有限断层地震波辐射能估算及其在合成强地面运动中的应用
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摘要
对有限断层地震波能量辐射的估算,通常采用断层面上子源能量的逐点求和方法.基于Brune圆盘模型,Anderson推导出有限断层地震波能量辐射S波的求解公式,即ESA=0.233(Δσd/Δσs)M0Δσs/μ.其中M0为断层面上地震矩,μ为剪切模量,Δσd和Δσs分别为动态应力降和静态应力降,并指出在复合震源模型强地面运动预测应用中Δσd>2Δσs以满足能量守恒.Rivera和Kanamori则从能量辐射表象定理出发,给出了有限断层中辐射能量的积分表达式,明确地指出了逐点求和所存在的问题.依据该积分表达式,本文推导出了复合源模型中新的辐射能完整的求解方法,指出Anderson方法实为断层面上点源辐射能量的简单叠加求和,后者则充分考虑了断层面上任一点在任一时刻能量传播过程中受到的断层面上所有位移破裂路径的交互影响.以1976年唐山MW7.6地震为例,应用上述方法分别计算了有限断层模型的辐射能量及近场强地面运动,如质点运动加速度,速度.结果表明,如果模型参数满足Δσd>2Δσs时,由本文给出的求解方法计算所得到的地震波辐射能已远远超出实际的辐射能量值,直接导致了对近场强地面运动参数如质点速度、加速度等的过高估算.因此,Zeng等和Anderson工作的局限性是非常明显的:地震矩守恒以及非物理的Δσd/Δσs>2无法准确地预测近场地面运动.未来工作中,对于有限断层模型的建立,在地震矩守恒这一约束条件的基础上,远场和近场能量解(或视应力)将可作为另一个重要的约束条件,为强地面运动的模拟提供一个更为恰当的求解方案.
The radiated seismic energy strongly depends on how the rupture propagates during an earthquake. In this study, we calculated the radiated energy and apparent stress from the known slip distribution described by Brune’s source function, which is commonly used in strong ground motion modeling, resulting from the composite source model. A new technique based on the far-field energy integrand over a simple finite fault is developed to estimate S-wave energy radiation with associated composite source model. Comparing with point source summation proposed by Anderson, in which EAS=0.233(Δσd/Δσs)M0Δσs/μ, where EAS is the energy radiated by S-wave, M0 and μ are scalar seismic moment and shear rigidity, respectively, Δσs and Δσd are static and dynamic stress drop, respectively. As Rivera and Kanamori pointed out that, in such case, the integration of energy flux from any point on the fault depend not only on the slip function at that point, but also on the slip function everywhere over the fault plane. Moreover, we discussed the frictional overshoot and undershoot behavior inherited in Anderson’s consideration and our current solution for the composite source model, and the scaling relation of radiated energy to the ratio of Δσd/Δσs given by Anderson may be incorrect in the source energy estimation. For comparison, we developed a composite source model to simulate the 1976 MW7.6 Tangshan earthquake and calculate the radiated S-wave energy based on Anderson’s solution and our new solution. The results show that, for Anderson’s solution, the energy conservation occurs when Δσd/Δσs>2, and the corresponding near-fault particle velocity or PGV (peak ground velocity) are much higher than real observation. We suggest that, for strong motion simulation, the seismic moment alone is insufficient to quantify the ground motion level, the radiated energy or apparent stress derived from earthquake source inversion should be an additional constraint in future development of numerical algorithm of strong motion prediction.
