計算蔵出しシリーズ 地震波動伝播  2020年7月16日新設
Computational Wave Propagation Series (Newly uploded on July 16, 2020), English ver. on 6th Apr.2024


Basically, the description follows the one at the time of uppladed (explanations for 3 and 4 are added this time).

The text was mainly used in the geoscience class of Tennoji high school at OKU at that time as well as in the 3rd grade course "Solid Earth Science II" of the Department of Liberal Arts at Osaka Kyoiku University, which the author has been in charge of since 2012.

1.地震波伝幡(PREMモデル)シミュレーション動画  地球内部の地震波の伝播は波線図がふつうであるが,津波にならって,媒質の動きをP-SV波の式(Vriuex,1986)を用いて計算した.地球内部構 造モデルのうち,PREMモデル(Dziewonsky & Anderson,1981)の弾性定数,密度を用いた.媒質の速度(2成分の絶対値 和ではなく,図の左右方向の速度成分表示だったと思います)をPovray3によるレンダリングで表現している.外核でS波が消えているのがわかるほか,各種屈折波,反射波が見える.(2001年07/06初出,201211/28更新


1. Seismic wave propagation in our earth interior (Prem Model).

The seismic wave propagation in the earth's interior is usually shown in wave ray paths, however the P-SV wave equation (Vriuex, 1986) was used to calculate the motion of the medium, as in the case of a tsunami. The elastic constants and density of the PREM model (Dziewonsky & Anderson, 1981) were used. The velocity of the medium (not the absolute sum of the two components, but the velocity components in the left and right directions in the figure) is represented by a Povray3 rendering. S-waves are seen to disappear in the outer core, and various refracted and reflected waves are also visible. (First uploaded 07/06/2001, updated 11/28/2012)

August 2020. I found the manuscript of the presentation at the Geoscience Education Society of Japan (1999), now only in Japanese, so I made it available as a pdf file. An example of tsunami calculation is also included.

2.地震波伝播(地殻とマントル)シミュレーション動画  高校地学でモホ面の発見は重要なテーマであるが,なぜ屈折波がモホ面から帰ってくるかを説明するのは至難の業である.P-SV波(P波と,S波のうち計算格子に平行な振動成分)の波動計算で2層構造下での屈折波の帰還を示した.図でhead waveと描かれているのが,モホ面から帰還する屈折P波.計算は(Vriuex,1986)を参考にし,x方向の速度成分で表示.ムービーファイルはPovRayでレンダリングした画像を動画化.(2001.11/26初出,2012.11/28改訂)

2. Seismic wave propagation at Moho dincontinuty (two layer model).

The P-SV wave (P waves and S waves parallel to the computational grid) simulation shows the return of refracted waves under a two-layered underground.
The head wave in the figure is the refracted P wave returning from the Moho boundary. The calculation is based on (Vriuex, 1986) and is shown with the velocity component in the x-direction. Movie files are animated images rendered by PovRay. (First uploaded on 2001.11/26, revised on 2012.11/28)

※ 上2種の各種波形のnomenclature画像 Nomenclature images of the above two types of waveforms

3.(PREMモデル)シミュレーションの走時曲線描画  上 記シミュレーションにおいて,地上に等間隔に置かれた地震
計が記録する揺れ(速度波形)をデータとして記録し,走時曲線のように表示したもの.実際の地震 による走時曲線(下記)とほぼ同じものがかける.これはつまりPremモデルの地下構造の推定が概略正しいことを示す.

実際の地震波形から読み取った顕著な位相による走時曲線の例: 例えばhttps://ds.iris.edu/ds/nodes/dmc/news/2014/09/global-stacks-poster-contest/
原辰彦(2005) https://www.jstage.jst.go.jp/article/jgeography1889/114/3/114_3_323/_pdf/-char/ja

3. The taver-time curve of the Prem Model simulation

The data of shaking (velocity waveform) recorded by the seismographs placed at equal intervals on the ground in the above simulation is recorded as data and displayed as a travel-time curve.
It is almost the same as the runtime curve of an actual earthquake (see below). This means that the Prem model's estimation of the subsurface structure is approximately correct.

