IMPROVEMENT OF EMPIRICAL GREEN'S FUNCTION METHOD USING A DYNAMIC CORNER FREQUENCY

doi:10.3969/j.issn.0253-4967.2015.02.015

Abstract

Abstract:

In traditional empirical Green's function method, the difference between corner frequencies of large and small events is seldom considered. Since the simulation is performed by the superposition of the small events records, the results would have same corner frequencies as the small events, which contradict the fact that the corner frequency decreases with the moment magnitude. The results by traditional empirical Green's function method underestimate the low-frequency content when n² small events are added. Assuming the corner frequency of a sub-fault is inversely proportional to the square root of the numbers of ruptured sub-faults, we construct a new function to apply the dynamic corner frequency to empirical Green's function method based on the ω² source model. In the constructed function, the corner frequency of each sub-fault changes with the rupture propagation. We also develop a schematic diagram to show how the improved empirical Green's function method works.
To validate the empirical Green's function method with dynamic corner frequency, we simulate the near fault strong ground motion of Wenchuan earthquake. Three aftershocks of Wenchuan earthquake are used as Green's functions of the asperities based on their magnitude and locations. Then ground motions of Wenchuan earthquake are synthesized by traditional empirical Green's function method and the empirical Green's function method with the dynamic corner frequency respectively. Comparison between the simulated results and observed data indicates that the traditional empirical Green's function method underestimates the low-frequency content of ground motions. While the empirical Green's function method with the dynamic corner frequency boosts the low-frequency motions without changing the high-frequency content. The results from the empirical Green's function method with the dynamic corner frequency show good agreement with the observed records after the low-frequency contents are improved, which proves that the dynamic corner frequency is valid to eliminate the underestimation due to the difference between the corner frequencies of large events and small ones.
This study also proves that the empirical Green's function method with the dynamic corner frequency is a powerful tool to synthesize the near fault strong ground motions from M_W7.9 earthquake.

Key words: Wenchuan earthquake, empirical Green's function method, dynamic corner frequency, ground motion simulation, ω² source model

摘要：

针对大小震拐角频率的差异, 假设大震断层上每个子源的拐角频率与已破裂的子源个数平方根成反比, 基于ω²震源谱模型, 通过理论推导构建了一个函数, 将动力学拐角频率引入经验格林函数法。以汶川地震余震记录为格林函数, 分别用改进前和引入动力学拐角频率后的经验格林函数法合成5 ·12汶川大地震强地面运动。对比合成结果与观测记录, 结果表明改进前经验格林函数法合成的地震动在低频部分相对实际记录偏低; 引入动力学拐角频率之后的经验格林函数法合成的结果在高频基本保持不变, 低频部分得到提高, 并与实际记录符合。引入动力学拐角频率后, 大部分合成结果很好地符合实际记录。说明动力学拐角频率可有效改善经验格林函数法的低频合成结果, 同时验证了经验格林函数法对M_W7.9特大地震地震动合成的有效性。

关键词: 汶川地震, 经验格林函数法, 动力学拐角频率, 地震动合成, &omega, ²震源谱模型

CLC Number:

P315.0

XIA Chen, ZHAO Bo-ming. IMPROVEMENT OF EMPIRICAL GREEN'S FUNCTION METHOD USING A DYNAMIC CORNER FREQUENCY[J]. SEISMOLOGY AND GEOLOGY, 2015, 37(2): 529-540.

夏晨, 赵伯明. 应用动力学拐角频率对经验格林函数法的改进[J]. 地震地质, 2015, 37(2): 529-540.

