Bulletin of the Seismological Society of America. Vol. 53, No. 5, pp. 905-919.
October, 1963
S O U R C E - M E C H A N I S M F R O M S P E C T R A OF L O N G - P E R I O D
S E I S M I C S U R F A C E WAVES.
3. T H E A L A S K A E A R T H Q U A K E OF J U L Y 10, 1958
BY AI~I BEN-MENAHEM AND M. NAFI TOKSSZ
ABSTRACT
Source-mechanism is derived from amplitude and phase spectra of mantle Love and Rayleigh
waves of the Alaska earthquake of July 10, 1958. The signals R2, Rz, G2, G4, G~ recorded on the
Gilman 80-90 and the Press-Ewing 30-90 seismograph systems at Pasadena, California, are
separated, digitized, filtered and Fourier-analyzed. An agreement between theory and observations is obtained for a unilateral fault of 300-350 km, which ruptured with a speed of 3-3.5
kin/see in the direction N40°W. Fault length is in good agreement with the extent of afterst,ock
distribution in the month of July, 1958, and the time of rupture checks with the duration of
an impressive T-phase recorded at Hawaii. The phases of the signals are corrected for propagation, instrumental shift and the source finiteness. Initial phases thus obtained agree on a
mechanism of a right double-couple with a unit step-function in time.
I~T~ODVCTION
I n previous work (Ben-Menahem and Toks6z, 1962, 1963), the source mechanism
of two m a j o r earthquakes were obtained from the Fourier spectra of Rayleigh and
G waves recorded at Pasadena, California. I n the present paper we use the same
data analysis procedure on a somewhat smaller shock recorded at Pasadena,
California. The theoretical background of the methods which were employed for
this purpose, are described in earlier publications.
The Alaska earthquake occurred on July 10, 1958, at 06:15:52 G C T at the
initial epicenter 58°20'N 136°55'W (Stauder, 1960). I t was given a Richter magnitude of 7~-8. Extensive field investigations (Tocher, 1960; Davis and Sanders, 1960)
revealed a strike-slip m o v e m e n t over a total distance of 200 k m along the Fairweather fault from N u n a t a k Fiord to P a l m a Bay, Southeast Alaska. The average
strike of the visible trace was N 38°W. Macroseismic evidence, such as reported
from Cap Y a k a t a g a (Davis and Sanders, 1960) 330 k m N W of Lituya Bay, suggests t h a t the actual fault m o v e m e n t extended beyond the reported trace of 200
kilometers.
Stauder (1960) studied initial P motions from 131 stations to obtain a fault plane
solution. There is a difference of 15 ° between his solution and the trend of the observed surface faulting, and a difference of about 8 ° between the solution and an
observed dip of 78°-81 degrees. Knopoff's solution (1961), as obtained b y machine
calculations, yields a strike of N 21.3°W ± 2.6 and a dip of 66.6°NE ± 2A °. Utsu
(1962) found an after-shock area extent of about 350 kin, from the distribution of
P-S time intervals at Sitka. Brune (1961, 1962) studied the source mechanism of
the Alaska earthquake from Mantle Rayleigh waves in the period range 150 < T <
225 sec as recorded on a net of 12 I G Y stations. F r o m the azimuthal distribution of
the average time domain amplitudes and initial phases, he concluded t h a t the fault
model is t h a t of a right lateral couple which acted as a unit step function in time,
and traveled from the epicenter northwestward along the strike of the fault (N
40°W) for 200 k m with a velocity of 3 km/sec. The Love-wave phase velocities for
905
906
BULLETIN OF THE SEISMOLOGICAL SOCIETY OF AMERICA
the great circles Alaska-Pasadena and Alaska-Wilkes were given by Toks6z and
Ben-Menahem (1963). The Rayleigh-wave phase velocities for various great-circle
paths through the epicenter of the Alaska earthquake were given by Brune (1961).
