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 UR F ACE WAVES.

3. T H E ALASKA 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 observa- tions 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 propa- gation, 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

In previous work (Ben-Menahem and Toks6z, 1962, 1963), the source mechanism of two major earthquakes were obtained from the Fourier spectra of Rayleigh and G waves recorded a t Pasadena, California. In 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 ear thquake occurred on July 10, 1958, a t 06:15:52 G C T at the initial epicenter 58°20'N 136°55'W (Stauder, 1960). I t was given a Richter magni- tude of 7~-8. Extensive field investigations (Tocher, 1960; Davis and Sanders, 1960) revealed a strike-slip movement over a total distance of 200 km along the Fair- weather fault f rom Nuna tak Fiord to Palma Bay, Southeast Alaska. The average strike of the visible trace was N 38°W. Macroseismic evidence, such as reported from Cap Yaka taga (Davis and Sanders, 1960) 330 km NW of Li tuya Bay, sug- gests tha t the actual fault movement 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 ob- served 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 by 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, f rom the distribution of P-S t ime intervals at Sitka. Brune (1961, 1962) studied the source mechanism of the Alaska ear thquake from Mantle Rayleigh waves in the period range 150 < T < 225 sec as recorded on a net of 12 I G Y stations. From the azimuthal distribution of the average t ime domain amplitudes and initial phases, he concluded tha t the fault model is tha 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 km 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 observa- tions 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 elec-

T A B L E I

LIST OF SIGNALS AND PERTINENT DATA

Signal

R2

R3 G2 G~ G4 G4 G5

Seismo- graph

System

8 ~ 9 0 8 ~ 9 0 3 ~ 9 0 3 ~ 9 0 3 ~ 9 0 80-90 3 ~ 9 0

Com- ponent

Z Z E W N S E W NS E W

Distance Traveled

km

36991 43041 36991 36991 77007 77007 83057

Onset of Wave h m s

08 54 17 09 20 05 08 35 05 08 33 05 11 04 06 11 06 05 11 28 41

I n ~ sec

9505 11053

8351 8231

17294 17413 18769

Group Velocity Window km/sec

_ _ B e g i n End _ _

3.89 / 3 .47 3.89 3.45 4.43 4 .10 4.49 4.22 4.45 4.28 4.42 4.29 4.42 4 .24

Record Length

see

1138 1440

682 540 670 502 780

P a s a d e n a c o o r d i n a t e s 34°08'54"N E p i c e n t r a l d i s t a n c e 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 C e n t r a l ang le 27.22 ° A z i m u t h to e p i c e n t e r 338.24 ° A z i m u t h f r o m e p i c e n t e r 144.40 °

118°10'18"W

40016 k m

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 dis- cussed 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/G5 EW are shown in fig. 9, for the period range

SOURCE-MECHANISM FROM SPECTRA OF SURFACE WAVES 907

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. Posit ion of Pasadena relative to the source of the Alaska earlJ~quake of July 10, 1958

iPE 06 :21 :40

~_~. ~ ~ ~ . . . . .- .

G4 ± 4, ~ k---Imin. Af=+4.TsIc. ALASKA- JULY 10,1958 G5 G2

E -W

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

" 1 ~ t F(~-) sin ~or d r ,so

~o

fo F(~-) cos ~ - d~'J

= 1, 2, . . . (1)

9 0 8 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 deter- mination of ~0 requires an accurate knowledge of the phase velocities in the spectral

A L A S K A -

P A S A D E N A

UAIFIL TERED

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

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 O F S U R F A C E W A V E S 909

ALASKA EARTHQUAKE /A~ JULY I0, 1958

' , , , ~ . . o 8 ' ' ' ' % / ' ' ',,:,'s:oc .-,,.I ~ h f = + 4 . 7 SEC

G 5 E-W 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 ,I R 3 Z U=3.45km/sec

09:20:00 v At=+j.Tsec U=5.9 km/sec I I

1 , R 2 Z

U =3.45 km/sec

l " ' IIV: v 09,,o:00 08:55:00 ALASKA

m . 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 SEISMOLOGICAL SOCIETY OF AMERICA

The average of b cos 00 over the per iod range 100 < T < 230 sec, y ie lded a fau l t l ength of a b o u t 280 k m as compared to 350 kin, de r ived ear l ier f rom the a m p l i t u d e s b y the d i r ec t i v i t y me thod .

