VOL. 84, NO. B II
JOURNAL
OF GEOPHYSICAL
RESEARCH
OCTOBER 10, 1979
Reevaluationof the Turn-of-the-CenturySeismicityPeak
HIRO0
KANAMORI
AND KATSUYUKI
ABE I
Seismological
Laboratory,CaliforniaInstituteof Technology,
Pasadena,California91125
Accordingto currentlyavailableseismicitycatalogues,
seismicity(for example,the numberof events
with Ms -->8) aroundthe turn of the century,from 1897to 1906,wassignificantly
higherthan in recent
years.However,the magnitudesof the earthquakeswhich occurredduring this periodwere determined
by Gutenberg,whousedtherecordsobtainedby the undampedMilne seismograph
with the assumption
that the effectivemagnification
is 5. Because
of saturationof the Milne seismogram
for verylargeevents
usedby Gutenbergfor calibration,the gain (-- 5) usedby Gutenbergcouldhave been underestimated,
and thereforethe magnitudeoverestimated.
Becauseof the lack of damping,the magnificationof thisinstrumentneedsto be calibratedcarefully.In orderto calibratethe instrumentresponse,
a Milne seismographwasconstructed
and hasbeenin operationsideby sidewith dampedseismographs
at Pasadena.
EleveneventshavebeenrecordedsinceFebruary1977.On the basisof (1) comparison
of the amplitudes
measuredon the Milne seismograms
with thoseof the standardseismograms,
(2) numericalexperiments
simulatingthe response
of the Milne seismographs
to surfacewaves,and (3) examinationof Gutenberg's
originalmaterialsusedfor thecalibration,we concludethat the averageeffectivegainis aslargeas20 for
very largeearthquakes,
resultingin systematic
reductionof the magnitudeof up to 0.6. This reductionis
largeenoughto suggest
that the turn-of-the-century
seismicitypeakis of marginalsignificance.
INTRODUCTION
The purposeof the presentstudyis to reevaluatethispeak
by
constructing
and operatingan undampedMilne seismoAccordingto currently available seismicitycatalogues[e.g.,
graph
at
Pasadena.
Fortunately,Gutenberg'soriginalwork
Gutenberg,1956a;Richter, 1958] the number of earthquakes
largerthan Ms (surfacewave magnitude)-- 8 was significantly sheetsusedfor the 1956paper were found in the archivesof
larger around the turn of the century,from 1897to 1906,than Millikan Memorial Library, California Institute of Techin recentyears (Figure 1). The data used in Figure 1 for the nology.Thismaterialis extremelyusefulfor thepresentstudy.
procedure.
period from 1897to 1903 are taken from Richter[1958], who By usingthismaterialwe firstfollowGutenberg's
converted the magnitudes, rn, determined by Gutenberg
GUTENBERG'S STUDY
[1956a]to the valuescorrespondingto the surfacewave magIn order to determinethe magnitudethe gain of the seismonitude, Ms. For the period 1904 to 1952 we used the surface
that Gutenberg
wave magnitudeMs listed by Gellerand Kanamori [1977]. Ex- graphmustbe known.The Milne seismograph
ceptfor a few eventsthe valuesof Ms of Geller and Kanamori [1956a]usedis an undampedsystem,and its effectivemagnifiare essentiallythe sameas the magnitudeslistedby Gutenberg cation for transientseismicwavesis not known very well. Guand Richter [1954]. For the period 1953 to 1977 the surface tenberg[1956a]calibratedthis instrumentby using 16 large
whichoccurredduringthe periodfrom 1904to
wave magnitude determined by Abe and Kanamori [1979] is earthquakes
used.Thus the magnitude scaleusedin Figure 1 is considered 1907. For these events both Milne seismogramsand the
seismograms
recordedby moreadvanceddampedinstruments
to be uniform throughoutthe entire period.
were
available.
The surface wave magnitude Ms of these
As was demonstratedby severalrecent studies[e.g., Kanamori, 1977],the surfacewave magnitudeMs saturatesfor very events had been determined from the amplitude data obIn thesedeterminations,
large earthquakes.Therefore the increasein the number of tainedby the dampedseismographs.
Gutenberg's
[1945]
method
was
employed.
Gutenbergusedthe
earthquakeswith a large Ms doesnot necessarilyindicate an
amplitude
of
surface
waves
having
periods
of about20 s and
increasein the total energy releasedby earthquakes.Nevertheless,this peak in the number of large eventsis so remark- determinedMs using the amplitude-distancefunction given
[1945,Table 3].
able that it has attractedconsiderableinterestof geophysicists by Gutenberg
Gutenberg's
[1956a]methodof calibrationis as follows:he
in the past.
Gutenberg[1956a] argued that the averageannual energy first usedthe maximum trace amplitude,4, (haft the peak-toreleaseduring the period 1896to 1906is about 3 times larger
than that for the period from 1907 to 1955. Unfortunately,
most seismographsoperated prior to 1904 were without a
dampingdevice,so the magnitudedeterminationwas inevitably unreliable.Gutenberg[1956a]madean extensiveinvestigation into this problem by using records obtained by undampedMilne seismographs
(see,for example,Reid [1912]for
the Milne seismograph;examplesof the seismogramswritten
by the Milne seismographare given by Richter [1958, p. 272]
and Walker [1913,Plates8 and 9]).
peak amplitude)on the Milne seismograms
reportedin the
publications
of the BritishAssociation
for the Advancement
of Science(for references,see Gutenberg[1956a]). Then he
calculatedthe magnitude Ms* by
Ms* = log (At/G) -1-Q(A) + s
(1)
whereQ(A) is the Q functionlistedby Gutenberg
[1945](i.e.,
Q -- 1.656log A + 1.818),s is the stationcorrection(listedby
Gutenberg[1956a]),and G is the effectivegain of the seismograph.The Q functionusedhereis identicalto that usedfor
the Ms determination.Gutenberg[1956a]adjustedG to make
Ms* equalto Ms.He foundthat G = 5 is mostsatisfactory.
