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Abstract

 An investigation has been in progress on submarine tsunamigenic earthquakes and the generation of tsunamis.This paper covers an investigation of all earthquakes and tsunamis which occurred in the vicinity of Japan during the 60−year period from 1900 to 1960.The magnitudes and energy of tsunamis are discussed;in particular,the relationship between the magnitude of an earthquake and a tsunami.Tsunami magnitude is related to the distance of the tsunami origin from the land and to the water depth at the epicenter of the earthquake.Tsunami energy is also discussed in connection with the area of tsunami origin,the water depth at the epicenter of the earthquake,and the height of the tsunami.A formula For tsunami energy is derived from these factors and tsunami magnitude is classified according to this energy.The minimum magnitude of shock which can cause a tsunami is estimated.Tsunami energy is equal to approximately one−tenth of seismic wave energy.
 The generation mechanism of tsunamis is also discussed on the basis of crustal deformations associated with earthquakes.The energy of tsunamigenic earthquakes is estimated by using the dimensions of the tsunami’s original domain.The domain is considered to be closely related to the scale of voluminal storage of stress energy in the earth’s crust and to the aftershock area associated with a crustal deformation.Earthquakes accompanied by tsunamis are always followed by many aftershocks.Some aftershocks,as generally defined,are accompanied by tsunamis even though the magnitude of the aftershocks may be small.The relationship between the earthquake’s potential energy and the released tsunamigenic seismic energy is obtained from the relationship between the volume of aftershock region and the earthquake magnitude.The energy contributed to the seismic waves as well as to the crustal deformation and to the tsunamis is estimated.

Introduction

 The Pacific coasts of Japan and adjacent areas are known as a region most frequently subjected to destructive tsunamis.These destructive tsunamis have been reported by many investigators,whereas,minor tsunamis have not received the same attention 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 previous papers (Iida,1956,1958);the author ascertained some characteristics of earthquakes that are accompained by tsunamis by paying close attention to the mareographic record of even minor tsunamis,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 aftershocks,and that tsunamis always follow shallow submarine earthquakes having a magnitude greater than 7.3.When the earthquake magnitude is greater than 7.8,a disastrous tsunami occurs.A formula for tsunami energy was derived from relationship that exists between the magnitude and the energy of earthquakes,and tsunami magnitude was classified according to this energy.
 In the present paper,the submarine tsunamigenic earthquakes which occurred in and near Japan during the 60−year period from 1900 to 1960 are investigated in connection with the generation of tsunamis.The magnitude and energy of tsunamis were obtained in more detail from the relationship between submarine earthquakes and tsunamis.Tsunami magnitude was further investigated in connection with focal depth and water depth at the epicenter of an earthquake.The generation mechanism of tsunamis was also studied on the basis of earthquake seismology.

