) (M w ) km 1km M w SN 3).2.331Hz.15.21Hz 1.4 3m S 12) (D) 3km (1) No. Earthquake Date Mw Focal Depth (km) Number of rec

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1 1) 2) (M) M M M 1)4).2.3(.4.7) 5) 6),7) 7)1) 6) 9) -59-

2 ) (M w ) km 1km M w SN 3).2.331Hz.15.21Hz 1.4 3m S 12) (D) 3km (1) No. Earthquake Date Mw Focal Depth (km) Number of recordings P.G.A. P.G.V. Fault Type 1 Off Tokachi Inter-plate 2 Off Nemuro Pen Inter-plate 3 Near Izu Oshima Crustal 4 Off Miyagi Pref Inter-plate 5 East off Izu Pen Crustal 6 Off Urakawa Crustal 7 Nihonkai-Chubu Inter-plate 8 Off Hyuganada Intra-plate 9 Central Iwate Pref Intra-plate 1 Northern Hidaka Mt Intra-plate 11 East off Chiba Pref Crustal 12 Off Kushiro Intra-plate 13 Off Noto Pen Crustal 14 Southwest off Hokkaido Inter-plate 15 East off Hokkaido Intra-plate 16 Far off Sanriku Inter-plate 17 Hyogo-ken Nanbu Crustal 18 Off Hyuganada Inter-plate 19 Northwestern Kagoshima Pref Crustal 2 Northwestern Kagoshima Pref Crustal 21 Northern Yamaguchi Pref Crustal 22 Off Shizuoka Pref Crustal 23 Northern Iwate Pref Crustal 24 Off Hyuganada Inter-plate 25 Southeastern Hokkaido Intra-plate 26 Northern Wakayama Pref Intra-plate 27 Off Nemuro Pen Intra-plate 28 Northeastern Chiba Pref Inter-plate 29 Off Ibaraki Pref Inter-plate 3 Tottori-ken Seibu Crustal 31 Central Mie Pref Intra-plate 32 Geiyo Intra-plate 33 Off Hyuganada Intra-plate -6-

3 3km (2) 11) A (cm/s 2 ) (cm/s)x (km)b C k log A = b log(x + C) kx (D3km) (1) log A = b +.6log(1.7D + C) 1.6 log(x + C) kx (D3km) (2) k 4).3.2 C (M w )(3)(4) C =.6 1.5Mw (for PGA) (3) C = Mw (for PGV) (4) b 4) (M w )(D) i (S i ) 3 b = am w + hd + d i S i + e (5) a h d Intra-event Inter-event Total e Crustal Inter-plate Intra-plate Standard deviation Standard deviation Standard deviation Peak ground acceleration Peak ground velocity ahd i e a h M w =7. 351km -61-

4 M w =7. 2km (Total Error) M w (5.8) M w =5.8 (Intra-event Error) (Inter-event Error) (.27)(.16) 2),7),9) Total error Intra-event error Inter-event error Frequency Acc. Acc. Acc. Inter-event error Intra-event error Data-Northern Yamaguchi Date-Northern Iwate Median for Northern Yamaguchi Median for Northern Iwate Median Attenuation Relationship Acc. Acc. Acc. -62-