The de r i va t i on of the source mechan i sm is s u m m e d up in t ab le IV. Before going into technica l deta i l s i t is useful to descr ibe the genera l a p p r o a c h briefly. To 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 5 0 0 2 5 0 167 125 50 i i i i

l O -

w a 7 8 I--

I:L

W > ~4 < J w

2

FIL TER RESPONSE

PERIOD (SECI) I00 85.5, ~ - - 7 1 ' ~ 2.5 55.5

n = 2 4 / coeff . z~l = 2 sec.

O0 I I I I I I I I I 0.01 0.02

FREQUENCY (GPS)

~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 func- tion 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 ex- pression b / 2 X ( ( C / V ) - - cos 00) with the observed average values of b = 300 km

PERIOD IN SEG. 333.3 200 142.8 IIl.I 90.9 76.9

IOO = I I I

(~ R2z R~

>. I,O I-

AL,aSK~4 ~- - n . V = 3 ,5 km /sec - ~[OOi~ /i JU'''O,'~" E~ E-W

I I f J J

b=350 km

5 I0 FREQUENCY IN MILLICYCLES/SEC

FIG. 9. O b s e r v e d ve r sus 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 and G4/G5 on a s emi log 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 = - t a n -1 (2) ~r Tgg -}- tan-1 T-~ 4

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

9 1 2 BULLETIN OF THE SEISMOLOGICAL SOCIETY OF AMERICA

of the trace Four ier componen t with respect to the phase of the ground motion.

E q u a t i o n (2) implies t h a t ~ i n ~ = ~ a t T = ~ and~ in~ t = - ~ a t T = 0. This

conven t ion is in agreement wi th the usual test of the ins t rument . The i n s t rumen ta l

correction (--~Jns~) is t abu l a t ed in table IV. Once the phase of the signal is corrected

for propagat ion, finiteness, and i n s t rumen ta l response, the remain ing phase con-

sists of the sum of the tempora l and spat ial phases.

TABLE II

SAMPLE OF DETAILED CALCULATION OF THE PHASE [G2] = 3.250 + ((36991/C) - 8351)--FouRIE~ PHASE,

FOR G.~ EW ALASKA-PASADENA JULY 10, 1958

.f c 3,25 (36~91 ) The Fourier Frequency Phase Velocity [G~] millicy/sec km/sec -4- f - 8351 Integral Phase

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

- .890 - .861 - .835 - •813 - . 792 - . 772 - . 752 - . 731 - . 710 - .686 - .664 - . 640 - .617 - .595 - .573 -- .553 --.533 - - .513 - . 494 - . 475 - . 455 --. 434 - . 407

- . 333 --.333 --.300 --. 258 - - . 2 1 4

--. 170 - . 128 --.088 - .050 - .014

.019

.051 • 082 .112 • 142 .171 • 201 • 231 • 262 .296 • 3 3 1

• 368 • 408

--.558 --. 527 --.535 -- •555 --. 578 --.602 --. 624 - . 643 - •660 -- .672 --.683 --.691 - . 700 --. 707 - - .715 -- .724 --.734 --.744 --. 756 --. 771 --.786 -- •802 - - .816

Phase angle is measured in circles. Phases corrected by ~r for instrumental directional sign reversal.

Since the tempora l phases of all the signals mus t agree, it is possible to find t ha t par t icu lar force configurat ion which renders equal t empora l phases for the analyzed phases of Love and Rayle igh waves• For the Alaska ea r thquake it was shown (Brune, 1961, 1962) t ha t the t ime func t ion of the source could be described b y the Heavis ide un i t step function• This implies a cons tan t tempora l phase augle equal to - 7 r / 2 (or to - 0 •250 , if measured in circles). To derive the force sys tem we used the phases of G2, which we considered as best fi t ted for this purpose. The scheme of computa t ions is described in table IV. The theoret ical Love-wave spat ia l phase for a r ight double couple is cos 20 exp @i/4) while t h a t of a r ight lateral couple is

