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 1960年5月24日未明に日本を襲つたチリ津波は過去に例を見ない大規模なもので,このようなスケールの大ぎな津波の諸性質を知るために,筆者らが調査した中部日本太平洋岸に限つて検討し,これをその地域に発生した過去の近地地震,すなわち,東南海地震(1944年12月7日),南海道地震(1946年12月21日)による津波の性質とを比較検討し,その相違点を明らかにした。
 各津波の高さの分布の特性を知るために,この地域における津波の高さの平均を求め,その平均値からの偏差を各地点について求めると,三つの津波の高さの分布の特徴が知られた。津波の到着時間の算定からチリ津波は海深数100m以上の外洋においては,波面はほぼ等深線に平行になり,平面波的の性質がみられた。また舞坂らの検潮記録の解析から沖合約35km,深さ1000mの海上では津波は周期が約60分,波高が約40cmで,かつ単純な波であることが推論された。
 海深200mの等深線上に配分される津波の高さを第一次的配分とし,沿岸地形,湾形などの影響により配分される高さを第二次的配分とすると,チリ津波のような遠地地震によるものは,波高の第一次配分は全地域ほとんど一定であり,むしろ第二次的波高分布が重要な要素となつている。すなわち,海岸近くの局地的な地形が波高分布に著しく大きな影響をおよぼしている。紀伊半島東岸においては,湾の形とその方向が津波の伝播方向および周期と著しく関係していて津波の高さが大ぎくなることが知られた。
 近地地震による津波の場合は一般に第一次および第二次的配分の相乗作用の結果として津波の高さが決まると考えられる。簡単な模型により理論的に津波の高さの分布を計算し,津波の波長による波高の相違を明らかにした。なお中部日本太平洋岸地域の各湾における波高や周期その他についても考察した。

1.Introduction

 The Chilean tsunami that attacked Japan before daybreak on May 24,1960,was of unprecedented magnitude,causing serious damage not only in Japan but also throughout the circum-Pacific region.Comparing the characteristics of the tsunami on the Pacific coast of Central Japan(from Hamamatsu to Wakayama)assigned to the writers with the characteristics of tsunamis caused by near earthquakes,the writers found that there are some considerable differences between them.In this paper the result of the writers’ investigation 1)is reported.
 Great tsunamis that swept over the Pacific coasts of Central Japan since 1700 are as follows:
1)The Moei tsunami(Oct.28,1707;Earthquake magnitude M=8.4).
2)The Ansei tsunami(Dec.23,1854;Earthquake magnitude M=8.4).
3)The Ansei tsunami(Dec.24,1854;Earthquake magnitude M=8.4).
4)The Tonankai tsunami(Dec.7,1944 ;Earthquake magnitude M=8.0).
5)The Nankaido tsunami(Dec.21,1946;Earthquake magnitude M=8.1).
 From the above list it will be understood that the above-mentioned region is high in the vulnerability rate of tsunamis with the coast of the Sanriku district.However,as the data on the tsunamis in olden times are poor,the writers made a comparison between the two tsunamis cited 4)and 5),the data on which are relatively rich,and the Chilean tsunami.