References

金星, 刘启方. 2002. 断层附近强地震动半经验合成方法的研究【J】. 地震工程与工程震动, 22(4): 22—27.
JIN Xing, LIU Qi-fang. 2002. Study on semi-empirical method of simulating strong ground motions near fault 【J】. Earthquake Engineering and Engineering Vibration, 22(4): 22—27(in Chinese).
罗奇峰, 胡聿贤, 壇一男. 1994. 估计近场地震动的统计经验格林函数法【J】. 自然灾害学报, 3(3): 3—10.
LUO Qi-feng, HU Yu-xian, DAN Yi-nan. 1994. Statistical-empirical Green's function method for estimating near-field earthquake ground motions 【J】. Journal of Natural Disasters, 3(3): 3—10(in Chinese).
孙晓丹, 陶夏新, 王国新, 等. 2009. 地震动随机合成中与震源谱相关的动力学拐角频率【J】. 地震学报, 31(5): 537—543.
SUN Xiao-dan, TAO Xia-xin, WANG Guo-xin, et al. 2009. Dynamic corner frequency in source spectral model for stochastic synthesis of ground motion 【J】. Acta Seismological Sinica, 31(5): 537—543(in Chinese).
王卫民, 赵连锋, 李娟, 等. 2008. 四川汶川8.0级地震震源过程【J】. 地球物理学报, 51(5): 1403—1410.
WANG Wei-min, ZHAO Lian-feng, LI Juan, et al. 2008. Rupture process of the M8.0 Wenchuan earthquake of Sichuan, China 【J】. Chinese Journal of Geophysics, 51(5): 1403—1410(in Chinese).
Boore D M. 1983. Stochastic simulation of high-frequency ground motion based on seismological models of the radiated spectra 【J】. Bulletin of the Seismological Society of America, 73(6): 1865—1894.
Brune J N. 1970. Tectonic stress and spectra of seismic shear waves from earthquakes 【J】. Journal of Geophysical Research, 75(26): 4997—5009.
Frankel A. 1995. Simulating strong motions of large earthquakes using recordings of small earthquakes: The Loma Prieta mainshock as a test case 【J】. Bulletin of the Seismological Society of America, 85(4): 1144—1160.
Hartzell S H. 1978. Earthquake aftershocks as Green's functions 【J】. Geophysical Research Letters, 5(1): 1—4.
Heaton T H, Hartzell S H. 1989. Estimation of strong ground motions from hypothetical earthquakes on Cascadia subduction zone, Pacific Northwest 【J】. Pure and Applied Geophysics, 129(1/2): 131—201.
Hough S E. 2001. Empirical Green's function analysis of recent moderate events in California 【J】. Bulletin of the Seismological Society of America, 91: 456—467.
Hutchings, L. 1991. Prediction of strong ground motion for the 1989 Loma Prieta earthquake using empirical Green's functions 【J】. Bulletin of the Seismological Society of America, 81:1813—1837.
Irikura K. 1983. Semi-empirical estimation of strong ground motions during large earthquakes 【J】. Bull Disas Prev Res Inst, Kyoto Univ, 33(2): 63—104.
Irikura K. 1986. Prediction of strong acceleration motion using empirical Green's function 【A】. In: Proceedings of the Seventh Japan Earthquake Engineering Symposium, Tokyo: 151—156.
Ji C, Hayes G. 2008. Preliminary result of the May 12, 2008 M_W7.9 eastern Sichuan, China earthquake【EB/OL】. http: //earthquake.usgs.gov/earthquakes/eqinthenews/us2008ryan/finite_fault.php(last accessed December 2013).
Joyner W B, Boore D M. 1986. On simulating large earthquakes by Green's function addition of smaller earthquakes 【A】. In: Earthquake Source Mechanics, American Geophysical Union Monograph, 37: 269—274.
Kamae K, Irikura K. 1992. Prediction of site-specific strong ground motion using semi-empirical methods 【A】. In: Proceedings of the 10th World Conference on Earthquake Engineering: 801—806.
Kanamori H. 1979. A semi-empirical approach to prediction of long-period ground motions from great earthquakes 【J】. Bulletin of the Seismological Society of America, 69(6): 1645—1670.
Kanamori H. Anderson D L. 1975. Theoretical basis of some empirical relations in seismology 【J】. Bulletin Seismological Society of America, 65: 1073—1095.
Koketsu K, Yokota Y, Ghasemi H, et al. 2009. Source process and ground motions of the 2008 Wenchuan earthquake 【R】. Investigation report of the May 12th 2008, Wenchuan earthquake, China, Grant-in-Aid for Special Purposes of 2008, Ministry of Education, Culture, Sports, Science and Technology(MEXT), No. 2900002: 201—212.
Kurahashi S, Irikura K. 2010. Characterized source model for simulating strong ground motions during the 2008 Wenchuan earthquake 【J】. Bulletin of the Seismological Society of America, 100(5B): 2450—2475.
Motazedian D, Atkinson G M. 2005. Stochastic finite-fault modeling based on a dynamic corner frequency 【J】. Bulletin of the Seismological Society of America, 95(3): 995—1010.
Shen Z K, Sun J, Wan Y, et al. 2008. Coseismic rupture distribution of the 2008 Wenchuan China earthquake inferred using GPS and InSAR measurements 【A】. In: American Geophysical Union, Fall Meeting, U22B-03.
Tanaka T. 1982. Estimation of acceleration characteristics of strong ground motion by synthesis of accelerogram obtained during a small earthquake 【J】. Bull Earthq Res Inst, Univ Tokyo, 57: 561—580.
Yarai H, Nishimura T, Tobita M, et al. 2008. A fault model of the Wenchuan earthquake estimated from SAR measurements 【A】. In: Proceedings of the 7th General Assembly of the Asian Seismological Commission, Tsukuba, Japan: 24—27.