Ac• Now at Department
of Geophysics,
Facultyof Science,
Hokkaido
ttmlly,Gutenberg
[1956a]madeall the calculations
by usingthe
University,Sapporo,Japan060.
magnitudescaleon the body wave basis,m, insteadof
Copyright¸ 1979by the AmericanGeophysicalUnion.
Papernumber9B0849.
0148-0227/79/009 B-0849501.00
SinceMs and rn are numericallyrelated by Ms = 1.59m- 4.0
6131
6132
KANAMORIAND ABE:TURN-OF-THE-CENTURY
SEISMICITYPEAK
Annualnumberof events,
Ms_>8
9
-
I
I / //1/,' /
/,,(,/ ß/
1897-1903
-
,
•
/•..•
o
1890
[- /
I
1900
1910
1920
1930
1940
19,50
1960
1970
7[,/
Fig. 1. Annual numberof earthquakeslargerthan M, = 8. Solid
circlesshowthe resultsobtainedfrom currentlyavailablecatalogues
(for 1897-1903:Richter[1958];for 1904-1952:Gutenbergand Richter
[1954] and Geller and Kanamori [1977]; and for 1953-1977:•4be and
Kanamori[ 1979]).Open circlesfor the period 1897-1903indicatethe
revisedvaluesobtainedby the presentstudy.
[Gutenberg, 1956a, b], there is no fundamental difference
whetherrn or M, is used.An illustrativeexamplefor the 1906
San Franciscoearthquakeis givenby Gutenberg[1956a].The
valuesof rn and M, for these16 eventsare listedby Gutenberg
1904
-1907
M:From
Milne
(G=5•
I /
1980
Yeor
-
/9, */
Ms FromDamped
I
7
I Seismøg,rap
h
8 Ms
.9
Fig. 2. Relation betweenM,* (the surfacewave magnitudedetermined from the Milne seismograms
with the assumptionthat the gain
is 5) and M, (the surfacewave magnitudedeterminedfrom the recordsof dampedseismographs).
Arrows indicatesaturatedcases.The
solidline indicatesthe relation betweenM,* and M, suggested
by the
present study. The dotted lines indicate the relations obtained with
different assumptions.
We firstrepeated
Gutenberg's
[1956a]procedure
'by using
[1956a] and Richter[ 1958],respectively.
M•. Table 1 showstwo examples,one for the 1906 Ecuador
earthquake(M• -- 8.7) and the other for the 1906 San Fran-
TABLE 1. M•* of the EcuadorEarthquakeof January31, 1906,and
the San FranciscoEarthquakeof April 18, 1906
ciscoearthquake(M• = 8.3). The resultsfor the remaining14
eventsare shownin Table A-3 (seealsoTable A-2) in the appendix.' The amplitude.4 in thesetablesrefersto the maxi-
Station
A,
deg
A,
tzm
M•*
mum ground displacement,in microns,calculatedwith the assumptionthat G = 5. Figure 2 comparesM, and M•* for the
Ecuador,M• = 8. 7
Shide
Kew
San Fernando
83
82
80
>4000
>3400
>3500
Capetown
99
1000
8.1
Azores
56
1600
7.9
Toronto
Victoria
43
59
>4000
3200
>8.1
8.3
Alicante
155
>4000
>9.0
Bombay
150
Kodaikanal
Beirut
Baltimore
156
112
39
>4400
2000
>3200
>9.1
8.5
>8.0
lrkutsk
Honolulu
126
79
>3400
>8000
>8.8
>8.9
3040
>8.6
>8.5
>8.5
8.9
Tokyo
127
1700
8.5
Christchurch
Colombo
102
160
3100
2800
8.6
8.9
Average
8.5
San Francisco,M• = 8.3
Shide
77
4000
8.5
73
113
1460
3400
8.1
8.7
Bombay
121
1260
8.4
Kodaikanal
128
500
8.0
Azores
Calcutta
Batavia
125
600
8.1
Helwan
Trinidad
Perth
108
61
132
900
2000
550
8.1
8.1
8.1
Wellington
Tokyo
95
73
1800
900
8.3
7.9
Christchurch
Colombo
Mauritius
Kew
100
120
162
75
1360
1500
1000
>3400
8.3
8.4
8.5
>8.5
Edinburgh
Paisley
73
75
>3400
>3400
>8.4
>8.5
San Fernando
Toronto
lrkutsk
85
33
81
>3500
>4000
>3400
>8.6
>7.9
>8.5
Average
8.3
A is the distance,and •4 is the amplitudeof the groundmotion,in
microns,calculatedfrom the maximumtraceamplitudeon the Milne
seismograms
with the assumption
that themagnificationis 5.
16 events.As Gutenberg[1956a]noted, M•* seemsto agree
very well with M•. However, during the courseof this comparisonwe noticed a rather seriousproblem.As indicated in
Table 1, many seismogramsused for the calibration were off
scale.In thesecases,Gutenberg[ 1956a]usedthe valueswhere
the saturationoccurred.SincemostMilne seismographs
used
recordingpapersabout 35 mm wide, saturationmust have occurred at M• = 8.6, 8.3, and 8.1 at a distanceof A -- 90ø, if G =
5, 10, and 15, respectively.As shownin Table A-3 in the mi-
croficheappendix,the saturationoccurredfor fiveout of eight
eventslargerthan M, = 8. In Figure 2 the saturatedcaseis indicatedby an upwardarrow attachedto the data point. Saturation could cause underestimation of M•*, which in turn
wouldresultin underestimation
of the effectivegain G.
For earthquakessmaller than M• = 7.7 the agreementbetween M•* and M• seemsvery good. Thus the effectivegain
appearsto depend on M,.
