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 0.210Hz 1.4 30m 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 1968.5.16 8.2 15 10 10 Inter-plate 2 Off Nemuro Pen. 1973.6.17 7.8 25 5 4 Inter-plate 3 Near Izu Oshima 1978.1.14 6.6 7 8 8 Crustal 4 Off Miyagi Pref. 1978.6.12 7.6 37 13 10 Inter-plate 5 East off Izu Pen. 1980.6.29 6.5 7 15 15 Crustal 6 Off Urakawa 1982.3.21 6.9 25 10 8 Crustal 7 Nihonkai-Chubu 1983.5.26 7.8 6 17 17 Inter-plate 8 Off Hyuganada 1984.8.7 6.9 30 9 7 Intra-plate 9 Central Iwate Pref. 1987.1.9 6.6 73 9 5 Intra-plate 10 Northern Hidaka Mt. 1987.1.14 6.8 120 13 6 Intra-plate 11 East off Chiba Pref. 1987.12.17 6.7 30 173 47 Crustal 12 Off Kushiro 1993.1.15 7.6 105 35 17 Intra-plate 13 Off Noto Pen. 1993.2.7 6.3 15 12 7 Crustal 14 Southwest off Hokkaido 1993.7.12 7.7 10 24 15 Inter-plate 15 East off Hokkaido 1994.10.4 8.3 35 41 17 Intra-plate 16 Far off Sanriku 1994.12.28 7.7 35 57 21 Inter-plate 17 Hyogo-ken Nanbu 1995.1.17 6.9 10 74 43 Crustal 18 Off Hyuganada 1996.10.19 6.7 25 159 98 Inter-plate 19 Northwestern Kagoshima Pref. 1997.3.26 6.1 6 121 65 Crustal 20 Northwestern Kagoshima Pref. 1997.5.13 6.0 7 133 71 Crustal 21 Northern Yamaguchi Pref. 1997.6.25 5.8 10 196 82 Crustal 22 Off Shizuoka Pref. 1998.5.3 5.5 3 77 46 Crustal 23 Northern Iwate Pref. 1998.9.3 5.8 10 66 26 Crustal 24 Off Hyuganada 1998.12.16 5.8 32 44 30 Inter-plate 25 Southeastern Hokkaido 1999.5.13 6.4 104 96 45 Intra-plate 26 Northern Wakayama Pref. 1999.8.21 5.8 70 249 172 Intra-plate 27 Off Nemuro Pen. 2000.1.28 6.7 56 46 21 Intra-plate 28 Northeastern Chiba Pref. 2000.6.3 5.9 48 135 90 Inter-plate 29 Off Ibaraki Pref. 2000.7.21 6.1 49 176 108 Inter-plate 30 Tottori-ken Seibu 2000.10.6 6.8 11 370 207 Crustal 31 Central Mie Pref. 2000.10.31 5.5 43 278 198 Intra-plate 32 Geiyo 2001.3.24 6.7 51 411 263 Intra-plate 33 Off Hyuganada 2001.4.25 5.6 42 253 201 Intra-plate -60-
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) 0.003 0.002 C (M w )(3)(4) C = 0.0060 10 0.5Mw (for PGA) (3) C = 0.0028 10 0.5Mw (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 0.59 0.0023 0.00 0.08 0.30 0.02 0.27 0.16 0.30 Peak ground velocity 0.65 0.0024 0.00 0.05 0.15-1.77 0.24 0.16 0.28 ahd i e a h M w =7.0 3050100km -61-
M w =7.0 20km 1.2 2.0 1.1 1.4 (Total Error) 10 0.30 0.28 9 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-
(Mw) M 5.55.96.06.56.6 6.97.68.3 M 9),13),14) M M 50km 200km 0.3 50km 0.3 50km 10km 0.2 15) M 7) 50cm/s 2 0.32 600cm/s 2 0.14 0.30 1) 2) 3) 50km 4) -63-
a1) a2) a1) 16) M 9) a2) 17) 3.5km/s 2.8km/s 3 1.7 0.16 0.08 18),19) Somerville et al. 20) M6.5 50km 0.6 3 1.5 21) 1/4 45 15Hz 22)24) ( 0.27) b) (Q) Lg 25) 100200km 26) -64-
2040km (Qs) 27) 50km K-net Qs 030km 3Hz Qs 1001000 28) 87 Qs 3Hz Qs 200400 Qs 200300300400 100km 0.1 200km 0.2 c) 1971 1km 0.10 29) SMART-1 ( 2km) M M M 45 0.14 M6.5 0.08 30) 30) 30) 25km20km 2km 150 31) Vs 600m/s Vs 100m/s 30m 10% 31) Vs 100 200m/s 10 50% 20m 10% Vs 300m/s 15% 31) 4.25.2 12 50150km 100km 0.21 0.20 0.02 0.2 10) ( 0.2 ) M 45 SMART-1 30) 0.14-65-
