24 October 2007

３次元複雑断層系における地震発生過程の理論的研究

Theoretical study on earthquake generation process in a 3D complex fault system

青地秀雄（仏・地質調査所） Hideo Aochi (BRGM, France)

24 October 2007 > 2

本日の目次

> 簡単な紹介> 問題設定とシミュレーション手法> １９９２年ランダース地震> 中部デュロンス断層帯（仏南東部）におけ

るシナリオ地震

24 October 2007 > 3

略歴

> 2004- BRGM （仏・地質調査所）： H. Modaressi 博士• 力学的計算に基づく地震ハザード・リスク研究（有限要素法）

> 2003-2004 IRSN （仏・放射線防護原子力安全研究所）： C. Berge-Thierry 博士• 地震ハザード研究への応用• Aki & Richards 翻訳

> 2000-2003 ENS Paris （パリ高等師範学校）： R. Madariaga 教授• 相互作用のある断層系における地震破壊過程の数値的研究• 近地地震動の計算（差分法）

> 2000 東大院理（博士） : 松浦充宏教授• ３次元複雑断層系における地震破壊過程の理論的研究（境界積分法）• 断層構成則の研究

> 1995 東北大理（学士）：大竹政和・佐藤春夫教授• 地震活動のフラクタル解析

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対象となった論文(a) Cruz-Atienza, V., J. Virieux and H. Aochi, 3D Finite-Difference Dynamic-Rupture Modelling Along Non-

Planar Fault, Geophysics, 72, SM123-SM137, 2007.(b) Aochi, H. and J. Douglas, Testing the validity of simulated strong ground motion from the dynamic

rupture of a fault system, by using empirical equations, Bull. Earthq. Engineering, DOI 10.1007/s10518-006-0001-3, 2006.

(c) Aochi, H., M. Cushing, O. Scotti, and C. Berge-Thierry, Estimating rupture scenario likelihood based on dynamic rupture simulations: the example of the segmented Middle Durance fault, southeastern France, Geophys. J. Int.,165, 436-446, 2006.

(d) Aochi, H., O. Scotti, and C. Berge-Thierry, 3D dynamic rupture propagation along complex segments with different mechanisms, Geophys. Res. Lett., 32, L21304, doi:10.1029/2005GL024158, 2005.

(e) Aochi, H. and K. B. Olsen, On the effects of non-planar geometry for blind thrust faults on strong ground motion, Pure appl. Geophys., 161, 2139-2153, 2004.

(f) Aochi, H. and R. Madariaga, The 1999 Izmit, Turkey, earthquake: Non-planar fault structure, dynamic rupture process and strong ground motion, Bull. Seism. Soc. Am., 93, 1249-1266, 2003.

(g) Aochi, H. and E. Fukuyama and R. Madariaga, Constraints of Fault Constitutive Parameters Inferred from Non-planar Fault Modeling, Geichemistry, Geophysics, Geosystems, 4(2), 10.1029/2001GC000207, 2003.

(h) Aochi, H., R. Madariaga and E. Fukuyama, Effect of Normal Stress During Rupture Propagation along Non-planar Fault, J. Geophys. Res., 107, 10.1029/2001JB000500, 2002.

(i) Aochi, H. and E. Fukuyama, Three-dimensional nonplanar simulation of the 1992 Landers earthquake, J. Geophys. Res., 107, 10.1029/2000JB000061, 2002.

(j) Aochi, H., E. Fukuyama and M. Matsu'ura, Selectivity of spontaneous rupture propagation on a branched fault, Geophys. Res. Lett., 27, 3635-3638, 2000.

(k) Aochi, H., E. Fukuyama and M. Matsu'ura, Spontaneous Rupture Propagation on a Non-planar Fault in 3D Elastic Medium, Pure appl. Geophys., 157, 2003-2027, 2000.

24 October 2007 > 7

King and Nabelek (1985)

破壊の開始・停止＝地震のサイズ

屈曲・セグメント化

断層形状と地震破壊

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差分法• Harris and Day (1991, 93, 99) • Kase and Kuge (1998, 2001)• Magistrale and Day (1999)

• Cruz-Atienza et al. (2007)

Harris and Day (1999)

境界条件の入れ方（断層形状）が限られる。

数値研究例

24 October 2007 > 9

• 無限均質弾性媒質のグリーン関数（解析解）• 仮想反射震源をおくことにより自由表面を近似• 解の精度• 計算量がべき乗で増える

• 歴史•2D anti-plaine …Cochard and Madariaga (1994) •3D plaine … Fukuyama and Madariaga (1995)

境界積分法

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1. Initial Condition Fault Geometry Tectonic Stress Rupture Criterion

2. Dynamic Rupture Propagation (BIEM)

3. Seismic wave Propagation (FDM)

4. Accelerogram

Strategy of dynamic simulation

Aochi and Fukuyama (JGR, 2002), Aochi et al. (G-cubed, 2003)

The 1992 Landers, CA (M7.3)

Aochi et al. (Pageoph, 2000)

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1. Initial Condition Geometry, Stress, Friction, etc.