MILNE
SEISMOGRAPH
In order to investigatethe calibrationproblemof the undamped Milne seismograph,we decidedto operatea Milne
seismograph
side by side with the standarddampedseismographsystems
at the Seismological
Laboratoryof the California Institute of Technology.To the authors'knowledge,at
least two original Milne seismographsstill exist, one at the
Science Museum in London and the other at the National
Sci-
ence Museum in Tokyo. However, both of theseare on exhibit
now and are not in operational condition. We therefore de-
cidedto build one followingthe originalmanufacturer's
manual [Munro, 1908]kindly made availableto us by A. McCannell of the ScienceMuseum, London. We also referred to Reid
[ 1912]and a detaileddescriptionkindly providedby T. Usami
• Tablesare availablewith entirearticleon microfiche.Order from
AmericanGeophysicalUnion, 2000 Florida Avenue,N. W., Washington, D.C. 20009. DocumentJ79-006;$01.00.Paymentmust accompanyorder.
KANAMORI AND ABE: TURN-OF-THE-CENTURY SEISMICITY PEAK
160 ø
i
120 ø
I
•
80 ø
I
40 ø
l•,.21
•,
,
0o
j
I
40 ø
•
I
80 ø
i
I
120 ø
•
613 3
160 ø
I
I
I
I
,•'
60 ø
I•
Toro_nto• Fernando.,
40 ø
20 ø
Honolulu
Trimdad
0o
20 ø
] e_r../
Capetown
/ ,covo
40 ø
'
(/
60 ø
P..-•--• •
'•
/
Christchurch-2
/
Wellington
/
(1897to 1903)
Fig. 3. Stationswhichoperatedthe Milne seismograph
duringthe periodfrom 1897to 1903.
of the University of Tokyo. In the constructionthe original figure, two curves are shown for two cases with different
seismograph
was copiedas closelyas possible,exceptfor the damping. In the figure, h is the damping constant,E -- exp
recordingdrum. We used a larger recordingdrum to obtain [•rh/(l - h2)'/2] is the damping ratio, and Q = l/2h is the
highertime resolution.It is unlikely that this modificationaf- quality factor. Sincethe magnificationchangesvery rapidly as
fectsthe overall responseof the instrument.Hereafter,we will a function of period, the effectivemagnificationof this system
call this newly built Milne seismographthe PasadenaMilne for a transient input signal dependsupon various factors,such
seismograph.
The natural period and the staticmagnification as the period, the wave form, the duration of the signal, the
of this instrumentare 15 s and 4.5, respectively.
complexity, and the dispersioncharacteristics.Sincethe wave
The details of the Milne seismographare describedby Reid form of earthquakesurfacewaves dependsvery stronglyon
[1912]. The instrumentconstantsof the Milne seismographs the nature of the path (oceanicor continental), the epicentral
which were in operation at various stations in the world distance,the magnitude of the event, and the depth of the
aroundthe turn of the centuryare listedin variousissuesof
the Bulletinof the BritishAssociation
for the Advancement
of
Science. These constants are summarized in Table A-1 in the
microficheappendix.The averagenatural period To is 17.5 s,
and the staticmagnification V is 6.0. Figure 3 showsthe distribution of the stations.In total, about 35 stationswere in operation. Although not all of thesestationswere operationalduring the entire period from 1897to 1903,the stationcoverage
was reasonablygood toward the end of this period. Thus if
calibration of the instrument could be made properly, a reasonablygoodestimateof the magnitudemay be expected.
The di•culty of the calibrationof undampedinstrumentsis
well known. As shown by Figure 4, the magnification becomesvery large at the resonantperiod (T = 17.5 s). In the
events,the effectivemagnificationof the undampedseismogram must stronglydependon thesefactorstoo. Therefore
calibration must be made by recordingvariousearthquakes
by both the Milne seismographand a damped seismograph
with known
characteristics.
Another uncertain element is the actual damping constant
of the Milne seismograph.Although the Milne seismograph
has no specialdamping mechanism,slight damping is caused
either by solid friction at the pivot and/or viscousfriction due
to air. Unfortunately,the dampingcharacteristics
of the original Milne seismographsare not describedin the literature in
detail. According to Walker [1913, p. 22] the damping constant h is 0.0257 (E - 1.084, Q = 19.5), and Knott [1908, p. 81]
noted that the Milne seismographat Edinburgh had h =
0.0683 (E = 1.24, Q = 7.32). Our Pasadena Milne seismo300
graph,when it wasinitially built, had very little damping,h =
0.014 (E = 1.05, Q -- 35). In order to increasethe dampingto
/Q: 50
h =001
_
_
that describedby Walker [1913] and Knott [1908], we had to
I00
add a very weak magneticdamper to the seismographboom.
50
The damping constant of the Pasadena Milne seismograph
c 30
with the magneticdamper is h = 0.05 (E -- 1.17, Q - 10). If
•_ 2o
the damping of the original instrument was mainly due to
solid friction at the pivot, damping characteristicscannot be
describedby the damping constanth. In this case,h should be
consideredthe effectivedamping constantthat approximates
V=6
3
the actual damping characteristics.The reasonwhy the PasaTo:175
dena Milne seismographwithout a damper had much smaller
damping than the original instrumentis not clear. One possibility is that the Pasadena Milne seismographhas a pivot
5
I0
15
20
25
0
35
made of hardened steel and sapphire,while the original inPeriod, sec
strumentprobably had a pivot made of hard metals.
Fig. 4. Static magnification curve for the Milne seismograph.
In any case,if h is smallerthan 0.1, the magnificationis sigNote that the gain is substantiallyhigher than 5 (value assumedby
Gutenberg) in the period rangefrom 10 to 23 s.
nificantly larger than the static magnificationover a period
_
6134
KANAMORI AND ABE: TURN-OF-THE-CENTURY SEISMICITY PEAK
TABLE 2. Comparisonof the MagnitudeDeterminationby Using the PasadenaMilne Seismograph
and the Standard Seismographs
Event
I
2
3
4
5
6
7
8
9
10
11
Date
Aug. 19, 1977
Feb. 19, 1977
Sept.4, 1977
Sept.4, 1977
Aug. 31, 1977
Sept.4, 1977
Nov. 23, 1977
March 24, 1978
Feb. 9, 1978
June 12, 1978
June 17, 1978
Epicenter
Indonesia
Aleutian Islands
Aleutian Islands
Aleutian Islands
Colombia
New HebridesIslands
Argentina
Kurile Islands
Kermadec Islands
Japan
Tonga Islands
ZX,
deg
M•
(Pasadena)
120
53
50
50
46
85
82
67
83
75
72
M $,t *
G
8.0
8.8
6.6
7.5
10.0
7.94
6.1
6.4
6.3
6.2
7.0
7.7
7.7
7.4
7.3
8.6
50.1
25.1
15.8
15.8
50.1
7:2
7.2
8.2
8.2
12.6
12.6
7.5
7.2
8.1
8.2
5.01
12.6
G is the effectivegain of the Milne seismographdeterminedfor the individual event.
range shorterthan 25 s, as shownin Figure 4. Sincethe average staticmagnificationis 6, it is difficultto understandwhy
Gutenbergobtainedan effectivegain as low as 5.
