JOURNALOF GEOPHYSICALRESEARCH
VOL. 70, No. 4
FEBRUARY15, 1965
Determination of Source Parameters by Amplitude Equalization
of Seismic
o
Surface
Waves
Release of Tectonic Strain by Underground Nuclear Explosionsand
Mechanismsof Earthquakest
M. I•AFI TOKSSZ,DAVIDG. HARKRIDER,
ANDARI BEN-MENAHEM
SeismologicalLaboratory
California Institute o[ Technology,Pasadena
Abstract. The radiationpatternsof Love and Rayleighwavesfrom three nuclearexplosions(Hardhat, Haymaker,and Shoal) are studiedto determinethe nature of the asymmetry
of radiation and the mechanismof Love wave generation.From a comparativestudy of
different explosionsit is reasonedthat the Love waves are generated at the source of the
explosion.The sourcefunction, representedas the superimpositionof an isotropicdilatational
component due to the explosion and a multipolar component due to the release of tectonic
strain energy, is consistent.
with the observedradiation patterns and the amplitude spectrums.
The amount of seismicenergy due to the strain releaseis computed. In some cases(Haymaker
and Shoal) it is found that this energy may be due to the relaxation of the pre-stressedmedium
by the explosion- formed cavity. In the case of Hardhat it is concluded that the explosion
must have triggered some other strain releasemechanism,such as an earthquake. The amplitude equalization method is applied to surface waves from an earthquake to determine the
source parameters. From only the amplitude spectrums and radiation patterns of Love and
Rayleigh waves, the sourcefunctions,sourcedepth, strike and dip of the fault plane, and the
rake of displacementare determined for the July 20, 1964, Fallon earthquake.
ambeau [1962] gave an example showingthat
the short-period SH waves from the Rainier
Many of the undergroundnuclear explosions
blast were of comparableamplitude with those
have generated horizontally polarized seismic
of an earthquake located in the vicinity of the
shear waves (SH and Love) along with P, SV,
explosionsite. Bmne and Pomeroy [1963] iland Rayleigh waves.Theoretically,an explosive
lustrated clear examples of relatively long pesourcein a horizontally layered, homogeneous, riod transverse waves from Hardhat and Missisisotropic medium should not generate SH or
sippi explosions.Other examplescan be found
Love waves. One purpose of this study is to
in the Long Range SeismicMeasurementsprojdeterminethe mechanismof generationof these
ect reports on undergroundexplosionsprepared
horizontally polarized transversewaves by nufor the Air Force TechnicalApplicationsCenter.
clear explosions.The secondpart of the paper
The important questionis not the verification
is devoted to a study of applicability of the
of the existenceof horizontally polarized waves
method of amplitude equalization to earthfrom the explosionbut the understandingof the
quakesfor determiningtheir sourceparameters. mechanismof the generationof these waves.To
INTRODUCTION
that end, several mechanismsneed to be con-
NUCLEAR EXPLOSIONS AND TECTONIC
sidered.
STRAIN RELEASE
The significanceof the magnitude of SH
waves radiated from explosionshas been demonstrated by many investigators.Press and Arch-
t Contribution 1290, Division of Geological Sciences, California Institute of Technology.
1. Wave conversion: P, SV, and Rayleigh
waves may be convertedto SH and Love waves
becauseof inhomogeneitiesalong the path of
propagation. However, SH and Love waves are
not always observedfrom explosionsfired in the
same general area. Examples of these would be
the Sedan and the Mississippiexplosionswhich
907
908
TOKSOZ, HARKRIDER,
were located less than 5 km apart. Although
there
were almost no horizontal
transverse
waves from Sedan, strong Love waves were
recordedfrom Mississippi.Most of the noncratering explosionsin alluvium were followed
by the collapseof the cavities.In somecases,
suchas Haymaker,the Rayleighwavesfrom the
collapsewere as largeas thosefrom the explosions.Although Love waveswere recordedfrom
the Haymaker and Mississippiexplosions,no
horizontally polarized waves were observed
from the collapsesthat followed lB rune and
Pomeroy,1963]. Sincethe paths were identical
for both the explosionand the collapse,any
conversionduring propagation could not affect
the waves from one event without affecting
thosefrom the other. In other words,we can
rule out wave conversionas a possiblesource
of SH waves observed from these nuclear explosions.
2. Near-source
effects:Althoughan explosion
would not generateany SH waves in an iso-
AND BEN-MENAHEM
function [Brune and Pomeroy,1963; Aki, 1964]
was explained by such a mechanism.
A secondmechanism of releasingthe strain
energy is directional cracking. When the shock
wave propagates from an explosionin a prestressedmedium, the cracking will occur in
preferred directions in such a way that the
existing strain energy is minimized. The radiation pattern of seismicwavesdue to an induced
rupture in a pre-strained medium was studied
by Archambeau [1964]. He found that all prestress conditions give symmetric quadrupole
radiation patterns.
Another sourceof strain energy that may be
released by an explosion is provided by the
cavity. This problem was investigatedby Press
and Archambeau [1962]. Not only would the
strain energy stored in the volume of material
that was molten and crushed be released,the
strain energy outsidethe linear zonewould also
be reduced.The latter releasewould primarily
be as elastic radiation.
tropic, homogeneous,
horizontallylayeredmeIf there is tectonic strain release,P, SV, SH,
dium,mostof the explosion
sitesdid not satisfy Love, and Rayleigh waves radiated from the
these conditions.The question,then, was releasewill be superimposedon the explosionwhether the SH waves could have been due to
generated waves--P, SV, and Rayleigh. Although the SH and Love waves will be due to
alsobe ruledoutwith the argument
that, if this the releasedstrain energy only, the P, SV, and
were the case,the collapseevents would also Rayleigh waves will contain fractions due to
generate SH waves.
both sources.It is not possibleto separatethe
3. Tectonicstrainrelease:A nuclearexplosion fraction of the energydue to the explosionalone
is not an ideal point source.The shock wave unless the space and time functions of both
generatedvaporizes,melts, crushes,and cracks sourcesare known exactly. Since this informathe rocks out to somedistance,dependingon tion is not available, we resort to someindirect
the yield of the explosionand the strengthof the techniquesand make certain assumptions.These
near-sourceirregularities.This possibilitycan
medium.The crackscausedby the explosion
are listed for each case.
would not generateany SH wavesunlessthere
were differentialmovementalong them. In a
mediumwhich is not pre-stressed
the cracksand
the movementalongcrackswould be distributed
uniformly, with radial symmetry around the
point of explosion.Therefore, one would not
expect an SH wave radiation pattern which
couldbe represented
by a dipoleor a quadru-
In this study we investigate three nuclear
explosions,the Hardhat and Haymaker explosionsfired at the Nevada test site and the
Shoal explosiondetonatedin the Sand Springs
Range, Nevada. In addition, two small earthquakes whose epicenterswere in the general
vicinity of the Shoal explosionsite are included
for comparison.Seismicsurfacewave recordings
pole source.
from these events at some or all of four CIT
In a pre-stressedreediron,all explosionmay
releasea part of the existingstrain energyby
one or more of three mechanisms.