2. Dynamic Rupture

3. Wave Propagation

Modelling StrategyModelling Strategy

Landers 1992 (M7.2) Eq.

4. Site Effect

5. Structure ResponseBIE

M,

FD

M,

FEM

Accord

ing

to t

he o

bje

cti

ves

24 October 2007 > 12

地表断層トレース (Hart et al., 1993)

古地震の研究(Rockwell et al., 2000)

• Kickapoo 小断層は過去に存在した。 • 同時代に各断層が前回破壊した。

１９９２年ランダース地震

24 October 2007 > 13

深さに依存する‘ Slip-weakning’ 構成則

すべり

剪断応力

p

cD

r0

Sibson (1982, 1984)Scholz (1988)

Ohnaka (1992)Ide and Takeo (1997)

断層構成則（境界条件）

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テクトニクスモデルUnruh et al. (1994)

テクトニクス応力のシステム

テクトニクス（初期条件）

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Example 1Tectonic stress

動的破壊シミュレーション（境界積分法）

Example 2Tectonic stress + heterogeneity

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Fréquence0.07-0.5Hz

地震動計算（波数積分法）

24 October 2007 > 23

中部 Durance 断層（フランス南東部）

24 October 2007 > 24

1. Moderate Seismicity

2. Repeated Historical Earthquake (M5-5.3, since 1509 every 100y)

3. Paleoseismological large earthquake (M=7)

One of the most important region for seismic risk assessment in France

Characteristic Features

What are Possible Earthquake Scenarios?

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After M. Rocher(IRSN/BERSSIN)

Durance

Compilation of Stress Field(geology, seismicity, in-situ measurements, …)

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Segmented Fault Model

5 Segments with different mechanismsSeg Length Width Strike Dip

1 10 km 8 km 225° 90°2 15 km 8 km 200° 80°3 18 km 8 km 215° 60°4 12 km 8 km 230° 45°5 10 km 8 km 230° 45°

Tectonic Stress (uni-axiale) 1 = N160°E

Rigidity 29.6 GPaP-wave velocity 5.8 km/sS-wave velocity 3.35 km/sGrid size s 500 mTime step t 0.04 sec

BIEM Param (infinite/homogeneous)

24 October 2007 > 27

Stress and Rupture Criterion

Fixed param.

Variable param.0

cD

r

p

O

slip

Shear stress

0 pr

=50cmcf. Aochi et al. (JGR, 2002)

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Probabilistic Approach

Focal Mechanism (Baroux et al., 2001)

Hypothesis (unknown)

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Simulations Results

Condition1. Tectonic Stress=N180E.2. Low Absolute Stress.3. Hypocenter on Seg 3.Probability=0.17%

Results• Ruptured Seg=4.• Rupture Length=55km.• Rupture Mode=bilateral• Mw=6.92.

rake=0°

4°19°

40°

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Simulations Results

Condition1. Tectonic Stress=N160E.2. Low Absolute Stress.3. Hypocenter on Seg 4.Probability=4.55%

Results• Ruptured Seg=3.• Rupture Length=45km.• Rupture Mode=uni-lateral• Mw=6.80.

rake=8°

36°

63°

24 October 2007 > 31

Simulations Results

Condition1. Tectonic Stress=N180E.2. Low Absolute Stress.3. Hypocenter on Seg 5.Probability=4.55%

Results• Ruptured Seg=1.• Rupture Length=10km.• Rupture Mode=single• Mw=6.32.

rake=63°

24 October 2007 > 32

Results of Earthquake Scenarios

Ruptured

Seg Numbe

r

Freq. Prob.

5 0 0%4 3 2%3 11 26%2 3 1%1 20 44%0 13 26%

Maximum event: 4 segment rupture Mw6.9

High possibility: Independent rupture on each segment, or 3 segment SN striking rupture

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Comparison between Segments

Easiest segment to be ruptured

Note: Initial stress is always the same on Seg 4 and 5.

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Rupture Directivity

Note: No propagation between Seg 5 and the others is found.

More favorable

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まとめ

> 断層構造の複雑さをシミュレーションし、地震破壊過程を３次元で議論することに成功した。

> マクロな断層構造が、破壊の進行方向、アスペリティーを支配することを実際の地震のシミュレーションから明らかにした。

> これらの知見は地震ハザード研究へ応用される。> より一層、実際に近い状況（周辺構造の複雑

さ）でモデル化されることが望まれる。> より一層の実際の地震の例を検証する必要があ

る。

24 October 2007 > 36

謝辞

> Thanks for the director of my theses, all my colleagues and friends I met.

> Thanks for all the professional opportunities I got mainly in Japan and France.