As will be shownlater, the dampinghasa very largeeffect
on the effective magnification. When h was increasedfrom h
- 0.016(E = 1.05,Q -- 32) to h -- 0.058(E - 1.2,Q = 8.6), the
effectivegain was reducedby approximatelya factor of 2.
Since installationof the PasadenaMilne seismograph
was
completedwe have recorded11 largeeventslistedin Table 2.
An example is shownin Figure 5. In the table the maximum
trace amplitudeson the PasadenaMilne seismogramA, and
the surfacewave magnitudesMs determinedat Pasadenaare
listed. Following Gutenberg[1956a],the determinationof the
effectivegain G was made as follows.
The surfacewave magnitudeMs can be written as
in the world and of the recentdeclinein the activity of large
earthquakes [Abe and Kanamori, 1979], the data shown in
Table 2 are inevitably biasedtoward oceanicpathsand smallmagnitude events. In order to supplementthe data we made
numerical experimentsby usingthe surfacewave signalsrecorded at Pasadena.
NUMERICAL
EXPERIMENTS
In order to investigatethe overall responseof the Milne
seismograph we calculated synthetic seismogramswhich
would be recordedby the Milne seismographby usingthe observedsurfacewave groundmotion as the input. We chose10
large events listed in Table 3. We used surfacewave records
obtained by a vertical component of short-period Benioff
seismograph(pendulum period, 1 s; galvanometerperiod, 0.2
s) and deconvolvedthem by usingthe instrumentresponseto
Ms = log (A,/G) + Q(A) = M $,t * - log G
(2)
obtain ground motions. Then we convolvedthem with the inwhere
strument responseof the Milne seismographto obtain synthetic seismograms.We assumedthat the amplitude of the
M * = log,4, + Q(a)
(3) horizontal component is 70% of that of the vertical comHere Q(A) is the Q functiondeterminedby Gutenberg
[1945]. ponent. As shown in Figure 7, the amplitude of the synthetic
Ms.,* definedby (3) can be calculateddirectlyfrom the record seismogramsdependson the damping of the instrument.We
and can be regardedasthe magnitudewhenthe effectivegain chosethe instrument constantsto be the same as the average
is assumedto be unity. The valuesof Ms.,* are listedin Table valuesgiven in Table A-1 (i.e., To-- 17.5s, V-- 6.0) and as2. In order to adjustthe differencebetweenthe averagestatic sumed that h -- 0.058. Then we measuredA, and calculated
magnificationof the Milne seismographswhich were in use Ms.,*. Two examplesare shownin Figure 8. Figures7 and 8
around the turn of the century (x6.0) and that of the Pasadena Milne seismograph(x4.5), the valuesof A, in Table 2
weremultipliedby 6/4.5 in the calculationof Ms.,..
The valuesof Ms.,*andMs areplottedin Figure6. The solid
linesshowthe trend for differentvaluesof G. From this figure
the value of G can be determinedfor eachevent.Althoughthe
value of G variesover a very wide range, G is larger than 5 in
all cases.The averageof G is 19.8.
Unfortunately, becauseof the geographicallocation of
Pasadena
with respectto the distribution
of largeearthquakes
Kur•le Is. Earthquake
March24, 1978 A=67ø, MS=7
2
•
/ •/•)?•,•.%0
ßNumericel
/6/ø/
/•/
6•
........
i'-•.......
Pasadena M•lne Seismograph E-W
To:IS sec, V:45, h:005
I m•nI tcm Cohbrohon
w
o3
Milne
8 M*
9
Fig. 6. RelationbetweenM• (Pasadena)
and M•,t* (surfacewave
magnitudedeterminedfrom the Milne seismograms
with the assumption that the gain is equal to 1. Solid lines indicate the relations for
Fig. 5. A surfacewave train from an earthquakein the Kurile Is- variousvaluesof G (gain). Solidcirclesare the resultsobtainedby the
landsrecordedby the PasadenaMilne seismograph.
Note the damp- numericalexperiments,
and opencirclesare the resultsobtainedwith
ingcharacteristic
indicatedby 'calibration.'
thePasadena
Milne seismograph.
KANAMORI AND ABE: TURN-OF-THE-CENTURY SEISMICITY PEAK
6135
TABLE 3. Resultsof NumericalExperimentto Simulatethe Response
of the Milne Seismograph
Event
Date
Epicenter
deg
(Pasadena) Mr,,*
G
I
Dec. 2, 1972
Mindanao Islands
105
7.5
8.7
15.8
2
3
4
May 26, 1975
May 10, 1975
July 20, 1975
North Atlantic
Chile
Solomon Islands
80
82
90
8.1
7.8
7.8
9.4
9.3
8.7
20.0
31.6
7.9
5
Dec. 28, 1973
New Hebrides Islands
6
7
Aug. 16, 1976
June 17, 1973
Mindanao Islands
Japan
8
9
10
Jan. 10, 1974
Oct. 3, 1974
Dec. 15, 1971
New Hebrides Islands
Peru
Kamchatka
89
7.0
8.6
39.8
108
72
7.7
7.7
9.0
9.0
20.0
20.0
88
62
59
7.0
7.5
7.3
8.5
8.5
8.4
31.6
10.0
12.6
illustrate the difficultiesof using undamped instrumentsfor
the amplitude measurement. For a prolonged wave train
caused by dispersionalong oceanic paths (Solomon Island,
Figure 7a; and New Hebrides,Figure 8a) the amplitudeof the
synthetic seismogramsbecomes very large owing to resonance.However, for wave trains with relatively short duration
(for example, central Chile, Figure 8b) the growth of the amplitude is relatively modest.Thus it is not surprisingthat the
effectivegain variesvery much accordingto the path.
