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ABSTRACT

 An investigation was conducted on the submarine earthquakes accompanied by tsunami which occurred in the vicinity of Japan during the 35 year period from 1923 to 1957.The magnitudes of these earthquakes are related to their focal depths and these various depths seemed to play an important role in the occurrence of tsunamis.The magnitude of an earthquake causing tsunami is generally found to be larger than
 M=6.42+0.017H,
and it is more than M=7.75+0.008H for disastrous tsunami.Shallow submarine earthquakes having a magnitude greater than 7.3 are always accompanied by tsunamis.
 Tsunami energy is derived from the relationship between the magnitudes of an earthquake and a tsunami.The tsunami magnitude m and the earthquake magnitude M are related through the empirical equation
 m=2.6M−18.4,
and the tsunami energy E_t or the earthquake energy E in ergs and the tsunami magnitude m are also related through the eqution
    logE_t=21.4+0.6m
  or logE=22.4+0.6m
From this,the tsunami magnitude is classified according to its energy,tsunami energy being about one tenth of seismic energy.
 The dimension of tsunami origin L is related to the earthquake or tsunami magnitude;
    logL=0.5M−1.8 or logE=3logL+17.3
and is approximately equal to the horizontal area of the after-shock activity which is associated with the crustal deformation.

INTRODUCTION

 Japan and its adjacent areas are known to be the most seismically active region in the world.Large earthquakes in the vicinity of these coasts occasionally produce great ocean waves known as tsunamis.The more destructive tsunamis have been reported by many investigators,whereas smaller tsunamis have not received the same attention from investigators and consequently complete knowledge of the type of earthquake which is accompanied by tsunamis is not yet available.This fact has already been reported in a previous paper(Iida,1956)[3];however,the author obtained some characteristics of earthquakes accompanied by tsunamis by paying close attention to the mareographic records of even minor seismic sea waves in addition to the major tsunamis occurring in association with earthquakes.It was found that earthquakes causing tsunamis are always followed by a series of after-shocks and that tsunamis follow submarine earthquakes having a magnitude of over 5.8.
 In the present paper,the magnitudes of the earthquakes accompanied by tsunamis are investigated in more detail.Since the focal depth of an earthquake seems to play an important role in the occurrence of tsunami,this focal depth is taken into consideration as well as its magnitude.The magnitude of a tsunami is further investigated to derive tsunami energy from the magnitude of an earthquake.The present paper covers an investigation of all earthquakes and tsunamis during the 35 year period from 1923 to 1957.

MAGNITUDES OF EARTHQUAKES ACCOMPANIED BY TSUNAMIS

 In order to compile and investigate the earthquakes accompanied by tsunamis that occurred in and near Japan,first,all the tsunamis of seismic origin were selected from the Kisyo-yoran(The Geophysical Review),the Zisin-geppo(The Seismological Bulletin of Japan Meteorological Agency),various reports and papers [1,3,4,5,8,9],and the mareographic records of some stations distributed along the Pacific Coast of northeastern Japan..The catalogue of these earthquakes are given in Table 1 along with tsunami data,such as its magnitude and the largest of its maximum amplitudes as recorded at one of the mareographic stations or the largest of its maximum heights that may have been observed at any specific location.
 It was noticed that the tsunamis associated with earthquakes could be observed easily when the earthquakes had large magnitudes of shallow focus ranging from 0 to 40 km; however,sometimes deeper shocks ranging 50 to 80 km caused tsunamis,but in the earthquakes of deeper focus above 80 km the tsunamis usually could hardly be observed even though the magnitude of these earthquakes was comparatively large.These circumstances seem to suggest that the magnitude and the focal depth of an earthquake play an important role in the occurrence of a tsunami.Under these considerations,it is necessary to obtain a general relation between the magnitude and the focal depth of an earthquake accompanied by a tsunami.Fig.1 graphically shows the relation between these factors,where earthquakes occurring off the coast accompanied by tsunamis and those not accompanied by tsunamis are depicted by filled-in circles and plain circles respectively.The magnitudes and the focal depths of the earthquakes used were taken mainly from the 「catalogue of major earthquakes which occurred in and near Japan」 published by the Japan Meteorological Agency [6],as in this catalogue these values have been elaborately estimated anew in the light of modern seismology.
 Taking these circumstances into consideration,it may be noticed that there is an approximate linear boundary between the earthquakes accompanied by tsunamis and those not accompanied by tsunamis.This means that there is a limiting magnitude for earthquakes under which tsunamis do not occur.If the two points(If we do not omit the two points,the earthquake magnitude for the limit may be expressed by M=5.7+0.005 H,a straight line passing through the two points,)(M=5.8, H=20 and M=6.0, H=60)in Fig.1 are omitted and the limit is determined by the least squares method,the earthquake magnitude M may be expressed by a relation which is linear with respect to the focal depth H.Thus the limit may be generally expressed by
   M=(6.42±0.04)+(0.017±0.001)H,(1)
in which H is measured in km.As seen in Fig.1,some earthquakes not accompanied by tsunamis are located on the right side of the straight line which represents the limit of(1).Most of these earthquakes are the after-shocks,associated with the great earthquake accompanied by tsunami,some shocks having occurred in the southwestern sea region of Kyushu,near Amami-Ooshima.
 The limit for disastrous tsunami also may be determined by
   M=7.75 + 0.008 H,(2)
as shown by the broken line in Fig.1.Thus it may be concluded that the magnitude of earthquakes which might have produced tsunami is generally larger than 6.4.Shallow submarine earthquake having a magnitude greater than 7.3 is always accompanied by tsunami and when its magnitude is greater than 7.8 disastrous tsunami occurs.It is interesting to note that the magnitude of land earthquakes accompanied by crustal deformations is almost located on the right side of the line expressing the magnitude limit of(1),as seen in Fig.2.

