Geophys. J. R. astr. Soc. (1971) 25,407-417
The Force System of The Chilean
Earthquake of 1960 May 22
Ari Ben-Menahem
(Received 1971 July 9)
Summary
The force system at the source of the colossal Chile earthquake of May
1960 was derived from spectral amplitudes of free oscillations and Mantle
surface waves recorded at Pasadena and Isabella California, Kyoto
Japan and Ogdensburg, New Jersey. Although the data are sparse and the
azimuthal coverage is partial, there is ample evidence to indicate a unique
solution which is a dip-slip motion on a fault dipping 45" to the east with
the oceanside downthrown.
Introduction
In a previous publication (Ben-Menahem, Israel & Levit6 1971a) we have
presented tables and charts that give the dependence of displacements and strains on
the source elements, the Earth's structural parameters and the station co-ordinates
with respect to the source. We have demonstrated therein that the theoretical calculations can indeed be used successfully to invert amplitude data in terms of the source
parameters. In another paper (Ben-Menahem, Rosenman & Israel 1971b) these
numerical results were used to derive the source parameters of the Alaskan earthquake
of 1964 March 28 from observed toroidal and spheroidal line spectra. The same
theory is applied in the present paper to derive the force system of the Chile earthquake
of 1960 May 22.
According to the theory, the spheroidal surface displacements u,, ue and u+ and
the surface strains 880, &e+, E++ are given as functions of the source parameters (depth
h, fault area ds, dislocation uo), the station co-ordinates with respect to the source
(0, r$ = q5-q50) and the structural parameters of the Earth. All field entities are
proportional to the source constant R = uo ds/4na2 which is expressed in microns.
Data analysis and interpretation
Benioff, Press & Smith (1961) recorded the spheroidal modes oS2, oS5 and oS19
on a linear-strain seismograph (N 32" W) at Isabella California, from the Chile
earthquake of 1960 May 22. At an epicentral distance of 84.3" and azimuth 6 ==45"
they reported a ground strain (mostly &Be) of 2 x lo-", 8 x lo-'' and 2 x lo-'
respectively, for the above modes. In order to find a source that could have produced
such a field at Isabella, we calculated displacements and strains for the three fundamental sources at depths 30,60 and 100 km with R = 2000 p. The results are presented
in Table 1. A comparison of the calculations with the observations immediately rules
out the possibility of pure dip-slip motion. Moreover, this must imply that the source
407
111
I1
I
III
I1
I
III
100
30
60
100
30
60
100
30
60
100
30
60
100
30
60
100
30
60
100
60
30
60
100
30
60
100
30
I
I1
(W
case
(1) Pasadena
(2) Isabella
(3) negligible
os19
oss
0%
Model
Depth
57
122
152
0.6
3
6
574
1033
1053
212
370
366
3
6
21
278
494
490
1330
2075
1740
5
90
210
1170
1800
1317
Q
IKl
(1)
810
680
8
141
330
471
726
531
520
0.6
0.1
0.5
1.2
8
14
14
276
480
475
1.8
3.0
10-7
355
631
625
0.5
0.2
IGI
0
(1)
1.8
23.1
41.6
41.3
342
532
447
1.32
23.0
53.7
303
466
340
0.5
7.8
14.1
14.4
15.8
27.6
27.3
0.3
-
-
0.85
1.83
2.29
1.7
4.0
17.6
27.2
20.0
-
-
0.1
0.4
5.1
9-3
8-7
23.5
36.6
30.7
16.0
16.2
5-8
10-1
10.0
9-0
-
-
0.81
1.75
2.19
21 .o
117
180
132
0.5
9.0
0.8
10.3
18.0
18.1
133-2
m7.6
174.2
0.2
6.1
11.2
11.3
7.9
13.7
13-6
0.1
-
-
-
0.6
1-3
1.6
(&"Ix loL1
(2)
Calculated displacements and strains for Pasadena and Isabella from the source of the Chilean earthquake of 1960 May 22. Amplitudes were
not corrected for attenuation. i2 = 2000 p.
