that in the magnitude range 3 < ML < 6 the seismicefficiency c is not a rapidly varying function of magnitude. This follows from the energymagnitude relation given by Richter [1958]

log Es = a + bM

(3)

and the relationship for work done during a disloeation

E = •A O'= •Mo/t•

(4)

In these equationsEs is the seismicenergy,E is the elastic energy, M is the magnitude, • is the averageacting stress(averageof the initial and the final stress),A is the fault plane area,

• is the mean relativedisplacement on the

The error is the mean deviation

(8) for the nine

analyzed shocks.Equation 6 suggeststhat the deviationsfrom a singlemoment versusmagnitude relation can reflect, among other things, Iocal differencesin the average stress. DATA rao•

OT•Ea

REmONS BASED ON AR

In a paper by Brune et al. [1963] the parameter AR, the sum of the area of the envelopes of the surfacewaves on three componentlongperiod Press-Ewinginstruments,was used as a measureof the long-periodwaves.AR is approximately proportional to spectral density and thus to seismic moment.

If

the

relation

of AR to moment is established,one can approximately convert AR (ram2) into spectral density and thus into seismic moment. The relationshipwas establishedby determiningAR for the thirteen analyzed shocksand plotting these values against seismicmoment. The resuit is shownin Figure 4. This relation is valid for shocks not exceeding depths of about 20 km. As expected,the points fall closelyalong a straightline with a slopeof 1. The conversion equationis

fault planeassociated with an earthquake,Mo is log Mo = log ARaoo• 20.1 (9) the seismicmoment,and t• is the shear modulus. where ARaoo is the sum of the surface wave Le• c be the seismic efficiencyfactor; then

4686

WYSS AND

BRUNE

io24

E 1023

i0 22

1021 I0

I00

I000

I0,000

Arec]onseismicrecords,mm2 Fig. 4. Moment as a function of surfacewave envelopearea AR correctedto a distance of 300 km. The data points are derived from the shockslisted in Table 1. This curve can be used to approximately convert AR into moment.

envelope areas normalized to a source distance period body waves at the continental margin, of 300 km. which could make the body wave magnitude as well as the This equation was used to obtain the seismic smaller. The Nevada-Arizona moments for seventy-sevenshocks whose AR Baja California earthquakesfall below the San

valuesat Pasadenawere determinedby Brune

Andreas values. If it is assumed that these re-

et al. [1963] as well as for 182 additional shocks.

gional differences in surface wave excitation are due to regionaldifferencesin stress,we can solve for •c by fitting a line with a slopeof 1.4

The resultsare shownin Figure 5. Shocksfrom the San Andreas and San Jacinto

faults

and

from the Imperial Valley and Gulf of California are shown as solid circles. Squaresrepresent shocksfrom off the coast of California; open circlesrepresentshocksfrom Nevada, Arizona, Utah, Baja California,and northern California. For these earthquakesthe fault plane orientationsare not knownand the depthis uncertain. The scatter is considerable. As pointed out in Brune et al. [1963],however,a groupingof shocks

through the data for each region. This yields a value of •c of about 110 bars for the Laguna Salada (Baja California) and California Nevada earthquakes. The regional variations observed here couldalsobe due to path effects,depth of source, and variations in faulting mechanism. However,the surfacewavepathsfor all analyzed earthquakesare short (A _• 1000km) and similar. All events were shallow, most of them not exfor various regions can be observed. The Gulf ceeding16 km depth. The AR method of deterof California shocks give moments that are mining the seismicmoment, adding Rayleigh somewhatsmalleron the averagethan the San and Love wave envelopes,averages out the Andreas values, but, since they are not much differencescausedby different faulting mechdifferent,the samesymbolwasused.The shocks anisms. Therefore, it is very likely that the from off the coast of northern

California

have

higherM0 valuesthan shocksof the same magnitude from the San Andreas. This similarity may in part be due to a strongfiltering of short-

regional variations in seismic moment are in part due to variations in tectonic stress. The relatively low stressesalong certain sections of the San Andreasfault may in part be caused

SEISMIC MOMENT, 3O

I

I



I

STRESS, AND SOURCE DIMENSIONS

I

Ms :

1.7ML-

4687

4.1

3 < ML < 6 (11a)

2.2

3 < M•. < 6 (11b)

Parkfield 28

Ms = 1.4M•.-

26

and are valid for very shallow earthquakes. These equations are in qualitative agreement with the statementsgiven by Richter [1958,

X20/X

p. 347]. He indicatesthat, althoughthe local

ø-;2'_'ø

_ o

22

f øø

earthquake magnitude and the surface wave magnitudes were originally constructed to be in agreement between magnitudes 6 and 7, later investigations indicated that for lower magnitudes the surface wave magnitudes are smaller than the local magnitude, in agreement with equations11.

o o

FIELD OBSERVATIONS OF FAULT I)ISPLACEMENT

08 •o• o

20

For

4

6

8

ML

I

MS

I0

the nine

in Table

Mognifude

Fig. 5. Logarithm of seismicmoment as a function of magnitude with data from the westernmost part of the United States. The slope of the straight line through the data is 1.7. Solid circles indicate San Andreas fault system; open circles, western United States; squares, region off the

shocks that

occurred

in the

Parkfield region, fault slip was measured in the field. The approximateaverageslip is given 1. The

detailed

nature

of the field

evidencefor each shockis given below. For shock 2 (M = 4.9) the offset of the

white line on Highway 46 near Cholame(Figure 6) was measuredrepeatedly after the Parkfield earthquake of June 20, 1966 [Smith and Wyss, 1968]. On June 29 it was measured at

coast of California. 36ø00

by geologicand tectonic features that control the amount

of stress the crust can withstand

[Allen, 1968]. The straight line that was fitted through all the available data for moment versus magnitude for the western United States (Figure 5) givesthe equation

log Mo = 1.7ML q- 15.1

3