2.Distribution of tsunami-height

 The materials of the Tonankai tsunami and the Nankaido tsunami were collected from the reports2)3)4)of these earthquakes published by the Central Meteorological Observatory and the Nagoya District Meteorological Observatory and the materials of the Chilean tsunami by the writers.1)The height of these tsunamis in each place is shown in Table1.As shown in the table,the height is considerably different in different places.Concerning damage caused by tsunamis the maximum height(inundation)is important,but for the purpose of disclosing the dynamic nature of tsunamis the range of sea-level(amplitude)may be necessary.In cases where the height of a measured tsunami is larger as compared with the amplitude of tides the maximum sea-level can be regarded as the maximum amplitude of the tsunami,but in cases where a measured height is in the order of 1-4m the above approximation cannot always be established.For this reason the writers,dividing the coast-line between Shizuoka and Wakayama into unit length(5km),investigated the mean height of the tsunami in each division and then calculated the mean height in the whole coast-line.
The result is as follows:
 Mean maximum tsunami-height in the Tonankai tsunami :2.65m.
 Mean maximum tsunami-height in the Nankaido tsunami :2.28m.
 Mean maximum tsunami-height in the Chilean tsunami :1.69m.
 These values are of use as a measure.Assuming that the tides are in the same condition in each place,differences between the above values and the measured values shown in Table1 indicate deviations from the mean inundation height of tsunami in the place.The differences are shown in three lines in the right column in Table1.
 Fig.1a shows the present surveyed area of the Chilean tsunami and the epicenter of Tonankai(A)and Nankaido(B)earthquakes.Fig.1b shows the general view of the topography of the sea floor in and near the present surveyed area.
 a)The Tonankai tsunami(1944)(Fig.2a)
 The geographical distribution of the height of this tsunami has been investigated by Omote 5)and classified into three regions.The first region includes the north coast of the Shima Peninsula and the coastal zones of Ise Bay and Atsumi Bay,the second region the coastal zone of the Enshu-nada,and the third region the south coast of the Shima Peninsula and the east coast of the Kii Peninsula.According to the writers’ classification,the first and second regions,generally speaking,correspond with a(−)region,the adjoining areas of the second and third regions(−)(+)regions.Of the third region,the coast extending as far as Shingii or vicinity,Mie Prefecture,corresponds with a(+)region,the coast south of it a(+)(−)region,and the coast extending from the cape of Shiono-misaki at the southern extremity of the Kii Peninsula to the west coast of the peninsula a(−)region.The above-mentioned three regions classified by Omote were not on the basis of the tsunami-height but whether the region is inland or not.Notwithstanding that,in comparison with the distribution of tsunami-height,both of them(Omote’s classification and the writers’)coincide well with each other.
 b)The Nankaida tsunami(1946)(Fig.2b)The(−)region corresponds with a region extending from Shizuoka to the cape of Miki-zaki,Mie Prefecture,the(−)(+)region a region from Kinomoto,Mie Prefecture,to Shimotsu,Wakayama Prefecture,and the(−)region a region west of Wakayama Prefecture,respectively,and it is noticed that,with the cape of Shiono-misaki at the extremity of the Kii Peninsula as a peak,the value becomes smaller on both sides of the peninsula with symmetry to a straight line connecting the epicenter with Shiono-misaki.(The values in the west side of the peninsula are somewhat larger.)
 c)The Chilean tsunami(1960)(Fig.2c)
 In this case it is impossible to make classification clearly unlike the cases of the above two tsunamis.With the exception of some regular distribution of tsunami-height,that is,(+)on the east coast of the Shima Peninsula and in the vicinity of Gokasho Bay and Owase,and(−)in the area extending from Kinomoto to Shingu.In fact the regions where the distribution of tsunami-height is remarkable cannot be distinguished from other regions.This is shown in Fig.2c.
 Below are given characteristics of the tsunami-height distribution in the above three tsunamis.
(1)The distributions of tsunami-height in the case of the Tonankai tsunami and the Nankaido tsunami closely resemble each other.That is,
(i)The tsunami-height is largest in the area directly facing and nearest the epicenter.It is a(+)region,and the tsunami-height diminishes symmetrically from the area.
(ii)In the area behind the epicenter(for example,the west coast of the Kii Peninsula in the case of the Tonankai tsunami)the height diminishes abruptly.
(2)Generally speaking,the tsunami-height is larger in bays.Owase Bay,Gokasho Bay,etc.in the cases of the Tonankai and Chilean tsunamis are the examples.
(3)In the area with a smooth coast the tsunami-height was low in cases of the above three tsunamis.
(4)In the Chilean tsunami the characteristic described in(i)of(1)was lacking.
 If,from the above,(i)and(ii)of(1)are regarded as the characteristics of tsunamis caused by near earthquakes,(4)is considered the characteristic of tsunamis generated by distant earthquakes.In the case of near earthquakes,tsunamis are discharged in a cylindrical manner from the wave origin.On the contrary,tsunamis generated from very distant places like the case of the Chilean tsunami are considered to be propagated in a plane wave.To study the characteristics of tsunamis on the basis of this difference may prove to be helpful.
 Then,the arrival time and wave fronts of the three tsunamis will be mentioned.
 Concerning the Tonankai tsunami and the Nankaido tsunami,a refraction diagram was published by Takehana 2)3)and Omote 5)6).According to the diagram,waves are generated in a radial way from the wave origin,the isobathyc lines and the wave fronts do not run with each other,and the arrival time of tsunamis calculated on the assumption that the velocity of wave propagation is √gh coincides with the arrival time on an actual tidegauge record within the extent of probable error of a diagram and record.
 In the Chilean tsunami the arrival times of the first,second,and third waves were read on the mareograms recorded at 20 tidegauge stations,and the result is shown in the third line of the left column in Table2.However,the initial phase of the tsunami was not read as the arrival time of the first wave,as is usually done but,as shown in Fig.3,the peak of the remarkable first phase was taken as the arrival time for the purpose of promoting accuracy of time by reading a distinct phase.As shown in Table2,it is known that the Chilean tsunami.arrived in this region from 3 to 5 o’clock on May 24.Probable error is only 2 or 3minutes.
 From these tidegauge stations 7 stations facing the open sea were selected,and the arrival times on the isobathyc lines were calculated in reverse order following Miyabe’s method 8).The result is shown in Table3.According to Table3,the arrival time on the 200-m isobathyc line t_200 3 h 15 m± 05 m,that on the 1000-m isobathyc line line t_1000= 3 h 09 m ±02 m.The former is not always within the extent of probable error,but it is beyond doubt that t_1000 is within the extent of probable error,and the result calculated in reverse from the arrival times of the first wave at 6 tidegauge stations coincides with above arrival time.From the above result it can be inferred that the Chilean tsunami was propagated almost parallel with the isobathyc lines in the open sea over 100 m deep.The mareogram obtained in Matoya Bay was excluded as the arrival time is rather late.