Table 1
P
Force system of the Chilean earthquake
409
was either close to the strike-slip type or close to a dip-slip motion on a 45" dipping
fault. If we accept the statement of Benioff et ul. (1961) that the vertical displacement u, at Pasadena was approximately l00Op for oSz, ,& and oS19,we must
favor the second alternative at an average source-depth of 60 km.
At Kyoto, Japan, Sat6 & Takeuchi (1963) recorded the modes ,S,, oS8and ,S9
on an Askania gravimeter with amplitudes 1.12, 0.97 and 1 - 1 1 pgal respectively.
At Ogdensburg, New Jersey, USA, Alsop, Sutton & Ewing (1961) recorded
relative strain and displacements for toroidal and spheroidal modes. Table 2 compares
the observed and the calculated amplitudes at both stations for the three fundamental
sources at various depths. Again, the observations favour the third case at average
depth of some 60 km.
Finally, records of surface waves from the Californian stations, PAS, BRK and
ISA were used to check on the above solution.
The positions of PAS and ISA relative to the source are shown in Fig. 1. Fig. 2
shows again the well-known Isabella strain recording with the multiple arrivals of
Mantle surface waves from the source of the Chilean earthquake, (Benioff 1962).
The azimuth of ISA with respect to the strike of the fault was 6 = 45"_+2". Since
Love waves from a strike-slip fault vary with azimuth like cos26, it is supposed to
have a nodal line at ISA. It appears however from Fig. 2 that Love and Rayleigh
waves are of comparable amplitudes in the period range T = 200-300 s. This
immediately rules out the possibility of transcurrent faulting, contrary to BeniofF's
assertion (Benioff 1962). The same phenomenon is repeated on a strain recording at
Pasadena (Fig. 3). A quantitative analysis of this observation is shown in Fig. 4
where we compare the observed spectral ratio G J R , from the NS Pasadena strain-
1
A Is. = lsabella
0 Pa.=Pasadena
FIG. 1. Location of source and recording stations of the Chile earthquake of
1960 May 22.
64
-
FIG.3. A low magnification strain recording at Pasadena.
R2
-
,
FIG. 2. Relative excitation of Love and Rayleigh waves from the Chilean earthquake of 1960 May 22.
0-21
0.23
0.24
0.26
0.55
0.70
5
10
0.44
0.01
-
-
-
-
II
osz
3620
(3)
-7.71
-7.80
-7.73
-7.71
-14.02
-14.48
III
-4.57
-4.54
-4.48
-4.43
-7.67
-7.53
I
0.71
-0.02
-
-
-
II
os3
OGDENSBURG, e(N 30" E) x 10"
3140
10
47
14
8
2
4
m
1528
1509
1470
1439
162
2369
Lu
I
-0.7
-0.7
-0.7
-0.7
-1.2
-1.2
I
427
262
446
273
271
266
= 3.086 x u,@)
-12.38
-12.32
-12.20
-12.10
-21.84
-22.22
(1) Transformed from gravimeter readings (Sato & Takeuchi 1963) according to the relation: 104 x A&gal)
(2) Calculated with 6 = cos'x ew+sin2X eM+cos x sin x e+e, for x = 30".
(3) Less than
No fit with observations.
(4) Observations (Alsop et 01. 1961) are given as relative amplitudes.
(4)
Observed
30
60
100
20
I
Depth (km)
(2)
Calculated
(1)
Observed
12
17
1
28
260
258
254
251
44
416
3
215
213
210
208
359
350
5
10
20
30
60
100
1062
1051
1029
1011
1760
1703
I1
6
oss
I
II
III
os7
I
Calculated
Depth (km)
KYOTO, u, microns
0.9
0.02
-0.19
-0.51
-
-
-
I1
O
s
4
3600
1
2
5
7
1
10
11
os9
Calculated us. observed strains and displacements at OGDENSBURG and KYOTO. Q = 2000 p.
