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Why does the shaking of the Earth not continue forever? なぜ地球は永遠に振動し続けないのか？

Why does the shaking of the Earth not continue forever? なぜ地球は永遠に振動し続けないのか？. Seismic Wave Amplitude Decreases with Distance (Time) 地震波の振幅は伝播する距離や時間とともに減衰する 　　1. Geometrical Spreading 地震波の幾何学的広がり 　　2. Attenuation 減衰 　　　- Intrinsic Attenuation 媒質固有の減衰

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Why does the shaking of the Earth not continue forever? なぜ地球は永遠に振動し続けないのか？

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  1. Why does the shaking of the Earth not continue forever? なぜ地球は永遠に振動し続けないのか？

  2. Seismic Wave Amplitude Decreases with Distance (Time) 地震波の振幅は伝播する距離や時間とともに減衰する 　　1. Geometrical Spreading 地震波の幾何学的広がり 　　2. Attenuation減衰 　　　- Intrinsic Attenuation媒質固有の減衰 　　　　　　Free Oscillations自由振動 　　　　　　Surface Waves表面波 　　　　　　Body Waves実体波 　　3. Scattering Attenuation散乱による減衰 　　　　　　Body Waves実体波 Traveling Waves vs Normal Modes (Standing Waves) 伝播する波 定常波

  3. Throwing a stone into a pond… 池に石を投げ入れると・・・

  4. Geometrical Spreading　地震波の幾何学的広がり Surface wave amplitudes  1/r 表面波の振幅

  5. Geometrical Spreading地震波の幾何学的広がり Body wave amplitudes  1/r 実体波の振幅

  6. Aki and Richards, Ch. 4.

  7. Amplitudes can increase with distance 振幅が距離とともに大きくなるのは - caustics - antipodes対蹠点（地球上の反対に当たる点）

  8. Large Amplitudes Small Amplitudes

  9. Satake 1988 May 22, 1960 Chile Earthquake, 5-6m tsunami in Tohoku, Hokkaido東北地方や北海道で5-6mの津波 142 dead and missing people 142名の死者・行方不明者

  10. Intrinsic Attenuation　媒質固有の減衰 Q = Quality factor = Fractional Loss of Energy per cycle 1周期でのエネルギー損失の割合

  11. freq. Range where • amplitude is of peak • 振幅が最大値の • になる周波数の範囲

  12. Earth Free Oscillations 地球の自由振動 1-D Vibrating String 弦の振動

  13. 地球の自由振動 周期 Alsop et al., 1961 周波数

  14. 観測されている地球の固有周期 S 0 8 Shearer Ch.8.6 Lay and Wallace, Ch. 4.6

  15. m nPl S Spheroidal T Toroidal n = 0 fundamental = 1 1st hgher mode = 2 2nd higher mode l = total no. of nodal lines m = no. of longitudal nodes

  16. Stein and Gellar, 1978

  17. The Earth is not a very good bell Q of the Earth is about 200 Q of a bell is about 3,000 福井県、大心時（だいしんじ）

  18. m nPl 3 nP8 l = ? m = ?

  19. Q of Bell 1/5 amplitude in 5 sec ⇒　1/25 energy 100 hz ⇒　500 cycles in 5 sec Energy loss per cycle is (24/25) /500 = 0.002 1/Q = energy loss/2/pi = 0.00032 ⇒　　 Q ~ 3000

  20. Surface Waves 表面波 観測点 地震 Lay and Wallace, Ch. 4.7

  21. Body Waves実体波

  22. Q Operator, Carpenter 1967

  23. t* ~ 1.0 for teleseismic P-waves遠地P波 t* ~ 4.0 for teleseismic S-waves遠地S波 independent of distance 距離に依存しない

  24. What is the physical mechanism for Q? Q（減衰）の物理的なメカニズムは何か？ - Grain boundary friction ? 粒子境界での摩擦？ - Creep ? クリープ？ If Q is due to shearing, もしQ（減衰）がせん断に伴って起こるならば Qp/Qs =2.25

  25. S波のQ（Qs) 深さ（km) Anderson and Hart, 1978

  26. 3-D Inversion for Qs Sekine et al., (2002)

  27. Sipkin and Jordan,1979

  28. Scattering Q 散乱による減衰 Q (intrinsic) ~ 5000

  29. Sato and Fehler, 1998

  30. Sato and Fehler, 1998 Single Scattering Model – Aki and Chouet, 1975

  31. コーダ波の Q Sato and Fehler, 1998

  32. 散乱によるQ 時間に対する全エネルギー密度 Hoshiba, 1993

  33. Seismic Wave Amplitude Decreases with Distance (Time) 地震波の振幅は伝播する距離や時間とともに減少する 　　　　1. Geometrical Spreading地震波の幾何学的ひろがり Same for all frequencies　　あらゆる周波数で同じ効果 　　　　2. Attenuation減衰 　　　　　- Intrinsic Attenuation媒質固有の減衰 High frequencies affected more　　高周波数でより減衰 　　　　　　　　　　　　 Large depth and spatial differences　深さや場所によって大きく変化 Frequency dependent　　周波数に依存する 　　- Scattering Attenuation散乱による減衰 Coda waves　コーダ波 Includes both scattering and intrinsic Q 散乱と媒質固有の減衰の両方を含む

  34. References Aki, K. and B. Chouet, Origin of coda waves; Source, attenuation and scattering effects, J. Geophys. Res., 80, 3322-33421975 Aki K. and P.G. Richards (AR), Quantitative Seismology, 2nd Edition., University Science Books, 2002 Alsop, L.E., G.H. Sutton, M. Ewing, Free oscillations of the Earth observed on strain and pendulum Seismographs, J. Geophys. Res., 66, 631-641, 1961. Anderson, D.L. and R.S. Hart, Q of the Earth, J. Geophys. Res., 83, 5869-5882, 1978 Carpenter, E.W., Teleseismic signals calculated fro underground, underwater, and atmospheric explosions, Geophysics, 32, 17-32, 1967 Hoshiba, M. Separation of scattering attenuation and intrinsic absorption in Japan using the multiple lapse time window analysis of full seismogram envelope, J. Geophys. Res., 98, 15809-15824, 1993 Lay T. and T.C. Wallace (LW), Modern Global Seismology, Academic Press, 1995. Rautian, T.G. and V.I. Khauturian, The use of coda for the determination of the earthquake source spectrum, Bull. Seismol. Soc. Am., 68, 949-971, 1978 Satake, K., Effects of bathymetry on tsunami propagation: Applications of ray tracing to tsunamis, Pure Appl. Geophys., 126, 27-36, 1988 Sato, H. and M. Fehler, Seismic wave propagation and scattering in the heterogeneous Earth, Springer-Verlag, 1998. Sekine, S., K. Koketsu, D. Zhou, Tomographic inversion of ground motion amplitudes for the 3-D attenuation structure beneath the Japanese Islands, S086-004, Abstracts, 2002, Japan Earth and Planetary Science Joint Meeting. Shearer, P. , Introduction to Seismology, Cambridge Univ. Press, 1999. Sipkin, S.A. and T.H. Jordan, Frequency dependence of QScS, Bull Seismol Soc Am. 69; 1055-1079, 1979 Stein, S. and R.J. Gellar, Time domain observation and synthesis of split spherical and torsional free oscillations of the 1960 Chile earthquake: Preliminary results, Bull. Seismol. Soc. Am., 68, 325-332, 1978.

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