་պ͈ఱ̧̈́ڛഎౣਔܢ଼͈ͬခ̳ͥೋ෨͈ഥඅ
ډઔȁఊɖȆ५ئȁȁɖȆ܅ၻȁࣝɖ
ˍȅ੬ȁȁა
2011ාཤ౷༷ఊဢؗ౷ૼೋ෨͈କ࿂
་൲̦Ȅ܊ࡇධ໐͈ؗକ૬ 204 m ͈౷ത
ͅ୭౾̯̹ͦ GPS ෨Ⴢࠗͤ͢ͅ௴̢̹ͣͦ1ȫȃ
̭͈ࠗ௶ͤ͢Ȅ0.5 m ഽ͈କպ೩ئ͈ࢃȄ
2.5 m ͈۱̥̈́͞କպષઌ̦ 10 ۼ̲Ȅ
̷̱̀Ȅ̷͈ࢃ͈ 4 ۼ́Ȅ 4.7 m ͈͜ݢ
ࠣ̈́କպષઌ̦อ̱̹̭̦̥̹͂ͩ̽ȃ̭
̠̱̹ 2 ٴ̹ͩͥͅକպષઌ͉Ȅ෨ࣞତ m
଼͈͂Ȅ་պ͈ͤ͢ఱ̧̈́ڛഎౣਔܢ͈
଼̥ͣ̈́ͥೋ෨̦ഥ̱̹̭͂ͬা̱̞̀
ͥȃ̷̭́Ḙ͈̠̏̈́͢ೋ෨̦͈̠̓̈́͢ഥ
අͬা̳͈̥ͬκΟσ౷ࠁͬచય̱̹͂
ତٜଢ଼͓ͤͥ͢ͅȃࢵͅȄ౷ࠁͬచય
̱̹͂ೋ෨͈ 1 ষࡓഥٜଢ଼࣐̞ͬ̈́Ȅષܱ
͈କ࿂་൲̹̳ͬͣ͜Ȅೋ෨෨࡙֖͈ܢକ
࿂ࠁͬদ࣐॒ࢋͤ͢ͅଔ̱̠̳͂ͥ͢ȃ
̤̈́Ḙ̭͈̏́ౣਔܢ͈փྙ͉Ȅఈ଼͈
෨Ȅ̱̩͉͜Ȅೋ෨͈ 1 ෨ఘ͈ਔܢ͂ڛ
̱̀ਔܢ̦ౣ̞̞̠̭̜͂͂́ͥȃ̹͘Ȅ࡛
ય͈ౙا͈̹͛ͅȄೋ෨͈ಿݻၗഥͬե
̠ष͜ͅȄ٬ೲླྀड़ݞ͍ၠఘුͬྫণ̱Ȅ
Coriolis ͈ႁͬࣉ̢̞̭̳̈́͂ͥͅȃ
ˎȅܖய༷ࠏ͂ତٜଢ଼༹
ුȆգੀၠఘͬచય̳͂ͥȃၠఘ
͈ྟഽ̦Ȅߗۼഎ֚ͅအ́Ȅশۼഎ֚́ͅ
̜̳ͥ͂ͥȃၠఘ͈൲̦ٝഢ̜́ͥ͂ب
̳ͥ͂Ȅষ͈̠̈́͢௸ഽεΞϋΏλσ ЋȪx,z,tȫ̦ంह̳ͥȃ
Ȫ1ȫ
̭̭́Ȅʞ=(/x,/y) ͉Ȅକ༷͈࢜
ॳঊ̜́ͤȄuݞ͍ w ͉Ȅ̷̸ͦͦȄକ
ݞ͍ೄ༷͈࢜ၠ௸̜́ͥȃ
ၠఘ͈൲ͅచ̱̀ȄȪ2ȫ͈ไ۾ତ2ȫ
ͬ͛ͥȃ
Ȫ2ȫ
̭̭́Ȅକ࿂ݞ͍ೲ࿂̷̸ͬͦͦz=(x ,t)
ݞ͍z=b(x,t)͂ນ̱̞ͩ̀ͥȃ̹͘Ȅg͉Ȅ
ਹႁح௸ഽ̜́ͤȄ9.8 m/s2̳͂ͥȃ
௸ഽεΞϋΏλσЋȪx,z,tȫͬষ͈̠͢
ͅକ࿂̥͈ͣೄݻၗz̧͈͓۾ତ͈ਹ͙
ັ̧ݭତͅജٳ̳ͥȃ
Ȫ3ȫ
̭̭́ȄȪडֲ༏ȫ̤̞̀ͅȄͅ۾̳ͥୟ
͈გܰͬဥ̞̞̀ͥȃ̹͘Ȅ႕̢͊Ȅf2͉Ȅ z2͈͈ࣜਹ͙߸ତ̜́ͥȃ
Ȫ3ȫ͈௸ഽεΞϋΏλσͬȪ2ȫ͈ไ
۾ତͅయව̱Ȅೄ༷࢜ୟٜͬଢ଼എ࣐ͅ
̥̈́̽̀ͣȄ་ࡔၑ͈ EulerLagrange ༷
ࠏͬ൵̳̭ͥ͂ͤ͢ͅȄ෨͈ޑࠁȆ ޑ८ͬࣉၪ̱̹෨൲༷ࠏ̦ංͣͦͥȃ
