长周期地震动衰减关系研究
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摘要
本文建立了我国水平向基岩长周期加速度反应谱衰减关系。根据长周期地震动研究的特点，本文从数据与方法两方面进行了以下工作。
在数据方面，主要使用了地震学研究所使用的数字宽频带记录，包括中国数字地震台网(CDSN)宽频带记录、法国全球数字地震台网(Geoscope)中国新疆乌什台的宽频带记录、美国南加州数字宽频带记录，另外也包括我国低放大倍数模拟式位移记录。
对观测数据着重考察了其长周期特性的可靠性。对于速度型和加速度型的数字宽频带记录，从仪器特性、恢复的地面运动对比、信噪比研究、反应谱对比等方面研究这类记录在长周期段的可靠性。建立了这类记录的处理方法，并计算了它们的反应谱。对于模拟式低放大倍数位移记录，以泰安地震台的513型中强地震仪所记录的1976年7月28日唐山地震的7.1级余震两个水平分向的记录图为例，详细说明了对记录图数字化、弧型校正、基线校正、等距插值、仪器响应校正等步骤，计算了周期T≤10s的反应谱，分析了它们的可靠性。
为弥补观测资料分布的不足，还发展了用面波震级定义估计长周期反应谱值的方法，与观测数据一起，作为统计分析的基础数据。
在方法上，采用了经验统计方法回归参考地区的反应谱衰减关系，用转换方法并加入中国数字地震台网记录得到中国东部地区和西部地区的反应谱衰减关系。对反应谱的长周期部分与短周期部分用不同的资料分别进行研究。将美国西部地区作为参考地区，对美国南加州地区的数字宽频带记录进行了搜集与处理后作为观测资料，共754条水平向记录，与利用震级定义所估计的反应谱值一起，用统计回归的方法建立美国西部长周期加速度反应谱衰减关系。与用模拟式强震仪记录所得出的美国西部地区短周期(T=0.04s-4s)加速度反应谱衰减关系结合，得出了美国西部地区水平向基岩宽周期(T=0.04-20s)加速度反应谱衰减关系。最后用常规的转换方法，并加入我国158条水平向宽频带数字记录，建立了中国东部和西部地区的水平向基岩宽周期(T=0.04-20s，ζ=5％)加速度反应谱衰减关系。
在本文工作中，得到了如下主要成果与认识：
(1)过去使用的低放大倍数位移式地震仪记录可用于长周期地震动研究。位移记录在经过适当的校正处理后，可得到周期长达10s的反应谱。本文给出了此类记录的处理方法。
（2地震学家攸用的数字宽频带地震仪具有良好的口 朋特性，其记录较适介十K川
朋地震动研究。木义发现，数宇宽频带记录的啪卢水平很低，在川朔K达 205时，即仗在
弱地震动的惰况下，还具有较高的信啪比，并且浊度型记录的信噪比禾厂加让度型门录的
信噪比。速度型和加速度型数字宽频带记录可以恢复出相同的地震动，在一定的川朋范田
内得到相同的反应谱，间接证明了这两种地恁记录的可靠性。相比较而言，介玫弱地震动
的情况下，速度型记录更适合于较长周期地震动的研究。数宇宽频带记录的处理方法较为
简单，不需要人多的校正步骤，从而保留了需要的K周朔成价，为长）刷田地恁动F］f究捉仪
’！
了条件。
（3）捉出了川震级定义估汁反应谱值的思想。泅过准级定义估计了个同川沏地汰波的
地而最大位移，进而估计了相应周期的反应谱值，作为实际观测数抓的补充，井。IJ以对让
立反应谱衰减关系起到一定的约火作用。
（叶山美国南加州地区数丫宽频带记录和震级定义所得到的反应以数掂述、＼的夭冈西
部长周期加诠度反应谱哀减关系，与用美国西部强发记录建立的短周期加边度反应谱哀测
关系在周期T＝l．ss左右衔接较好，从一个侧面说明了这两种数据在1．ss刷田附近部是可靠
的。通过将这两个哀减关系相接，本文建立了美国西部地区宽周期（T＝0．04205）水平向基岩
加诬度反应谱哀减人系。与用枚拟记录得到的郁戍大系w比，小义得到的加注度反应谐哀
减关系既解决了高人级时对长川朋估汁小足的问题，同时也尤服了低浴级一in场时俏吹比
低的缺点，史为合理。
（5）利用美国西部的地震烈度哀减关系与中国东部和西部地区的地震烈度及4a义系，
用转换方法分别得到了中国东部与中国西部地区的宽周期（T＝0刀4－205）水‘卜向基岩加洼度反
应谱衰减关系。在用转换方法建立中国分区长周期反应谱哀减关系时，还加入了中冈的数
字宽频带记录及模拟式位移记录资料重新回归，使转换得到的反应谱哀减关系少为合理。
J
（6）通过对新疆乌什台所记录的新疆伽师强震群宽频带数字记录的分析，发现地震震
级大小对长周期地震动的影响程度较大，地震越大，长周期成份越丰富。与上滑型地震相 多
比，倾滑型地震的长周
The goal of this paper is to develop the long period attenuation relationships for horizontal acceleration response spectrum of rock site in China. The study is carried out both in database and methodology aspects.