Attenuation coefficients of Love waves over the Pasadena-Alaska great circle were
computed by Ben-Menahem and ToksSz (1963). B a t h (1959) reported observations on ultra-long period waves from the Alaska earthquake recorded at Uppsala,
Sweden.
D A T A ANALYSIS
The list of the phases used in the analysis are given in table I. Each wave-train
was digitized at 2 second intervals and Fourier analyzed on the IBM 7090 elecTABLE
I
L I S T OF SIGNALS AND P E R T I N E N T D A T A
Signal
Seismograph
System
Component
Distance
Traveled
km
Onset of Wave
h m s
In ~
sec
Group Velocity Window
km/sec
__Begin
R2
R3
G2
G~
G4
G4
G5
8~90
8~90
3~90
3~90
3~90
80-90
3~90
Z
Z
EW
NS
EW
NS
EW
36991
43041
36991
36991
77007
77007
83057
08
09
08
08
11
11
11
54
20
35
33
04
06
28
17
05
05
05
06
05
41
9505
11053
8351
8231
17294
17413
18769
3.89
3.89
4.43
4.49
4.45
4.42
4.42
End
/ 3.47
3.45
4.10
4.22
4.28
4.29
4.24
Record
Length
see
_ _
1138
1440
682
540
670
502
780
Pasadena coordinates
34°08'54"N 118°10'18"W
Epicentral distance
3025 k m
C i r c u m f e r e n c e of n o r m a l s e c t i o n
40016 k m
Central angle
27.22 °
A z i m u t h to e p i c e n t e r
338.24 °
Azimuth from epicenter
144.40 °
tronic computer. Before the analysis, the data were filtered with a low-pass digital
filter. In table I, tr~ is the time delay of the window onset with respect to the time of
origin.
The source-station geometry is shown in figure 1. The original record of the
Pasadena EW 30-90 is shown in figure 2. The separated traces of the signals which
were used in the analysis are given in figures 3-5. In figs. 6-7 some of the filtered
signals are shown. The filter response is shown in figure 8
AMPLITUDE-SPECTRA
The theoretical background for the derivation of the source parameters from the
ratio of the spectral amplitudes of even and odd order surface waves has been discussed in detail in a previous paper (Ben-Menahem, 1961). Phase velocities and
attenuation coefficients for the Alaska earthquake were reported elsewhere (Toks6z
and Ben-Menahem, 1963; Ben-Menahem and Toks6z, 1963).
The direetivities R~/R~Z and G4/G5EW are shown in fig. 9, for the period range
907
SOURCE-MECHANISM FROM SPECTRA OF SURFACE WAVES
330 > T > 70 see. The best fit was obtained for both Love and Rayleigh waves
with b = 350 km V = 3.5 km/sec and 0 = 176 °. While the fit of the observed and
calculated poles is satisfactory there exists a considerable deviation in the region
between these poles.
'~%
N (+)
E (+)
FIG. 1. Position of Pasadena relative to the source of the Alaska earlJ~quake of July 10, 1958
iPE
06:21:40
~_~. ~
~
~
G4
±
G5
ALASKA- JULY 10,1958
E-W
4,
G2
.
.
~
.
.
k---Imin.
.-
.
Af=+4.TsIc.
FIG. 2. The Pasadena E-W 30-90 record of the Alaska eart.hquake of July 10, 1958.
PHASE-SPECTRA
I t is shown (Ben-Menahem and Toks6z, 1963) that ~0, the total initial phase
(which is the sum of the phases of the time function, the force system and the
source finiteness) is given by
t " F(~-) sin
~
~o
,so
~or d r
1
fo F(~-) cos ~- d~'J
=
1, 2, ...