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Fig.1a.Showing the surveyed area and epicenters of Tonankai(A)(Dec.7,1944)and Nankaido(B)(Dec.21,1946)earthquakes.
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Fig.1b.Showing the topography of the sea floor in the surveyed area.
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Fig.2a.Height of Tonankai tsunami.
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Fig.2b.Height of Nankaido tsunami.
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Fig.2c.Height of Chilean tsunami.
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Table1.Maximum height of tsunamis and deviation from its mean height.
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Table2.Arrival time of the first,second,and third waves and the maximum wave amplitude.
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Fig.3.Initial part of mareogram at various tidegauge stations.
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Table3.Arrival time of tsunami on the isobathyc line.

3.The height of tsunamis on the 100-misobathyc line.

 From the above description the height of tsunamis is considered constant in the direction parallel to the same wave-front.In the present case the tsunami-height on the isobathyc line of more than several hundred meters,generally speaking,is regarded as constant on the sea off the Kinki and Tokaido districts.
 Based on an example of a mareogram(recorded at Maisaka)obtained at a tidegauge station facing the open sea and free from local effect due to the topography in the vicinity of the coast,the height of tsunami on the 1000m isobathyc line was calculated.The mareogram recorded at Maisaka and the section of the open sea facing Maisaka are shown in Fig.4 and Fig.5.Aiming at about 10 waves in the mareogram from the beginning,excluding the tides of 12-hour period,the running mean was calculated.Then a spectrum shown in Fig.6 was obtained using Sato’s method9).From this result it was confirmed that waves of 50-60 min in period particularly predominate.
 In order to calculate a spectrum at a depth of 200m from a spectrum shown in Fig.6,the wave-height j_0(2p√a^2/gH_0)e^ipt at B determined mined assuming existence of a wave of e^ipt at A was calculated by being multiplied by the amplitude of each period.In this case a=18 km(the distance from A to B in Fig.7),H_0=200 m(water depth),and g=9.8 m/ sect.The result is shown in Fig.8.According to the result,tsunamis at a depth of 200 m are believed to consist of extremely simple waves as the spectrum is narrowed as compared with the case of Fig.6.In Table2 also it is noticed that periods of the order of 60 min predominate.Consequently,assuming amplitude =760cm,T=60min as the value representing Fig.8,as in the vicinity of a coast the wave propagating direction makes a right angle with the coast and,according to Green’s rule ^10):A_1 :A_2=h_1^1/4:h_2^1/4,we get A_2=40cm from A_1=60cm,h_1=200m,h_2=-1000m.It is,therefore,inferred that on the sea 1000m deep about 35km off Maisaka the period of tsunami is 60 min and the wave-height is in the order of 40cm.
 Assuming that the wave-height in the direction parallel to the same wave-front is constant,it is inferred that a tsunami of about 60min in period and about 40cm in amplitude in the open sea arrived at the 1km isobathyc line at about 3h 9m to affect the Kinki and Takai districts.
 In order to check the above view,calculations will be carried out by using Takahasi’s function^7)T(p).In the Chilean tsunami the amplitude of the tsunami is considered almost on the sea several hundred meters off this region,so the difference of amplitude of tsunami recorded at each place on the coast indicates the local characteristic of the coast and between the coasts.Hence,taking a square of the amplitude in the present case,this is in proportion to T(p).Then,as shown in Fig.9,the values of T(p)against A^2 at 53 places where the tsunami-height(actually the maximum sea-level)common to both were plotted.Though the relation between both is not very distinct,except for several points marked with ○,the relation may be regarded as T(p)∞A^2.The circles are arranged sporadically.One of the reasons is that in fact both are not the wave-height of tsunami but the maximum sea-level.Moreover,there may be errors of measured values,and,further,it is neglected in calculation that the amplitude in a depth of 200m may be different in different places.Next,local difference of the tsunami-height will be discussed.