Discussion

ArrayMagnitudes of Earthquakes Accompanied by Tsunamis
 A catalogue of tsunamigenic earthquakes,compiled from various reports and papers and from mareographic recordsof tidal stations distributed along the coasts of Japan,is presented in Table1,along with tsunami magnitudes.
 As previously noted (Iida,1958),tsunamis associated with earthquakes can be easily observed when the earthquakes have large magnitudes of shallow focus ranging from 0 to 40km;also,deeper shocks with focus ranging from 0 to 40km;also,deeper shocks with focus ranging from 50 to 80km sometimes cause tsunamis;but,in the earthquakes with focus greater than 80km,the tsunamis are usually unobservable even though the magnitude of these earthquakes may be comparatively large.These circumstances seem to suggest that the magnitude and focal depth of an earthquake play an important role in the occurrence of a tsunami.Under these circumstances,it is necessary to obtain a general relationship between the magnitude and focal depth of an earthquake that is accompanied by a tsunami.Figure 1 shows the relationship between these factors;earthquakes occurring off the coast accompanied by tsunamis and those not accompanied by tsunamis are depicted by filled−in circles and by plain circles,respectively.Data for the magnitudes and focal depths of the earthquakes were taken mainly from the 「Catalogue of major earthquakes which occurred in and near Japan,」 published by the Japan Meteorological Agency(1958),as,in this catalogue,these values have been elaborately estimated a new in the light of modern seismology.
 Figure1 shows that there is an approximate linear boundary between earthquakes accompanied by tsunamis and those that are not accompanied by tsunamis.This means that there is a limiting magnitude for earthquakes below which tsunamis do not occur.The limit is determined by the least squares method;the earthquake magnitude M may be expressed by a relationship which is linear with respect to the focal depth H.Thus the limit may be generally expressed by
   M = 6.3 + 0.01 H,   (1)
in which H is measured in km.As seen in figure 1,some earthquakes not accompanied by tsunamis are located on the right of the straight line A which represents the limit of (1).Most of these earthquakes are aftershocks associated with great earthquakes that were accompanied by tsunamis,some shocks having occurred in the southwestern sea region of Kyushu,near Amami−Oshima.There are two tsunamigenic earthquakes located on the left of the straight line expressing the limit of (1).Taking these two earthquakes into consideration,the limit may be expressed by
   M = 5.6 + 0.01 H.
 The limit for disastrous tsunamis having a magnitude of more than 2 may also be determined by
   M = 7.75+0.008 H,    (2)
as shown by the broken line B in Figure 1.Thus the earthquakes accompanied by tsunamis having magnitude of less than 2 are located between lines A and B,and those accompanied by tsunamis having magnitudes of more than 2 are located on the right of line B.The limit for the tsunamis having a magnitude of more than 1 may be determined by
   M = 6.5 + 0.017H.    (2)’
The percentage of tsunamigenic earthquakes is given in Table2.It may be concluded from these figures that the magnitude of earthquakes which might produce tsunamis should be,generally,larger than 6.3;however,in some instances when the earthquake magnitude was 5.6,tsunamis have also occasionally occurred;5.6 may therefore be the minimum magnitude for shocks which are accompanied by tsunamis.Shallow submarine earthquakes having a magnitude greater than 7.3 are always accompanied by tsunamis;and when magnitude is greater than 7.7,a disastrous tsunami occurs.It is interesting to note that the magnitude of land earthquakes which accompany crustal deformations is located almost to the right of the line expressing the magnitude limit of(1),as previously reported by Iida(1958).
Magnitude of Tsunamis
 A magnitude classification for tsunamis has been given in a previous paper(Iida,1958).Magnitude is separated into six classifications −1,0,1,2,3,and 4,according to the maximum wave height,the wave height of each higher classification being doubled in each succeeding classification.The first grade of magnitude (−1) includes minor tsunamis having a wave height less than 50 cm;thus,the other magnitude classifications are as follows:magnitude 0,maximum wave height in the order of 1;magnitude 1 m,maximum wave height in the order of 2m;magnitude 2,maximum wave height in the order of 4−6m;magnitude 3,maximum wave height in the order of 10−20m;and magnitude 4,maximum wave height in excess of 30m.Tsunamis which have occurred during the last 60years were classified in Table1 according to their magnitude.The epicenters for the earthquakes which were accompanied by these tsunamis are shown in Figure2;the numerals outside the circles correspond to the serial numbers in Table1.From Figure2,we can easily determine the active regions of tsunamis,such as the Pacific side of Japan and Kamchatka,especially the Hokkaido−Sanriku−Boso region.Table3 presents tsunamis listed in Table1 classified according to their magnitude and region of occurrence.
 Taking the depth of water at the epicenters of the earthquakes into consideration,the relationship between tsunami magnitude and water depth was investigated.This relationship,which is shown in Figure3,was obtained from data of about one hundred tsunamigenic earthquakes which occurred during the 260−year period from 1700 to 1960.As indicated in Figure3,there appears to be an approximate boundary between tsunami magnitude m and water depth h.This seems to suggest that there is a limiting magnitude of tsunamis by the water depth at the epicenter of the earthquake.The limit may be expressed by
    m = 1.66 log h −1.62    (3)
in which h is measured in m.Thus the limiting tsunami magnitude may be obtained by determining the epicenters of tsunamigenic earthquakes.This seems to be important in tsunami warning.
 Further,the tsunami magnitude was investigated in connection with distance from the epicenter to the land and water depth at the epicenter.Figure4 shows the relationship between these factors;tsunami magnitude is plotted against the log of S,the ratio of the water depth h to the distance D.As seen in Figure4,the ratio S tends to increase with increase in tsunami magnitude.The relationship between them is determined by the least squares method as follows:
   log S = 0.12 m + 2.12,    (4)
  or m = 8.33 log S −17.0    (4)’
Since the ratio S is a quantity relating to the slope of the sea bottom at the epicenter,it may be shown that the larger the slope,the larger the tsunami magnitude.On the other hand,the ratio S also depends on D and h,so,comparatively,the effect of water depth on tsunami magnitude is greater than the effect of distance from the epicenter of the earthquake.
Earthquake Energy and Tsunami Energy
 For the period from 1900 to 1960,the smallest magnitude for an earthquake accompanied by a tsunami was 5.8,and the largest,8.5(Table1).In order to find the relationship between the magnitudes of earthquakes and tsunamis,the magnitudes of the tsunamis(m) were plotted against the magnitudes of the earthquakes(M)(Fig.5).From this figure it can be noted that,as previously observed,in general,the greater the magnitude of an earthquake,the greater the magnitude of the tsunami.Thus the relationship between the magnitude of a tsunami and that of an earthquake has been found to be
    m = aM + b,    (5)
in which a and b are the constants,the numerical values of which are determined by the least squares method as follows:
    m = (2.61±0.22) M−(18.44±0.52)    (6)
Thus,with this formula,tsunami magnitude may be estimated from earthquake magnitude.The computation of tsunami energy is,therefore,executed by means of the following formula(Gutenberg and Richter,1956)showing the relationship between the earthquake magnitude M and the seismic wave energy Es:
   logEs = 11.8+1.5M.    (7)
Equating M in (6) and (7),we get
   logEs = 22.4+0.6m,    (8)
 or Es = Eo10^0.6m    (9)
where Eo = 2.5×10^22ergs.
   With respect to the tsunami of magnitude m,(9)is similar to the following relationship (Takahasi,1951)
   Et = Eo 10^0.6m,    (10)
where E´o = 2.5×10^21ergs.From(9)and(10)tsunami energy can be derived as
   Es/Et = Eo/E´o    (11)
and
   log Et = 21.4+0.6m,    (12)
or
   log Et = 10.3+1.5M.    (12)
From(11),tsunami energy is found to be equal to approximately one−tenth of the seismic wave energy Thus,we can determine the energy of a tsunami from earthquake mag nitude or from seismic wave energy Tsunami magnitude classified according to its energy,is presented in Table4.The revised relationships between the magnitude,energy,and maximum wave height of tsunamis are also listed in Table4.
 In order to investigate the generation mechanism of tsunamis,the area of tsunami origin must be taken into consideration.As reported in previous papers(Iida,1956,1958),there is a close relationship between the area of tsunami origin and the area of aftershock activity.Some examples are shown in Figure6.This relationship can be understood from another point of view also.The data in Figure 7 wherein the after−shock area A is plotted against earthquake magnitude M by the least squares method,may be expressed as(similar to Utsu and Seki’s relationship,1955).
   log A = 0.9M−3.0,    (13)
where A is measured in km^2 This relationship shows that the greater the magnitude of an earthquake,the larger the area of aftershock activity.If the horizontal area of aftershock activity is assumed to be a circular one with diameter f,,the following relationship may be derived from(13):
   log L’ = 0.5M−1.6    (14)
On the other hand.however.as previously Postulated,the area of tsunami origin is related to earthquake magnitude.Reconsidering this relationship from the data in Figure 8,the dimension of tsunami domain L by least squares method may be expressed as
   log L = 0.5M−1.7,    (15)
where L is measured in km.Comparing(14)and(15),L’is approximately equal to L.This relationship suggestes the identity of two separate areas,the area of origin of a tsunami and the area of aftershock.The area of crustal deformation caused by the main shock is known to correspond approximately to that of aftershock activity.
 Tsunamis are therefore considered to occur at the epicentral area of an earthquake resulting from a crustal deformation of the sea bottom,such as rising,sinking,faulting,and so forth,and the area of tsunami origin may be approximately estimated by the aftershock area,which can be clearly fixed by seismic observation.
 In addition to the aftershock area,aftershock volume was investigated in connection with earthquake energy.Figure9 shows the relationship between the earthquake magnitude and maximum aftershock volume.The data in Figure8 may be expressed by the least squares method as
   log V = M−2.1,    (16)
where V is the volume of aftershock activity in km^3.If the aftershock volume is assumed to be an earthquake volume V,the energy of the released seismic waves,Es is
   Es=1/2fex^2V,    (17)
  =f Ep’    (18)
in which Ep is the potential energy of a volume V of the crustal material having an average elastic constant strained an ultimate amount x immediately before an earthquake,and f the fraction of the energy released as seismic waves Es.Assuming reasonable values of e = 5 x 10^11 C.G.S.and x = 10^−4 for an understanding of the nature of the problem and combining(7),(16),and (17),the following relationship may be derived
   0.5 M = log f + 4.5.(19)
Thus,the fraction of the energy released as seismic waves may depend upon the magnitude of the earthquake.We may calculate the fraction of conversion of elastic energy to wave energy.For instance,the fraction is found to be about one−third or one−fourth for a great earthquake having a magnitude of 8,and about one−thirtieth,for an earthquake of magnitude 6.
 It may be concluded that the greater the magnitude of the earthquake,the closer the value of f will approach unity;and also,the greater the earthquake,the more often will the efficiency of conversion of earthquake potential energy to seismic wave energy become unity.Thus,the greatest tsunamigenic seismic wave energy recorded in the past may be estimated to be about one−half of the potential energy of a tsunamigenic earthquake and the average energy of a tsunami,as about one−tenth of such seismic wave energy.