(1)
908
BULLETIN OF THE SEISMOLOGICAL SOCIETY OF AMERICA
Where F(r) is the time function of the digitized signal, An is the distance, C the
phase velocity, (n - 1)/4 the polar phase shift, and N an integer. Thus the determination of ~0 requires an accurate knowledge of the phase velocities in the spectral
ALASKA
-
PASADENA
UAIFILTERED
08"55"~,
I
,,-oooo
II / \
A
,,-,5-oo
FIG. 3. Unfiltered G~and G4 phases (E-W 30-90) from the Alaska earthquake,
recorded at Pasadena.
range of interest. An example for a detailed computation of the propagation phase
which is equal to ~0 + ~i~t is shown in table II for the signal G2 EW recorded on
the 30-90 seismograph system at Pasadena. Phase velocities are those obtained
from G2-G4 (ToksSz and Ben-Menahem, 1963). In table I I I the faultlength is
SOURCE-MECHANISM
FROM SPECTRA
ALASKA EARTHQUAKE
',,,~..o8
'
'
G5 E-W
/A~
'
.-,,.I
OF SURFACE
WAVES
909
J U L Y I0, 1958
'%/
'
~
'
',,:,'s:oc
h f = + 4 . 7 SEC
J MIN.
11:30:00
11:40:00
FIG. 4. Unfiltered G4 and G5 phases from the Alaska earthquake reeorded at Pasadena.
/
U=3.9km/sec
09:20:00
U=5.9 km/sec
,I
R3 Z
v
I
U=3.45km/sec
At=+j.Tsec
I
1
,
R2 Z
U=3.45 km/sec
l"' IIV: v
08:55:00
m .
09,,o:00
ALASKA
dULY 10,1958
FIG. 5. Unfiltered R2 and Rz (Z component) recorded at Pasadena on the Gilman
80-90 seismograph system.
determined from the differential phases of the Z component of Rayleigh waves
R2 and Ra. Since the finiteness phase equals b/2X((C/V) - cos 00) for R2 and
b/2X((C/V) + cos 00) for R3, the differential phase is equal to b/X cos 00 . Hence,
upon the multiplication of the observed a~0 by X, the value of b cos 00 is obtained.
910
B U L L E T I N OF T H E S E I S M O L O G I C A L S O C I E T Y OF A M E R I C A
T h e a v e r a g e of b cos 00 o v e r t h e p e r i o d range 100 < T < 230 sec, y i e l d e d a f a u l t
l e n g t h of a b o u t 280 k m as c o m p a r e d to 350 kin, d e r i v e d earlier f r o m t h e a m p l i t u d e s
by the directivity method.
T h e d e r i v a t i o n of t h e source m e c h a n i s m is s u m m e d u p in t a b l e IV. Before going
into t e c h n i c a l details it is useful to describe t h e general a p p r o a c h briefly. T o begin
-~,
m;o I.._
E-W
FIG. 6. Mantle Love wave G2 E-W filtered with two different low pass digital filters : (A) cut-off
at T = 25 sec, (B) cut-off at T = 125 seconds.
FIG. 7. Mantle Rayleigh waves R~ and Rz (80-90 Z) filtered with a low pass digital filter.
Amplitude scales are not uniform.
~o
PERIOD (SECI)
I00
85.5,
~--71'~
500
250
167
125
i
i
i
i
2.5
55.5
I
I
50
lOw
n = 2 4 / coeff.
z~l = 2 sec.
a
78
I--
I:L
F I L TER RESPONSE
W
>
~4
<
J
w
2
O0
I
I
I
I
I
I
0.01
FREQUENCY (GPS)
I
0.02
~FIG. 8. Response of a digital filter used to eliminate high frequency noise from the
digitized signals.
SOURCE-MECHANISM FROM SPECTRA OF SURFACE WAVES
911
with, one must make a basic assumption that the total phase is the sum of the phase
due to the force system at the source (spatial phase) the phase due to the time function at the source (temporal phase) and the phase due to the finite motion of the
source (propagation phase).
In table IV the phase [G2] is corrected for the instrumental phase shift and for
finiteness effect. The finiteness correction was computed from the theoretical expression b / 2 X ( ( C / V )
- - cos 00) with the observed average values of b = 300 km
333.3
IOO =
PERIOD IN SEG.