An example of a runtime curve with a significant phase read from an actual seismic waveform: e.g. https://ds.iris.edu/ds/nodes/dmc/news/2014/09/global-stacks-poster-contest/

In practice, when there is still a discrepancy between the model and observations, the model is naturally modified to reveal a more detailed structure of the Earth's interior. This process can be seen, for example, in Tatsuhiko Hara (2005) https://www.jstage.jst.go.jp/article/jgeography1889/114/3/114_3_323/_pdf/-char/ja (Sorry, in Japanese)
English ver. ref. will be uploaded soon (6th Apr. 2024).

4.(ドラえもんモデル)シミュレーション動画 と 走時曲線描画   比較のために上記Premモデルではなく,私が勝手に作った地球内部構造モデル(「ドラえもん」モデル,荒唐無稽なモデル)による地震波伝播とその走時 曲線を示す(Captionがないが,上のPremモデルと同じ).これにより”地球内部空洞説”などトンデモ説は地震波観測により完璧に否定されること は明らか! 

4. (Doraemon model) Simulation movie and drawing of travel time curves

For comparison, I show the seismic wave propagation and its travel time curves by my own model of the Earth's interior structure (named "Doraemon" model, a ridiculous model) instead of the above Prem model (There is no caption, but it is the same as the Prem model above). ). It is clear that the "Earth's interior cavity theory" and other demo theories are completely disproved by seismic wave observations! 

地震波伝幡(震災の帯)シミュレーション画像  神戸の地震における「震災の帯」の生成は数多くの専門家の研究テーマとなったが,ここでは地下構造に起因する地震波の屈折と表面波との干渉による振幅の増 幅の説明をシミュレートしてみた.ただし,この計算のみ上記に用いたP-SV波の波動式ではなく,より簡単なSH波の計算式にしたがっている.計算の概要と地下構造は入倉(1996)等を参考にした.さらに波形表現も上記で用いた媒質速度ではなく変位で表現 していることに注意.N88BASICによる計算画面である.

六甲山から大阪湾に至る南北断面を表示している.灰色は固い花崗岩の岩盤.色のついた地層は柔らかい堆積層であるが,底から地上にむけて順に柔らかくな る.つまり地震波速度が遅くなる.そのため地下からみると堆積層がいわば凸レンズの役割をして,地震波を屈折させ地上に焦点を結ぼうとする.一方地表に露 出する花崗岩と固い扇状地堆積層(青色)は表面波にとって壁となり,柔らかい堆積層側の表面波を反射する.これらの効果が組み合わされて図で Disaster Beltと書かれた地上部分に振幅を大きな震動を生じさせた.これが震災の帯の成因とされる.しかしこれらの事実はこの神戸の地震のあと,研究者によって 初めて見いだされ,現在は世界の地震防災の教訓となっている(追記).

5. "Disaster belt" at Kobe in 1995 Kobe earthquake

Simulated images of seismic wave propagation ("Disaster Belt") The generation of the "Disaster Belt" in the Kobe earthquake has been the subject of research by many experts. However, for this calculation we use a simpler SH wave equationon (followed Irikura (1996) and others) instead of above P-SV wave equation. The following is a screen shot of our calculation using N88BASIC. http://seagull.stars.ne.jp/wave_simulations/Propagation/Kobe_Disaster_Belt.png

The figure shows the north-south section from Mt. Rokko to Osaka Bay through Kobe urban area. The gray color shows hard granite bedrock. The colored layers are soft sedimentary layers, which become softer from the bottom to the ground. This means that seismic wave velocities slow down. The sedimentary layers act as a convex lens, refracting the seismic waves to focus them on the ground. On the other hand, the exposed granite and hard fan sediments (blue) act as a barrier to the surface waves and reflect them away from the softer sedimentary layers. The combination of these effects produced large amplitude ground motions at the surface level, which is indicated as the "Disaster Belt" in the figure. This is believed to be the cause of the strong shaking disaster belt. However, these facts were first discovered by researchers after the Kobe earthquake and are now lessons for earthquake disaster prevention around the world (see postscript).


岡本義雄:モデルを意識した地学教材,特に地震分野,地球惑星科学関連学会2004年合同大会セッション報告「新しい地学教育の試み」64-75, 2004  口絵 mgp_files


Yoshio Okamoto (2004): Model-oriented teaching materials for geoscience, especially in the field of earthquakes, Report of the 2004 Joint Meeting of Societies of Earth and Planetary Sciences "An Attempt at New Geoscience Education", 64-75, 2004, (in Japanese) Frontispiece     mgp_files

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