Table 2
11.21
11.13
10.96
10.83
19-63
19.82
1830
1803
1750
1706
2923
2737
m
CL
f:
s
1
P
b
v
4
412
Ari Ben-Menahem
meter to calculated values that were taken from tables of Ben-Menahem, Rosenman &
Harkrider (1970). Two theoretical solutions were obtained:
(1) A dip-slip fault at h = 60 km with 6 = 80".
(2) A dip-slip fault at h = 10 km with 6 = 45".
The fit with the second solution is shown in Fig. 4.
The observed spectral ratios in this figure were multiplied by (CJC,) x cot ct
where a is the angle that the strain rod made with the direction of the wave approach.
The calculated values were divided by the surface Rayleigh ellipticity, in order to
convert tabulated values of u, to u,.
To determine the polarity of the motion at the source we have used initial phases
of some well recorded surface waves. Details of their phase equalization is shown in
Table 3 and data pertinent to these signals is given in Table 4. Fig. 3 shows the NS
low-magnification strainmeter at Pasadena from which the signals G2 and R z were
taken. Phase velocities were calculated from the combinations G2- G4 and R, - R4
of the same record. Inversion of the observed initial phases yielded a solution
1 = 90"6 = 45" -go", h = 10- 60 km. where in all cases the oceanside is downthrown
and dipping under the continent.
In conclusion, the combined evidence from free oscillation amplitudes, spectral
ratio of G,/R, and initial phases of Mantle surface waves, point to a unique solution.
(Table 4). There is some freedom in the determination of the vertical extent. Surfacewave data require a shallow depth of 10-20 km but the longer wavelengths of the free
oscillations ' see ' a greater depth which does not exceed 100 km. We have therefore
fixed our final result midway between these two extremes.
300
250
200
150
I
I
I
I
A :90'
h = lOkm
-2
\
\
\
+
\
'.
.
+ - -+
Observed
-- --- --- ----
+ +
---------+ + -I
+
+
-----_-_
+
+
+ +
+
+
+ +
30
40
50
60
Frequency (mc s '1
FIG.4. Spectral ratio G Z / R 2of surface waves recorded at Pasadena, California,
from the Chile earthquake of 1960 May 22.
10
151.5
312.5
294-1
277.8
263-1
250-0
238.1
227.3
217.4
208 * 3
200.0
192.3
185.2
178.6
172-4
166.6
161-3
156.2
(s)
Period
5.383
5.251
5.132
5.012
4.917
4.824
4.754
4-674
4.616
4.569
4-517
4.469
4.436
4.407
4.374
4-348
4.319
4.299
CR
(km s-1)
-0.336
-0.344
-0.323
-0.283
-0.282
-0.240
-0.300
-0.254
-0.282
-0.329
-0.2%
-0.250
-0.290
-0.331
-0.328
-0.370
-0.374
-0.405
(Rz)
(4)
(4) ( R d =f((30796/Cd -7744)+f (step) -f (polar)+7- -(Fourier phase)
5.2
5.4
5-6
5.8
6.0
6-2
6.4
6.6
5.0
3.2
3.4
3-6
3.8
4.0
4.2
4.4
4.6
4.8
Frequency
(mc s-l)
-0.273
-0.270
-0.268
-0.265
-0.263
-0.261
-0.259
-0.257
-0.255
-0.254
-0.253
-0.251
-0.250
-0.248
-0.247
-0.245
-0.244
-0.243
0.169
0-175
0.181
0.188
0.194
0.200
0.205
0.21 1
0.217
0.223
0.229
0.235
0.240
0.246
0.252
0.258
0.264
0.270
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
Ra, Pasadena NS Strain, To = 180 ses:
corrections
Instrumental
finiteness
force system
Calculated us. observed initial phases of surface waves from the Chilean earthquake of 1960 May 22.