142.8
IIl.I
90.9
I
I
200
I
(~
>. I,O
I-
~[OOi~
R2z
R~
AL,aSK~4
/i JU'''O,'~"
~--
76.9
n
E~
b=350 km
.
V = 3,5
km/sec-
E-W
I
I
5
f
J
J
I0
FREQUENCY IN MILLICYCLES/SEC
FIG. 9. O b s e r v e d v e r s u s c a l c u l a t e d d i r e e t i v i t y for M a n t l e R a y l e i g h w a v e s R=/Ra a n d G4/G5 on
a s e m i l o g scale.
V = 3.5 km/sec and 00 = 176 degrees. The instrumental correction was computed
for a seismometer-galvanometer system in critical damping and zero coupling
(Benioff and Gutenberg, 1952; Hagiwara, 1958; Gilman, 1960). The instrumental
phase shift for a system of this type is given by:
~inst = -
~r
t a n -1
Tgg -}- tan-1 T-~
4
(2)
where Tg is the period of the galvanometer, T~ is the period of the seismometer.
~ns~ is measured in parts of circle. A positive value of ~n~ means a phase advance
912
B U L L E T I N OF T H E SEISMOLOGICAL SOCIETY OF AMERICA
of the trace F o u r i e r c o m p o n e n t with respect to the phase of the g r o u n d m o t i o n .
E q u a t i o n (2) implies t h a t ~ i n ~ = ~ a t T = ~ a n d ~ i n ~ t = - ~ a t
T = 0. This
c o n v e n t i o n is in a g r e e m e n t w i t h the u s u a l test of the i n s t r u m e n t . T h e i n s t r u m e n t a l
correction (--~Jns~) is t a b u l a t e d in table IV. Once the phase of the signal is corrected
for p r o p a g a t i o n , finiteness, a n d i n s t r u m e n t a l response, the r e m a i n i n g phase consists of the s u m of the t e m p o r a l a n d spatial phases.
TABLE II
SAMPLE OF DETAILED CALCULATIONOF THE PHASE
[G2] = 3.250 + ((36991/C) - 8351)--FouRIE~ PHASE,
FOR G.~E W ALASKA-PASADENAJULY 10, 1958
.f
Frequency
millicy/sec
c
Phase Velocity
km/sec
3.6
3.8
4.0
4.2
4.4
4.6
4.8
5.0
5.2
5.4
5.6
5.8
6.0
6.2
6.4
6.6
6.8
7.0
7.2
7.4
7.6
7.8
8.0
5.137
5.089
5.047
5.010
4.977
4. 948
4•921
4.896
4.874
4.853
4.834
4.816
4.800
4.785
4. 771
4. 758
4. 746
4.734
4. 724
4.714
4.704
4.695
4.686
3,25 (36~91
)
-4-f
- 8351
- .890
.861
-.835
•813
- . 792
- . 772
- . 752
- . 731
- . 710
-.686
- .664
- . 640
.617
-.595
-.573
-- .553
--.533
.513
- . 494
- . 475
- . 455
--. 434
- . 407
-
-
-
- -
The Fourier
Integral Phase
[G~]
- . 333
--.333
--.300
--. 258
--.558
--. 527
--.535
-- •555
--. 578
--.602
--. 624
- . 643
- •660
-- .672
--.683
--.691
- . 700
--. 707
.715
-- .724
--.734
--.744
--. 756
--. 771
--.786
-- •802
.816
-
-
.
2
1
4
--. 170
128
--.088
-.050
.014
.019
.051
•082
.112
142
.171
201
231
•262
.296
-
.
-
•
•
•
• 3 3 1
•368
•408
- -
- -
Phase angle is measured in circles. Phases corrected by ~r for instrumental directional sign
reversal.