First, intense
stresswaves near the explosionmay trigger a
small earthquake. The radiation pattern of
stations(Pasadena,California; Ruth, Nevada;
Jamestown,California; and Albuquerque,New
Mexico) equipped with narrow-band, highsensitivityBenioffseismographs
and from LRSM
program mobile stationsare usedin the study
Love and Rayleigh waves from the Hardhat
(see Table i and Figure 1).
explosion which fits a double-couplesource
Shoal explosion. The method of amplitude
SOURCE PARAMETERS
OF EXPLOSIONS
TABLE la.
Origin Time,
UT
h m
s
Event
AND EARTHQUAKES,
2
909
Epicenter Data
Location
Latitude, N
Longitude, W
Shot or
Focal Depth,
km
Magnitude
Yield
or
Explosion
Hardhat
(Feb. 15, 1962)
Haymaker
(June 27, 1962)
18
O0
O0
37013'35"
116003'34"
0.290
6 kt
18
00
00
37ø02•30"
116ø02•07"
0.410
56 kt
17
00
00
39ø12•01"
118ø22•49 •
0.367
12.5 kt
15
09
38
02
47
08
38.4 ø
39.5 ø
Shoal
(Oct. 26, 1963)
Earthquake
April 13, 1962
June 20, 1962
TABLE
lb.
119.2 ø
118.3 ø
Station
Data
Distance
Location
Station
Latitude, N
Longitude, W
Haymaker
34ø57'00"
37056'53"
34008'53"
39015'00"
106027'29"
120ø27'17"
118ø10'16"
115000'00"
894
402
Albuquerque,New Mexico
Jamestown,California
Pasadena,California
Ruth, Nevada
equalization as describedin our earlier paper
[ToksSz et al., 1964] will be utilized to determine the sourcefunction of the explosionand
the nature of the multipolar component of the
source responsiblefor Love waves. Since the
isotropic explosive source does not contribute
to the radiatedLove waves,the propertiesof the
multipolar sourcefunction can be deducedfrom
the transverse
waves alone. The
time
function
m--4.8
m --5.2
25
25
375
261
km
Shoal
358
A horizontalquadrupoleof the type described
above will have an azimuthal radiation pattern
for Rayleighwavesgivenby sin20,and for Love
wavesby cos20.Thus in the caseof an explosion
with a superimposedquadrupolecomponent,the
Rayleigh waves recorded at stations set up
along 0 = n•r/2, where n: 0, 1, 2, 3, 4, would
be due to the explosivesourceonly. The ideal
method of studying the explosion-generated
of the explosive source, however, cannot be
readily determinedfrom the Rayleigh wavesbe-
waves,then, would be to find a station or stations situatedalongtheseazimuthsand usetheir
cause of contamination
recorded
with
waves
from
the
multipolar source.
We make two assumptionsconcerning the
superimposed
multipolarsource:(1) The space
function of the source can be representedas a
horizontal (strike-slip) couple or orthogonal
doublecouple; (2) the orientationof the axisof
the couple or the double coupleis parallel to
those of earthquakesoccurringin the region.
The validity of theseassumptions
will be justified by showingthe consistencyof theoretical
models with
observations at all stations sur-
roundingthe explosionsite.
waves.
The Shoal explosionwas in a region of moderate seismic activity where numerous shallow
earthquakeshave occurred.'The movementsassociated with the earthquakes that have been
investigatedwere alongfaults whosestrikesare,
in general, in the N-S direction [Slemmons,
1956, 1957; Benio#, 1962]. The recordingsof
these earthquakes in Pasadena, which is due
south of the epicentral areas, show that the
Rayleigh wave amplitudes are much smaller
than the Love wave amplitudes. The examples
shownin Figure 2 clearly illustrate the passage
910
TOKSOZ, HARKRIDER,
7-20-63
!
i
/•HOAt .....
39øN
I
-
/
--0
?.
14'
/ 4_13•_
' 62 II
I
c
--37 •
-
I
•
I
--36•
i/
I
i
•
II
I
-35 •
I
I
Fig. 1. Locations of the Shoal explosion, Fallon
earthquake epicenters,and CIT stations.
AND BEN-MENAHEM
the layer thicknessesand the velocities were
computedas the weightedaverageof thosealong
the paths (Table 2).
To determine
the source-time
function
of the
Shoal explosion we corrected the amplitude
spectrum of the Rayleigh wave recorded at
Pasadena for the responseof the instrument
[ToksSz and Ben-Menahem, 1964] and the responseof the layered medium for an explosive
source buried at a depth of 370 m (i.e., shot
depth). The observed vertical displacementof
the ground and the theoretical responseof the
medium are shown in Figure 3.
The ground displacementwas corrected for
the responseof the layered medium by pointwise division to obtain the amplitude spectrum
of the source function at the boundary of the
linear
zone. The
time
function
of the source
was then assumedto be of the form p(t)
=
P•te-•t, where p(t) is the pressure,Po is a
constant,t is time, and '1 is the sourceparameter
[ToksSzet al., 1964]. For a value of r/ = 1.0
sec-• the amplitude spectrumof the theoretical
pressure pulse, which is shown in Figure 4,
agrees with the spectrum of the experimental
pulsebetter than other valuesof r/.
Three points shouldbe clarified in regard to
the shape of the pressurepulse: (1) The observed spectrum is not a true experimental
quantity, since we computed the layering responsetheoreticallyusing an assumedstructure.
The complexitiesof the structure, such as the
as the tectonic axis as determined by earth- lateral inhomogeneities,could not be taken into
quakes--wecan state that the Rayleighwaves account. The oscillationsof the observedspecrecordedin Pasadenawere primarily due to the trum are probably due to such complications.
explosivesourceonly. Using thesewaves,we can (2) The uniquenessof the particular pressure
determine the source-time function of the exfunction is not proved. There are other pulses
with similar amplitude spectrums.Someof these
plosion.