In the database aspect,the digital broad-band records originally used by seismological studies are used. These data mainly come from the digital broad-band records which are used by seismologists. The recordings include the CDSN records,the Wushi station records of the Geoscope,the TERRAScope records of southern California. The analog low-gain displacement-type records of China are also used.
The reliability of the observation data in long period range is particularly inspected. This is done "by verifying the instrument response characteristic,examining the signal-to-noise ratio,comparing the recovered ground motions and response spectra from the velocity type and acceleration type digital broad-band records. The processing method for the digital broad-band records is developed. For the analog low-gain displacement-type records,two horizontal-component records of a M7.1 aftershock of Tangshan earthquake,July 28,1976,in Tai'an seismic station are used as the example to show the procedures of digitizing,arc-shape correction,baseline correction,equal-interval interpolation and instrument response correction. The reliability of the analog low-gain displacement-type records for long period study is also discussed.
In order the database to have a better magnitude-distance distribution,a method to estimate the long period response spectrum values from earthquake magnitude definition is developed.
The empirical attenuation relationship for horizontal acceleration response spectrum in reference region is developed by regression,and the relationships for eastern China and western China are obtained by transform method and the data from China. The western North America is set as the reference region. 754 horizontal-component digital broad-band records in western North America are processed. The acceleration response spectra are calculated and used as part of the database. The response spectrum values are estimated by the earthquake magnitude definition and are used as another part of the database. The long period attenuation relationship of acceleration response spectrum is developed using this database. The short-period attenuation equation is
developed by using the analog strong motion records of western North America. By connecting the short period and the long period attenuation relationships together,the wide period (7"=0.04-20sec) attenuation relationships for horizontal acceleration response spectrum of western North America are obtained. Then the transform method and the digital broad-band data from China is applied to obtain the wide period attenuation relationships for horizontal acceleration response spectra of eastern China and western China in rock sites (C,=5%).
We have got the following knowledge and conclusions:
(1) The records of low-gain analog displacement-type seismograph can be used to study long period ground motion. After proper correction procedures the usable period can be up to 10 sec. The processing procedures are showed in the paper.