Since the t e m p o r a l phases of all the signals m u s t agree, it is possible to find t h a t
p a r t i c u l a r force configuration which renders equal t e m p o r a l phases for the a n a l y z e d
phases of Love a n d R a y l e i g h waves• F o r the A l a s k a e a r t h q u a k e it was shown
(Brune, 1961, 1962) t h a t the t i m e f u n c t i o n of the source could be described b y the
Heaviside u n i t step function• T h i s implies a c o n s t a n t t e m p o r a l phase augle equal
to - 7 r / 2 (or to - 0 • 2 5 0 , if m e a s u r e d i n circles). T o derive the force s y s t e m we used
the phases of G2, which we considered as best fitted for this purpose. T h e scheme of
c o m p u t a t i o n s is described i n table IV. T h e theoretical Love-wave s p a t i a l phase
for a right double couple is cos 20 exp @ i / 4 ) while t h a t of a right lateral couple is
913
SOURCE-MECHANISM FROM SPECTRA OF SURFACE WAVES
sin 2 0 exp (--3~ri/4). The angle 0 for the Pasadena-Alaska
g e o d e s i c w a s 176 °. T h e r e -
f o r e , t h e s p a t i a l p h a s e a n g l e s of - 3 ~ r / 4 a n d q - r / 4 a r e p r e d i c t e d f o r t h e e a s e s of
couple and double-couple respectively. The results given in table IV show very
TABLE III
DERIVATION OF THE FAULT LENGTtt OF THE ALASKA EARTHQUAKE OF JULY 10, 1958
FROM THE DIFFERENTIAL PHASES OF RAYLEIGH WAVES R 2 AND /~3
RECORDED AT PASADENA~ CALIFORNIA
f
Frequency
railliey/sec
T
Period
see
[R~]
4.4
4.6
4.8
5.0
5.2
5.4
5.6
5.8
6.0
6.2
6.4
6.6
6.8
7.0
7.2
7.4
7.6
7.8
8.0
8.2
8.4
8.6
8.8
9.0
9.2
9.4
9.6
9.8
10.0
227.2
217.4
208.3
200.0
192.3
185.1
178.6
172.4
166.6
161.2
156.2
151.5
147.0
142.8
138.9
135.1
131.6
128.2
125.0
121.9
119.0
116.2
113.6
111.1
108.6
106.3
104.1
102•0
100.0
--.384
--.376
--.341
--•342
--.319
--.364
--.382
--.351
--.360
--.434
--.407
--.436
--.507
--.543
--.645
--.816
--.909
--.927
--.977
--.956
--.913
--.926
--1.038
-.985
-1.093
-1.108
-1.123
-1.096
-1.070
[R~]
3~o= [R~]
-- [R~]
Xkm
X(6~) = bcos0
km
.112
- . 077
- . 053
--. 050
--. 040
--.022
--.029
- - .010
--.005
- . 025
- . 054
- . 070
-.097
.272
.299
•288
•292
.279
.342
.353
• 341
•365
•409
.353
•366
•410
•422
•489
•465
.473
•500
.523
.556
.591
.620
•634
•670
.674
•686
•692
•708
•704
1078.9
1018.5
961.4
914.0
868-3
829.8
792.1
759.6
728.7
702.6
674.8
650.0
629.6
610.0
591.2
574.2
557.4
540.1
525.6
510.7
496.5
483.5
471.7
459.6
448.9
438.3
428.2
418.5
409.3
293
304
277
267
242
284
280
259
266
287
238
238
258
257
289
267
263
27O
274
284
293
300
3OO
3O8
302
3OO
296
296
288
Average
279
-
--.121
--. 156
-.
351
-.436
--.428
- . 454
- . 400
--. 322
--. 306
--. 404
--.315
- - .419
--.422
--.431
--.388
- .