[1]	SONG Dong-mei, WANG Hui, SHAN Xin-jian, WANG Bin, CUI Jian-yong. A NOVEL EXTRACTION METHOD OF PRE-EARTHQUAKE GRACE GRAVITY ANOMALY INFORMATION BASED ON MAXIMUM SHEAR STRAIN [J]. SEISMOLOGY AND GEOLOGY, 2022, 44(6): 1539-1556.
[2]	CHEN Li-juan, CHEN Xue-zhong, LI Yan-e, GONG Li-wen. RELATIONSHIP BETWEEN DECREASING AMPLITUDE OF b-VALUE AND THE SEISMOGENIC ZONE OF THE WENCHUAN M_S8.0 EARTHQUAKE [J]. SEISMOLOGY AND GEOLOGY, 2022, 44(4): 1046-1058.
[3]	WANG Xiao-shan, WAN Yong-ge. CHARACTERISTICS OF THE CRUSTAL STRESS FIELD AND ITS DIRECTION CONVERGENCE BEFORE THE WENCHUAN EARTHQUAKE [J]. SEISMOLOGY AND GEOLOGY, 2022, 44(2): 363-377.
[4]	GUO Shu-song, ZHU Yi-qing, XU Yun-ma, LIU Fang, ZHAO Yun-feng, ZHANG Guo-qing, ZHU Hui. GRAVITY EVIDENCE OF META-INSTABLE STATE BEFORE THE 2008 WENCHUAN EARTHQUAKE [J]. SEISMOLOGY AND EGOLOGY, 2021, 43(6): 1368-1380.
[5]	LI Chun-guo, WANG Hong-wei, WEN Rui-zhi, QIANG Sheng-yin, REN Ye-fei. THREE-COMPONENT GROUND MOTION SIMULATIONS BASED ON THE STOCHASTIC FINITE-FAULT METHOD FOR THE 2021 MADUO M_S7.4 EARTHQUAKE, QINGHAI PROVINCE [J]. SEISMOLOGY AND EGOLOGY, 2021, 43(5): 1085-1100.
[6]	WANG Hong-wei, WEN Rui-zhi, REN Ye-fei. SEISMIC GROUND MOTION SIMULATION CONSIDERING REGIONAL CHARACTERISTICS: A CASE STUDY OF THE JIASHI M_S6.4 EARTHQUAKE IN 2020 [J]. SEISMOLOGY AND GEOLOGY, 2021, 43(2): 430-446.
[7]	LAN Jian, CHEN Xiao-li. EVOLUTION CHARACTERISTICS OF LANDSLIDES TRIGGERED BY 2008 M_S8.0 WENCHUAN EARTHQUAKE IN YINGXIU AREA [J]. SEISMOLOGY AND GEOLOGY, 2020, 42(1): 125-146.
[8]	ZHU Chuan-hua, SHAN Xin-jian, ZHANG Guo-hong, JIAO Zhong-hu, ZHANG Ying-feng, LI Yan-chuan, QIAO Xin. TWO DIMENSIONAL MODEL ON RELATION BETWEEN THERMAL ANOMALY BEFORE WENCHUAN EARTHQUAKE AND TECTONIC STRESS [J]. SEISMOLOGY AND GEOLOGY, 2019, 41(6): 1497-1510.