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FIG.1.Showing the relationship between magnitude and focal depth of submarine earthquakes during the period from1923 to 1957.
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TABLE1.CATALOGUE OF EARTHQUAKES ACCOMPANIED BY
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TSUNAMIS IN AND NEAR JAPAN FROM 1923 TO 1957
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FIG.2.Showing the relationship between magnitude and focal depth of earthquakes occurred in land during the period from 1923 to 1957.

MAGNITUDE OF TSUNAMI

 In the previous paper(Iida,1956)[3] the magnitude classification of tsunami by Imamura [5] was used.Magnitude is separated into five classifications,0,1,2,3,and 4 according to the maximum wave-height and the amount of damage sustained,the wave height of each higher classification from 0 through 4 being doubled in each succeeding classification.In this paper,a classification smaller than magnitude 0 is introduced.This classification is designated as the magnitude -1 and includes minor tsunamis having a waveheight of less than 50 cm.These tsunamis cause negligible damage.The other classifications of magnitude are designated as follows: magnitude 0:tsunami having a wave-height in the order of one meter causing no appreciable damage;magnitude 1:tsunami having a wave-height in the order of 2 meters causing damage to houses along the coast or to ships washed ashore;magnitude 2:tsunami having a wave-height in the order of 4-6 meters causing the destruction of some houses and considerable loss of life; magnitude 3:tsunami having a wave-height of 10-20 meters and producing a damaged area of about 400 kilometers in length along the coast;magnitude 4:the severest tsunami having a maximum wave height of more than 30 meters and producing a large damaged area of more than 500 kilometers in length along the coast.This classification is finally to be related to the classification of tsunamis according to their total energy,as described in the next section.
 The number of tsunamis which have occurred during the last 35 years in Table1,classified according to their magnitude and region of occurrence is given in Table2.
 A close study of these classifications shows that severe tsunamis with magnitude 3 occurred along the Pacific Coasts of northeastern and southwestern Japan while the tsunamis in the lowest class with magnitude −1 occurred most frequently in northeastern Japan(Sanriku-Boso region),and much less frequently along the coast of southwestern Japan(Tokaido-Nankaido region).Tsunamis of magnitude 2 and 3 sometimes occurred off the east and south coast of Hokkaido and Kamchatka area.Tsunamis of magnitude 1 sometimes occurred along the Japan Sea Coast,especially along the west coast of Hokkaido.The epicenters of earthquakes accompanied by these tsunamis for the period from 1923 to 1937 are plotted in Fig.3,where the radius of the circle indicates the magnitude of the tsunami and the numerals outside the circles are the serial numbers in Table1.From Fig.3 we can easily determine the active region of tsunamis.