Table 3
0.109
0.075
0.042
0.052
0.018
0.048
-0.003
0.055
0.024
0.074
0.021
0.075
0.055
0.015
0.015
-0.035
-0.065
-0.064
Residuals
3
ew
B
1
B
cm
P
w
5
9
3
m
3
0.030
-0.020
-0.041
0.022
-0.048
0.109
0.027
0.094
0.086
-0.018
0.030
0.063
-0.026
-0.085
-0.089
-0.128
-0.052
-0.145
(km s-')
5.383
5.251
5.132
5.012
4.917
4-824
4.754
4 * 674
4-616
4.569
4.517
4.469
4.436
4.407
4.374
4.348
4.319
4.299
6)
312.5
294.1
277.8
263.1
250.0
238.1
227.3
217-4
208.3
200.0
192.3
185.2
178.6
172.4
166.6
161.3
156-2
151-5
(mc s-l)
3.2
3.4
3.6
3.8
4.0
4-2
4.4
4.6
4.8
-0.542
-0.536
-0.529
-0.523
-0.517
-0.555
-0.548
-0.595
-0.588
-0.581
-0.574
-0.568
-0.561
-0.602
-0.630
-0.623
-0.616
-0.609
Instrumental
(6) (R4) = f((70269/C~)--17618)ft (step)1-2 (polar)+&(change to u,)+16- -(Fourier phase)
5.2
5.4
5.6
5.8
6-0
6-2
6.4
6-6
5.0
(6)
(R4)
CX
Period
Frequency
Table 3-conrinued
0.21 1
0.217
.0*223
0.229
0.235
0.240
0.246
0.252
0.258
0.264
0.270
0.205
0-169
0.175
0.181
0.188
0.194
0.200
R4, Berkeley Z, 30-90
Corrections
finiteness
-0.056
-0.093
-0.100
-0.024
-0.081
0.089
0.019
0.099
0.104
0.012
0.073
0.118
0.041
0.375
0.375
0.375
0-375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0-375
0.375
0.375
0.375
0.375
0.375
0.375
-0.017
0.064
0.002
-0.024
-0406
Residuals
force system
P
P
a
c
if
k
%
e
km s - 1
(s)
312.5
294.1
277.8
263.1
250.0
238.1
227.3
217.4
208.3
200.0
192.3
185.2
178.6
172.4
166.6
161.3
156.2
151.5
3.2
3.4
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
-0.471
-0.464
-0.430
-0.427
-0.422
-0.422
-0.442
-0.458
-0.435
-0.243
-0.281
-0.317
-0.349
-0.376
-0.400
-0.412
-0.423
-0.432
(5)
(Gal
-0.273
-0.270
-0.268
-0.265
-0.263
-0.261
-0.259
-0.257
-0.255
-0.254
-0.253
-0.251
-0.250
-0.248
4.247
-0.245
-0.244
-0.243
Instrumental
0-217
0.225
0.234
0.242
0.251
0.260
0.268
0.276
0.285
0.293
0.302
0.310
0.208
0.166
0.175
0.183
0.192
0.200
Corrections
finiteness
0.375
0.375
0.375
0.375
0.375
0-375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0.375
0-375
0.375
0.375
force. system
Gz,Pasadena NS Strain, TI= 180 sec
(5) (Gz)= f((30796/CL) -6694)+$ (step)-* (polar)++ (strain polarity)+4-(Fourier phase)
4.972
4.940
4.911
4.885
4.861
4.840
4.821
4.804
4,790
4.776
4.761
4.748
5.008
5.047
5.088
5.243
5-185
5.134
C'
Period
Frequency
(mc s- ')
Table >-continued
-0.078
-0.072
-0.057
-0.043
-0.029
-0.019
-0.029
-0.035
-0.031
-0.029
-0.064
-0.078
-0.080
-0.080
0-025
-0*001
-0.027
-0.047
Residuals
O S 5 r o s19
R4, G4
os2, os5, os19
9381 (84.3")
40,023
324.6"
315'f 2"
145-9"
N32" W, strain
9775 (87.9")
40,024
323.5"
314"f 2"
143.5"
Z, Press-Ewing
30-90
70&-1000 km
3-4 km s - 1
-6okm
-20 m
20ooP
step
9" k 2" West of South
90"
-45" to the east with oceanside down
N
38" S
73.5" w
19-11-17 GCT
M, 2: 8+
Source parameters
Rz, Gz
osz,
9226 (82-9")
40,024
324.0"
315"f 2"
146"
NS, strain
2,Press-Ewing
30-90
Pasadena (1,2)
Isabella (1,2)
Berkeley (1,2)
34.150"N 118.171" W 35.663" N 118.473" W 37.876"N 122.235" W
(1) Ben-Menahem, A., Ph.D Thesis, California Institute of Technology, Pasadena, California (1961)
(2) Smith, S.W.,Ph.D. Thesis, California Institute of Technology, Pasadena, California (1961)
(3) Alsop et al. (1961); (4) Sato & Takeuchi (1963)
Fault-length, b (1)