The radiated seismic energy strongly depends on how the rupture propagates during an earthquake. In this study, we calculated the radiated energy and apparent stress from the known slip distribution described by Brune’s source function, which is commonly used in strong ground motion modeling, resulting from the composite source model. A new technique based on the far-field energy integrand over a simple finite fault is developed to estimate S-wave energy radiation with associated composite source model. Comparing with point source summation proposed by Anderson, in which EAS=0.233(Δσd/Δσs)M0Δσs/μ, where EAS is the energy radiated by S-wave, M0 and μ are scalar seismic moment and shear rigidity, respectively, Δσs and Δσd are static and dynamic stress drop, respectively. As Rivera and Kanamori pointed out that, in such case, the integration of energy flux from any point on the fault depend not only on the slip function at that point, but also on the slip function everywhere over the fault plane. Moreover, we discussed the frictional overshoot and undershoot behavior inherited in Anderson’s consideration and our current solution for the composite source model, and the scaling relation of radiated energy to the ratio of Δσd/Δσs given by Anderson may be incorrect in the source energy estimation. For comparison, we developed a composite source model to simulate the 1976 MW7.6 Tangshan earthquake and calculate the radiated S-wave energy based on Anderson’s solution and our new solution. The results show that, for Anderson’s solution, the energy conservation occurs when Δσd/Δσs>2, and the corresponding near-fault particle velocity or PGV (peak ground velocity) are much higher than real observation. We suggest that, for strong motion simulation, the seismic moment alone is insufficient to quantify the ground motion level, the radiated energy or apparent stress derived from earthquake source inversion should be an additional constraint in future development of numerical algorithm of strong motion prediction.
引文
蔡永恩,何涛,王仁.1999.1976年唐山地震震源动力过程的数值模拟[J].地震学报,21(5):469-477.
Aki K,Richards F G.1980.Quantitative Seismology:Theory and Methods[M].New York:W H Freeman and Company Press:127.
Anderson J G.1997.Seismic energy and stress-drop parameters for a composite source model[J].Bull Seism Soc Amer,87(1):85-96.
Boatwright J A.1980.Spectral theory for circular seismic sources;simple estimates of source dimension,dynamic stress drop,and radiated seismic energy[J].Bull Seism Soc Amer,70(1):1-27.
Boore D M,Atkinson G M.2007.Boore-Atkinson NGA Ground Motion Relations for the Geometric Mean Horizontal Component of Peak and Spectral Ground Motion Parameters[R].PEER Report 2007/01.Pacific Earthquake Engineering Research Center.University of California,Berkeley.
Brune J N.1970.Tectonic stress and spectra of seismic shear waves from earthquakes[J].J Geophys Res,75(26):4997-5009.
Brune J N.1971.Correction to“tectonic stress and spectra of seismic shear waves from earthquakes”[J].J Geophys Res,76(20):5002.
Butler R,Stewart G S,Kanamori H.1979.The July 27,1976Tangshan,China earthquake:A complex sequence of interpolate events[J].Bull Seism Soc Amer,69(1):207-220.
Choy G L,Boatwright J L.2009.Differential energy radiation from two earthquakes in Japan with Identical MW:The Kyushu 1996and Tottori 2000earthquakes[J].Bull Seism Soc Amer,99(6):1815-1826.
Haskell N A.1964.Total-energy and energy spectral density of elastic wave propagation from propagating faults[J].Bull Seism Soc Amer,54(6):1811-1841.
Huang B S,Yeh Y T.1997.The fault rupture of the 1976Tangshan earthquake sequence inferred from coseismic crustal deformation[J].Bull Seism Soc Amer,87(4):1046-1057.
Kanamori H,Rivera L.2006.Energy partitioning during an earthquake[M]∥Earthquakes:Radiated Energy and the Physics of Faulting.Geophysical Monograph Series,170:American Geophysical Union:3-13.
Madariaga R.1976.Dynamics of an expanding circular fault[J].Bull Seism Soc Amer,66(3):639-666.
McGarr A,Fletcher J B.2001.A method for mapping apparent stress and energy radiation applied to the 1994Northridge earthquake fault zone-revisited[J].Geophys Res Lett,28(18):3529-2532.
Patricia Grossi,Domenico del Re,Wang Zifa.2006.The 1976 Great Tangshan Earthquake 30-year Retrospective[G].Risk Management Solutions,Inc:3.
Rivera L,Kanamori H.2005.Representations of the radiated energy in earthquakes[J].Geophys J Int,162:148-155.