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Fig.4.Mareogram record at Maisaka.
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Fig.5.Profile of sea bottom along the path of tsunami from 1000-m depth line to Maisaka mareogram station.  — Real depth.  ・・・・Assumed depth for estimation.
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Fig.6.Spectra of tsunami at Maisaka.
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Fig.7.Calculation of spectrum at a depth of H_0.
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Fig.8.Spectra of tsunami at a water depth of 200m off Maisaka.

4.Primary distribution of the height of tsunami.

 To begin with,the distribution of the wave-height of the three tsunamis which attacked this region will be mentioned.In this case it is necessary to bear in mind a concrete shape of Takahashi’s D(P,Q)function ^7).This D(P,Q)is the rate at which the energy of a tsunami released from a point Q is distributed to a division off the point P on the 200-m isobathyc line,and it is a function determined by the mutual positions of P and Q and the distribution of depth.In the present case the tsunami-height was taken in place of the energy of tsunami.This is called by the writers the primary distribution of the height of tsunami.Accordingly the quantity related to T(p)which was previously calculated is regarded as the secondary distribution of tsunami-height connected with the topography and others which are very near the coast.
 Taking account of the fact that a refraction diagram of tsunamis generated by near earthquakes is almost cylindrical but that of the Chilean tsunami can be regarded as plane waves,the distribution of tsunami-heights in the surrounding regions can be inferred by a simple model.
 The method is,assuming a cylindrical island in the sea and a point A in Fig.10 as the origin of a tsunami,to investigate how the wave-height in the surroundings of the island is changed by 0.Calculation is shown in an appendix,and the pattern P(θ)is represented by formulae(I)and(II).
(I)is a case when a is finite:
【数式・1】
(II)is a case when a is infinite,that is,an incident tsunami may be called plane waves:
【数式・2】
in which ξ_0,=2π/λ(angular wave number),E_m=i for m=0,Em=2 for m=1,2,3.・・・,b is the radius of the island.
 The writers will discuss this problem from the standpoint that as the first approximation the south coast area of the Kii Peninsula can be regarded as part of a cylindrical island.In the present case,assuming b=50km and a=100 km,a tsunami was generated by a near earthquake and assuming incidence of plane waves,the phenomena are not inconsistent with those of the Chilean tsunami.In the case of the Tonankai tsunami the depth of sea was assumed to be 3km and the wave length 300km.In the present case,if the period is assumed to be 60 min and the depth 2~3km,the wave length will be 500~600 km.Taking account of this,P(θ)was calculated in the following 4 cases and a result calculated on the assumption P(0)=1 is shown in Fig.10:
(1)ξ_0 b=0.5,ξ_0 a=20:λ=628km.
(2)λ_0 b 0.5 :λ=628 km.
 (Case of incidence of plane wave).
(3)λ_0 b__=1:λ=314 km.
 (Case of incidence of plane wave).
(4)ξ_0 b =1,ξ_0a=2 :λ=314km.
 Concerning,0~180° is shown,but it is 0~100° or so that is necessary for the writers.In respect to θ in both(I)and(II)only cos mθ being given,the pattern is quite the same in the direction of —θ as shown in Fig.11.
(i)In the order of the wave-length λ=300km,λ/b=6 considerable changes take place due to θ.
(ii)With the maximum of P(0)and the increase of θ P(θ)decreases abruptly.
(iii)In the case of incidence of plane waves the decrease of P(θ)is small in degree.
(iv)When the wave-length is 600 km,in θ=0-100° both of them become P(θ)=1.0~0.8,and there is no considerable change due to θ.As the last extremity,in the case of λ→∞ P(θ)becomes non-relative to θ.
 From the above it is known that,with λ/b=10 or so as a boundary,when more than the value P(θ)is non-relative to θ and when less the effect of θ is remarkable.Comparing this result with the distribution of waveheight in cases of the three tsunamis,it is concluded that the magnitude of wave-length in comparison with the dimension of topography primarily affect tsunamis much more than the distance of the origin of tsunami.
 In case of tsunamis generated by near earthquakes(the case of a=finite),besides the above,it is possible that wave-height declines due to spread.However,as the effect is in the order of r^-1/2,and the difference of distance is slight,it is out of question in the region in question.In the Chilean tsunami the wave-length is exceedingly long and on the sea about 1000m off this region the waveheight may be considered almost constant.Hence,if it is considered that the wave-height was distributed in a different way from tsunamis which originated from near regions,the distribution of wave-height will be elucidated temporarily.
 The above discussion is not free from weak points,that is,(1)in this discussion the change of depth of the sea is neglected,(2)a peninsula is regarded as part of a cylindrical island,and(3)the origin of tsunami is re-garded as a single point.However,(1)in this region the 1000-m and 2000-m isobathyc lines lie generally in the distance of 20~50km from the coast-line,though different in different places,and the shape of the isobathyc lines is not without resemblance to that of the peninsula.This corresponds with the case when b is the above-mentioned formulae is assumed to be larger and means that the θ-effect becomes more remarkable.11)(2)Concerning this assumption,there is no means to check it,but,judging from the fact that,as will be discussed later,in the cases of the three tsunamis the maximum wave-height appeared in the waves which arrived relatively early,that is,the second to fourth wave,it may be concluded that there is no effect due to the topography of the interior of the peninsula.(3)The weak point cited in(3)may be com-pensated by the fact that the wave-length is considerably long.