̭͉ͦȄఱܨգͬ 0 ̳͂ͥ͂Ȅষ͂̈́ͥȃ
Ȫ4ȫ
Ȫ5ȫ
ɖോఱڠఱڠ֭ȁၑࢥڠࡄݪش
Ȫ4ȫݞ͍Ȫ5ȫ͉ȄȪ3ȫ͈௸ഽεΞϋΏλ σ͈ജٳࣜତͬNɁ1 ̳͂ͥ͂Ȅࠁஃ କ༷ࠏ3ȫ֚͂౿̳ͥȃ̭̭͉́Ȅ෨͈
८ͬࣉၪ̱ȄNɁ2 ̱͂̀ତٜଢ଼࣐ͬ
̠̈́ȃ
౯࿂ 2 ষࡓඤ͈࡛યͬచય̱͂Ȅ2 ཿ͈ࡥ
କโ́ޖ̹ͦ͘ 2 ࿚ఴٜ̩̹͈ͬ͛ତ
κΟσ̜́ͥ NakayamaȆKakinuma4ȫ͂൳ အ͈ओ༹ͬဥ̞̀ȄȪ4ȫݞ͍Ȫ5ȫٜ̩ͬȃ
ˏȅ་պ͈ఱ̧̈́ڛഎౣਔܢ଼͈ͬ
ခ̳ͥೋ෨͈ഥඅ
2011 ාཤ౷༷ఊဢؗ౷ૼೋ෨͈କ࿂
་൲ͅ۾̱̀Ȅஜ̱̹ͤȄ1 ͅা̳
̠̈́͢ಲպ༊ओ̦ං̞ͣͦ̀ͥ1ȫȃ̷̭́Ȅ 2 ٴ͈କպષઌ͈ࠫضȄ་պ͈ఱ̧̈́ڛ എౣਔܢ଼͈̦܄̹ͦ͘ાࣣͅȄೋ෨̦̓
͈̠̈́͢ഥඅͬা̳͈̥͓ͬͥȃ
̤̈́Ḙ̭͉̏́Ȅ౷ࠁͬඵ͈֚̾အକ૬ ໐̷͂ͦͣͬࠒ̪֚အ࢙০࿂ͤ̈́ͥ͢κΟ σ౷ࠁ̱͂Ȅೋ෨͈ 1 ষࡓഥͬచય̳͂ͥȃ
̳̻̈́ͩȄ2 ͈̠͢ͅȄ600 kmɅxɅ
650 km ֚ͅအ࢙০࿂̦̜ͤȄ০࿂ͤؗ͢
௰͈କ૬ͬ 204 mȄ০࿂ͤ͢܅௰͈କ૬
ͬ 60 m ̳͂ͥȃ̭͈০࿂͈࢙͉Ȅ0.00288
̜́ͥȃ
1 ͈ಲպ༊ओ͈ͬ 2 ̱Ȅೋ෨̦
GPS ෨Ⴢ͈ࠗ୭౾պ౾ͬࠁஃକ෨͈෨௸
ً̱̹́͂ب̱̀Ȅ3 ͈̠̈́͢ߗۼ ෨ࠁͬංͥȃ̭ͦͬ Case A ͈ೋ෨ܢ෨ࠁ
̳͂ͥȃ
̭͈ Case A ͈෨ࠁ̥ͣȄ୶̧࣐̳ͥ֨෨
ͬࠁ଼̳ͥ໐ͬੰٸ̱̀କ࿂̱̹͂෨ ࠁͬ4Ȫaȫͅা̳ȃ̭ͦͬ Case B ͈ܢ ෨ࠁ̳͂ͥȃ̹͘Ḙ͈̏ Case B ͈෨ࠁ͉ͅȄ
་պ͈ఱ̧̈́ڛഎౣਔܢ଼͈ͅ୶࣐̳ͥ
෨ͬࠁ଼̳ͥ໐Ȅ̳̻̈́ͩȄల 1 ٴ͈କ պષઌ໐̦̜̦ͥḘ͈̏໐ͬ෨ࠁ̦ڲ̥ͣ
̠̈́ͥ͢ͅͅੰٸ̱̹෨ࠁͬ4Ȫbȫͅা
̳ȃ̭ͦͬ Case C ͈ܢ෨ࠁ̳͂ͥȃఈ༷Ȅ
Case A ͈෨ࠁ̥ͣȄల 2 ٴ͈କպષઌ໐
ͬੰٸ̱̹෨ࠁͬ4Ȫcȫͅা̳ȃ̭ͦͬ
Ƚ1ȁ܊ධ໐ؗ GPS ෨Ⴢ̦ࠗ௴̢̹
2011ාཤ౷༷ఊဢؗ౷ૼೋ෨͈
ಲպ༊ओ1ȫ
Ƚ2ȁೋ෨͈ഥٜଢ଼͈̹͈͛κΟσ౷ࠁ
Case D ͈ܢ෨ࠁ̳͂ͥȃ
Case AȡD͈ܢ෨ࠁͬܢশ࣫Ȫt = 0 sȫ
̤̫ͥͅକ࿂ࠁ̱͂Ȅܢၠ௸ͬঢͥਫ਼́ 0