(2) The digital broad-band seismographs used by seismologists have high quality long period characteristics and the records are suitable for studying long period ground motions. We find that the noise level of the record is very low. Even in weak ground motion condition the digital broad-band record has high signal-to-noise ratio when the period is as long as 20 sec. The signal-to-noise ratio of the velocity-type records is lower than that of the acceleration-type records. From the velocity-type records and the acceleration-type records in one station the same ground motions can be recovered,and the calculated response spectra are the same in a specific period range. This indirectly proves the reliability of the two types of records. When in the weak ground motion condition,the velocity-type digital broad-band records are more suitable fo
在数据方面，主要使用了地震学研究所使用的数字宽频带记录，包括中国数字地震台网(CDSN)宽频带记录、法国全球数字地震台网(Geoscope)中国新疆乌什台的宽频带记录、美国南加州数字宽频带记录，另外也包括我国低放大倍数模拟式位移记录。
对观测数据着重考察了其长周期特性的可靠性。对于速度型和加速度型的数字宽频带记录，从仪器特性、恢复的地面运动对比、信噪比研究、反应谱对比等方面研究这类记录在长周期段的可靠性。建立了这类记录的处理方法，并计算了它们的反应谱。对于模拟式低放大倍数位移记录，以泰安地震台的513型中强地震仪所记录的1976年7月28日唐山地震的7.1级余震两个水平分向的记录图为例，详细说明了对记录图数字化、弧型校正、基线校正、等距插值、仪器响应校正等步骤，计算了周期T≤10s的反应谱，分析了它们的可靠性。
为弥补观测资料分布的不足，还发展了用面波震级定义估计长周期反应谱值的方法，与观测数据一起，作为统计分析的基础数据。
在方法上，采用了经验统计方法回归参考地区的反应谱衰减关系，用转换方法并加入中国数字地震台网记录得到中国东部地区和西部地区的反应谱衰减关系。对反应谱的长周期部分与短周期部分用不同的资料分别进行研究。将美国西部地区作为参考地区，对美国南加州地区的数字宽频带记录进行了搜集与处理后作为观测资料，共754条水平向记录，与利用震级定义所估计的反应谱值一起，用统计回归的方法建立美国西部长周期加速度反应谱衰减关系。与用模拟式强震仪记录所得出的美国西部地区短周期(T=0.04s-4s)加速度反应谱衰减关系结合，得出了美国西部地区水平向基岩宽周期(T=0.04-20s)加速度反应谱衰减关系。最后用常规的转换方法，并加入我国158条水平向宽频带数字记录，建立了中国东部和西部地区的水平向基岩宽周期(T=0.04-20s，ζ=5％)加速度反应谱衰减关系。
在本文工作中，得到了如下主要成果与认识：
(1)过去使用的低放大倍数位移式地震仪记录可用于长周期地震动研究。位移记录在经过适当的校正处理后，可得到周期长达10s的反应谱。本文给出了此类记录的处理方法。
（2地震学家攸用的数字宽频带地震仪具有良好的口 朋特性，其记录较适介十K川
朋地震动研究。木义发现，数宇宽频带记录的啪卢水平很低，在川朔K达 205时，即仗在
弱地震动的惰况下，还具有较高的信啪比，并且浊度型记录的信噪比禾厂加让度型门录的
信噪比。速度型和加速度型数字宽频带记录可以恢复出相同的地震动，在一定的川朋范田
内得到相同的反应谱，间接证明了这两种地恁记录的可靠性。相比较而言，介玫弱地震动
的情况下，速度型记录更适合于较长周期地震动的研究。数宇宽频带记录的处理方法较为
简单，不需要人多的校正步骤，从而保留了需要的K周朔成价，为长）刷田地恁动F］f究捉仪
’！
了条件。
（3）捉出了川震级定义估汁反应谱值的思想。泅过准级定义估计了个同川沏地汰波的
地而最大位移，进而估计了相应周期的反应谱值，作为实际观测数抓的补充，井。IJ以对让
立反应谱衰减关系起到一定的约火作用。
（叶山美国南加州地区数丫宽频带记录和震级定义所得到的反应以数掂述、＼的夭冈西
部长周期加诠度反应谱哀减关系，与用美国西部强发记录建立的短周期加边度反应谱哀测
关系在周期T＝l．ss左右衔接较好，从一个侧面说明了这两种数据在1．ss刷田附近部是可靠
的。通过将这两个哀减关系相接，本文建立了美国西部地区宽周期（T＝0．04205）水平向基岩
加诬度反应谱哀减人系。与用枚拟记录得到的郁戍大系w比，小义得到的加注度反应谐哀
减关系既解决了高人级时对长川朋估汁小足的问题，同时也尤服了低浴级一in场时俏吹比
低的缺点，史为合理。
（5）利用美国西部的地震烈度哀减关系与中国东部和西部地区的地震烈度及4a义系，
用转换方法分别得到了中国东部与中国西部地区的宽周期（T＝0刀4－205）水‘卜向基岩加洼度反
应谱衰减关系。在用转换方法建立中国分区长周期反应谱哀减关系时，还加入了中冈的数
字宽频带记录及模拟式位移记录资料重新回归，使转换得到的反应谱哀减关系少为合理。
J
（6）通过对新疆乌什台所记录的新疆伽师强震群宽频带数字记录的分析，发现地震震
级大小对长周期地震动的影响程度较大，地震越大，长周期成份越丰富。与上滑型地震相 多
比，倾滑型地震的长周
The goal of this paper is to develop the long period attenuation relationships for horizontal acceleration response spectrum of rock site in China. The study is carried out both in database and methodology aspects.