[9]	SONG Dong-mei, XIANG Liang, SHAN Xin-jian, YIN Jing-yuan, WANG Bin, CUI Jian-yong. THE METHOD OF CONSTRUCTING IONOSPHERIC TEC BACKGROUND FIELD BASED ON SVR MODEL [J]. SEISMOLOGY AND GEOLOGY, 2019, 41(6): 1511-1528.
[10]	MA Si-yuan, XU Chong, WANG Tao, LIU Jia-mei. APPLICATION OF TWO SIMPLIFIED NEWMARK MODELS TO THE ASSESSMENT OF LANDSLIDES TRIGGERED BY THE 2008 WENCHUAN EARTHQUAKE [J]. SEISMOLOGY AND GEOLOGY, 2019, 41(3): 774-788.
[11]	XU Zhi-ping, WANG Fu-yun, JIANG Lei, ZHAO Yan-na, YANG Li-pu, TANG Lin. THE THREE DIMENSIONAL DENSITY STRUCTURE OF CRUST AND UPPER MANTLE IN THE CENTRAL-SOUTHERN PART OF LONGMENSHAN [J]. SEISMOLOGY AND GEOLOGY, 2019, 41(1): 84-98.
[12]	YIN De-yu, LIU Qi-fang, LIU Chang, JI Xin-yang. ESTIMATING THE WENCHUAN EARTHQUAKE RUPTURE PROCESS USING NEAR FIELD STRONG MOTION RECORDS AND COSEISMIC DISPLACEMENTS [J]. SEISMOLOGY AND GEOLOGY, 2018, 40(3): 698-717.
[13]	ZHAO You-jia, ZHANG Guo-hong, ZHANG Ying-feng, SHAN Xin-jian, QU Chun-yan. TWO-DIMENSIONAL WHOLE CYCLE SIMULATION OF SPONTANE-OUS RUPTURE OF THE 2008 WENCHUAN EARTHQUAKE USING THE CONTINUOUS-DISCRETE ELEMENT METHOD [J]. SEISMOLOGY AND GEOLOGY, 2018, 40(1): 12-26.
[14]	LIU Yuan-zheng, MA Jin, MA Wen-tao, JIANG Tong. INFLUENCE OF PRESSURE HEAD CHANGE AND ITS CHANGE RATE ON RESERVOIR TRIGGERED SEISMICITY -A CASE STUDY OF ZIPINGPU RESERVOIR [J]. SEISMOLOGY AND GEOLOGY, 2017, 39(3): 437-450.
[15]	YAO Lu, MA Sheng-li, WANG Yu, HE Hong-lin, CHEN Jian-ye, YANG Xiao-song, SHIMAMOTO Toshihiko. THE VITRINITE REFLECTANCE OF FAULT ROCKS FROM THE WENCHUAN EARTHQUAKE FAULT ZONE: CONSTRAINTS ON FRICTIONAL PROPERTIES OF THE FAULT DURING THE EARTHQUAKE [J]. SEISMOLOGY AND GEOLOGY, 2016, 38(4): 817-829.