̱͂̀Ḙ͈̏ͦͣܢેఠ଼̳ͤͥ͢ೋ෨
͈ഥٜଢ଼࣐̠ͬ̈́ȃ̤̈́Ȅࠗॳڒঊۼڞݞ
͍ࠗॳশۼۼڞ͉Ȅ̷̸ͦͦȄxɁ100 m ݞ͍tɁ0.02 s ̳͂ͥȃ
5 ͅȄCase AȡD͈ೋ෨͈Ȅশ࣫tɁ 8,000Ȅ9,000 ݞ͍ 10,000 s ̤̫ͥͅକ࿂ࠁ͈
Ƚ3ȁ2 ͈κΟσ౷ࠁષ́ଔ̯̹ͦ
ೋ෨ܢ෨ࠁȪCase Aȫ
໐ȪCase C ͈ܢ෨ࠁ́ੰٸ̱̹໐ȫ
͜Ȅஃକ་ࠁͤ͢ͅ༰͈̯̦ࣞ੭șͅ௩ح̱Ȅ ତ෨ͅႨ̱̞̀ͥȃ̹͘Ȅশ࣫ tɁ8,000Ȅ 9,000 ݞ͍ 10,000 s ̴͈̞͈ͦশ̤̞࣫̀ͅ
͜ȄCase A ͈ೋ෨̯ࣞȄ̳̻̈́ͩȄ༰͈άȜ
·͈କպ͈डఱ̦ȄCase AȡD ͈ಎ́ड
Ƚ4ȁب̯̹ͦೋ෨ܢ෨ࠁȪCase BȡDȫ
Ȫaȫ Case A ͈ܢ෨ࠁ̥ͣ୶̧࣐̳ͥ֨෨
ͬࠁ଼̳ͥ໐ͬॉੰ̱̹෨ࠁȪCase Bȫ
Ƚ5ȁ3 ݞ͍ 4 ͈ೋ෨ܢ෨ࠁͅచ̳
ͥೋ෨͈ڎশ̤̫࣫ͥͅକ࿂ࠁ͈ࠗ
ॳࠫض
Ȫbȫ Case A ͈ܢ෨ࠁ̥ͣ୶̧࣐̳ͥ֨෨
͂ڛഎౣਔܢ଼͈ͅ୶࣐̳ͥ෨ͬࠁ଼̳
ͥ໐ͬॉੰ̱̹෨ࠁȪCase Cȫ
Ȫcȫ Case A ͈ܢ෨ࠁ̥ͣల 2 ٴ͈କպ ષઌ໐ͬॉੰ̱̹෨ࠁȪCase Dȫ
ତٜଢ଼ࠫضͬা̳ȃ
5 ٜͅଢ଼ࠫضͬা̱̹শ̤̞࣫̀ͅȄ
ೋ෨͉Ȅ2 ͈ஃ̞֚အକ૬ႀ֖ͬഥ
̱̞̀ͥȃ̭̭́ȄCase AȄB ݞ͍ D ͉́Ȅ
་պ͈ఱ̧̈́ڛഎౣਔܢ଼͈͈͙̈́ͣ
̴Ḙ̏ͦͅ୶࣐̳ͥȄକպ̞ͤࣞ͢କպ͈
Ȫaȫ tɁ8,000 s
Ȫbȫ tɁ9,000 s
Ȫcȫ tɁ10,000 s
͜ఱ̧̞ȃ̷̱̀ȄCase A ͈άȜ·ൢోশ
̦࣫ड்̩̞̈́̽̀ͥ͜ȃ
Case B ͂ Case C ͈άȜ·ൢోশ͉࣫Ȅশ
࣫tɁ8,000 s ͉́Ȅ͕͖֚౿̱̞̀ͥȃ̱
̥̱̦̈́ͣȄশ࣫ tɁ9,000 s ͉́ȄCase B
͈ల 2ȡ4 ෨̦ȄCase C ͈చ؊̳ͥల 1ȡ 3 ෨̷̸ͦͦͅ୶࣐̱̞̀ͥȃ̭͉ͦȄCase B ̤̞̀ͅȄڛഎౣਔܢ଼͈͈ೄஜ͈କ
պ̦ Case C ̩ͤࣞ͢Ḙ͈̭̦̏͂କ૬ͬ
చഎͅ૬̩̳ͥ࢘ض̱͂̀൱̧Ȅ෨௸̦͢
ͤఱ̧̩̹̜̈́ͥ͛́ͥ͂ࣉ̢ͣͦͥȃ̈́
̤ȄCase B ͈ల 5 ෨͉ȄCase C ͈చ؊̳ͥ
ల 4 ෨͂պ̜֑̞̦̩ͤ̈́͘ͅȄCase B