The method used in determining the source might evenhave a negativephase,wherea
functionis the amplitudeequalizationtechnique dilatation phase follows the initial compression.
which was previouslyused in the caseof some This particular pulse was chosenbecauseof our
other nuclear explosions[ToksSz et al., 1964]. earlier study, in which pulses of this nature
To determinethe amplitude responseof the lay- were justified by physical reasoningand by
ered medium for a source,we employthe avail- the consistencywith initial phase studies.We
able information on the structure of the crust
should also mention that the p (t) = P•te-'
and the upper mantle. For propagationpaths representsthe shape of the pressurefunction
from Fallon to Pasadena,Ruth, and James- at the boundary of the regionwhere the motion
town, the structuresare complicatedand the is elastic. (3) The long-period waves from
thicknessesof the layers change along a given which the source function is determined would
path [Eaton, 1963; Healy, 1963]. In eachcase, not yield information on the sharper features
however, we representedthe structure as a of the pulse. Therefore, the pressure pulse
horizontallylayeredhomogeneous
mediumwhere shown in Figure 4 should be regarded as a
of the Rayleighwavenodalline throughor near
Pasadena.The recordsof Rayleigh and Love
wavesfrom the Shoalexplosionshowthat their
amplitudesare approximatelyequal. Invoking
our first assumption--thatthe orientationof the
quadrupolecomponentof the field is the same
SOURCE PARAMETERS
OF EXPLOSIONS
AND EARTHQUAKES,
2
911
Fig. 2. Pasadenaseismograms
of the July 6, 1954,August 23, 1954,April 13, 1962,earthquakes and the Shoal explosion.July 6 and August 23 events are recordedwith strong-motion
instrument, others with narrow-band Benioff seismograph.The N-S component is almost
purely radial, and the E-W componentis purely transverse.
smoothed approximation rather than as the
exact pulse.
The source of the Love waves generated by
TABLE 2. Structures Used in Computing
the Medium Layering Responses
CompresThick-
ness,
km
Region
sional
Shear
Velocity,
km/sec
Velocity,
km/sec
Den-
sity,
g/cm 3
Fallon to
Pasadena
I
21
15
50
c•
5.00
6.09
6.69
7.82
8. O0
2.75
3.40
3.70
4.35
4.40
2.60
2.75
3.00
3.35
3.40
Fallon
Ruth
1
21
9
50
•o
5.00
6.00
6.60
7.82
8. O0
2.75
3.40
3.70
4.35
4.40
2.60
3.75
3.00
3.35
3.40
I
19
15
50
•o
5.00
6.00
6.70
7.90
8. O0
2.75
3.40
3.75
4.37
4.40
2.60
2.75
3.05
3.35
3.40
to
Fallon to
Jamestown
the Shoal explosioncan be investigatedwith
the same amplitude equalization technique.
Other difficulties,however,result from the uncertainty of the depth and the spatial distribution of the source. Let us assume that the force
configurationat the source can be represented
as a double couple similar to that of the majority of earthquakes. For further simplification we take this to be an orthogonal double
couplein the horizontal plane. Sincethe medium
is going from a stressedto a relaxed state in releasingthe strain energy, we would also expect
the source-timefunction to be similar to a step
function. It may seem that we have assumed
everything about the mechanismof the generation of Love waves.However, we will showlater
that these assumptionsare consistentwith the
observations.
Comparisonof the Love wavesgeneratedby
the explosionand the two small earthquakes
providescluesto the nature of the explosiongenerated waves. The Pasadena records from
one set of instruments for three events with
almost identical source-stationpaths were used
in computingthe graphs shown in Figure 5.
912
TOKSOZ, HARKRIDER,
[
]
[
[
[
[
AND BEN-MENAHEM
[
- SHO•I
[
• 1.0
• Pasadena
Z
•
[
[
I
I
•
[
[
[
•
-
--
•
-
VE' -
•
-
_
õo.• -•
-
0•02
I
I
I
0.04
I
•
I
•
I
•
I
I
I
0.06Freq.,
cps.
0.08
[
I-
0.1
0.4•' I • I • I • I * I • I • I •
m0.2•
Fig. 3. Observed ground displacement at Pasadena and amplitude responseof layered
medium for an explosivesurfacesourcewith impulsive time function.
\
F•a.vle/•h Wave
[.0•
-
F'----••
••
Pasadena
Z --
••
--• Observed-
.•0.8
--
0.02
0.04
Freq., 0.06
cps.
0.08
0.•
,o.5
o
0
I
2
Time,
3
sec.
4
5
Fig. 4. Comparisonof the theoretical and experimentalamplitude spectrumsof the Shoal
pressurepulse and the shapeof the pressurepulse at the boundary of the linear zone.
SOURCE PARAMETERS
1.0••_
•
.o_ I œovE •_VES _ _-
•
• Eorthq.-Expl.
Ratio
.; o.5 /
-o
I
0.03
•
I
I
0.04
I
OF EXPLOSIONS AND EARTHQUAKES, 2
X.
I
I
•
Freq., cps. 0.06
I
I-
i
0.07
I
0.08
913
would generate Love waves whose amplitudes
are nearly three times as large as those of the
sourceat the depth of 25 km. Comparing Figures 5 and 6, we can state that the source of
the Love waves generatedby the Shoal explosion was near
the
surface
and
those
of the
earthquakeswcrc deeper, provided that all the
other source parameters were the same.
With the source near the surface, we can
investigatewhether the theoreticaldouble-couple
O.5
I
•
I
•
I
•
I
•
I
•
I
force configurationand the step-functionsourceLove
Fig. 5. The ratios of the amplitude spectrums time variation of the explosion-generated
of the Love waves from earthquakesto the amplitude spectrumsof the Love waves generated
by the Shoal explosion.
waves are consistent with the observations. Cor-
recting the amplitude spectrum of the Love
waves recordedat Pasadenafor the responseof
the seismograph,we obtain the grounddisplaceThe outstanding feature of these curves is ment spectrum. The theoretical spectrum is
that the earthquake-explosionamplitude ratio simply the product of the transform of the
decreaseswith increasing frequency. The rela- source-timefunction (i.e., .•-• for a step functive enhancementof the long-periodLove waves tion) and the amplitude responseof the medium
in the case of earthquakes cannot be explained shown in Figure 6 (h -- 0 km). The ratio of
simply by the volume of the source,sincethe the observedground displacementspectrum to
equivalentmagnitude of the explosionand those the theoreticalis shownin Figure 7. If the theoof the earthquakeswere fairly close.The depth retical model exactly represented the actual
of the source,however, could affect the spec- source, this ratio would be a constant indetrums of the seismicsurface waves generated, pendent of frequency.The ratios plotted in Figthe deeper events producing relatively less am- ure 7 show a slight increase with frequency.
plitude of the short-periodsurfacewaves.These This increasecan be due either to experimental
curves,shown in Figure 6, were computedby errors or to the inexact representation of the
using the idealized structure from Fallon to
structure, as well as somevariation of the theoPasadena that is listed in Table 2 and medium
retical source from the actual. However, the
responseprogramsbasedon the matrix solutions effect shown in Figure 7 is so small that it can
in Harkrider [1964]. From the figure it is be neglected, and the consistencyof the obobviousthat at f -- 0.03 cps the amplitudesare served Love wave amplitudes with theoretical
nearly equal for sourcesat depthsof 0, 11.5,and amplitudescan be accepted.