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Fig.9.Showing the relationship between T(p)and A^2.
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Fig.10.Showing the azimuthal angle between cylindrical island and tsunami origin A.
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【数式・1】
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【数式・2】
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Fig.11.Variation of azimuthal wave pattern with wave-length of tsunamis.

5.The secondary distribution of the height of tsunamis;effect of coast topography,shape of bays,etc.

Array As described above,in cases of tsunamis generated by near earthquakes the tsunamis were classified into certain regions according to the wave-height,but in the case of the Chilean tsunami it is noticed that the boundaries of regions are ambiguous.It was described in the preceding paragraph that the difference between both cases can be elucidated tem-porarily by the difference in the manner of spread of waves,wave-length,and period in each tsunami.This is applicable to the rela-tion between the local topography and tsu-namis,and it is considered to be one of the reasons that on the difference between the proper period peculiar to the shape of bays and the period in the open sea in the case of each tsunami the above-mentioned relation between T(P)and A^2 is not in direct proportion.Concerning the predominant period of each tsunami,it is 20~40min in the Tonankai tsunami,15~35min in the Nankaido tsunami,and 60min in the Chilean tsunami.In order to solve the problem the tsunami-heights in coast topography and bays in several places and the reason of difference will be investigated.
(1)Smooth coast-line.Kinomoto-Shingu;cape of Irako-saki-Maisaka-cape of Omai-saki.
 Both coast-lines are devoid of indentation and the topography of continental shelf is nearly in parallel with the coast-line.The continental shelf of the latter is much wider.It is considered that the concentration of tsunami arriving on such a coast to a special part does not occur as the wave-front is parallel to the coast-line as far as a fairly distant offing,and the increase of tsunami-height is due to only the difference of depth.Green’s rule seems to be simply established.Hence,the tsunami-height in such a region ought to be extremely small as compared with other regions.In Table4 such a region is shown as a(−)region.
(2)Rias coast.Kinomoto-Owase-Nagashima-cape of Goza.
 Exclusive of the Nankaido tsunami,in the two cases of the Tonankai tsunami and the Chilean tsunami the tsunami-height in this region,on the whole,was large.In particular the tsunami-height was remarkable in the region east of Owase(see Table1).In the Tonankai tsunami the tsunami-height in this region seems to have been exceedingly large by reason of the multiplication of the fact that this region corresponds with a large region of the primary distribution of tsunami and topographical effect.However,in the Chilean tsunami(+)and(−)regions were arranged irregularly.As understood by the above discussion,even if there were the effect of multiplication in this region,as in the case of the Tonankai tsunami,it would have been slight.Supposing that it is true,it is considered that the secondary distribution of tsunami-height determined by the topography of the region very near the coast-line had a powerful ,effect upon the irregular arrangement of(+)and(−)regions.Hence,the writers’ standpoint regarding a square of the inundation-height of tsunami as topographical vulnerability rate against tsunamis in a local zone will be approved.However,it is necessary to bear in mind that this rate of tsunami risk differs with the period of tsunamis arriving in the region.
 Cape of Daio-saki-Toba;In the case of the Tonankai tsunami the tsunami-height in Matoya Bay was exceedingly large,unlike the case of the Chilean tsunami.
        Tonankai tsunami:
   Matoya{ 3m(above T.P.)
        Chilean tsunami:
        1m(above T.P.)