In the database aspect,the digital broad-band records originally used by seismological studies are used. These data mainly come from the digital broad-band records which are used by seismologists. The recordings include the CDSN records,the Wushi station records of the Geoscope,the TERRAScope records of southern California. The analog low-gain displacement-type records of China are also used.
The reliability of the observation data in long period range is particularly inspected. This is done "by verifying the instrument response characteristic,examining the signal-to-noise ratio,comparing the recovered ground motions and response spectra from the velocity type and acceleration type digital broad-band records. The processing method for the digital broad-band records is developed. For the analog low-gain displacement-type records,two horizontal-component records of a M7.1 aftershock of Tangshan earthquake,July 28,1976,in Tai'an seismic station are used as the example to show the procedures of digitizing,arc-shape correction,baseline correction,equal-interval interpolation and instrument response correction. The reliability of the analog low-gain displacement-type records for long period study is also discussed.
In order the database to have a better magnitude-distance distribution,a method to estimate the long period response spectrum values from earthquake magnitude definition is developed.
The empirical attenuation relationship for horizontal acceleration response spectrum in reference region is developed by regression,and the relationships for eastern China and western China are obtained by transform method and the data from China. The western North America is set as the reference region. 754 horizontal-component digital broad-band records in western North America are processed. The acceleration response spectra are calculated and used as part of the database. The response spectrum values are estimated by the earthquake magnitude definition and are used as another part of the database. The long period attenuation relationship of acceleration response spectrum is developed using this database. The short-period attenuation equation is
developed by using the analog strong motion records of western North America. By connecting the short period and the long period attenuation relationships together,the wide period (7"=0.04-20sec) attenuation relationships for horizontal acceleration response spectrum of western North America are obtained. Then the transform method and the digital broad-band data from China is applied to obtain the wide period attenuation relationships for horizontal acceleration response spectra of eastern China and western China in rock sites (C,=5%).
We have got the following knowledge and conclusions:
(1) The records of low-gain analog displacement-type seismograph can be used to study long period ground motion. After proper correction procedures the usable period can be up to 10 sec. The processing procedures are showed in the paper.
(2) The digital broad-band seismographs used by seismologists have high quality long period characteristics and the records are suitable for studying long period ground motions. We find that the noise level of the record is very low. Even in weak ground motion condition the digital broad-band record has high signal-to-noise ratio when the period is as long as 20 sec. The signal-to-noise ratio of the velocity-type records is lower than that of the acceleration-type records. From the velocity-type records and the acceleration-type records in one station the same ground motions can be recovered,and the calculated response spectra are the same in a specific period range. This indirectly proves the reliability of the two types of records. When in the weak ground motion condition,the velocity-type digital broad-band records are more suitable fo
引文
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Lam N., Wilson J., Chandler A. and Hutchinson G., 2000b. Response spectrum modelling for rock sites in Iow and moderate seismicity regions combining velocity, displacement and acceleration predictions. Earthquake Engng. Struct. Dyn., 29:1491～1525