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TABLE2.NUMBER OF TSUNAMIS ACCORDING TO MAGNITUDE AND REGION OF OCCURRENCE
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FIG.3.Geographic distribution of epicenter of earthquakes accompanied by tsunamis during the 35 year period from 1923 to 1957,classifying the earthquakes according to the tsunami magnitude.

EARTHQUAKE ENERGY AND TSUNAMI ENERGY

 As shown in Table1, for the period from 1923 to 1957, the smallest magnitude of an earthquake accompanied by a tsunami is 5.8 and the largest magnitude is 8.3.In order to study the relationship between the magnitude of an earthquake and a tsunami,the magnitude of the tsunami(m)was plotted against the magnitude of the earthquake(M)as in Fig.4.From this figure we find that in general the greater the magnitude of the earthquake,the greater the magnitude of the tsunami and thus the relation has been found to be
   m=aM+b. (3)
When the numerical values of the constants a and b in this formula are determined by the least squares method,the following equation is obtained:
   m=(2.61±0.28)M−(18.44±0.61). (4)
Since the magnitudes of tsunamis are related to those of earthquakes,the computation of tsunami energy may be performed by using the following formula derived by Gutenberg and Richter(1956)[2] showing the relationship between the magnitude M and the energy E of earthquakes:
   logE=11.8+1.5 M. (5)
Combining equations(4)and(5)so as to eliminate M,the formula showing the relationship between the earthquake energy E and the tsunami magnitude m may be written as
   logE=22.4+0.6 m.(6)
This equation also may be expressed as
   E=E_0 10^0.6m, (7)
where E_0=2.5 × 10^22 ergs.(7)is similar to the following equation obtained by
Takahashi(1951)[9]:
   E_t=E´_0 10^0.6m, (8)
where E´_0=2.5 × 10^22 ergs and E_t,is the total energy of a tsunami of magnitude m.From(7)and(8)the following may be expressed by
【数式】 (9)
and
logE_t=21.4+0.6m. (10)
From the above it may be determined that the energy of an earthquake is ten times larger than that of a tsunami.Thus,the tsunami magnitude may be classified according to its energy, as given in Table3.
 From Table3 we may ascertain the energy of small or large tsunami.For instance,the energy of a large tsunami,magnitude 3, corresponding to the Sanriku Tsunami of 1933, is found to be about 1.6×10^23 ergs,which is approxi-mately one tenth that of the earthquake energy derived from(5).
 The earthquake energy accompanied by a tsunami also may be estimated approximately by means of the linear dimension of tsunami domain which is obtained from the circle.enveloped by the curves of imaginary wave fronts stanting from several station points.As reported in the previous paper(Iida,1956)[3],the original area of a tsunami is related to the earthquake magnitude.Reconsidering this relation,though the estimation of the area involves some errors due to the inaccuracy in measuring the time necessary for the tsunami waves to reach the mareographic station and to the uncertainty of the tsunami velocity near the sea coast,a reliable relation may be derived from averaging the available statistical data.The data in Fig.5 by the least squares method may be expressed as
   logL=(0.46±0.06)M−(1.82±0.58), (11)
   or logL =0.2m + 1.7, (12)
where L in km is the linear dimension of tsunami domain.Equating M in(5)and(11),the following equation may be written as
   logE=3logL+17.3. (13)
From(13)the earthquake energy E related to the linear dimension of tsunami domain may be determined and it may be shown that the greater the magnitude of the earthquake,the larger the domain of the tsunami becomes.
 To estimate the conceivable earthquake energy in another way,Tsuboi’s hypothesis [10,11] regarding the voluminal storage of stress energy in the earth’s crust may be asumed.In this case,let this volume of the earthquake energy field be a spherical volume with a diameter L´.
 Then E may be written as
 【数式】 (14)
where μ is the effective elastic constant and ε the ultimate strain of the crustal material.If and E may be taken approximately to be μ = 5×10^11 C.G.S.and ε=10^-4 for understanding of the nature of the problem,the following equation may be derived
  logE=3logL´+18.0. (15)
From this relation we can see that(15)approximately agrees with(13),provided L= L´.
 Further,if the horizontal area of after-shock activity is assumed to be a circular one with diameter r,the following relation may be derived from the statistical relation of logA=M+6 obtained by Utsu and Seki(1954)[12]:
  logr=0.5M−1.9. (16)
The area of after-shock activity is approximately that of crustal deformation.The original area of a tsunami is assumed to correspond with the crustal deformation.Comparing(16)with(11),r is approximately equal to L.This relationship suggests the identity of two separate areas,the area of origin of the tsunami and the after-shock area.
The tsunami is therefore considered to be produced at the epicentral area of an earthquake by a crustal deformation of the sea bottom,in the region where the seismic energy has been stored.