25 km, while at f -- 0.09 cps a surfacesource
So far we have shown that our assumed source
is an adequate model at this azimuth. There is
0.4
_ love WavelayeringResponse
Source
atdepth
h
•
•
o
'-
--
SHOAL
_
Amplitude normalized
LOVE
to step func t/on
I
I
I
Frequency,
0.05
Freq., cps. 0.07
.
I
O.O7
0.05
0.05
WAVE
cps.
0.09
Fig. 7. The ratio of the observeddisplacement
Fig. 6. The Love wave amplitude response of
the medium to a double-couple,impulsive sourcetime function buried at depth h.
spectrum of Love waves from the Shoal explosion
to the theoretical spectrum for a double-couple
source with step-function time variation.
914
TOKSOZ, HARKRIDER,
AND BEN-MENAHEM
a problem of lack of uniquenessin this procedure,and variouscombinationsof sourcespace
configurationsand time functions may produce
the same results. For example, in amplitude
studies at one station
ßexp kr--t--
it makes no difference
whether the sourceis a coupleor double couple
[Ben-Menahem and ToksSz, 1963]. Furthermore, a single horizontal force with impulsive
time function would give approximately the
same results as a double-couple source with
step-function time dependence. The doublecouple (or couple) nature of the source,rather
than a singleforce, will be shown in the next
section.
Radiation patterns •rom three nuclear explosions. When tectonic strain energy is released in the form of seismicenergy, the isotropic radiation pattern of an explosionis altered. It was shownearlier that, at least in the
case of the Shoal explosion,this strain energy
was released from a shallow depth. It will be
assumed that
ßexp
(--q/Rr)kR
1 ]
the same condition
= o
wherewe, go,and ve are the vertical, radial, and
tangential componentsof the displacement,k•
is the wave number,r is the radial distancefrom
the source,7• is the Rayleighwave attenuation
coefficient,A•(•o) is the medium responsefor
Rayleigh waves from a vertical force at the
surfacepoint, •ois the angular frequency,/;oand
fv• are componentsof particle velocity at the
surface,and T(•o) and .•(•o) are the amplitude
and phase responseof the source-timefunction.
The approximate ground displacementdue to a
near-surfaceorthogonal,horizontaldoublecouple is [Ben-Menahemand Toksb'z,1963, BenMenahem and Harkrider, 1964]
will hold for
the two other explosions,Haymaker and Hardhat, which are included in this study. The geometry of the strain-releasesource function is
assumedto be an orthogonal,horizontal double
couple. This double-couplecondition was observedfor many earthquakes,and it is a reasonable assumption.The horizontal orientation is
the simplestgeometry for an initial assumption.
We will now determine two parameters of the
sourcefunction, the orientation of the principal
axis and the relative strength of the multipolar
source compared to the explosivesource.
The displacementsobserved at distant stations are the vectorial sum of displacementsdue
to the explosionand the tectonic strain release.
In a cylindrical coordinatesystem,the far-field
expressions
for the approximategrounddisplacements from a near-surfaceexplosivepoint source
are [Harkrider, 1964; ToksSzetal., 1964]
C!
Wdc(O,)
) -- (271.r)1/2
ßexp
(--'y•r)k•
1/•sin \lbo
/
ßexp
[i(•t-ksr--4t'+
qdc(O•)
-ß
!
sin 20 (t•o*/•
---exp
(_.Rr)k•
1/a
\•o /
ß exp
Ii(o•t
--kRr
--•St
•
(2•-r)TM
ßexp(--'y•.r)k•.
'/• cos20A•(co)T'(½o)
C1
We((.D
) '--
ßexp[i(•t--k,•r--4t'3_ff)](2)
\tbo /
ß exp
Cl
qe(w)
= (27rr)1/2
The subscriptsR and L refer to Rayleigh and
Love waves, respectively;azimuthal angle 0 is
measuredcounterclockwise
from the fault plane.
If the time delay betweenthe explosionand the
strain releaseis negligible,the observedRayleigh and Love wave displacementscan be written
as
SOURCE PARAMETERS
OF EXPLOSIONS
AND EARTHQUAKES,
I
U•(w) - w•(w) q- w•,•(w)
/
0ø
/
..
I
-- We(W)
1q-F•w•-sin
20.e'
2
915
Hardhat
\
\
4
½o)=
The term 3p in (3) is the phasedifferencebetween
source-time
functions
and
the
905--
source-
spacefunctions.The constant F is the strength
of the multipolar sourcerelative to that of the
explosion.
Assumingthe differencebetween time functions T(•o) and T'(•o) to be negligible,we computed theoretical radiation patterns for Haymaker and Hardhat explosionsto fit the observed Rayleigh wave amplitudes of the longperiod recordsfrom the LRSM stations.We can
ignorethe effectsof geometricspreading,instrument magnification,and the layering in the case
of the Haymaker explosionby normalizing the
Rayleigh wave amplitudes to those of the Haymaker collapseevent. It was concludedearlier
[Brune and Pomeroy,1963; ToksSzet al., 1964]
that the Haymaker collapsewas a symmetric
event. The experimental amplitude ratios are
taken from the report Haymaker (prepared for
AFTAC by the GeotechnicalCorporation,1962)
and are the ratios of the maximum amplitudes
in the period range of 13 to 16 seconds.We
have also computed four ratios from CIT stations. The radiation pattern shown in Figure 8
is well defined, and the amplitude along the
20ø azimuth is approximately one-half of that
alongazimuth 110ø. To explainthis theoretically
,4Ibq.
•
- - Tectonic
• Composite
x
//
ß Observed
amplitude
/
I
Fig. 9. The observed and the theoretical Rayleigh wave radiation pattern for the Hardhat explosion. The data is from LRSM stations.
we superimposeda double-couplesource over
the isotropic explosion and determined the
orientation and the relative strength as given
in (3) with 3• = 0. The best-fit theoretical
double-couplepattern and the compositepattern are also shown in Figure 8. The doublecouple orientation is such that it represents
either a right-hand strike-slip fault striking at
340ø azimuth or a left-hand fault striking at
70ø azimuth. The relative strength of the
double coupleis F ----0.333.