366
c l e a r l y t h a t a f o r c e s y s t e m of t h e s i n g l e c o u p l e t y p e d o e s n o t a g r e e w i t h a t e m p o r a l
p h a s e of - 0 . 2 5 0 , w h i l e a c o r r e c t i o n of - 0 . 1 2 5 l e a v e s r e s i d u a l s t h a t c o n f i r m B r u n e ' s
f i n d i n g s . T h e f o r c e s y s t e m w a s g i v e n i n f i g u r e 1. T h e i n n e r r i n g i n t h i s f i g u r e d e s c r i b e s t h e q u a d r a n t d i s t r i b u t i o n s i n 20 a p p r o p r i a t e f o r t h e R a y l e i g h w a v e r a d i a tion fi'om a right lateral couple or a right double couple, whereas the outer ring
g i v e s t h e d i s t r i b u t i o n cos 20 c o r r e s p o n d i n g t o t h e L o v e w a v e r a d i a t i o n f r o m a r i g h t
d o u b l e c o u p l e • P r e v i o u s e v i d e n c e f o r t h e o c c u r r e n c e of t h e d o u b l e - c o u p l e m e c h a -
914
BULLETIN
OF THE SEISMOLOGICAL SOCIETY OF AMERICA
TABLE
IV
DERIVATION OF THE TEMPORAL P H A S E FUNCTION OF THE ALASKA E A R T H Q U A K E
OF J U L Y 10, 1958 FROM THE ABSOLUTE P H A S E S OF G2 E - W RECORDED ON THE
3 0 - 9 0 SEISMOGRAPH AT PASADENA, CALIFORNIA
Corrections
f
Frequency in
millicy/sec.
T
Period
in see.
[G~]
3.6
3.8
4.0
4•2
4.4
4.6
4.8
5.0
5.2
5.4
5.6
5.8
6.0
6.2
6.4
6.6
6.8
7.0
7.2
7.4
7.6
7.8
8.0
8.2
8.4
8.6
8.8
9.0
9.2
9.4
9.6
9.8
10.0
10.2
10.4
10.6
10.8
11.0
11.2
11.4
11.6
11.8
12.0
277•7
263.1
250
238.1
227.1
217.4
208.3
200
192.3
185.1
178.6
172.4
166.6
161.2
156.2
151.5
147.0
142.8
138.9
135.1
131.6
128.2
125
121.9
119.0
116.2
113.6
111.1
108.6
106.3
1.401
102.0
100
98.0
96.1
94.3
92.6
90.9
89.3
87.7
86.2
84.7
83.3
--•558
--.527
-.535
-.555
-.578
-.602
-.624
-.643
-.660
-.672
-.683
-.691
--.700
--.707
--.715
-.724
-.734
-.744
-.756
-.771
-.786
-.802
-.816
-.724
--.737
-.730
-.745
-.752
-.752
--.760
--.761
--.771
~ .754
--.763
-.760
-.772
-.785
-.794
-.801
-.805
-.826
-.842
-.864
Instrument
•616
--.609
- - . 602
- . 595
-.588
-.581
-.574
- . 568
.561
- . 555
--. 548
-- . 5 4 2
--.536
--.529
--.523
-.517
-.511
--. 505
--. 500
- - . 493
--. 487
--. 482
- - . 476
-.471
--.405
--.460
- - . 454
--.450
--.444
- - . 433
--. 434
- - . 429
- - . 424
-.419
-- . 4 1 4
- - . 409
- - . 405
--.400
- - . 395
-.391
- - . 386
- - . 382
-- . 3 7 7
--
The Resulting
Temporal Phase
Finiteness
• O58
•0 6 0
• 062
• 064
• 066
• 068
•0 7 0
• 072
•0 7 4
• 076
.078
.080
.082
.084
• 086
• 088
•0 9 0
•0 9 2
•094
Force system
--0.125
I
.096
• 098
• 100
.102
10~
106
108
110
112
114
117
118
120
122
125
127
128
131
133
135
137
139
141
143
-.241
.201
--.200
-.211
--.225
-.240
-.253
- - . 264
--. 272
- - . 276
--.278
--.278
- . 279
- . 277
- .277
--.278
- - . 280
- - . 282
- - . 287
- - . 293
- - . 300
- . 300
.315
.216
-.221
- . 207
- . 2 1 4
.215
--.207
--.207
--.202
--.205
-
--.181
- 0 . 1 2 5
- - . 182
- - . 174
- .