(3)Wave-height in bays.
(a)Ise Bay and Mikawa Bay.The height of tsunamis caused by near earthquakes is in the order of from 0.5 to 1.0 m in both bays and these regions were(−)regions(from —2 to —1m)in the cases of the above two tsunamis.Nevertheless,these regions were(+)(−)regions in the Chilean tsunami,and the value of wave-height was 1.69m which is nearly the mean value.This is a great difference as compared with tsunamis generated by near earthquakes.In the Tonankai tsunami Ise Bay is in a position not directly attacked by the progressing tsunami,and in the case of the Chilean tsunami the direction of the bay is almost parallel with the propagating direction of tsunami waves.Judging from this,the difference between the cases of the two tsunamis may be reasonably regarded as a result of the difference of the primary distribution of tsunami-height.The reason why the tsunami-height in Mikawa Bay was of the same order as that in Ise Bay may be the connection of both bays with a wide channel.Assuming tentatively the tsunami-height at Irako-saki or Moro-saki(98cm and 94cm respectively)as the tsunami-height at the mouth of bay,the tsunami-height becomes 134cm,144cm respectively at the head of the bay(Nagoya Harbor and Kiso-saki),that is,the tsunami-height of the west coast is larger by from 30 to 50cm.In Ise Bay,generally speaking,the tsunami-height of the west coast is larger.In Kuwana,Tsu and Chiyosaki the wave-height of 2m was recorded,but the reason remains unsolved.Possibly the phases of the direct waves and the reflected waves are in harmony with each other and the two waves may have been doubled.However,this is impossible because the maximum wave arrived in the early period in each tsunami and the period is very long.In addition,there are about 10 tidegauge stations in both bays,and the time of the initial phase of tsunami seems to coincide,in general,with the time calculated with velocity √gh.
(b)Lake Hamana.This lake is connected with the open sea by a narrow outlet of the southern extremity.The Maisaka Tidegauge Station is situated near the outlet.In this lake there are 9 tidegauge stations,at 7 of which the Chilean tsunami was recorded.Judging from the wave-height which is 0.2m in the lake and 1.10m at Maisaka near the outlet,it is convincible how the secondary distribution of tsunami-height is affected by topographic features,that is,a rush of tsunami into the lake is obstructed by the narrow and shallow outlet of the lake.In the case of the Nankaido tsunami the tsunami-height has been reported to have been 1m in the outside of a bay and 60cm in the inside of the same bay.Comparing with the present case,the tsunami-height in the outside of the bay is nearly of the same order but that in the inside of the bay is smaller by more than 40cm.It is considered that the difference of period of both tsunamis gave rise to the difference of effect causing vibrations in the bay.
(c)Ago Bay.In the cases of the Tonankai tsunamis,the Nankaido,and the Chilean the tsunami-height in the bay was 2m,1m,and from 1.5 to 2.0m respectively(Table1).Only in the Chilean tsunami(+)and(−)regions were recognized and approximated to the mean value of the tsunami-height in this bay,that is,1.69m.In the cases of other two tsunamis this region was a(−)region.The value of 1m in the Nankaido tsunami is recognizable from the position of tsunami origin,but the wave-height in the case of the Tonankai tsunami seems to be smaller than the value expected in the bay,even if only the primary distribution of tsunami-height is taken into account.Then,let us consider the next case.
(d)Gokasho Bay.The tsunami-height in this bay was from 3 to 3.5m in the Tonankai tsunami,from 1 to 2m in the case of the Nankaido tsunami,and from 1.7 to 3.5m in the Chilean tsunami.The value is larger without exception as compared with those obtained in Ago Bay.The shape and direc-tion of the two bays are as follows:
        Shape of Bay  Direction of Bay
 Gokasho Bay  U-shape      SW
         narrow-mouth
 Ago Bay    wide-head type  WSW-W
A narrow mouth is a characteristic common to both bays,but,concerning the direction,Gokasho Bay is in parallel to the propagating direction of tsunami wave in case of any tsunami,and Ago Bay is nearly at right angles to the propagating direction of tsunami wave.From the direction toward which Ago Bay opens it may be understood that the tsunami-height is larger in Gokasho Bay.Though trustworthy data on ancient tsunamis are scarce,in Funakoshi the side facing the open sea and the side facing Ago Bay are different by 20 to 60 cm in the tsunami-height in any tsunami,and it is noticed that the tsunami-height is larger in the inner side of the bay.
(e)Owase Bay.As described in many historical materials,this bay is a notorious place where great damage due to tsunamis was frequently repeated like the Sanriku district.In the Tonankai and Chilean tsunamis the height in the bay was large.The cause of the remarkable height of the former tsunami was the position of the bay which is very near the origin of tsunami.However,the height of tsunami,locally from 8 to 10m,was due to the powerful secondary effect.In Sugari Bay(length:about 5km),an indentation of Owase Bay,the tsunami-height was measured in detail.The result disclosed that the tsunami-height was 2.2m at the mouth of bay and On the height of the Chilean tsunami on the Pacific Coasts of Cental Japan from 2.5 to 2.7m at the head of bay.This is a good example that a difference of as much as 50cm is caused even in such a small area(see our report ^1)).
 The features of the distribution of tsunami-height in various topography were described above,but,besides these,there are not a few features worthy of special mention.That is,the tsunami-height in the region between Owase and Goza was considerably large in the cases of the Tonankai tsunami and the Chilean tsunami.This feature can be elucidated by the examples cited above.In connection with this feature,the relation between the shape of coast line viewed as general features of this region and the distribution of isobathyc lines must be noticed.The coast line in this region,topographically speaking,is concave on the whole and the isobathyc lines are arranged,in general,in accordance with the coast line.That is,a deep zone extends at a right angle in this region.In such a feature the energy of tsunami is liable to be accumulated as compared with straight or convex coasts.In the Tonankai tsunami the origin of which was on the extension of the above deep zone,it is possible that when the tsunami propagates it selects the deep zone.In other words,there is a tendency that the deep zone promotes the primary distribution of tsunami-height.This is regarded as a factor of the large tsunami-height in the region between Owase and Goza.
 The value of 2 to 3m was recorded in the Tomita-Shirahama area near Wakayama on the west coast of the Kii Peninsula.This is a characteristic vastly different from the Tonankai tsunami.In the Uragami area a difference in tsunami-height of as much as more than 1m was found in the mouth and head of the bay.This is also a remarkable case.