For the Hardhat explosionwe corrected the
maximum amplitudes of the Rayleigh waves
given in the AFTAC report Hardhat (prepared
for ARPA, 1962) for the geometricspreading.
We assumedthat the responseof the medium
AR remained constant for all azimuths, and we
neglected the effect of attenuation due to absorption. From the observed radiation pattern
(Figure 9) we determined the compositetheoretical sourcewith a proceduresimilar to that
followed for Haymaker. In this case,the data
scatteredmore than with Haymaker, but the intensity of the sourcein the southeasterlydirection is seen to be definitely larger than it is in
the northeasterly direction. For this event, the
double-couplesource can be the model of a
right-hand strike-slip fault with the azimuth of
the strike at 330ø, and the conjugateof this
(left-hand strike-slip fault at azimuth 60ø) is
also a possiblesolution. The amplitude of the
Fig. 8. The observed and the theoretical Raydouble coupleis F = 3.0 relative to the exploleigh wave radiation pattern for the Haymaker
sion. The polarity of the composite source
explosion and the theoretical source components.
changesfrom one quadrant to the other. The
Observed amplitudes are normalized to those of
change of polarity of the Rayleigh waves rethe Haymaker collapse.
916
TOKSOZ, HARKRIDER,
corded at Ruth
AND BEN-MENAHEM
and Pasadena relative to that
recorded in Albuquerque was observedin our
earlier study [ToksSzet al., 1964]. From a study
of the Hardhat, Love and Rayleigh wave phases
and amplitudes,Aki [1964] obtainedexactly the
same double couple for the source.The contribution from the explosionin his casewas onehalf of that from the doublecouple,as compared
with our value of one-third. It is, however,very
encouragingto obtain almost the same source
functionsfrom two independenttechniques.
The generalagreementbetweenthe orienta-
the report Shoal (prepared for AFTAC by the
United Electrodynamics,Inc., 1963). The average period of the maximum amplitude waves
was about 14 seconds.
The
value
of F and the orientation
of the
double couplewere determinedso that the theoretical values from (4) and the observedvalues
were in agreement (Figure 10). The amplitude
of the double couplerelative to the explosionis
F -- 0.9. The azimuth
of the strike of the fault
plane is 346ø. In this case, the choicebetween
the two possibleconjugateorientationswasmade
tion and the sense of the double-couple com- from the initial phase of the Love waves obponentsfor both Haymaker and Hardhat ex- servedin Pasadena.This orientation is in agreeplosions
suggests
that the strainenergyreleased ment with the generaltectonicaxisof the region.
The tectonic strain energy. The strength of
waspart of the regionalstrainfield.
To determine the mechanism at the source of
the multipolar component relative to the isothe Shoal explosionwe use the ratios of Love tropic componentdemonstratesthe significance
wave to Rayleigh wave amplitudes.Neglecting of the tectonic strain release in each case. In
the difference between the source time functions determiningthe sourceof the strain energy,it is
of the explosionand the doublecoupleand using of great importance to know the total amount
(1), (2), and (3), we canwrite the ratio of the of seismic energy released by the multipolar
observedLove wave amplitude to the amplitude component.
of the vertical componentof the Rayleigh wave.
In general, the determination of the absolute
value of the seismicenergy releasedfrom a disturbanceinvolvesmany corrections.In this case,
I UL•I
FkL•/2ALcos26
(4)
however,we can computethe seismicenergydue
to
the multipolar source relative to the explo\•bo !
sion, and we can then compute the seismic
energy of the explosionfrom the magnitude asThe quantitieskL, AL, k•, and [A•(•/tVo)]
were computedtheoretically for the structure signedto it and the energy-magnituderelation.
described earlier.
Since the magnitude is measured from ampli-
The amplitude ratios of the observedLove
and Rayleighwaveswere determinedfrom the
recordings
of the LRSM stationsas reportedin
•
/
- 27
o
tudes of the waves from a number of stations
along variousazimuths,the effectof the multipolar components
shouldcancelout.
SHOAL
Tectonic
oø1
Explosion•
ILl
IRzl
\
90
270
/
Theo.
/80 ß Observed
Fig. 10. The theoreticaland observed[L[/[R•[ (Love to verticalcomponent
of Rayleigh)
amplitude ratios for the Shoal explosion. The theoretical model of the explosion and tectonic strain release are shown on the left-hand
side.
SOURCE PARAMETERS OF EXPLOSIONS AND EARTHQUAKES, 2
The energydensityof Rayleigh or Love waves
recordedat a station is given by
=
whereV is the groupvelocity,p isdensity,and
is the particle velocity. The time integration is
taken
over the duration
of the surface wave
In
the above derivation
the source-time
917
func-
tions are assumed to be the same for both events.
Since itoø*/•o,AL, AR, /eL, /oR,V=, and V• are
frequency-dependent
quantities,the ratio of energy densities would also depend on the frequency.However,sincethe ratios/to*/•o, A•/A•,
/c•//c•,and V•/V• generallyvary graduallywith
frequencyEtect/Eexp
alsovariesvery gradually
with frequency.
arrival. To computethe total energyof surface
We computedthe ratios of the strain energy
waves, we need to correct for the effect of georeleased(i.e., energy of the multipolar compometric spreadingand then to integrate over the
nent of the source) and the explosionenergy
azimuth and over the depth. The geometric
for the three explosionsat successive
periods
spreading factor and the depth factor are inbetween10 and 40 seconds.
We shouldpoint out
dependent of the source type. Since we are that the values shown in Table 3 are the ratios
interested in the energy of one event, relative
of the surfacewaveenergies.
They alsorepresent
to the other, we can excludethe commonfactors
the ratios of the total energies,sincethe partiand integrate over the azimuthal variation to
tion of the energybetweenthe body and surface
determine an energy factor, E{ t, which is the
wavesis not likely to changesignificantlyfrom
surfaceenergydensityat a unit distance.
one sourceto another if the source depth and
type are not changed.