0.12 M 0.08 0.12 0.15 d) 6),9) km 500cm/s 2 100km 1993 1978 30m S (AVS30) AVS30 100300m/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-
() 4.1 a1)( INTER ) M M M 100km 4.2 0.1 0.15 ( INTER-S ) 0.1 INTER-S M INTER-S = 0.1 (6) ( INTRA ) 4.1 a2) ( INTRA-S )4.1 17) 0.1 21) 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) 4.2 26) 40km 27),28) 4.2 4.3 0.1 0.1 0.15 ( INTRA-G )4.4 INTRA-G = ( 0.08 2 + 0.12 2 ) 0.5 = 0.14 (9) ()( INTER )( INTRA ) -67-
( 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 0 0.18 INTER-S INTRA-S INTRA-G 0.3 INTRA-P INTRA-P (8) 0.004 (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.757-783. 2) 87 24 1997 pp.161-164. 3) No.523, 1999 pp.63-70. -68-
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.2011-2038. 5) Abrahamson, N.A. and K.M. ShedlockOverview, Seism. Res. Lett., Vol.68, 1997, pp.9-23. 6) Donovan, N.C. and A.E. BornsteinUncertainties in Seismic Risk ProceduresJournal of the Geotechnical Engineering Division, American Society of Civil Engineers, 104, 1978, pp.869-887. 7) 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.283-292. 8) 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.255-320. 9) 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.1161-1176. 10) Douglas, J. and P. M. SmitHow Accurate Can Strong Ground Motion Attenuation Relations be?, Bull. Seism. Soc. Am., Vol.91, 2001, pp.1917-1923. 11), 11 (CD-ROM), 2002, 117. 12) Midorikawa, S., M. Matsuoka and K. SakugawaSite Effects on Strong-Motion Records Observed During The 1987 Chiba-ken-toho-oki, Japan Earthquake, 9 1994 pp.e085-e090. 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.58-73. 14) 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.154-179. 15) Abrahamson, N.A. and W.J. SilvaEmpirical Response Spectral Attenuation Relations for Shallow Crustal Earthquakes, Seism. Res. Lett., Vol.68, 1997, pp.94-127. 16),, 545, 2001, pp.51-62. 17) 2 40 1987 pp.397-404. 18) 546 2001 pp.47-53. 19), 2001, pp.59-60. 20) 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.199-222. 21) 10, Vol.1, 1998, pp.133-138. 22) Satoh, T. : Empirical Frequency-Dependent Radiation Pattern of the 1998 Miyagiken-Nanbu Earthquake in JapanBull. Seism. Soc. Am., Vol.92, 2002, pp.1032-1039. 23) 2002 pp.141-142. 24) (1Hz ) 2002 pp.143-144. -69-
25) 27 1999 pp.17-28. 26), 1997, 1997, B41-P02. 27),, Vol.54, 2002, pp.475-488. 28) JMA87 9 1994 pp.751-756 29) 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.615-632. 30) Abrahamson, N.A. Statistical Properties of Peak Ground Accelerations Recorded by the SMART 1 Array, Bull. Seism. Soc. Am., Vol.78, 1988, pp.26-41. 31) 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.261-279. 2002 9 7 2003 1 7 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-