͈෨ಿ̦ Case C ͤ͢͜ಿ̱̹̭̦̥͂ͩ
ͥȃ̹͘ȄCase C ͈ೋ෨͉Ȅڛഎౣਔܢ
଼͈ͅ୶࣐̳ͥȄକպ̞ͤࣞ͢କպ͈໐
̹̞̹ͬ̈́͛Ȅ̷͈ల 1ȡ3 ෨͉ȄCase B ͈చ؊̳ͥల 2ȡ4 ෨ͤ͢͜Ȅ͈ड೩ କպ̷̸̦ͦͦ೩̞ȃশ࣫ t=10,000 s ͉́Ȅ Case B ͈ల 1Ȅ3 ݞ͍ 4 ෨̦ȄCase C ͈చ؊
̳ͥల 1ȡ3 ෨ͤ͢͜Ȅ̷̸ͦͦࢵͅஜ༷ͅ
պ౾̱̞̀ͥȃ
Case B ͂ Case C ͈ల 1 ෨͈डࣞକպ ϼmax
ͬࡉͥ͂Ȅt=9,000 s ͉́͘ȄCase C ͈༷̦
ఱ̧̞ȃ̭͉ͦȄCase B ͈༷̦Ȅ་պ͈ఱ
̧̈́ڛഎౣਔܢ଼͈͈ೄஜ͈କպ̦̩ࣞȄ
̭ͦͬକպ͂ࣉ̢ͥ͂Ȅచഎ̈́෨̦ࣞఱ
̧̩̞̹̈́͛ȄCase B ̤̞̀ͅȄஃକ་ࠁ
͈࢘ض̦̜࡛̞̞̥̜ͤͦ̀̈́ͣ́ͥ͘ȃ̭
ͦͅచ̱̀Ȅশ࣫ t=10,000 s ͉́Ȅϼmax͉Ȅ Case B ͈༷̦ Case C ͤ͢͜ఱ̧̩̞̈́̽̀
ͥȃ̭͉ͦȄt=10,000 s ̤̞̀ͅȄCase B
͈་պ͈ఱ̧̈́ڛഎౣਔܢ଼͈͈ల 1 ๔
࿒͈෨̦Ȅ̷͈ೄஜͅంह̱̹໐̥ͣࠁ଼
̯̹ͦ෨̞ͬา̞̤̀ͤȄ་պ͈ఱ̧̈́
ڛഎౣਔܢ଼͈͈ల 1 ๔࿒͈෨͈ೄஜ͈କ պ̦೩̩Ȅஃକ་ࠁ͈࢘ض̦ఱ̧̩࡛ͦͥ͢
̠̹̹̜̈́̽͛́ͥͅȃ
̭̭́ಕփ̧̳͓̭͉͂ȄCase A ͈ೋ෨͉Ȅ
་պ̦̭͕ͦ̓ఱ̧̩̞̈́ڛഎౣਔܢ଼͈
̦ȄCase D ͈̠̈́͢ಿਔܢ෨଼ͅਹ̈́̽
̲̹̀෨͂։̞̠̭̜̈́ͥ͂͂́ͥȃ̳̈́
̻ͩḘ͈̏ڛഎౣਔܢ଼͈͉Ȅౙඊ́
ϼmax̞̠͂डࣞକպͬခ̳ͥ෨̜́ͥȃ̭
ͦͬ࿅എͅນ࡛̳̹ͥ͛ͅȄ6 ͅা̳
̠̈́͢Ȅڛഎౣਔܢ଼͈ P ̦ಿਔܢ଼͈
Q ̞ͅັ̞̀ਹ̹̈́̽ેఠ̜́ͥ෨ R
͂Ȅܢକպ I ̦ၗ̱̲̹̀ 2 ෨͈̠̻
͈ 1 ෨̜́ͥ෨ J ͂ͬࣉ̢ͥȃஜ৪͉́Ȅ෨ P ݞ͍෨ Q ̦ΕςΠϋഎ̈́૦ͥໍ̞̳ͬͥ͂
ب̳ͥ͂Ȅ෨ R ͈ڛഎౣਔܢ଼͈̦
ಿਔܢ଼͈̞ͬา̞̹ࢃȄڛഎౣਔܢ
଼͈͈डࣞକպ͉Ȅࡓ͈෨P͈डࣞକպ
ഽ̈́ͥͅȃ̭ͦͅచ̱̀Ȅࢃ৪͉́Ȅ෨ J
ͅ܄ͦͥ͘Ȅ་պ͈ఱ̧̈́ڛഎౣਔܢ଼͈
͉Ȅ̷͈ೄஜ͈໐̞ͬา̞̀͜Ȅ̷͈
डࣞକպ̦෨ J ͈डࣞକպ̥̜ͣͤ͘་ا̱