The absolutevalues of the strain energy released in each case were computed from the
seismicenergy of the explosion.The equivalent
magnitude of each explosionis listed in the explosion reports. Using the formula given by
where {(0) is the azimuthal factor of the source
Gutenbergand Richter [1956],
,
and [U (m)[• is the power spectrumdensity,
[(0) : 1 for explosions,and [(0) : F sin 20,
F cos20 for the double-coupletype sourcefunctions where F is the sourcestrength. From (6),
(1), and (2), and after the azimuthal integration, the ratio of the energy of the tectonic
strain releaseto the energy of the explosioncan
be derived
Etect
log E = 5.8-+- 2.4m
(8)
wherem is the unifiedmagnitude,we computed
the seismicenergyradiatedfrom the Haymaker
and Shoalexplosions.
In the caseof Hardhat, it
is very difficult to justify the assumptionthat
the measuredmagnitude would represent the
magnitude of the explosionand that the effect
of the multipolar componentswould cancelout.
The source o{ strain energy. The sourceof
the strain energy and the mechanismof its release by the explosionis of great interest. An
explosiondetonated in a strained medium would
releasesome strain energy in the form of seis-
F2
J•l-](•o./:•r
1(•o.]•1(--•••
)(k•.•)(-F•'•
'l
\t•o / L
\t•o / _1
(7)
mic wavesbecauseof the insertionof the cavity
TABLE 3. SeismicEnergiesfrom Explosionsand the AssociatedTectonic Strain Release
Assigned
Seismic
Magnitude
Explosion
(m)
Energy from
F
Ratio of
SeismicEnergy
Strain Releaseto
from Tectonic Strain
Explosion,ergs ExplosionEnergy
Release,ergs
4.3 X 10x8(?)
Hardhat
4.9(?)
3.00
3.63 X 10x7(?)
Haymaker
Shoal
4.9
4.9
0.33
0.9
3.63 X 10•7
3.63 X 10l*
12.00
0.14
1.05
5.1 X 10•6
3.8 X 10l*
TOKSOZ, HARKRIDER,
918
AND BEN-MENAHEM
in the medium
and the relaxation of the stress
likely to be radiated in the form of seismic
field in the elastic zone around the cavity. This energy.
problem was studiedby Press and Archambeau
Let us comparethesevalueswith the seismic
[1962] for a sphericalcavity in a pre-strained energy due to the multipolar componentof the
elastic space.The expressionthey derive for the sourceslisted in Table 3. For Haymaker the
reductionof the strain energy due to the cavity maximum available strain energy was 5.4 X
is
10•ø ergs,and the observedseismicenergywas
5.1 x 10•ø ergs. For Shoal, the values were
5.4 X 10•7ergsand 3.8 x 10•7ergs,respectively.
In both of thesecasesthe seismicenergydue to
2
where • = fi.opis the modulusof rigidity of the
medium,S is the strain, and a is the radius of
the cavity. The function /(•/X)
is approximately equal to 1. The first term in (9) representsthe reduction in strain energy in the elastic
zoneoutsidethe cavity, and the secondterm the
reduction of strain energy within the cavity.
The maximum value of seismicenergy radiated
from stress relaxation must be equal to or less
the multipolar component of the source is less
than the maximum value of strain energy releasedbecauseof the explosion-generated
'cav-
ity.' All of the observedstrain energy could
therefore be due to the relaxation
of the stress
field aroundthe 'cavity,' and it is not necessary
to have movements along the faults to radiate
the strain energy in these cases.
The Hardhat explosionposesa completely
different problem. Here our estimate of the
lhan AW.
seismic energy due to release of tectonic strain
An undergroundnuclearexplosioncrushesand
is
not very accurate; it is probably higher than
cracks rocks far beyond the cavity. So, in
the
true value. However,this figure (4.3 X 10•
applying (9), we can assumethat the effective
ergs) is about 18 times higher than maximum
cavity radius is equal to the radius of the nonavailable strain energy released due to the
linear zone around the explosion.These radii can
'cavity.' Therefore, tectonic strain energy must
be computed from the yields and strengthsof
the mediums as describedin our earlier paper be releasedfrom a volume that is much larger
than the volume of the cavity and relaxed zone.
[Toks6z et al., 1964]. The value of strain S is
This would mean that the shock wave from the
a difficult quantity to estimate. 8 : 10-* was
explosion triggered a strain release mechanism
chosento be the upper limit for Nevada test
outside the nonlinear zone. An earthquake,
site by Press and Archambeau [1962]. For the
triggered in this manner near the explosion,
regionwhere Shoalwas located,8: 10-* is probwould be an explanationof the magnitude of
ably a good average value, judging from the
the observedstrain energy. This was also conseismicity of the Fallon area. With these values
eludedby Brune and Pomeroy [1963] from the
we computed the strain energy reduction AW
after shocksthat followedthe explosiom
by each of the three explosions.These results,
listed in Table 4, represent the upper limit of
SOURCEPARAMETERS
OF EARTt-IQUAKES
the seismicenergy that can be attributed to the
The radiation patterns of seismic surface
strain release,since not all the strain energy is
wavesfrom buried dipolar sourcesin a stratified
earth were studied theoretically by BenTABLE 4. Theoretical Values of Strain Energy
That May Be Releasedby Explosions
Menahemand Harkrider [1964]. The necessary
source-depththeory was given by Harkrider
[1964]. We will determine the source char-
Nonlinear
Strain
Zone
RigidRadius,
ity t•,
Strain
Explosion
m
dynes/cm2
s,
Energy
Reduction
AW, ergs
Hardhat
270
3 •( 1011
10 -4
2.4 •( 1017
Haymaker
400
2 X 10lø
10-4
5.4 •( 1016
Shoal
350
3 X 10"
10 -4
5.4 X 1017
acteristicsof the July 20, 1962, Fallon earthquake using the amplitude equalizationmethod
and the radiation patterns from buried sources.
The earthquake was a relatively small event
(m = 5.2), and the finiteheSSof the sourcecan
be neglected when seismicsurface waves of 40
km or longerwavelengthsare used.The parameters that will be determined are the source-
SOURCE PARAMETERS
/
J'ILI ]
•'•
I
k 0oo 7-20-62
4•- [] 4-13-62
\ ß 7-20-62 (LRSM)
/
[
! /"-"N
]1R---•I
•'dc; /
OF EXPLOSIONS
\
Theoreticol:
•',
---8 =76• 230•
-270
ø•
••/ß 9
--2
I
•.•
I
/
I
iI/l,i
AND EARTHQUAKES,
2
919
A set of sourceparameterscan be determined
by fitting a theoretical radiation pattern curve
to the experimentaldata, and the solid curve
shown in Figure 11 is our 'best' fit. It is for a
fault plane with a strike at azimuth 355ø and
an easterly dip of 76ø. The slip angle X is 230ø
(i.e., the direction if displacementis 50ø from
horizontal, rake is 50øS) and the sourcedepth
is 20 km. Although the agreementbetween the
theoretical and observed radiation patterns is
good, it is essentiallybased on three experimental points. The LRSM data that were added
to the figure later do not strengthenor contradict this picture.