The values of Mr,,* and Ms determined at Pasadenawith
damped seismographs
are plotted in Figure 6. Again, the effectivemagnificationis larger than 5 in all cases.The average
of the effectivegain G is 20.9.
However, the following two problems need be considered
further. First, Gutenberg[1956a] obtained a good agreement
between Ms* and Mr for smaller earthquakesunder the assumption that G -- 5. Second,the damping of the original instrument appears significantly larger than that of the Pasadena Milne seismograph (without a magnetic damper),
suggestingthat the dampingof the original instrumentis partially due to solid friction at the pivot.
As is well known [e.g., Cloud and Hudson, 1961], the effect
of solid friction is more pronouncedwhen the amplitude is
very small. Once the amplitude exceedsa certain threshold,
motion of the pendulum overcomessolid friction. Thus one
possibilityis that for relatively small magnitude (Mr --<7.7)
events, the amplitude of the pendulum motion is not large
enough to overcome solid friction completely, resulting in a
THE EFFECTIVE GAIN OF THE MILNE SEISMOGRAPH
relatively small effective magnification. On the other hand,
As shown by Figure 6, the resultsobtained by both the
when the magnitude is large, the effect of solid friction bePasadenaMilne seismographexperimentand the numerical
comesrelativelyunimportant,and the effectivemagnification
experiment suggestthat the effective gain is significantly increases.
larger than 5, probably about 20. This resultsuggests
that satWith theseconsiderationswe estimatedthe effectivegain in
uration of the Milne seismograms
for very large earthquakes
the following manner. Our basicphilosophyis that inasmuch
causedunderestimationof the effectivemagnification(Figure
as Gutenberg used a very large number of Milne recordsfor
2). If the gain is 20 insteadof 5, it would causean error in the
calibration,we use Gutenberg's
[1956a]resultsas much as posmagnitudeof 0.6, which is very significant.
sible with only modification to remove the effectof saturation.
We thus assumedthat the effectivegain G is 5 for Mr --<7.7
(a)
(seeFigure 2) but gradually increasesto 20 until Mr = 8.7 (the
Solomon
Is. July20, 1975 Ms=7.8
&=90 ø
magnitude of the largestevent usedfor calibration) is reached.
For Mr -->8.7, G is set equal to 20. Although there is no com••
•••
Io.z
pelling reason why the maximum gain G = 20 should be
E:I2
,• I
reachedat Ms -- 8.7, it is probably reasonableto assumethat
/•••
mm
the transition
from
friction-controlled
state to friction-free
E:I.O$
(a)
T :17.$
sec, V:6
i rain
New HebridesDec 28, 1973 Ms=7.0
A =89ø
mm
(b)
N Afionfic•oy 26, 1975 •=8.1
•:80 •
u
_•c)J
(b)
CentralChile,MayI0, 197.5 Ms=78
A=82ø
mm
o:
,
:
E
=1.2
Fig. 7. Surfacewavegroundmotions(U) and the response
of the
Milne seismograph
computedfor two dampingconstants.(a) SoloFig. 8. Surfacewave ground motionsand the responseof the
mon Islandsearthquakeof July 20, 1975. (b) North Atlantic earth- Milne seismograph.
(a) New HebridesIslandsearthquakeof Decemquake of May 26, 1975.
ber 28, 1973.(b) Central Chile earthquakeof May 10, 1975.
6136
KANAMORI AND ABE: TURN-OF-THE-CENTURY SEISMICITY PEAK
statetakesplacein I magnitudeunit, or a factorof 10 increase
in the amplitude [seeCloudand Hudson,1961,Figure 4]. The
Ms (real surfacewave magnitude)versusMs* (surfacewave
magnitude determinedfrom Milne seismograms
with G -- 5)
TABLE 4.
relationwe thus assumedis shownby the solidline in Figure
2. Actually, changingthe upper boundin the magnitudefrom
8.4 to 9 does not substantially affect the Ms versus M•* as
shownby the dashedlinesin Figure2.
List of Great Shallow Earthquakes 1897-1903
Time,
Earthquake
Date
GMT
Epicenter
Q
Ms*
C
C
(7.8)
(>7.5)
Region
1897
I
2
Feb. 7
Feb. 19
7.6
3
Feb. 19
20.8
23.8
4
May 13
12.5
5
June 12
11.1
6
7
8
9
10
Aug. 5
Aug. 15
Aug. 16
Sep. 20
Sept. 2 l
0.2
11
12
Oct. 18
Oct. 20
23.8
13
Jan. 24
23«
14
15
April 22
April 29
23.6
16.3
40øN, 140øE
38øN, 142øE
38øN, 142øE
C
12øN, 124øE
26øN,91øE
38øN,143øE
D
A
C
12.3_+
18øN, 120øE
D
7.9
39øN,143øE
6øN,122øE
6øN,122øE
12øN,126øE
12øN,126øE
C
D
D
D
D
19.1
5.2
14.4
'--
(7.7)
(>8.4)
(>8.2)
(7.8)
(>7.5)
...
(7.7)
(>8.2)
(>8.1)
'"
(7.7)
(>8.2)
(>8.2)
(8.1)
(8.0)
(7.7)
(>8.1)
(>8.1)
(8.0)
(7.9)
Japan
Japan
Japan
Philippine Islands
India
Japan
Philippine Islands
Japan
Philippine Islands
Philippine Islands
Philippine Islands
Philippine Islands
1898
16
June 29
17
Aug. 31
18.6_+
19.9_+
18
Nov.