̞̈́ȃ̭̭͉́Ḙ͈̏෨ J ͅࡉ࡛ͣͦͥય̦Ȅ Case A ݞ͍ B ࡛̞ͦ̀ͥͅȃ
Ƚ6ȁ་պ͈ఱ̧̈́ڛഎౣਔܢ଼͈ͬ
܄͚ 2 ਅ႒͈ೋ෨͈࿅Ȫ෨ R ͉Ȅ ෨ P ̦෨ Q ̞ͅັ̞̀ਹࣣ̱̹෨
̜́ͥȃఈ༷Ȅ෨ J ͉Ȅೋ෨ܢ෨ ࠁ I ̦ऒֲͅၗ̱̹̠̻͈Ȅ͈
ֲ༷࢜ͅૺ࣐̳ͥ෨̜́ͥȃȫ
Case A ͈ܢ෨ࠁͬࡉͥ͂ȄCase D ͈
ܢ෨ࠁͅȄڛഎౣਔܢ଼͈ͬࠁ଼̳ͥ໐
̦̞̠̽̀ͥ͢ͅࡉ̢̦ͥḘ͈̏ࡉ༷
͉Ȅࢋ̜ͤ́ͤȄCase C ͈ܢ෨ࠁ͈ఘ
̦Ȅౣਔܢ෨଼ͬࠁ଼̳ͥ͂ࣉ̢ͥຈါ̦
̜ͥȃ̷̱̀Ȅϼmax̞̠͂डࣞକպͬခ̳
ͥڛഎౣਔܢ଼͈͈ೄஜ͈କպ̦ڛഎ
̞ࣞાࣣ̦ȄCase A ݞ͍ B ͈ೋ෨ͅࡉͣͦȄ
̧̭͈͂Ȅକպ̦̞ࣞેఠ̜͙̯́ͥ͂̈́
ͦȄஃକ་ࠁ͈࢘ضͥ͢ͅ෨͈ࣞ௩໙ݞ͍
Ⴈ̦࡛̩̞ͦͅȃ
̱̥̱̦̈́ͣȄশ࣫tɁ10,000 s ͉́Ȅ
Case A ݞ͍ B ͂͜Ȅ་պ͈ఱ̧̈́ڛഎౣ
ਔܢ଼͈͈ల 1 ๔࿒͈෨̦Ȅ̷͈ஜ̜̽ͅ
̹໐̥ͣࠁ଼̯̹ͦ༰ͬา̧ݲ̤̽̀ͤȄ
ೄஜ͈କպ̦೩̞̹͛Ȅஃକ་ࠁ͈࢘ض̦࡛
̳̩̞ͦ̈́̽̀ͥ͞ȃ̤̈́Ȅ་պ͈ఱ̧̈́
ڛഎౣਔܢ଼͈͂Ȅ̷͈ஜ̜̹̽ͅ໐̥
ͣࠁ଼̯̹ͦႨ෨̦͂ਹ̈́ͥΗͼηϋΈͅ
ջం̱̀Ȅೋ෨͈ల 2 ෨̦ల 1 ෨ͤ͢͜डࣞ
କպ̦̩̞̹ࣞ̈́ͥ͂̽ેఠ̦̲ංͥȃ ఈ ༷ȄCase A ͂ Case B ͬ ڛ ̳ ͥ ͂Ȅ Case A ͈༷̦ల 1 ෨͈डࣞକպϼmax̦ఱ̧
̞̦Ḙ͈̏ၑဇ͉Ȅ࡛শത́ྶږ̞́̈́ȃ̹
̺̱ȄCase A ̧̦֨෨Ȫ̭͈໐ͬ p ͂ࡤ
̭̳͐͂ͥͅȃȫ̥ͣই̤̽̀ͤ͘ȄCase A ͈Ȅ
་պ͈ఱ̧̈́ڛഎౣਔܢ଼͈ r ͈ೄஜ͈
໐ q ͈Ȅࢵͅஜ͈໐ p ͈କպ̦ڛഎ೩
̩Ȅ̷͈̹͛Ȅ໐ q ͈෨̦ࣞచഎͅఱ̧
̩̤̈́̽̀ͤȄ໐ q ͅஃକ་ࠁ͈࢘ض̦ఱ
̧̩࡛̞ͦ̀ͥȃ̭̠̱̹໐ q ͬڛഎౣ
ਔܢ଼͈ r ̦าً̞࣐̩̤̞̀̀ͅȄة
̥͈ͣၑဇ́ Case A ͈ϼmax̦ఱ̧̩̈́̽̀
̞ͥȃ໐ p ͈גޣ̦Ȅq ̱ͬٚ̀ r ͅݞ͐
͈̜́ͦ͊Ȅq ͈෨ಿ͜Ȅr ͈ഥͅגޣ̳
ͥ͂ࣉ̢ͣͦͥȃ
ːȅೋ෨ܢ෨ࠁ͈ଔ
౷ࠁͬచય̱̹͂ೋ෨͈ 1 ষࡓഥٜ
ଢ଼࣐̞ͬ̈́Ȅ1 ͅা̳କ࿂ࠁ̹̳ͬͣ͜Ȅ
ೋ෨෨࡙֖̤̫ͥͅܢକ࿂ࠁͬদ࣐॒ࢋͅ