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Table4.Tsunami-height at smooth coast.

6.Arrival time of the maximum wave and period.

(a)As have been known,in field work,generally speaking,there is a tendency that the wave number of the maximum wave is determined too late,and sometimes the maximum sea-level that was reported does not always mean the maximum amplitude of the tsunami waves.In this paper,making use of about 20 mareograms recorded in the Kinki and Takai districts,the number of the maximum amplitude was read.The result is shown in the right side of Table2.In the case of the Chilean tsunami the number of waves of the maximum amplitude was largest in the second and third waves and next come from the fourth to the sixth wave.It is interesting that the tsunami-height is divided into two groups,that is,one group in which the second and third waves show distinctly the waves of the maximum amplitude as seen in the mareograms recorded at the tidegauge stations situated in the two bays of Ise and Mikawa like Toyohashi,Katanohara,and Nagoya,and the other group in which several waves have the equal amplitude like the second to the fifth and the second to the eighth wave as seen in the records of Irako,Matoya,Komatsujima,and Kochi.In the latter,taking the wave number cited before,the second or third wave is the maximum(here,as the wave as shown in Fig.3 is taken as the first wave,in the ordinary enumeration the first wave corresponds with the third or fourth wave.)On the other hand,according to the report of the Tonankai or Nankaida tsunami,the second or the third wave is the maximum in both cases.This is very different from the present case.In any case the waves of the maximum amplitude are considered the direct waves
(b)Period.The period of the Chilean tsunami is remarkably long as compared with tsunamis generated by near earthquakes(from Table2 and Fig.6).Hence,the wave-length of the tsunami is long.Assuming T=60min and the depth 2000m,the wave-length is in the order of 500km.It is considered that this magnitude is correlated to the magnitude ^12)^13)of the hypocentral region and it is related to the magnitude of the earthquake that generated the tsunami.The depth of the sea at the epicenters of earthquakes under consideration were from 2000 to 3000m.From the resemblance it is inferred that the difference of the period of the tsunamis can be regarded to be due to the magnitude of the earthquakes.It is an interesting problem to take a spectrum from each mareogram and to inquire in detail into the relation between the spectrum and the coast topography in the vicinity of the tidegauge station.However,attention must be paid to the predominant period of 20min in the mareogarm recorded in Owase and the cape of Shiono-misaki.
(c)Others.In the cases of the Tonankai and the Nankaida tsunamis crustal movements of as much as 1 m occurred in the Kii Peninsula and Shikoku.The effect of the crustal movements on the height of the tsunamis cannot be overlooked.As a matter of course,this is out of the question in the case of the Chilean tsunami.Besides,in the case of the Nankaido tsunami,taking account of(1)slow velocity and(2)low tsunami-height as compared with the magnitude of earthquake,some scientists maintain that,in most places,it is not impossible to consider that the waves generated at the wave origin went ashore before the waves change completely from the phase to the progressive waves.If this view is correct,this is a characteristic of tsunamis caused by near earthquakes.In the case of the Chilean tsunami a velocity of from 8 to 10 knots was observed.