178
- .
184
- .
186
- .
186
- .
184
- .
198
.210
- - . 223
-
SOURCE-MECHANISM FROM SPECTRA OF SURFACE WAVES
915
nism for some Japanese earthquakes has been produced by H. Honda and his
collaborators (Honda 1952, 1962).
In an analysis of this kind, one must pay attention to the sign convention of
the source system relative to that of the station-system. Consider for example the
G2 EW signal which was used to determine the force-system at the source. If we
adopt the convention that the angles in the source-system are measured positively
in the counter-clockwise direction and that east is positive in the station system
(this is dictated by the choice of the positive amplitude axis for the Fourier analysis) then one must add an angle of ~r to the absolute phase of G2 in order to conform to the convention of the station-system. If the signals were recorded on a
150 °
146 °
142 °
138 °
134 °
130 °
126 °
FIG. 10. Aftershock distribution in the m o n t h of July 1958 at the source region of the
Alaska earthquake.
linear strain seismograph, this COlTection would not be needed. Similar arguments
hold for the horizontal component of the gayleigh wave.
SUPPORTING EVIDENCE
The aftershock distribution in the month of July 1958 are shown in figure 10.
These aftershocks describe an area which probably contributed to the strain-release
of the main shock.
An additional cheek on our results is supplied by the duration of the T-phase as
recorded by short period instruments on the islands of Hawaii and Oahu. The use
of the T-phase as a measure of the duration of the seismic event at the source has
been demonstrated by Eaton, Richter, and Ault (1961) in the case of the Chile
earthquake of May 22, 1960.
Figure 11 shows a T-phase recorded at the Hawaiian Volcano Observatory
(19°26'N 155°16'W) on a short period instrument. The P wave from the main
916
BULLETIN OF THE SEISMOLOGICAL SOCIETY OF AMERICA
shock of the Alaska earthquake arrived at this station at 06:23:37 and the Tphase at about 07:06:52. It is found that the initial T arrival traveled a distance
of 4565 km with a velocity of VT = 1.69 km/sec. Assuming that the T-phase in
this case was caused by a seismic source which moved with an average speed of
VI = 3 km/sec over a distance of b = 300 kin, one obtains a duration at the recording station given by the expression b/2Vr (cos 0 + (Vr/VI)), where 0 is the angle
between the fault line and the geodesic passing through the initial epicenter and
the station (0 = 113°). This implies that the contribution of the fault's propagation
to the duration of the T-phase is around 1.5 rain. Additional contributions to the
duration may arise from dispersion (Northrop, 1962) and lateral as well as vertical
time delays when the conversion to seismic waves takes place at both the trans-
FIG. 11. A short-period smoked paper seismogram of the T-phases from the main shock and
two aftershocks of the Alaska earthquake recorded at the HVO, MAUNA LOA, Hawaii.
mission and the reception ends. The derivation of the source parameters from the
duration of an observed T-phase is thus hampered b y two serious difficulties:
First, we are not able to remove the propagation effects from the signal and second,
we cannot determine accurately the terminals of the signal on the l~cord because
of the microseismic noise level which prevails on most short-period records. The
first difficulty may be overcome by a comparison of the T-phase from the main
shock to a T-phase from a localized source (both in time and space) at an equivalent
epicentral distance. Such a source may be realized by a submarine explosion or an
aftershock. Figure 11 shows T-phases from two small aftershocks. The amplitudes
of these signals drop down to the ambient noise level in 60-70 seconds. Their durations are apparently shorter than that of the main shock, but no quantitative
statement can be obtained.