ͤ͢ଔ̳̭ͥ͂ͬদ͙ͥȃ̷͈षͅḘ̭̏
͉́Ȅষ͈̠̈́͢ඵ͈̾بͬ୭̫ͥȃ ب Ȫ1ȫ:ೋ ෨ ̦Ȅ ܊ ධ ໐ ؗ GPS ෨ Ⴢ
͈ࠗ୭౾ത߃ཌྷͬͥཤ 39ɋ 15ȧ58ȩ͈ೄષ̥ͬͣୌͅ 1 ষࡓഎͅഥ̱̹ȃ
بȪ2ȫ:ߗۼഎ֚ͅအ̈́௸ഽ͈౷་̦Ȅ1 ഽ̺̫อ̱̀Ȅೋ෨଼̦̯ͦ
̹ȃ
7 ͅȄཤ 39ɋ15ȧ58ȩ͈ೄષ͈٬
ೲ౷ࠁͬা̳ȃ̹̺̱Ḙ͈̏ࠗॳႀ֖͈܅௰
Ȫֲ͈༷ȫ֚ͬအକ૬ 70 m ͈بே֖̱͂Ȅ
̭̭ͅ෨͈ৣͬཡ̪̹͈͛ sponge layer ͬ
౾̩ȃ̹͘Ȅ௰༷ޏٮͅȄSommerfeld ͈༶
ৣૄͬഐဥ̳ͥȃ܊ධ໐ؗ GPS ෨Ⴢࠗ
͈୭౾ത͉ȄxɁ478.7 km ͈պ౾̜́ͥȃࠗ
ॳڒঊۼڞݞ͍ࠗॳশۼۼڞ͉Ȅ̷̸ͦͦȄ xɁ100 m ݞ͍tɁ0.01 s ̳͂ͥȃ
Ƚ7ȁೋ෨ܢ෨ࠁ͈ଔ͈̹͈͛ࠗॳచ યႀ֖͈٬ೲ౷ࠁ
ܢକ࿂ࠁ͈ଔ͉Ȅষ͈̠̈́͢ਜ਼࣐́
̠̈́ȃ
Ȫ1ȫೋ෨̦ࠁஃକ෨͈෨௸́ഥ̱̹͂
ب̱̀Ȅ1 ͈ಲպ༊ओϼȪtȫ̥ͣȄ
౷ૼٳইশ࣫ t = t0̤̫ͥͅೋ෨෨ࠁͬ
ݥ͛ȄGreen ༹͈௱ͬဥ̞̀କպͬ
୯̳ͥȃ̳̻̈́ͩȄষ̽̀͢ͅȄକ
࿂་൲ϼ0Ȫxȫͬݥ͛ͥȃ
Ȫ6ȫ
Ȫ7ȫ
Ȫ8ȫ
̭̭́ȄhȪxȫɁbȪxȫ͉Ȅକ૬̜́
ͤȄ̹͘ȄxGPSݞ͍hGPS͉Ȅ̷̸ͦͦȄ
܊ධ໐ؗ GPS ෨Ⴢ͈ࠗ୭౾ത͈պ౾ ݞ͍କ૬̜́ͥȃ
Ȫ2ȫං̹ͣͦϼ0Ȫxȫ͈ 2 ͈ͬକ࿂་൲
̱͂̀ခ̳ͥ෨ࠁͬೋ෨ܢ෨ࠁ̳͂
ͥȃ
Ȫ3ȫೋ෨ܢ෨ࠁͬܢକ࿂ͅဓ̢Ȅܢ
ၠ௸ͬঢͥਫ਼́ 0 ̱͂̀Ȅೋ෨͈ 1 ষ ࡓഥٜଢ଼࣐̠ͬ̈́ȃ
Ȫ4ȫ܊ධ໐ؗ GPS ෨Ⴢ͈ࠗ୭౾ത̤̫ͅ
ͥକ࿂་൲͈ࠗॳࠫضͬ1 ͅা̱̹
ࠗ௶ࠫض͂ڛ̳ͥȃ
Ȫ5ȫܢ෨ࠁ͈༞ୃ࣐̞ͬ̈́Ȅષܱ͈Ȫ3ȫ ȡȪ4ȫͬ߫ͤ༐̱̀Ȅࠗ௶ࠫض̩ͬ͢
ठ࡛̳ͥೋ෨ܢ෨ࠁͬࠨ̳ͥȃ
̭̠̱̀ං̹ͣͦೋ෨ܢ෨ࠁͬ8 ͅ
া̳ȃ
̞͛ͣͦ̈́ȃ̭͈Ⴈ෨͉Ȅೋ෨ܢ෨ࠁ̦
ஜࢃͅၗ̳ͥष̲ͅȄഥ̱̹͈̜́͜
ͥȃࠗॳ͂ࠗ௶̭̠̱̹ͅओ։̦࡛̹ͦ
ࡔ֦͈͉֚̾ȄبȪ1ȫͬ୭̫̹̭̜͂́ͥȃ
̳̻̈́ͩȄೋ෨͈ 2 ষࡓഥ̦ࣉ̢̞ͣͦ̀
̞̹̈́͛Ḙ̭̏́చય̱̹͂ഥࠐႹ̥ͣٸ
̹ͦ෨ࡘ̥͈ͣೋ෨͈ഥ̦๛̯̞ͦ̀ͥȃ
8 ͉́ȄάȜ·ུ̦٬ࢾͤؗ͢͜௰ͅ