Nuttli O. W., 1973. Seismic wave attenuation and magnitude relations of Eastern North America. J. Geophys. Res., 78:876～885
Park S. and Elrick S., 1998. Predictions of shear-wave velocities in southern California using surface geology. Bull. Seism. Soc. Am., 88, 677～685
Richter C. F., 1935. An instrumental earthquake magnitude scale. Bull. Seism. Soc. Am., 25, 1～32
Sadigh K., Chang C.-Y., Egan J. A., Makdisi F. and Youngs R. R., 1997. Attenuation relationships for shallow crustal earthquakes based on California strong motion data. Seism. Res. Lett., 68(1):180～189
Sato T., Graves R. W., Somerville P. G., 1999. Three-dimensional finite-difference simulations of long-period strong motions in the Tokyo Metropolitan area during the
1990 Odawara earthquake (M_J5.1) and the great 1923 Kanto earthquake (M_s 8.2) in Japan. Bull. Seism. Soc. Am., 89(3):579～607
Takeo M., Kanamori H., 1992. Simulation of long-period ground motions for the 1923 Kanto earthquake (M≈8). Bulletin of the Earthquake Research Institute, University of Tokyo, 67, 389～436
Takeo M., Kanamori H., 1997. Simulation of long-period ground motion near a large earthquake. Bull. Seism. Soc. Am., 87(1): 140～156
Tamura K, Sasaki Y., Aizawa K, 1990. Attenuation characteristics of ground motions in the period of 2 to 20 seconds. Proceedings of Fourth U.S. National Conference on Earthquake Engineering, May 20-24, 1990, Palm Springs, California
Trifunac M. D., 1993. Long period Fourier amplitude spectra of strong motion acceleration. Soil Dynam. Earthq. Engng., 12, 363～382
Trifunac M. D., 1995. Pseudo relative velocity spectra of earthquake ground motion at long period. Soil Dynam. Earthq. Engng., 14, 331～346
Trifunac M. D., Lee V. W., 1974. A note on the accuracy of computed ground displacements from strong-motion accelerograms. Bull. Seism. Soc. Am., 64, 1209～1219
Trifunac M. D., Todorovska M. I., 2001. Evolution of accelerographs, data processing, strong motion arrays and amplitude and spatial resolution in recording strong earthquake motion. Soil Dynam. Earthq. Engng., 21(6), 537～555
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Wang S. Y., Yu Y. X., Gao A. J., Yan X. J., 2000. Development of attenuation relations for ground motion in China. J. Earthquake Prediction Res., 8:32～20
Wills C. J., Peterson M., Bryant W. A., Reichle M., Saucedo G. J., Tan S., Taylor G., and
Treiman J., 2000. A Site-Conditions Map for California Based on Geology and Shear-Wave Velocity. Bull. Seism. Soc. Am., 90, S187～S208
Wyss M. and J. N. Brune, 1968. Seismic moment, stress, and source dimensions for earthquakes in the Califomia-Nevada region, J. Geophys. Res., 73:4681～4694
Xiang Z. F. and Li Y. M., 2000. Statistical characteristics of long period response spectra of earhtquake ground motion. 12th World Conference on Earthquake Engineering, Paper No. 0745
Yu Y. X., Hu Y. X., 2001. A combine method to establish attenuation relation of long-period response spectrum. in Earthquake Engineering Frontiers in the New Millennium, Edited by B. F. Spencer, Jr and Y.X. Hu, A. A. Balkema Publishers, 177～182
Zama S., 1996. Regionality of long-period ground motion using JMA strong motion displacement records. Eleventh World Conference on Earthquake Engineering, Paper No. 1891
Zama S., 2000. Characteristics of long-period strong ground motions due to earthquakes in the eastern margin of the Japan Sea. 12th World Conference on Earthquake Engineering, Paper No. 1987
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Lam N., Wilson J., Chandler A. and Hutchinson G., 2000a. Response spectral relationships for rock sites derived from the component attenuation model. Earthquake Engng. Struct. Dyn., 29:1457～1489
Lam N., Wilson J., Chandler A. and Hutchinson G., 2000b. Response spectrum modelling for rock sites in Iow and moderate seismicity regions combining velocity, displacement and acceleration predictions. Earthquake Engng. Struct. Dyn., 29:1491～1525
Nuttli O. W., 1973. Seismic wave attenuation and magnitude relations of Eastern North America. J. Geophys. Res., 78:876～885