Rupture velocity, u (1)
Vertical extent, H
Dislocation, uo
Specific amplitude, Q
Time function, H ( t )
Azimuth of strike ( I )
Slip of fault, X
Dip of fault, 6
Source coordinates (USCGS)
Origin time
Richter's magnitude
Signals
Distance, km
Great circle, km
Azimuth (from north)
Azimuth (from strike)
Inverse azimuth
sensors
Station
Co-ordinates
350.1"
8"f 2"
179.1"
N30" E, strain
40,009
8756 (78.7")
Ogdensburg (3)
41.067'N 74.617" W
17392 (156.3")
40,05 1
271.8"
263' f 2"
105-8"
Gravimeter
Kyoto (4)
35.030" N 135.787" E
Data used for the determination of the force system at the source of the Chilean earthquake of 1960 May 22.
Table 4
Force system of the Chilean earthquake
417
We have noticed that all USCGS aftershock epicentres up to 1960 November 1
were limited to focal depths less than 100 km. Furthermore, all aftershocks with
magnitudes above 6-75 were likewise restricted to a depth range of 60-90 km during
the period May 1960-May 1961. This supports our previous determination.
A few words must be said about the resulting force system. Benioff (1962) believed
that the large amplitudes of G waves in Fig. 2 (Fig. 13 in his paper) are evidence for
transcurrent faulting. But Isabella lies on a nodal line of the radiation pattern for a
pure strike-slip fault and one should not expect to see large Love waves there. Our
Tables 1 and 2 also show that one could not hope to explain the free oscillations
amplitudes at Kyoto, Isabella and Ogdensburg on the basis of a strike-slip source.
The Chile earthquake of 1960 May 22 could be best represented by dipslip faulting
on a fault dipping about 45" to the east, with the oceanside under-thrusting the
continent. This does not contradict Benioff's own model of western South America
tectonics. (Benioff 1962, p. 123, Fig. 14).
Acknowledgments
This research has been sponsored by the Air-Force Cambridge Research Laboratories under contract AF61(052)-954 through the European office of Aerospace
Research, OAR USAF, as part of the Advanced Research projects Agency's Project
VELA UNIFORM.
Departmed of Applied Mathematics
The Weizmann Institute of Science
Rehovot, Israel
References
Alsop, L. E., Sutton, G. H. & Ewing, M., 1961. Free oscillations of the earth
observed on strain and pendulum seismographs, J. geophys. Res., 66,631-641.
Benioff, H., Press, F. & Smith, S., 1961. Excitation of the free oscillations of the
earth by earthquakes, J. geophys. Res., 66,605-619.
Benioff, H., 1962. Movements on major transcurrent faults, pp. 103-134 in
Continental Drift edited by S . K. Runcorn, Academic Press.
Ben-Menahem, A., Israel, M. & Levit6, U., 1971a. Theory and computation of
amplitudes of terrestrial line spectra, Geophys. J. R. astr. Soc., 25, 309408.
Ben-Menahem, A., Rosenman, M. & Israel, M., 1971b. Source mechanism of the
Alaskan earthquake of 1964 from amplitudes of free oscillations and surface
waves, in press.
Ben-Menahem, A., Rosenman, M. & Harkrider, D. G., 1970. Fast evaluation of
source parameters from isolated surface-wave signals, Bull. seism. SOC.Am., 60,
337-387.
Sato, Y.& Takeuchi, H., 1963. Free oscillations of the earth observed by gravimeters
installed in Kyoto, Japan, Bull. Earth. Res. Inst., 41, 699-703.