պ౾̱̞̦̀ͥȄ෨࡙̦Ḙ̭̏́చય̱̹͂
ഥࠐႹ̥ͣٸ̹̞ͦպ౾̜̹̽̈́ͣ͊ͅȄ
ೋ෨ܢ෨ࠁ͈άȜ·ུ̦٬ࢾͤؗ͢௰ͅ
̜ͥຈါ̦̞̈́ȃ̹̺̱Ȅष͉ͅȄஜ̱
̹Ⴈ෨̦อ̱̞̞͈̀̈́́ȄάȜ·໐
͈෨࡙̦̭̭́చય̱̹͂ഥࠐႹ̥ͣٸͦ
̹̞պ౾̜ͤͅȄ̷͈౷ത̥ͣάȜ·໐̦Ȅ
ೋ෨̯͈ࣞڛഎ೩଼̞ͤ͢͜ಁͦ̀ഥ
̱Ḙ̦̏ͦͣਹࣣ̱̀ȄGPS ෨Ⴢࠗ୭౾ത
́ 2 ٴ͈କպષઌ̦ࠗ௶̯̹ͦ͂ࣉ̢ͣͦ
ͥȃ̧̭͈͂ȄGPS ෨Ⴢࠗ୭౾തً̱ͬ
̹ೋ෨͉Ȅ6 ͈ષͅা̱̹Ȅ2 ෨͈ਹ
ࣣ͈ࠫض̲̹෨ R ͅ൚̳̭ͥ͂̈́ͥͅȃ
̹͘ȄبȪ2ȫ͉́Ȅ౷་̦ 1 ഽ̺̫
̲̹̯̞͂ܰͦ̀ͥȃIde et al.5ȫ͉Ȅ։̈́
ͥાਫ਼́Ȅٴͬࠐ̀౷་̦̲̹̭̳͂ͬ
͓ͤ௸ഽͅܖ̧̿া̱̤̀ͤḘ̠̱̹̏ࠫض
ͬࣉၪ̱̀ೋ෨ܢ෨ࠁͬଔ̳ͥຈါ̦̜
ͥȃ႕̢͊Ȅډઔ3ȫ́া̱̹̠̈́͢ȶાਫ਼
ͬ་̢̧̀ܳͥ౷་ȷ̦ఉٴ̲́Ȅഥ
ಎ͈ೋ෨̦ȄठഽȄ٬ೲၦฺ̠ܳͅକպષઌ
̫̹ͬ͂ࣉ̢ͥ͂Ȅ٬ೲ͈ၦུ֖̦ܳ٬
ࢾͤ͢܅௰̜ͤͅȄ̹͘Ȅ9 ͅࡉͣͦͥ
শ࣫ t=30 ஜࢃ͈Ⴈ෨̦̲̞̈́ૄ
ͬࡉ̳̭̦͂خෝ͂̈́ͥȃ
ˑȅࠫȁȁა
෨͈ࠁ͂८ͬࣉၪ̱ȄκΟσ౷
ࠁͬచય̱͂̀Ȅೋ෨͈ 1 ষࡓഥٜଢ଼࣐ͬ
̹̈́̽ȃ་պ͈ఱ̧̈́ڛഎౣਔܢ଼͈ͬ
܄͚ೋ෨͉́Ȅ̷଼͈͈ೄஜ͈କպ̦କ պ̞ͤࣞ͂͢Ȅచഎ̈́༰͈̯̦ࣞ೩̞̹͛Ȅ ஃକ་ࠁฺ̠ͅ෨͈ࣞ௩໙͞෨͈Ⴈ̦࡛ͦ
̩̩ͅȄ̹͘Ȅ෨௸̦ఱ̧̩Ȅ෨ಿ͈ಿၚ
Ƚ8ȁ1 ͈କ࿂་൲̥ͣଔ̯̹ͦೋ
෨ܢ෨ࠁ
Ƚ9ȁ܊ධ໐ؗ GPS ෨Ⴢ͈ࠗ୭౾തȪx
Ɂ478.7 kmȫ̤̫ͥͅକ࿂་൲͈ࠗ
௶ࠫض1ȫ͂8 ͅা̳ೋ෨ܢ෨ ࠁ଼̥̯ͣͦͥೋ෨͈ࠗॳࠫض
̭͈ೋ෨ܢ෨ࠁͬဓ̢̀ 1 ষࡓഥٜଢ଼
̧࣐̹͈ͬ̈́̽͂Ȅ܊ධ໐ؗ GPS ෨Ⴢࠗ
͈୭౾ത̤̫ͥͅକ࿂་൲͈ࠗॳࠫض͂ࠗ௶
ࠫضͬ9 ͅা̳ȃ
9 ͤ͢Ȅల 1 ෨͈άȜ·͞պ̦̩͢
ठ࡛̯̞ͦ̀ͥ͂࡞̢ͥȃ̱̥̱̦̈́ͣȄࠗ
ॳࠫض͉́Ȅల 1 ෨͈άȜ·ࢃͅႨ෨̦
อ̱Ḙ̦̏ͦ9 ̤̞̀ͅȄশ࣫ t=30
ஜࢃͅࡉ̦ͣͦͥḘ͉̏ͦȄࠗ௶ࠫضͅ
̦̞ࣞȃ̱̥̱̦̈́ͣḘ͈̏ڛഎౣਔܢ͈
଼̦Ȅ̷͈ೄஜ̜̹̽ͅȄକպͤ͢କպ
͈̞ࣞ໐͈෨ͬา̧ݲͥ͂Ȅచഎ̈́༰͈
̯̦̩ࣞࣞ̈́ͤȄஃକ་ࠁ͈࢘ض̦௩ఱ̳ͥȃ
