On　the　Height　of　the　Chilean　Tsunami　on　the　Pacific　Coasts　of　Central　Japan　and　the　Effect　of　Coasts　on　the　Tsunami,particularly　on　the　comparison　between　the　Tsunami　and　those　that　accompanied　the　Tonankai　and　Nankaido　Earthquakes（中部日本太平洋岸におけるチリ津波の高さと海岸の影響,特に東南海地震および南海道地震に伴なつた津波との比較）

　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.

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.

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.

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

　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.

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）

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）.
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