12.8_
19
Jan. 24
2343_+
20
21
June 14
1109_+
July 14
Aug. 24
Sept. 4
Sept. 10
Sept. l0
Sept. 29
13327
17
9
39øN,142øE
C
'7.9
7.9
12øN,86øW
B
7.5
7.5
(52øN,172øE)
G
8.1
8.0
(26øS,68«øE)
(16«øS,168«øE)
G
G
7.8
7.6
7.8
7.6
D
E
8.0
7.8
7.9
7.8
(60øN, 150øW)
(27øS,165øE)
G
G
7.7
......
7.7
60øN,142øW
60øN,140øW
60øN, 140øW
B
B
A
8.4
7.8
8.4
8.2
7.8
8.2
A
7.6
7.6
E
B
B
7.9
7.7
......
7.9
7.7
(5øS,148øE)
G
7.5
7.5
20øN, 105øW
20øN, 105øW
20øN,80øW
10øS,165øE
4øS, 140øE
60øN, 142øW
11øN,66øW
43øN, 146øE
C
D
F
F
F
C
B
C
7.9
7.4
7.7
8.1
7.4
8.2
8.2
7.6
7.9
7.4
7.7
8.0
7.4
8.1
8.1
7.6
E
C
E
C
E
C
D
D
7.7
7.9
7.7
7.8
8.4
8.0
7.5
7.7
7.9
7.7
7.8
8.2
7.9
7.5
7.5
7.5
Aleutian
55øN,165øW
8øS, 150øE
20øS, 174øW
D
D
D
7.5
7.7
7.4
7.5
7.7
7.4
off Alaska?
14øN,91øW
C
8.0
7.9
Guatemala
40øN,77øE
18øN,146øE
!6øN,93øW
29øN, 114øW
B
C
C
E
8.2
8.0
8.2
7.6
8.2
7.9
8.2
7.6
Marianne Islands
off' south Mexico
Gulf of California
Japan
Nicaragua
Aleutian Islands?
Indian Ocean?
SW Pacific?
1899
22
23
24
25
26
27
28
29
Nov.
23
Nov.
24
Nov.
24
1509_+
0022
1704
2141
1703
0949_+
1842
1855
17øN,98øW
18øN,77øW
3øS,128«øE
53øN, 159øE
32øN,131øE
32øN, 131øE
Mexico
Jamaica
Arctic near Alaska
SW Pacific
Alaska
Alaska
Alaska
Ceram
Kamchatka
Japan
Japan
1900
30
31
32
33
34
35
36
37
38
0907
Jan. ll
Jan. 20
0633«
May 16
2012
June 21
2052
July 29
0659
Oct.
Oct.
Oct.
Dec.
2104
7
9
29
25
1228
0911
0504
SW Pacific?
Mexico
Mexico
Caribbean?
New Hebrides?
New Guinea?
Alaska
Venezuela
Japan
1901
39
Jan. 7
40
April 5
41
June 24
42
Aug. 9
Aug. 9
Aug. 9
43
44
0029«
2330:]
0702«
0923.5
1301
45
Dec.
46
Dec. 31
1833,•
2257:]
0902«
47
Jan. 1
o52o«
48
49
Jan. 24
Feb. 9
2327
5O
52
53
April 19
Aug. 22
Sept. 22
Sept. 23
54
Dec.
14
2øS,82øW
45øN, 148øE
27øN,130øE
40øN,144øE
22øS, 170øE
40øN, 144øE
14øN, 122øE
52øN, 177øW
Ecuador
South Kurile
Islands
Ryukyu Islands
Japan
New Hebrides?
Japan
Philippine Islands
Islands
1902
51
12
0735«
0223«
0300
0146«
2o•8¬
2310_+
Bismarck
Islands
Tonga Islands
Turkestan
KANAMORIAND ABE:TURN-OF-THE-CENTURY
SEISMICITYPEAK
6137
TABLE 4. (continued)
Time,
Earthquake
Date
GMT
Epicenter
15øN,98øW
48øN,98øE
8øS,106øE
Q
Mr*
Mr
Region
D
D
D
8.2
7.5
7.9
8.1
7.5
7.9
off Mexico
SW of Lake Baikal
East Indies
1903
55
56
57
Jan. 14
Feb. I
Feb. 27
0147.6
0934.5
0043.3
58
May 13
0634.1
17øS,168øE
E
7.5
7.5
New Hebrides(h = 60 ñ km?)
59
Dec. 28
0256.0
7øN, 127øE
D
7.6
7.6
off Mindanao
This table lists all of the 59 eventslisted by Gutenberg[1956a, Table 3]. Epicenter:Gutenberg'sdetermination.Gutenbergassumedthe
epicentersof 16, 17, and 18 on the basisof seismicity.Gutenberg used the location noted by Milne for the epicentersof 21, 22, and 30. Q:
quality of location. See Gutenberg[1956a]. Mr*: surfacewave magnitudesdeterminedwith the assumptionthat the magnificationis 5.
Parenthesesindicate that Mr* was determinedonly from one or two station data. Mr* = log •4max+ 1.656log A + 1.818.Mr: correctedsurface
wavemagnitude.
The averagenumberof stations
usedin thecalculation
of Mr* is 2 (1897),4.(1898),•7(1899),9 (1900),13(1901),14 (1902),
and 15(1903).For theorigintimesof 49 and53,minorcorrections
weremadeon thebasisof theoriginalworksheets.
SURFACE WAVE
MAGNITUDE
FROM
OF THE EVENTS
1897 TO 1903
The amplitude data of Milne seismogramsfor the events
from 1897to 1903are listed in Gutenberg'sunpublishedwork
sheetsfor the 1956 paper. We used the publicationsof the
British Association
for the Advancement
of Science for the
period 1897-1903 to check and supplement Gutenberg's
notes. Gutenberg[1956a] determined rn by using these data
(with the assumptionof G -- 5), and Richter[1958]converted
rn to M by usingthe relation M -- 1.59m- 3.97. In order to
maintain consistencywith the scaleusedin our calibration,we
calculatedMr* from the original amplitude data by assuming
G -- 5. The results are listed in Table 4. Theoretically,
should agree with M, but our calculationsshowedthat M is
consistentlylarger than Mr*. This differenceis due to the fact
that Gutenberg[1956a] always rounded off the hundredths
digit and raisedthe tenthsdigit by I (for example,7.82 to 7.9).