5 Total error Residual ε(logv) Residual ε(loga) Total error P.G.A. 1 Acc. 2 Standard Deviation σ(logv).3-1 Acc Standard Deviation σ(loga) 図５に地震規模(Mw)と全バラツキ地震内のバラツキ地震間のバラツキとの関係を示す図の上段は個々のデータのバラツキを示し下段は M をの４つの範囲に分類しそれぞれの M の範囲でのバラツキの値を示したものである図には米国の記録等に基づく既往の結果 9),13),14)も示してあるバラツキは M が増大するにつれて小さくなる傾向がみえるが M 依存性は既往の結果に比べてあまり明瞭ではない図５と同様な形で図６に震源からの距離と全バラツキとの関係を示すなお震源 3 図６ Fault Distance (km) Vel. P.G.V. 1 Vel. 2 3 Fault Distance (km) 距離とバラツキの関係 Residual ε(logv) Standard Deviation σ(logv) Standard Deviation σ(loga) Residual ε(loga) からの距離毎や後述の振幅レベル毎の地震 Total error Total error 間のバラツキは意味をなさないのでここで 1 1 は地震内と地震間のバラツキにわけずに全.5.5 バラツキだけを示した震源からの距離が km 程度以上の場合にはバラツキの大きさ -1 Acc. -1 Vel. は距離が近づくにつれてやや小さくなる傾.4.4 向がみられる例えば最大加速度の場合.3.3 バラツキは距離が 2km で.3 強距離が.2.2 5km で.3 弱である距離が 5km 程度以下.1.1 になると距離が小さくなるにつれてバラツ P.G.V. P.G.A. Vel. Acc. キはかなり小さくなり最大加速度の場合距 P.G.A.(Pred.) P.G.V.(Pred.) 離が 1km で.2 程度となる既往の研究で距離との関係について議論されている例は図７振幅レベルとバラツキの関係みあたらないが例えばカリフォルニアでの地殻内地震による記録の解析結果 15)をみると本研究と同様に距離が近づくにつれてバラツキが小さくなる傾向が読みとれる図７に振幅レベルと全バラツキとの関係を示す図の横軸は距離減衰式からの予測値を示すバラツキの大きさは明らかに振幅レベルに依存しており M に対する依存性よりも強く既往の指摘 7) とも一致している最大加速度の場合全バラツキは振幅レベルが 5cm/s2 以下の場合には.32 であるが振幅レベルとともに減少し 6cm/s2 以上の場合にはその半分弱の.14 となる前述したように全データに対する全バラツキは.3 でありこの値がデータ数の多い振幅レベルの小さな記録に対するバラツキでほぼ決まっていることを示している最大速度の場合も同様の傾向である以上の検討から距離減衰式における地震動強さのバラツキの特徴として 1)地震間のバラツキに比べて地震内のバラツキが大きいこと 2) あまり明瞭ではないがバラツキのＭ依存性がみられること 3)距離が 5km 程度以下でバラツキの距離依存性が強くみられること 4)バラツキの振幅依存性が最も明瞭にみられることがわかった４距離減衰式における地震動強さのバラツキの要因 4.1 震源特性の影響距離減衰式におけるバラツキの原因について地震動特性を支配する３つの要素震源特性伝播 -63-

6 a1) a2) a1) 16) M 9) a2) 17) 3.5km/s 2.8km/s ),19) Somerville et al. 2) M6.5 5km ) 1/ Hz 22)24) (.27) b) (Q) Lg 25) 12km 26) -64-

7 24km (Qs) 27) 5km K-net Qs 3km 3Hz Qs 11 28) 87 Qs 3Hz Qs 24 Qs km.1 2km.2 c) km.1 29) SMART-1 ( 2km) M M M M ) 3) 3) 25km2km 2km 15 31) Vs 6m/s Vs 1m/s 3m 1% 31) Vs 1 2m/s 1 5% 2m 1% Vs 3m/s 15% 31) km 1km ) (.2 ) M 45 SMART-1 3)

8 .12 M d) 6),9) km 5cm/s 2 1km m S (AVS3) AVS3 13m/s36m/s6m/s 3 (AVS3=13m/s) Variance vs. P.G.A.(pred.) Acc. Variance vs. P.G.V.(pred.) Vel. AVS3=1 ~3m/s AVS3=3 ~6m/s AVS3=6 ~26m/s -66-

9 () 4.1 a1)( INTER ) M M M 1km ( INTER-S ).1 INTER-S M INTER-S =.1 (6) ( INTRA ) 4.1 a2) ( INTRA-S )4.1 17).1 21).5 INTRA-S =.5 (7) 4.2 ( INTRA- P ) INTRA-P = ( (X) 2 + (.1X) 2 ).5 (X4km) ( (44 -.1X) 2 + (.1X) 2 ).5 (X4km) (8) ) 4km 27),28) ( INTRA-G )4.4 INTRA-G = ( ).5 =.14 (9) ()( INTER )( INTRA ) -67-

10 ( INTER )(6)( INTRA )(7)(9) () = ( INTER 2 + INTRA 2 ).5 = ( INTER-S 2 + INTRA-S 2 + INTRA-P 2 + INTRA-G 2 ).5 (1) INTRA-P.18 INTER-S INTRA-S INTRA-G.3 INTRA-P INTRA-P (8).4 (1) M M M M M 1) Fukushima, Y. and T. TanakaA New Attenuation Relation for Peak Horizontal Acceleration of Strong Earthquake Ground Motion in Japan, Bull. Seism. Soc. Am., Vol.8, 199, pp ) pp ) No.523, 1999 pp