̹͘Ȩ̏֨෨̥ͣইͥ͘ાࣣȄ̳̻̈́ͩȄ
་պ͈ఱ̧̈́ڛഎౣਔܢ଼͈͈ೄஜ͈໐
͈Ȅࢵͅஜ͈໐͈କպ̦କպͤ͢೩̞
ાࣣȄచય̱̹͂ΉȜΆ͉Ȅڛഎౣਔܢ
଼͈͈डࣞକպ̦Ȩ̏֨෨̦୶࣐̱̞̈́ા
ࣣ͓̩̹͂̀ࣞ̈́̽ȃ
ࢵͅȄ1 ষࡓ͈ೋ෨ഥ͂Ȅ1 ٴ͈౷་
ͬب̱Ȅ܊ධ໐ؗ GPS ෨Ⴢ̦ࠗ௴̢̹
କ࿂་൲͈ࠗ௶ͤ͢Ȅ2011ාཤ౷༷ఊ
ဢؗ౷ૼೋ෨͈ܢ෨ࠁͬଔ̱̹ȃ̷͈
ࠫضȄల 1 ෨͈෨ࠁ̷̤̤ͬ͢ठ̧࡛̹̦́Ȅ
ٜଢ଼ࠫض͉́Ȅࠗ௶ͅࡉ̞ͣͦ̈́Ⴈ෨̦
࡛ͦȄ̹͘ȄάȜ·໐͈෨࡙֖̦Ȅུ٬ࢾ
ͤؗ͢௰ͅպ౾̳̭̹ͥ͂͂̈́̽ȃ̭ͦͤ͢Ȅ GPS ෨Ⴢࠗ୭౾ത͉́Ȅ̞ͤ͢෨࡙̥ͣ
ഥ̱̹άȜ·໐͂Ȅೋ෨̯͈ࣞڛഎ೩̞
଼̦ਹࣣ̱̞̹̭̀͂Ȅ̱̩͉͜Ȅ౷་̦
ાਫ਼ͬ་̢̀ఉٴ̲̹̭̦́͂ଔ௶̯ͦ
ͥȃ
ུࡄݪ̦Ȅ໐شڠજشڠࡄݪ༞੩߄Ȫܖ
๕ࡄݪȪCȫȪ21560544ȫȫͥ͢ͅࡄݪ͈֚໐
̜̭́ͥ͂ͬັܱ̳ͥȃ
४ࣉࡃ
1ȫعࣣࢬణȆऎȁ૯Ȇ࢛ࢼඵȆ۾ȁ࣪ࡨ:
଼23ාȪ2011ාȫཤ౷༷ఊဢؗ౷
ૼೋ෨͈අ, ࢽსߗࢽܿࡄݪਫ਼༭࣬, ల50ے, ల4, pp. 363, 2011.
2ȫډઔఊ: ൫କ٬ຩ̤̫ͥͅඤ໐෨͈ݷ
൲͈ତࠗॳ, ٬܅ࢥڠაਬ, ల48ے, pp.146150, 2001.
3ȫډઔఊ: ೋ෨౷ૼ̹̯̽̀ͣͦͥ͢͜ͅ
̜̠́ͧܜ̥͈̾౷་ࠁఠ͂ࠁ଼̯ͦͥೋ
෨͈ତٜଢ଼, ೋ෨ࢥڠࡄݪ༭࣬, ల23, pp. 6986, 2006.
4ȫ Nakayama, K. and Kakinuma, T.: Internal waves in a twolayer system using fully non linear internalwave equations, Int. J. Numer.
Meth. Fluids, Vol. 62, pp. 574590, 2010.
5ȫ Ide, S., Baltay, A., and Beroza, G. C.: Shallow dynamic overshoot and energetic deep rupture in the 2011 Mw 9.0 TohokuOki Earthquake, Sciencexpress, www.sciencexpress.org.