Also, small roundofferrorsresultedfrom conversionof rn to M.
For many events in 1897, only one or two stationswere
available for the magnitude determination. The results for
theseeventsare very unreliable and are in the parenthesesin
Table 4. Apparently, Gutenberg[1956a] assignedthe magnitude to theseeventson his own judgments.The averagenumber of stations used for the calculation of Mr* in Table 4 is as
follows: 2 (1897), 4 (1898), 7 (1899), 9 (1900), 13 (1901), 14
(1902), and 15 (1903). Sinceonly 2 and 4 stationsare usedfor
1897and 1898,respectively,the resultsfor thesetwo yearsare
lessreliable. The station data for the larger earthquakesare
listed in Table A-4 (see also Table A-2) (microficheappendix).
If many stationswent off scale,the measurementof Mr* is
meaningless.However, as shown in Table A-4, most of the
stationswere on scalefor the eventsfrom 1897 to 1903. Only
for two events, the 1902 Turkestan event and the 1902 event
off south Mexico, four or more stations were off scale. We
therefore consider that most of the Mr* measurements in
Table 4 are meaningful.
We then convertedMr* to Mr by usingthe relation given by
the solid line in Figure 2. This Mr scalecan be consideredto
be identical to that defined originally by Gutenberg[1945].
Table 4 lists Mr thus obtained for the period from 1897 to
1903. For the two events, the 1902 Turkestan event and the
1902 event off south Mexico, the present calibration is not
meaningful becauseof the saturationof the records.We substituted the value of Mr* for Mr for theseevents.A small number of recordsobtained by Nicolajew instrumentswere also
used in Gutenberg's[1956a] study. However, •ince the deter-
minationsof the magnitudeswith the recordsof the Nicolajew
instruments were very few, we paid no particular consideration to thosedata in this study.
Recently,Thatcherand Plafker [1977]determinedthe magnitudes of three Yakutat Bay, Alaska, earthquakesin 1899
and 1900 by using a small number of early damped seismographicrecords.They obtained8.4 and 8.1 for the September 10, 1899, event and the October9, 1900,event, respectively, which comparereasonablywell with the valueslistedin
Table 4, 8.2 and 8.1, respectively.However, for the event on
September4, 1899, Thatcherand Plafker [1977] obtained 8.5,
which is significantlylarger than our value, 8.2. The causeof
this discrepancyis presentlyunknown.
From Table 4 the annual number of eventswith Mr -->8 was
obtained and plotted in Figure 1. If we ignore the unreliable
result for 1897, the peak around the turn of the century no
longerexists.The peak in 1906consistsof the January31 Colombia earthquake(Mr = 8.7), the April 18 San Francisco
earthquake(Mr -- 8.3), the August 17 Aleutian Islandsearthquake (Mr = 8.2), the August 17 Chilean earthquake(Mr =
8.4), and the September14 New Britain Islandsearthquake
(Mr = 8.1).
While studying Gutenberg'soriginal work sheetsfor the
1956 paper, we found additional data for 49 events,some of
which were mentionedin the 1956 paper. We determinedMr
for theseeventsby usingthe method describedabove.The resultsare listedin Table 5. The amplitudeand magnitudedata
for major earthquakeslistedin this table are givenin Table A5 (see also Table A-2, microfiche appendix). As mentioned
earlier, the resultsfor the 1896 and 1897 eventsare very uncertain.
CONCLUSION
Becauseof saturationof the Milne seismogramsfor very
large eventsusedby Gutenberg[1956a]for calibration,we suspect that the gain (-- 5) used by Gutenberg[1956a] is underestimatedand thereforethe magnitudeoverestimated.Our experiments using a newly constructedMilne seismographas
well as the numerical experiments using observed surface
wavessuggestthat the effectivegain can be as large as 20. Becauseof the unknown damping characteristicsof the original
Milne seismograph,we could not make definitive calibration
of the instrument.However, it is almostcertain from Figure 2
that the magnitudesof earthquakeslarger than Mr -- 7.7 listed
by Gutenberg[1956a]were considerablyoverestimated,in the
extremecaseby as much as 0.6 (-- log (20/5)). Assumingthat
the correction increaseslinearly from 0 to 0.6 as Mr increases
from 7.7 to 8.7, we correctedMr* (surfacewave magnitude
6138
KANAMORI AND ABE: TURN-OF-THE-CENTURY
TABLE 5.
SEISMICITY PEAK
List of Large Shallow Earthquakes 1896-1903
Time,
Earthquake
Date
GMT
Epicenter
Q
Ms
Region
1896
110
Jan. 9
13.3
120
March
130
140
150
160
May 5
June 15
Aug. 26
Aug. 31
23
10.5
23.3+
8.1
170
Nov. 1
5
4
5
(36øN, 141øE)
?
?
(40øN, 144øE)
?
(40øN, 141øE)
?
'"
(7.9)
Japan
G
..-
?
G
......
......
--.
'"
(>7.5)
G
---
?
Japan
Iceland
Japan
Tashkent?
1897
180
190
200
210
March 16
July 21
Sept. 17
Sept. 17
6.3+_
13
15.5+_
17.6+_
?
?
40øN,68øE
40øN,68øE
G
G
D
D
..'"
(7.1)
(7.3)
220
Dec. 29
11.3
19øN,73øW
C
7.4
Philippine Islands
North Atlantic?