In obtaininga best fit, it was found that the
source depth had relatively little effect. From
Figure 11 it is clear that the strike direction
cannot be changedappreciably.The dip of the
fault plane affectsthe (Love/Rayleigh) amplitude ratios very strongly, and the effect of the
slip angle is significant on the small lobes,
especially in the directions of 0 = 90ø and 0
= 270ø. The dashed curve in Figure 11 demonstrates the results of varying the dip angle by
2 ø and the slip angle by 10ø. The differencebetween the two theoretical curves is outstanding.
To check the validity of the source parameters, we computedthe theoreticalground displacements for the Love and Rayleigh waves
from
the
above source at three
stations
and
compared the results with the observed ampli-
for •he July 90, 1969,earthquake.Open symbolsare
da•a from CIT stations. • is •he dip angie and k is
tudes. The time variation
Caltech stations from which to determine the
is included.
of the source was as-
sumed to be a step function. At Jamestown and
the slip angie.
Ruth, the Rayleigh waves were recordedwith
much greater amplitudesthan at Pasadena,since
spacefunction (i.e., singlet,couple,or double the latter is very close to a nodal point. The
couple), strike and dip of fault plane, source Love waves, however,were very clear, with no
depth, and the orientationof the force vector interference on the transverse component at
(i.e., strike-slipand the dip-slip components
of Pasadena.The Fourier amplitude spectrumsof
Rayleigh wave pulses at Ruth and Jamestown
the motion).
The radiation patterns and the ground dis- were corrected for the instrument responseto
placementspectrumsof both and Love and the determine the ground displacement.These obRayleighwaveswereusedin determiningall the served spectrums are shown in Figure 12 along
parameters.Unfortunately,when this work was with the theoretical spectrums.In each part of
done,we had only the seismograms
from three the figure an arbitrary amplitude scalingfactor
radiation patterns, and we were not, aware of
the LRSM data. Instead of using absolute
amplitudes at each station, we used the ratio
of the Love to Rayleigh wave peak amplitudes
(T = 16 sec) to determine the points that
are shownin Figure 11.
In comparingthe observedand the theoretical
curves,we seethat at Jamestownthe Rayleigh
wave spectrums are almost identical over the
entire frequencyband (]:
0.025 to 0.10 cps).
At Ruth and Pasadena,however,the agreement
between the experimental and the theoretical
920
TOKSOZ, HARKRIDER, AND BEN-MENAHEM
oo
z7øøm
t --o*
18 o o
• PASADENA
08
E/ •Rz
a/
Theoretical
Observed
l0
......
ß•
09
Ruth
•xx.
_ _ _ Pasadena
•
05
/O•
C•4
C•5
Freq•)incy
'•),P7
s)
•8
O?
X ////!!
Frequency(cps)
•)•) 04 05 O•B07 0t8
,\
_
/
• •""', /" --.
o.
•
o4'\,,/,/,//__
__o•
•,•
•
04
Frequency
(cps)
05
06
07
08
COMPARISON
OFOBSERVED
ANDTHEORETICAL
DISPLACEMENT
SPECTRUMS
FROM
JULY
•,19•
EARTHQ
Fig. 12. Observedandtheoreticalgrounddisplacement
spectrums
of Rayleighand Love waves.
The theoreticalsourceparametersare the sameas in Figure 11.
curves is not as good. There is a 'dip' in the
a better fit with the records for Pasadena and
observedspectrumscenteredaroundI = 0.035 Ruth. This can be done by moving the source
cps. This is present in Love waves recordedat
to a shallowerdepth (see Figures 6 and 13).
Pasadenaand in Love and Rayleighwavesre- Comparing each of these theoretical curveswith
cordedat Ruth. A similar dip was alsoobserved the observedcurve (Figure 12), we can imin the spectrumsof Love and Rayleigh waves mediately rule out the depth of 5.5 km. The
recordedat Pasadenafrom the Shoalexplosion. h = lzi km casegives a fair fit at frequencies
The structures from the epicentral area to lower than • = 0.06 cps, but at higher frePasadenaand to Ruth are far from beinghori- quencies
it divergesfrom the experimentalcurve,
zontally layered, as assumedin our theoretical
computations.The dips in the spectrumsare
which reaches a maximum
and then declines.
The depth of 20 km gives the best over-all fit.
probablydue either to the selectivefilteringof We also computedthe theoreticalcurvesfor the
some geologicstructure in the path or to the listed focal depth of 25 km and deeper source
interferenceof waves traveling along slightly depths, but these did not fit the observed
different paths.
spectrumsand were ruled out.
At Ruth the shapeof the theoreticalRayleigh
It should be noted that the source is not a
wave spectrum is different from that at James-
town. This is primarily becausethe azimuths of
the stationsrelative to the strike of the asymmetric sourceare different..The agreementbetween the theoreticaland observedspectrums -1.5.,:
is fair, considering
the big 'dip' in the observed
E
spectrum.
The theoretical curves for Love waves at
Pasadenaand Ruth are almostidenticalexcept
for a scalefactor.For this reasonwe plottedthe
-I
h=14 km
-•
>•
-
= . km
experimentalLove wave spectrumsof both sta-
tions on the samegraph (Figure 12). Again,
--
,5
•
the agreement between the theoretical and obFrequency(cps)
servedcurvesis excellentfor frequencies
higher
.05
.04
.05
.06
.07
.08
.09
.10
than 0.05 cps.At lower frequencies,
however,
I
I
I
I
I
I
, I
I
the curvesdivergebecauseof the 'dip.'
Fig. 13. The frequencyresponseof the medium
It may appearthat the theoreticalspectrums to Rayleigh wavesgeneratedby the sourceof Fig-.
shouldbe shiftedtowardhigherfrequencies
for ure 11 placed at three different depths.
SOURCE PARAMETERS
OF EXPLOSIONS
singlepoint and that it has a finite volume. The
depth of the sourcein this caseis the center of
the volume, and it may differ from the focal
depth. In general,the focal depth refers to the
depth of the point where the first motion occurred at the source.If the rupture along the
fault propagated upward or downward, the
source depth would refer to the depth of a
central point and the focal depth would be the
depth of the initial point.
Let us summarize the source parameters of
AND EARTHQUAKES,
2
921
plained by superimposinga quadrupole force
systemover the isotropicexplosionsource.The
quadrupole source representsthe radiation of
seismicenergy from tectonic strain release.