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Table1 Catalogue of earthquakes accompanied by tsunamis in and near Japan,1900−1960
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Fig.1−Relationship between magnitude M and focal depth H submarine earthquakes during the period from 1900 to 1960.
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Table2 Earthquake magnitude and percentage of earthquakes accompanied by tsunamis during the period from 1900 to 1960
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Table3 Number of tsunamis,according to magnitude and region of occurrence Region
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Fig.2−Geographic distribution of the epicenters of earthquakes accompanied by tsunamis during the 60−year period from 1900 to 1960,classifying the earthquakes according to the tsunami magnitude.
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Fig.3−Relationship between tsunami magnitude m and water depth h at the earthquake epicenter.
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Fig.4−Relationship between tsunami magnitude m and the ratio S of water depth at the earthquake epicenter in relation to the distance D from epicenter to land.
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Fig.5−Relationship between earthquake magnitude M and tsunami magnitude m.
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Table4.Tsunami magnitude,energy,and height.
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Fig.6−Area of tsunami origin and area of aftershock activity.
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Fig.7−Relationship between aftershock area and magnitude M of tsunamigenic earthquakes.
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Fig.8−Relationship between dimension of tsunami origin area L and magnitude of tsunamigenic earthquakes.
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Fig.9−Relationship between maximum aftershock volume V and magnitude M of tsunamigenic earthquakes.

