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

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1 1) 2) (M) M M M 1)4) ( ) 5) 6),7) 7)10) 6) 9) -59-

2 ) (M w ) km 100km M w SN 3) Hz Hz m S 12) (D) 30km (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 10 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 20 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 30 Tottori-ken Seibu Crustal 31 Central Mie Pref Intra-plate 32 Geiyo Intra-plate 33 Off Hyuganada Intra-plate -60-

3 30km (2) 11) A (cm/s 2 ) (cm/s)x (km)b C k log A = b log(x + C) kx (D30km) (1) log A = b + 0.6log(1.7D + C) 1.6 log(x + C) kx (D30km) (2) k 4) C (M w )(3)(4) C = Mw (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 = km -61-

4 M w =7.0 20km (Total Error) M w (5.8) M w =5.8 (Intra-event Error) (Inter-event Error) ( 0.27)( 0.16) 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 (Mw) M M 9),13),14) M M 50km 200km km km 10km ) M 7) 50cm/s cm/s ) 2) 3) 50km 4) -63-

6 a1) a2) a1) 16) M 9) a2) 17) 3.5km/s 2.8km/s ),19) Somerville et al. 20) M6.5 50km ) 1/ Hz 22)24) ( 0.27) b) (Q) Lg 25) km 26) -64-

7 2040km (Qs) 27) 50km K-net Qs 030km 3Hz Qs ) 87 Qs 3Hz Qs Qs km km 0.2 c) km ) SMART-1 ( 2km) M M M M ) 30) 30) 25km20km 2km ) Vs 600m/s Vs 100m/s 30m 10% 31) Vs m/s 10 50% 20m 10% Vs 300m/s 15% 31) km 100km ) ( 0.2 ) M 45 SMART-1 30)

8 0.12 M d) 6),9) km 500cm/s 2 100km m S (AVS30) AVS m/s300600m/s600m/s 3 (AVS30=100300m/s) Variance vs. P.G.A.(pred.) Acc. Variance vs. P.G.V.(pred.) Vel. AVS30=100 ~300m/s AVS30=300 ~600m/s AVS30=600 ~2600m/s -66-

9 () 4.1 a1)( INTER ) M M M 100km ( INTER-S ) 0.1 INTER-S M INTER-S = 0.1 (6) ( INTRA ) 4.1 a2) ( INTRA-S )4.1 17) ) 0.05 INTRA-S = 0.05 (7) 4.2 ( INTRA- P ) INTRA-P = ( (X) 2 + (0.001X) 2 ) 0.5 (X40km) ( (44-0.1X) 2 + (0.001X) 2 ) 0.5 (X40km) (8) ) 40km 27),28) ( INTRA-G )4.4 INTRA-G = ( ) 0.5 = 0.14 (9) ()( INTER )( INTRA ) -67-

10 ( INTER )(6)( INTRA )(7)(9) () = ( INTER 2 + INTRA 2 ) 0.5 = ( INTER-S 2 + INTRA-S 2 + INTRA-P 2 + INTRA-G 2 ) 0.5 (10) 0 INTRA-P INTER-S INTRA-S INTRA-G 0.3 INTRA-P INTRA-P (8) (10) 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.80, 1990, 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, 104, 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, 2001, pp ), 11 (CD-ROM), 2002, ) Midorikawa, S., M. Matsuoka and K. SakugawaSite Effects on Strong-Motion Records Observed During The 1987 Chiba-ken-toho-oki, Japan Earthquake, pp.e085-e ) 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, 2001, pp ) pp ) pp ), 2001, 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 ) 10, Vol.1, 1998, pp ) Satoh, T. : Empirical Frequency-Dependent Radiation Pattern of the 1998 Miyagiken-Nanbu Earthquake in JapanBull. Seism. Soc. Am., Vol.92, 2002, pp ) 2002 pp ) (1Hz ) 2002 pp

12 25) pp ), 1997, 1997, B41-P02. 27),, Vol.54, 2002, 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, 2002, 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 -70-

) (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

) (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 1) e-mailsmidorik@enveng.titech.ac.jp 2) e-mailootake@ctie.co.jp (M) M M M 1)4).2.3(.4.7) 5) 6),7) 7)1) 6) 9) -59- 1968 21 33 11) (M w ) 5.5 8.3 km 1km M w 3335 198 SN 3).2.331Hz.15.21Hz 1.4 3m S 12) (D)