Turkestan
Turkestan
Haiti
1898
230
April 15
7.2+_
39øN,123«øW
A
7.4
California
240
Oct. 11
1637«
50øN,180ø
D
7.4
Aleutian Islands
250
260
270
280
290
Jan. 14
April 12
April 16
Sept.4
Sept. 17
0236+_
1724+_
1342+_
0440+_
1250
(20øN, 110øW)
28øS,67øW
(58øN,138øW)
60øN,142øW
59øN,136øW
G
D
G
C
D
7.5
7.5
7.4
(7.4)
,7.3
300
Sept.20
0211«
38øN,28øE
B
7.3
Turkey
310
320
330
Sept.23
Sept.23
Dec. 25
1104
1250+_
1228+_
60øN,143øW
60øN,143øW
334aøN,117øW
D
D
A
7.4
7.5
7.1
Alaska
Alaska
California
340
Jan. 5
19007
3øS, 102øE
D
7.5
Sumatra
350
April 24
2313
(27øN,126«øE)
G
7.4
RyukyuIslands?
360
Nov. 9
1610
F
7.5
Mexico
370
380
Jan. 18
Oct. 8
0439?
0214«
(60øN,135øW)
13øN,87øW
G
F
7.6
7.6
off BritishColumbia?
Nicaragua
390
400
Nov. 15
Dec. 9
2015
0217
43øS, 173øE
26øN, 110øW
D
F
7.3
7.6
New Zealand
Mexico
410
Jan. 12
2218«
D
7.2
Celebes
420
Jan. 30
1400
41øN, 144øE
D
7.3
Japan
430
Feb. 13
0939
40«øN,48«øE
A
7.0
Caucasus
440
450
460
Feb. 17
March 28
June 11
0031
1444
0609+_
20øN,70øW
0ø,133øE
53øN,142øE
F
D
...
7.3
7.4
7.1
Antilles?
West New Guinea
Sakhalin?
1899
off Mexico?
Brazil
off BritishColumbia?
Alaska
Alaska
1900
13øN,90øW
1901
1902
3øN,122øE
470
Aug. 30
2148
40øN,77øE
...
7.3
Turkestan
480
Nov. 4
1133«
36øN,96øE
D
6.9
KunlunMountains
490
500
510
Nov. 20
Nov. 21
Dec. 16
2027
0703
0507
22øS, 170øE
23øN, 121øE
40øN,73øE
D
D
D
7.3
7.2
6.8
New Hebrides
Formosa
Turkestan
520
Jan. 17
1605
50øN, 170øW
'"
7.4
Aleutian Islands
530
540
Jan.24
Feb. 10
5.5
0253¬
31«øN,115øW
17øN,144øE
"'
D
7.2
7.0
lowerCalifornia
Guam(h = 60+_km?)
550
560
Oct. 21
Nov. 26
0957.0
1148.1
34øS,52øE
53øN, 107øE
D
D
7.1
7.0
Indian Ocean
Lake Baikal
570
Dec.7
1444«
27øS,70øW
C
7.3
Chile
1903
The epicentersof 110;140,and 160weretakenfrom the TokyoAstronomical
Observatory[ 1975]. For 250, 270, 350, and 370,Gutenbergused
the epicentersgivenby Milne, only for calculatingepicentraldistances.
For othercolumnheads,seefootnotefor Table 4.
obtained with the assumptionthat G -- 5) to obtain Ms. Thus
the values of Ms* in Table 4 may be consideredthe upper
limit of the surfacewave magnitude.Although we believe that
the values of Ms listed in Table 4 are the best estimateswe can
make under various considerations,they are still subject to
some uncertainty due to the rather erratic responseand the
limited dynamic rangeof the Milne seismograph.
Nevertheless,the suggested
reductionsin the magnitudeare
systematicand large enough to indicate that the turn-of-thecentury peak, if it exists,is of marginal significance.A recent
study by Abe [1979] showsthat the activity of tsunamigenic
earthquakes
duringthisperiodisnot higherthan that during
any other periods.Abe's result is consistentwith the present
conclusion.
KANAMORIAND ABE:TURN-OF-THE-CENTURYSEISMICITYPEAK
•4cknowledgments.
We thank N. Ambraseysof the Imperial Collegeof Scienceand Technology,London,England;A. McConnell of
the ScienceMuseum, London, England;and T. Usami of the Earthquake ResearchInstitute, Tokyo University,for providingus with
valuableinformationregardingthe originalMilne seismograph.
We
thank Karen MeNally for reviewingthe manuscript.We thank David
Hadley for providingus with the digitizedseismograms
usedfor the
numerical experiments.Francis Lehner and the technicalstaff of the
Seismological
Laboratoryof the CaliforniaInstituteof Technology
designedand operatedthe PasadenaMilne seismograph.
This research was supported by the National Science Foundation under
grant EAR77-13641.Contribution3179, Division of Geologicaland
Planetary Sciences,California Institute of Technology,Pasadena,
California
91125.
6139
Gutenberg,B., Great earthquakes1896-1903,Eos Trans.•4GU, 37,
608-614, 1956a.
Gutenberg,B., The energyof earthquakes,
Quart.J. Geol.Soc.London, 112, 1-14, 1956b.
Gutenberg,B., andC. F. Richter,Seismicity
of theEarth,2nded.,310
pp., PrincetonUniversityPress,Princeton,N.J., 1954.
Kanamori,H., The energyreleasein greatearthquakes,
J. Geophys.
Res., 82, 2981-2987, 1977.
Knott,C. G., ThePhysics
of Earthquake
Phenomena,
283pp.,Oxford
•t the Clarendon Press,London, 1908.
Munro, R. W., The Seismograph,15 pp., 103 Cornwall Road, South
Tottenham, London, 1908.
Reid, H. F., On the choice of a seismograph,Bull. Seismol. Soc.
•4mer., 2, 8-30, 1912.
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Abe, K., Size of great earthquakesof 1837-1974 inferred from tsunami data, J. Geophys.Res.,84, 1561-1568, 1979.
Abe, K., and H. Kanamori,Magnitudesof greatshallowearthquakes
from 1953to 1977,Tectonophysics,
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Tokyo AstronomicalObservatory,Science•41manac,
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Cloud, W. K., and D. E. Hudson,A simplifiedinstrumentfor record1975.
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(ReceivedNovember 14, 1978;
revisedApril 11, 1979;
acceptedMay 18, 1979.)