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FIG.4.Showing the relationship between earthquake magnitude M and tsunami magnitude m.
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【数式】(9)
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TABLE3.EARTHQUAKE ENERGY AND TSUNAMI ENERGY ACCORDING TO TSUNAMI MAGNITUDE
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FIG.5.Showing the relationship between dimension of tsunami domain and earthquake magnitude.
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【数式】(14)

CONCLUDING REMARKS

 Earthquakes accompanied by tsunamis were investigated and a compilation was made of those tsunamis including minor ones occurring in and near Japan during the period from 1923 to 1957.During this period the number of tsunamis accompanying submarine earthquakes totaled 44.
 The magnitudes of earthquakes accompanied by tsunamis were found to be related to the focal depths of the earthquakes.After introducing the magnitude of minor tsunami,the relationship between the magnitudes of the various earthquakes and their related tsunamis was established.The formula for tsunami energy was derived from the relationship existing between the magnitude and the energy of earthquakes,and the tsunami magnitude was classified according to the energy.The present results show that tsunami energy is approximately one tenth of seismic energy.The earthquake energy is also estimated by the dimension of tsunami domain.This domain is considered to have a close relationship to the scale of voluminal storage of stress energy in the earth’s crust and to the after-shock area associated with the crustal deformation,and the tsunami is believed to originate at the epicentral area of an earthquake by a deformation of the sea bottom.

ACKNOWLEDGMENT

 This work was supported by funds donated by the Scripps Institution of Oceanography,University of California,under a contract with the Japanese Organization for Tsunami Investigation,for which the author expresses his sincere appreciation.

REFERENCES

[1] ■■■■■■■■■■ ■■■■■■ ■■ ■■■■■■■■■■■■ No.4 ■■■■■■ 4-5 ■■■■■■ 1952 T.:■■■■■■■■■■■■■■ ■■■■ ■■■■ ■■■■,■■■■■■(1958).
[2] GUTENBERG,B.,The energy of earthquakes: Quart.J.Geol.Soc.London,112,1-14
(1956).
[3] IIDA.K.,Earthquakes accompanied by tsunamis occurrig under the sea off the Islands of Japan:J.Earth Sri.,Nagoya Univ.,4,1-43(1956).
[4] IMAMURA,A.,and MOYAYA,M.,Mareographic observations of tsunamis in Japan during the period from 1894 to 1924:Japan.J.Astron.and Geophys.,17,733-740(1939).
[5] —,List of tsunamis in Japan(in Japanese):Zisin,Ser.2,2,23-28(1949).
[6]Japan Meteorological Agency,Catalogue of major earthquakes which occurred in and near  Japan:Seism.Bull.,Suppl.Volume No.1(1958).
[7] —,The Seismological Bulletin,1926-1957.
[8] ■■■■■■■■■■■■,A.E.,■■■■■■:■■■■■■■■■■■■ ■■■■.■■■■ ■■■■,■■■■■■(1957).
[9] TAKAHASHI,R.,An estimate of future tsunami damage along the Pacific coast ofJapan:Bull.Earthquake Research Inst.,Tokyo Univ.,29,71-95(1951).
[10] TSUBOI,C.,Earthquake energy,earthquake volume,aftershock area,and strength of the earth’s  crust:J.Phys.Earth,4,63-66(1956).
[11] —,On seismic activities in and near Japan:Contributions in Geophysics in Honor of Beno Gutenberg,Pergamon Press,London,1,87-112(1958).
[12] UTSU,T.,and SEKI,A.,Relation between the area of after-shock region and the energy of main shock(in Japanese):Zisin,Ser.2,7,233-250(1955).