SOURCE-MECHANISM FROM SPECTRA OF SURFACE WAVES 913

s in 2 0 exp ( - - 3 ~ r i / 4 ) . T h e a n g l e 0 f o r t h e P a s a d e n a - A l a s k a geodes i c w a s 176 °. T h e r e -

fore , 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 fo r t h e e a s e s of

c o u p l e a n d d o u b l e - c o u p l e r e s p e c t i v e l y . T h e r e s u l t s g i v e n i n t a b l e I V s h o w v e r y

TABLE I I I

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 T X(6~) = bcos0 Frequency Period [R~] [R~] 3~o = [R~] X km railliey/sec see -- [R~] km

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 - - . 3 1 9

--.364 --.382 - - . 3 5 1

-- .360 --.434 --.407 --.436 --.507 --.543 --.645 --.816 --.909 --.927 --.977 --.956 --.913 --.926

--1.038 - . 9 8 5

- 1 . 0 9 3 - 1 . 1 0 8 - 1 . 1 2 3 - 1 . 0 9 6 - 1 . 0 7 0

- .112 - . 077 - . 053 -- . 050 -- . 040 --.022 --.029 - - .010 --.005 - . 025 - . 054 - . 070 - . 0 9 7 - - . 1 2 1

-- . 156 - . 3 5 1

- . 4 3 6 --.428 - . 454 - . 400 -- . 322 -- . 306 -- . 404 - - . 3 1 5

- - .419 --.422 --.431 --.388 - . 366

.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

c l e a r l y t h a t a fo rce s y s t e m of t h e s ing le c o u p l e t y p e does 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 nd ings . T h e force s y s t e m w a s g i v e n in f igure 1. T h e i n n e r r i n g in t h i s f igu re de -

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 for t h e R a y l e i g h w a v e r a d i a -

t i o n f i ' om a r i g h t l a t e r a l c o u p l e o r a r i g h t d o u b l e coup le , w h e r e a s t h e o u t e r r i n g

g ives 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 couple• P r e v i o u s e v i d e n c e for 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 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 O F A M E R I C A

T A B L E I V

DERIVATION OF THE TEMPORAL PHASE FUNCTION OF THE ALASKA EARTHQUAKE

OF JULY 10, 1958 FROM THE ABSOLUTE PHASES OF G2 E - W RECORDED ON THE

3 0 - 9 0 SEISMOGRAPH AT PASADENA, CALIFORNIA

f Frequency in millicy/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

8 . 2

8 . 4

8 . 6

8 . 8

9 . 0

9 . 2

9 . 4

9 . 6

9 . 8

1 0 . 0

1 0 . 2

1 0 . 4

1 0 . 6

1 0 . 8

1 1 . 0

1 1 . 2

1 1 . 4

1 1 . 6

1 1 . 8

1 2 . 0

T Period [G~] in see.