Park S. and Elrick S., 1998. Predictions of shear-wave velocities in southern California using surface geology. Bull. Seism. Soc. Am., 88, 677～685
Richter C. F., 1935. An instrumental earthquake magnitude scale. Bull. Seism. Soc. Am., 25, 1～32
Sadigh K., Chang C.-Y., Egan J. A., Makdisi F. and Youngs R. R., 1997. Attenuation relationships for shallow crustal earthquakes based on California strong motion data. Seism. Res. Lett., 68(1):180～189
Sato T., Graves R. W., Somerville P. G., 1999. Three-dimensional finite-difference simulations of long-period strong motions in the Tokyo Metropolitan area during the
1990 Odawara earthquake (M_J5.1) and the great 1923 Kanto earthquake (M_s 8.2) in Japan. Bull. Seism. Soc. Am., 89(3):579～607
Takeo M., Kanamori H., 1992. Simulation of long-period ground motions for the 1923 Kanto earthquake (M≈8). Bulletin of the Earthquake Research Institute, University of Tokyo, 67, 389～436
Takeo M., Kanamori H., 1997. Simulation of long-period ground motion near a large earthquake. Bull. Seism. Soc. Am., 87(1): 140～156
Tamura K, Sasaki Y., Aizawa K, 1990. Attenuation characteristics of ground motions in the period of 2 to 20 seconds. Proceedings of Fourth U.S. National Conference on Earthquake Engineering, May 20-24, 1990, Palm Springs, California
Trifunac M. D., 1993. Long period Fourier amplitude spectra of strong motion acceleration. Soil Dynam. Earthq. Engng., 12, 363～382
Trifunac M. D., 1995. Pseudo relative velocity spectra of earthquake ground motion at long period. Soil Dynam. Earthq. Engng., 14, 331～346
Trifunac M. D., Lee V. W., 1974. A note on the accuracy of computed ground displacements from strong-motion accelerograms. Bull. Seism. Soc. Am., 64, 1209～1219
Trifunac M. D., Todorovska M. I., 2001. Evolution of accelerographs, data processing, strong motion arrays and amplitude and spatial resolution in recording strong earthquake motion. Soil Dynam. Earthq. Engng., 21(6), 537～555
Trifunac M. D., Udwadia, F. E. and Brady, A. G., 1973. Analysis of errors in digitized strongmotion accelerograms. Bull. Seism. Soc. Am., 63, 157～187
Wald D. J., Graves R. W., 1998. The seismic response of the Los Angeles basin, California. Bull. Seism. Soc. Am., 88(2):337～356
Wang S. Y., Yu Y. X., Gao A. J., Yan X. J., 2000. Development of attenuation relations for ground motion in China. J. Earthquake Prediction Res., 8:32～20
Wills C. J., Peterson M., Bryant W. A., Reichle M., Saucedo G. J., Tan S., Taylor G., and
Treiman J., 2000. A Site-Conditions Map for California Based on Geology and Shear-Wave Velocity. Bull. Seism. Soc. Am., 90, S187～S208
Wyss M. and J. N. Brune, 1968. Seismic moment, stress, and source dimensions for earthquakes in the Califomia-Nevada region, J. Geophys. Res., 73:4681～4694
Xiang Z. F. and Li Y. M., 2000. Statistical characteristics of long period response spectra of earhtquake ground motion. 12th World Conference on Earthquake Engineering, Paper No. 0745
Yu Y. X., Hu Y. X., 2001. A combine method to establish attenuation relation of long-period response spectrum. in Earthquake Engineering Frontiers in the New Millennium, Edited by B. F. Spencer, Jr and Y.X. Hu, A. A. Balkema Publishers, 177～182
Zama S., 1996. Regionality of long-period ground motion using JMA strong motion displacement records. Eleventh World Conference on Earthquake Engineering, Paper No. 1891
Zama S., 2000. Characteristics of long-period strong ground motions due to earthquakes in the eastern margin of the Japan Sea. 12th World Conference on Earthquake Engineering, Paper No. 1987
陈达生、刘汉兴，1989．地震烈度椭圆衰减关系．华北地震科学，7(3)：31～42
陈培善，1981．国际上测定地震震级的现状．地震地磁观测与研究，2(3)：12～16
陈培善、白彤霞，1991．震源参数之间的定量关系．地震学报，13(4)：401～411
陈培善、成瑾，1998．中国地震基本台网测定面波震级的偏差．国际地震动态，7：6～8
陈培善、李保昆、白彤霞，1998．根据构造环境应力场预测峰值水平加速度．地球物理学报，41(4)：502～517
崔鸿超，1997．高层建筑钢结构在我国的发展．建筑结构学报，18(2)：60～71
大崎顺彦，1980．地震动的谱分析入门．吕敏申、谢礼立译，地震出版社，283pp
傅淑芳、刘宝诚、李文艺编，1984．地震学教程，上册．地震出版社，332pp
冈本舜三，1980．地震工程学．国立台湾大学工学院地震工程研究中心编译，台北：科技图书股份有限公司，pp561
葛焕称，1982．震级的标度．地震地磁观测与研究，3(3)：34～39
葛焕称，1997．震级概念和测量方法的历史演变．中国地震学研究进展，141～151，地震出版社，北京
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