3. The strength of the quadrupolesourcerelative to the explosion,and its orientation,can be
determined from the radiation patterns of the
Love and/or Rayleigh waves. The orientation
seemsto agree with the general tectonic features of the region.
4. The seismicenergy releasedby the quadthe Fallon earthquakeof July 20, 1962. The rupole component of the source varies from a
azimuth of the strike is 355ø and the dip is 76øE. small fraction of the explosionenergy to many
The force system is double couple.The projec- times the value of it. In the Haymaker and
tion of the displacementvector on the footwall Shoal explosions,the relaxation of the tectonic
makes an angle of 50ø from the horizontal (i.e., stress field due to the explosion-generated
rake is 50øS), which means that the dip- and 'cavity' can accountfor all of the seismicenergy
strike-slip componentsof the motion were apfrom the multipolar source. The Hardhat exproximately equal. The senseof the strike-slip plosion,however, must have triggered a small
motion is dextral. The source depth is 20 km.
earthquake or some other strain releasemechaAlthough we make no claim of uniqueness,the nism besidesthe cavity.
result is in agreementwith the data and general
5. No attempt was made to determine the
tectonic features of the region.
time delay, if any, between the explosionand
the tectonic strain release.This can be done by
I)ISCUSSION AND CONCLUSIONS
checkingthe radiation pattern of the first cycle
In the first part of this paper we utilized some of the P waves. In the Hardhat explosion the
assumptionsand qualitative physical arguments polarity of the first motion around the explosion
to reach to the conclusions about the nature of
would yield an answer. If time delay was much
the complicatedsource of explosion-generated, less than about 0.2 sec the polarity of the first
transverseseismicwaves.In comparingthe ob- motion (compressionor tension) would have a
servations and theoretical results we did not
quadrant distribution similar to the Rayleigh
always find perfect agreement. Some dis- wave polarities.All of the reported first motions
crepanciesare expected in this type of study from LRSM stations were compression(TWG
because of the errors and scatter in the data a.nd
2), although many stations did not specify the
because of the simplified theoretical models polarity.
chosen to represent complicated cases. There
6. The application of the amplitude equalizaare also some uncertainties about the param- tion method with the theoretical radiation pateters we chose,such as values of strain in en- terns from dipolar sourcesyields much useful
ergy computations.In spite of these limita- information about the source mechanism of
tions, we found modelsfor complicatedsources earthquakes. The procedure to be followed in
that are consistent with the observations for
determiningthe sourceparametersis a step by
different explosions.
The conclusions
stated be- step process, as demonstrated for the Fallon
low about the source mechanism of these exearthquake. The strike, dip, and displacement
plosions must be consideredalong with the direction are determined from the radiation
limiting assumptions.
pattern of the Love and Rayleigh wavesor from
1. The source-time function of the Shoal exthe azimuthal variation of Love to Rayleigh
plosion at the boundary of the linear zone as amplitude ratios. In such a ratio, the time and
determined by amplitude equalization of sur- space variation of the source,as well as the
face wavesis of the form p (t) : Pore-'.
effect of its depth, nearly cancelout. The sense
2. The asymmetry of the radiation patterns of the motion must be determined from the
of the Rayleighwavesand the generationof the initial phaseof the Love or the Rayleigh waves.
Love waves from nuclear explosionscan be ex- The spatial sourcefunction and the depth are
922
TOKSOZ, HARKRIDER,
AND BEN-MENAHEM
determined from the ground displacement Eaton, J.P., Crustal structure from San Francisco,
California, to Eureka, Nevada, from seismic-respectrums. Thus, the source is completely
fraction measurements, J. Geophys. t•es., 68,
specifiedusing only seismicsurfacewaves.The
5789-5806, 1963.
uniqueness,however, remains a problem when Gutenberg,B., and C. F. Richter, Magnitude and
the data are scattered.
energy of earthquakes, Ann. Geofis, t•ome, 9,
1-15, 1956.
Acknowledgment. This researchwas supported Harkrider, D. G., Surface waves in multilayered
by contract AF-49(638)-1337 of the Air Force Office of Scientific Research as part of the Advanced
ResearchProjects Agency project Vela.
REFERENCES
Aki, K., A note on surface wave generation from
the Hardhat nuclear explosion,J. Geophys.Res.,
69, 1131-1134, 1964.
Archambeau, C. B., Elastodynamic sourcetheory,
Ph.D. thesis, California Institute of Technology,
Pasadena, 1964.
Benioff, H., Movements on major transcurrent
faults, in Continental Drift, edited by S. K. Runcorn, pp. 103-134, Academic Press, New York,
1962.
Ben-Menahem, A., and M. N. ToksSz, Source
mechanism from spectrums of long-period sur-
face waves,2, Kamchatka earthquake of November 4, 1952,J. Geophys.Res., 68, 5207-5222,1963.
Ben-Menahem, A., and D. G. Harkrider, Radiation
patterns of seismic surface waves from buried
dipolar point sourcesin a flat stratified earth, J.
Geophys. Res., 69, 2605-2620, 1964.
Brune, J. N., and P. W. Pomeroy, Surface wave
radiation patterns for underground nuclear explosions and small-magnitude earthquakes, J.
Geophy•. Res., 63, 5005-5028, 1963.
elastic media, 1, Rayleigh and Love waves from
buried sources in a multilayered elastic halfspace, Bull. Seismol. Soc. Am., 54, 627-680, 1964.
Healy, J. H., Crustal structure along the coast of
California from seismic-refraction measurements,
J. Geophys. Res., 63, 5777-5787, 1963.
Press,F., and C. Archambeau, Release of tectonic
strain by underground nuclear explosions, J.
Geophys. Res., 67, 337-343, 1962.
S!emmons, D. B., Geologic setting for the FallonStillwater earthquakes of 1954, Bull. Seismol.
Soc. Am., 46, 4-9, 1956.
Slemmons, D. B., Geologic effects of the Dixie
Valley-Fairview Peak, Nevada, earthquakes of
December 16, 1954, Bull. Seismol.Soc. Am., •7,
353-375, 1957.
ToksSz, M. N., and A. Ben-Menahem, Excitation
of seismic surface waves by atmospheric nuclear
explosions,J. Geophys. Res., 69, 1639-1648, 1964.
ToksSz, M. N., A. Ben-Menahem, and D. G. Harkrider, Determination of source parameters by
a•nplitude equalization of seismic surface waves,
1, Underground nuclear explosions,J. Geophys.
Res., 69, 4355-4366, 1964.
(Manuscript received September 18, 1964;
revised November 11, 1964.)