On M a y 10, 1962, the seismographs throughout Hawaii recorded a T-phase
arriving from the northeast with no detectable P or S phase (J. P. Eaton, private
communication). The event has been attributed to a submarine, manmade ex-
SOURCE-MECHANISM FROM SPECTRA OF SURFACE WAVES
917
plosion. F r o m t h e a r r i v a l t i m e s of t h e P a n d T - p h a s e s of this e v e n t to P a s a d e n a a n d
H a w a i i we were able to e s t i m a t e t h e e p i c e n t e r to be a b o u t 3000 k m n o r t h e a s t of
H a w a i i . T h i s p o i n t lies a p p r o x i m a t e l y on t h e geodesic f r o m t h e source of t h e A l a s k a
e a r t h q u a k e to H a w a i i , a n d b o t h e p i c e n t r a l d i s t a n c e s are of t h e s a m e order. F i g u r e
12 shows a r e c o r d i n g of t h e explosion T - p h a s e a t t h e H V O on t h e s a m e i n s t r u m e n t
w h i c h r e c o r d e d t h e A l a s k a n e a r t h q u a k e in J u l y 1958. Since b o t h signals h a v e similar
a m p l i t u d e s one m a y safely c o m p a r e t h e d u r a t i o n of t h e t i m e i n t e r v a l s a b o v e t h e
noise level. One t h e n finds t h a t t h e A l a s k a n T - p h a s e h a d a d u r a t i o n of a b o u t zi
m i n u t e s while t h e explosion T - p h a s e s u b s i d e d a f t e r a b o u t 2½ m i n u t e s . T h e difference
b e t w e e n these i n t e r v a l s agrees w i t h t h e t h e o r e t i c a l v a l u e of 1.5 m i n u t e s o b t a i n e d
FIG. 12. A short-period smoked paper seismogram of a T-phase of a submarine man-made
explosion recorded at the nvo, M£UNA LOA, Hawaii.
earlier on the assumption that the earthquake source propagated over a distance
of 300-350 km with a rupture speed of 3-3.5 km/sec.
ACKNOWLEDGMENTS
This research was supported by Grant No. AF-AFOSR-25-63 of the Air Force Office of Scientific Research as part of the Advanced Research Projects Agency project VELA UNIFORM.
We wish to express our sincere thanks to Dr. J. P. Eaton and Dr. Harold J. Krivoy of the U.S.
Geological Survey and to Dr. Robert A. Earle of the U.S.C.G.S. for sending us the Hawaii
T-phase seismograms of the Alaska earthquake.
Acknowledgment is also due to Drs. Keiiti Aki and Augustine Furumoto for helpful discussions. The time series analysis and azimuth-distance computer programs used in the data
analysis were written by Dr. Shelton S. Alexander.
918
BULLETIN OF THE SEISMOLOGICAL SOCIETY OF AMERICA
REFERENCES
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1952. "The Response of Strain and Pendulum Seismographs to Surface Waves," Bull.
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Ben-Menahem, Ari, and M. Nail Toksoz
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Ben-Menahem, Ari, and M. Nail Toksoz
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(Supplement).
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Northrop, J.
1962. "Evidence of Dispersion in Earthquake T-phases," J. Geophys. Res., 67, 2823.
Stauder, W.
1960. "The Alaska Earthquake of July 10, 1958," Bull. Seism. Soc. Am., 50, 293.
Toeher, D.
1960. "The Alaska Earthquake of July 10, 1958," Bull. Seism. Soc. Am., 59, 217-220, 267.
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SOURCE-MECHANISM FROM SPECTRA OF SURFACE WAVES
919
Utsu, T.
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SEISMOLOGICAL LABORATORY
CALIFORNIA INSTITUTE OF TECHNOLOGY
PASADENA~ CALIFORNIA
(Division of the Geological Sciences, Contribution No. 1164)
Manuscript received May 31, 1963.