Conclusion

 Earthquakes accompanied by tsunamis were investigated,and a compilation was made of those tsunamis which had occurred in and near Japan during the period from 1900 to 1960.During this period,the number of tsunamis accompanying submarine earthquakes totaled 61.
 The magnitude of earthquakes accompanied by tsunamis was found to be related to focal depth.Tsunami magnitude was found to be limited by water depth at the epicenter of the earthquake and to be related to the distance of the area of tsunami origin from land and water depth at the epicenter.
 After introducing the magnitudes of minor tsunamis,the relationship between the magnitude 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 energy of earthquakes,and the tsunami magnitude was classified according to the energy.The present results show that the average tsunami energy is approximately one−tenth of seismic wave energy.The greatest tsunami−genic seismic wave energy was found to be about one−half of the earthquake potential energy.In this way,the partition of earthquake energy may be estimated.
 Earthquakes that generate tsunamis are always followed by a series of aftershocks;some are followed by a great number of aftershocks,while others are followed by only a few.The generation mechanism of tsunamis was discussed on the basis of crustal deformations,such as rising,subsiding,faulting,and so forth,in relation to the main shocks.Tsunamis are believed to originate at the epicentral area of an earthquake resulting from a deformation of the sea bottom,and are modified by the aftershock area and the area of tsunami origin.
 Since earthquake data such as magnitude,focal depth,location of epicenter,and aftershock activity all have a close relationship to tsumani generation and tsunami magnitude,the accurate determination of all of these factors is considered to be important in tsunami warning.

References:

1.Gutenberg,B.1956.The energy of earthquakes.Quart.J.Geol.Soc.London 112:1−14.
2.lida,K.1956.Earthquakes accompanied by tsunamis occurring under the sea off the Islands of Japan.J.Earth Sci.,Nagoya Univ.,4:1−43.
3.lida,K.1958.Magnitude and energy of earthquakes accompanied by tsunami,and tsunami energy.J Earth Sci.,Nagoya Univ.,6:101−112.
4.Japan Meteorological Agency.1958.Catalogue of major earthquakes which occurred in and near Japan.Seismol.Bull.,Suppl.Vol.No.1.
5.Solovev,S.L.− I.Ferchev M.A.,1961.Summary of Data on tsunamis in the USSR.Bull.Soveta Po Seismologii an CCCP No.9−23−55.
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7.Utsu,T.,and Seki,A.1955.Relation between the area of aftershock region and the energy of main shock.Zisin,Ser.2(7):233−250.(In Japanese).