11 4) Joyner, W.B. and D.M. BoorePeak Horizontal Acceleration and Velocity from Strong-Motion Records Including Records from the 1979 Imperial Valley, California, Earthquake, Bull. Seism. Soc. Am., Vol.71, 1981, pp ) Abrahamson, N.A. and K.M. ShedlockOverview, Seism. Res. Lett., Vol.68, 1997, pp ) Donovan, N.C. and A.E. BornsteinUncertainties in Seismic Risk ProceduresJournal of the Geotechnical Engineering Division, American Society of Civil Engineers, 14, 1978, pp ) Campbell, K.W. and Y. BozorgniaNear-Source Attenuation of Peak Horizontal Acceleration from Worldwide Accelerograms Recorded from 1957 to 1993, Proc. Fifth U.S. National Conf. on Earthquake Engineering, Vol.3, 1994, pp ) Idriss, I.M.Evaluating seismic risk in engineering practice, Proceedings of the Eleventh International Conference on Soil Mechanics and Foundation Engineering, San Francisco, 1985, pp ) Youngs, R.R., N. Abrahamson, F.I. Mkdisi, and K. SadighMagnitude Dependence Variance of Peak Ground Acceleration, Bull. Seism. Soc. Am., Vol. 85, 1995, pp ) Douglas, J. and P. M. SmitHow Accurate Can Strong Ground Motion Attenuation Relations be?, Bull. Seism. Soc. Am., Vol.91, 21, pp ), 11 (CD-ROM), 22, ) Midorikawa, S., M. Matsuoka and K. SakugawaSite Effects on Strong-Motion Records Observed During The 1987 Chiba-ken-toho-oki, Japan Earthquake, pp.e85-e9. 13) Youngs R.R., S.J. Chiou, W.J. Silva and J.R. Humphrey Strong Ground Motion Attenuation Relationships for Subduction Zone Earthquakes, Seism. Res. Lett., Vol.68, 1997, pp ) Campbell, K.W.Empirical Near-Source Attenuation Relationships for Horizontal and Vertical Components of Peak Ground Acceleration, Peak Ground Velocity and Pseudo-Absolute Acceleration Response Spectra, Seism. Res. Lett., Vol.68, 1997, pp ) Abrahamson, N.A. and W.J. SilvaEmpirical Response Spectral Attenuation Relations for Shallow Crustal Earthquakes, Seism. Res. Lett., Vol.68, 1997, pp ),, 545, 21, pp ) pp ) pp ), 21, pp ) Somerville, P. et al.: Modification of Empirical Strong Motion Attenuation Relations to Include the Amplitude and Duration Effects of Rupture Directivity, Seism. Res. Lett., Vol.68, 1997, pp ) 1, Vol.1, 1998, pp ) Satoh, T. : Empirical Frequency-Dependent Radiation Pattern of the 1998 Miyagiken-Nanbu Earthquake in JapanBull. Seism. Soc. Am., Vol.92, 22, pp ) 22 pp ) (1Hz ) 22 pp

12 25) pp ), 1997, 1997, B41-P2. 27),, Vol.54, 22, pp ) JMA pp ) McCann, M.W. and D.M. BooreVariability in Ground Motions: Root Mean Square Acceleration and Peak Acceleration for the 1971 San Fernando, California, Earthquake, Bull. Seism. Soc. Am., Vol.73, 1983, pp ) Abrahamson, N.A. Statistical Properties of Peak Ground Accelerations Recorded by the SMART 1 Array, Bull. Seism. Soc. Am., Vol.78, 1988, pp ) Rodriguez, V.H.S. and S. Midorikawa: Applicability of the H/V Spectral Ratio of Microtremors in Assessing Site Effects on Seismic Motion, Earthquake Engineering & Structural Dynamics, Vol.31, 22, pp Empirical Analysis of Variance of Ground Motion Intensity in Attenuation Relationships MIDORIKAWA Saburoh 1) and OHTAKE Yu 2) 1) Member, Professor, Department of Built Environment, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Dr. Eng. 2) Graduate Student, Department of Built Environment, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Ms. Eng. (Currently Engineer, CTI Engineering Co., Ltd.) ABSTRACT The variance of peak horizontal accelerations and velocities of the Japanese strong-motion data set is examined. The standard errors of the data from the empirical attenuation relationships are calculated. The standard error decreases with increasing magnitude, with decreasing the distance, and with increasing the amplitude. The amplitude dependence of the error seems much stronger than the magnitude and distance dependences. The distance dependence can be caused by the effects of scattering and absorption of seismic waves in the path. The strong amplitude dependence can be interpreted by multiplying of the effects of the maginitude and distance dependences. Key Words: Attenuation Relationship, Variance, Magnitude Dependence, Distance Dependence, Amplitude Dependence -7-

) (M w ) km 100km M w SN 3) Hz Hz m S 12) (D) 30km (1) No. Earthquake Date Mw Focal Depth (

) (M w ) km 100km M w SN 3) Hz Hz m S 12) (D) 30km (1) No. Earthquake Date Mw Focal Depth ( 1) e-mailsmidorik@enveng.titech.ac.jp 2) e-mailootake@ctie.co.jp (M) M M M 1)4) 0.20.3( 0.40.7) 5) 6),7) 7)10) 6) 9) -59- 1968 2001 33 11) (M w ) 5.5 8.3 km 100km M w 3335 1980 SN 3) 0.2 0.3310Hz 0.15