7.Conculusion

 Various characters of the three tsunamis were discussed.Though it is not reasonable to attempt a general discussion,limiting the extent to the Kinki and Takai districts,on a tsunami of extraordinary magnitude like the Chilean tsunami,so far as this region is concerned,the primary distribution of height of tsunami is almost constant throughout the region and the secondary distribution of height of tsunami is considered an important factor.That is,it is considered that the effect of local topography near the coast on the distribution of tsunami-height is considered to be larger.This is considered mainly to be due to the following causes:(1)The tsunami being generated by a distant earthquake,the propagating direction of tsunami wave is,almost parallel to the direction of the bay;i.e.,the wave front is almost parallel to the isobathyc lines.(2)The wave-length of tsunami is exceedingly long(that is,the period is long).On the other hand,in the case of a tsunami caused by a near earthquake the distribution of tsunami-height is regarded generally to be determined as a result of multiplication of the primary and secondary effects.However,in this case also it is supposed that the features are considerably different when the period of tsunami is exceedingly large.

Appendix

The displacement of tsunami at any point(r,θ)is given by
【数式】(1)
where
【数式】(2)
in which φ is the velocity potential,h the water depth,b the radius of the island,a the distance from the origin of a tsunami to the island(Fig.10),and p the angular frequency.(2)can be obtained from the equations of continuity and free surface and boundary conditions,as usual.Addition to this,we used here the Hankel transformation with respect to R.Then,.(1)can be written as
【数式】(3)
Thus we get at the boundary r=b
【数式】(4)
【数式】(5)
【数式】(6)

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【数式】(1)
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【数式】(2)
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【数式】(3)
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【数式】(4)
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【数式】(5)
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【数式】(6)

References

1.Chilean Tsunami Survey Group,Preliminary survey report on the Chilean tsunami of May 24,1960(in Japanese)1-870,(1960).
2.Central Meteorological Observatory,Reports on the Tonankai earthquake(in Japanese).Special Publication(1945).
3.Central Meteorlogical Observatory,Report on the great Nankaido earthquakes(in Japanese),Special Publication(1947).
4.NAGOYA Meteorological Observatory,Report on the Tonankai and Nankaido earthquakes(in Japanese,unpublished).
5.S.OMOTE:The tsunami,the earthquake sea waves,that accompanied the great earthquake of Dec.7,1944(in Japanese):Bull.Earthq.Res.Inst.24,31-51(1946).
6.S.OMOTE:On the central area of seismic sea waves.Bull.Earthq.Res.Inst.25,15-19(1947).
7.R.TAKAHASHI:An estimate of future Tsunamidamage along the Pacific coast of Japan.Bull.Earthq.Res.Inst.,29,71-95(1951).
8.N.MIYABE:An investigation of the Sanriku Tsunami based on mareogram data.Bull.Earthq.Res.Inst.Suppl.1.,112-126(1934).
9.Y.SATO:Analysis of dispersed surface waves by means of Fourier transform I.Bull.Earthq.Res.Inst.33,33-48(1955).
10.H.WATANABE:Studies on the Tsunamis on the Pacific coast of northern Japan.Geophys.Mag.27,61-75(1956).
11.S.HOMMA:On the behaviour of seismic sea waves around a circular island.Geophys.Mag.21,199-208(1950).
12.K.IIDA:Earthquakes accompanied by tsu-namis occurring under the sea off the Islands of Japan.J.Earth Sciences,Nagoya Univ.,4,1-43(1956).
13.K.IIDA:Magnitude and energy of earthquakes accompanied by tsunami,and tsunami energy:J.Earth Sciences,Nagoya Univ.,6,101-112(1958).