2 7 7 • 7 - - • 5 5 8

2 6 3 . 1 - - . 5 2 7

250 - . 5 3 5

2 3 8 . 1 - . 5 5 5

2 2 7 . 1 - . 5 7 8

2 1 7 . 4 - . 6 0 2

2 0 8 . 3 - . 6 2 4

200 - . 6 4 3

1 9 2 . 3 - . 6 6 0

1 8 5 . 1 - . 6 7 2

1 7 8 . 6 - . 6 8 3

1 7 2 . 4 - . 6 9 1

1 6 6 . 6 - - . 7 0 0

1 6 1 . 2 - - . 7 0 7

1 5 6 . 2 - - . 7 1 5

1 5 1 . 5 - . 7 2 4

1 4 7 . 0 - . 7 3 4

1 4 2 . 8 - . 7 4 4

1 3 8 . 9 - . 7 5 6

1 3 5 . 1 - . 7 7 1

1 3 1 . 6 - . 7 8 6

1 2 8 . 2 - . 8 0 2

125 - . 8 1 6

1 2 1 . 9 - . 7 2 4

1 1 9 . 0 - - . 7 3 7

1 1 6 . 2 - . 7 3 0

1 1 3 . 6 - . 7 4 5

1 1 1 . 1 - . 7 5 2

1 0 8 . 6 - . 7 5 2

1 0 6 . 3 - - . 7 6 0

1 . 4 0 1 - - . 7 6 1

1 0 2 . 0 - - . 7 7 1

100 ~ .754

9 8 . 0 - - . 7 6 3

9 6 . 1 - . 7 6 0

9 4 . 3 - . 7 7 2

9 2 . 6 - . 7 8 5

9 0 . 9 - . 7 9 4

8 9 . 3 - . 8 0 1

8 7 . 7 - . 8 0 5

8 6 . 2 - . 8 2 6

8 4 . 7 - . 8 4 2

8 3 . 3 - . 8 6 4

Instrument

- - •616

- - . 6 0 9

- - . 602

- . 595

- . 5 8 8

- . 5 8 1

- . 5 7 4

- . 568

- .561

- . 555

- - . 548

- - . 542

- - . 5 3 6

- - . 5 2 9

- - . 5 2 3

- - .517

- - .511

- - . 505

- - . 500

- - . 493

- - . 487

- - . 482

- - . 476

- - .471

- - . 4 0 5

- - . 4 6 0

- - . 454

- - . 4 5 0

- - . 4 4 4

- - . 433

- - . 434

- - . 429

- - . 424

- - .419

- - .414

- - . 409

- - . 405

- - . 4 0 0

- - . 395

- - .391

- - . 386

- - . 382

- - .377

Corrections

Finiteness

• O58

• 060

• 062

• 064

• 066

• 068

• 070

• 072

• 074

• 076

.078

.080

.082

.084

• 086

• 088

• 090

• 092

• 094 I

.096 • 098

• 100

. 1 0 2

10~

106

108

110

112

114

117

118

120

122

125

127

128

131

133

135

137

139

141

143

Force system

- - 0 . 1 2 5

- 0 . 1 2 5

The Resulting Temporal Phase

- . 2 4 1

- .201

- - . 2 0 0

- - .211

- - . 2 2 5

- . 2 4 0

- . 2 5 3

- - . 264

- - . 272

- - . 276

- - . 2 7 8

- - . 2 7 8

- . 279

- . 277

- .277

- - . 2 7 8

- - . 280

- - . 282

- - . 287

- - . 293

- - . 300

- . 300

- .315

- .216

- . 2 2 1

- . 207

- . 2 1 4

- .215

- - . 2 0 7

- - . 2 0 7

- - . 2 0 2

- - . 2 0 5

- - . 1 8 1

- - . 182

- - . 174

- . 178

- . 1 8 4

- . 1 8 6

- . 1 8 6

- . 1 8 4

- . 1 9 8

- .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 anal- ysis) then one must add an angle of ~r to the absolute phase of G2 in order to con- form to the convention of the station-system. If the signals were recorded on a

1 5 0 ° 1 4 6 ° 1 4 2 ° 1 3 8 ° 1 3 4 ° 1 3 0 ° 1 2 6 °

FIG. 10. Aftershock distr ibution in the month 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

9 1 6 BULLETIN OF THE SEISMOLOGICAL SOCIETY OF AMERICA

shock of the Alaska earthquake arrived at this station at 06:23:37 and the T- phase at about 07:06:52. I t 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 record- ing 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 by 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 dura- tions are apparently shorter than that of the main shock, but no quantitative statement can be obtained.

On May 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 at tr ibuted to a submarine, manmade ex-

SOURCE-MECHANISM FROM SPECTRA OF SURFACE WAVES 917

plosion. F r o m the a r r iva l t imes of t he P and T-phases of th is even t to P a s a d e n a and

H a w a i i we were able to e s t ima te the ep icenter to be a b o u t 3000 k m nor theas t of Hawai i . Th is po in t lies a p p r o x i m a t e l y on the geodesic f rom the source of the A la ska e a r t h q u a k e to Hawai i , and b o t h ep icen t ra l d is tances are of the same order. F igu re 12 shows a recording of the explosion T-phase a t the HVO on the same i n s t rumen t which recorded the A l a s k a n e a r t h q u a k e in J u l y 1958. Since bo th signals have s imi lar amp l i t udes one m a y safely compare the d u r a t i o n of the t ime in te rva l s above the noise level. One t hen finds t h a t the A l a s k a n T-phase had a d u r a t i o n of a b o u t zi minu te s while the explosion T-phase subs ided a f te r a b o u t 2½ minutes . The difference

be tween these in te rva l s agrees wi th the theore t i ca l va lue of 1.5 minu tes ob t a ined

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 Scien- tific 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 dis- cussions. 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

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SOURCE-MECHANISM FROM SPECTRA OF SURFACE WAVES 919

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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.