Robinson R,Zhou S Y.2005.Stress interactions within the Tangshan,China,earthquake sequence of 1976[J].Bull Seism Soc Amer,95(6):2501-2505.
Rudnicki J W,Freund L B.1981.On energy radiation from seismic sources[J].Bull Seism Soc Amer,71(3):583-595.
Savage J C,Wood M D.1971.The relation between apparent stress and stress drop[J].Bull Seism Soc Amer,61(5):1381-1338.
Scholz C H.2002.The Mechanics of Earthquakes and Faulting[M].2nd.Cambridge:Cambridge University Press:194.
Tumarkin G,Archuleta J,Madariaga R.1994.Scaling relations for composite earthquake models[J].Bull Seism Soc A-mer,84(4):1279-1283.
Wald D J,Quitoriano V,Thomas H H,Kanamori H,Scrivner C W,Worden C B.1999.Relations between peak ground acceleration,peak ground velocity,and Modified Mercalli intensity in California[J].Earthquake Spectra,15(3):557-564.
Wyss M,Brune J N.1968.Seismic moment,stress,and source dimensions for earthquakes in the California-Nevada region[J].J Geophys Res,73(14):4681-4694.
Xie L L,Zhang M Z,Qu C J.1994.Simulation of strong seismic motions for the Tangshan earthquake[J].Earthquake Engineering and Engineering Vibration,14(3):1-10.
Zeng Y,Anderson J G,Yu G.1994.A composite source model for computing realistic synthetic strong ground motions[J].Geophys Res Lett,21(8):725-728.
Aki K,Richards F G.1980.Quantitative Seismology:Theory and Methods[M].New York:W H Freeman and Company Press:127.
Anderson J G.1997.Seismic energy and stress-drop parameters for a composite source model[J].Bull Seism Soc Amer,87(1):85-96.
Boatwright J A.1980.Spectral theory for circular seismic sources;simple estimates of source dimension,dynamic stress drop,and radiated seismic energy[J].Bull Seism Soc Amer,70(1):1-27.
Boore D M,Atkinson G M.2007.Boore-Atkinson NGA Ground Motion Relations for the Geometric Mean Horizontal Component of Peak and Spectral Ground Motion Parameters[R].PEER Report 2007/01.Pacific Earthquake Engineering Research Center.University of California,Berkeley.
Brune J N.1970.Tectonic stress and spectra of seismic shear waves from earthquakes[J].J Geophys Res,75(26):4997-5009.
Brune J N.1971.Correction to“tectonic stress and spectra of seismic shear waves from earthquakes”[J].J Geophys Res,76(20):5002.
Butler R,Stewart G S,Kanamori H.1979.The July 27,1976Tangshan,China earthquake:A complex sequence of interpolate events[J].Bull Seism Soc Amer,69(1):207-220.
Choy G L,Boatwright J L.2009.Differential energy radiation from two earthquakes in Japan with Identical MW:The Kyushu 1996and Tottori 2000earthquakes[J].Bull Seism Soc Amer,99(6):1815-1826.
Haskell N A.1964.Total-energy and energy spectral density of elastic wave propagation from propagating faults[J].Bull Seism Soc Amer,54(6):1811-1841.
Huang B S,Yeh Y T.1997.The fault rupture of the 1976Tangshan earthquake sequence inferred from coseismic crustal deformation[J].Bull Seism Soc Amer,87(4):1046-1057.
Kanamori H,Rivera L.2006.Energy partitioning during an earthquake[M]∥Earthquakes:Radiated Energy and the Physics of Faulting.Geophysical Monograph Series,170:American Geophysical Union:3-13.
Madariaga R.1976.Dynamics of an expanding circular fault[J].Bull Seism Soc Amer,66(3):639-666.
McGarr A,Fletcher J B.2001.A method for mapping apparent stress and energy radiation applied to the 1994Northridge earthquake fault zone-revisited[J].Geophys Res Lett,28(18):3529-2532.
Patricia Grossi,Domenico del Re,Wang Zifa.2006.The 1976 Great Tangshan Earthquake 30-year Retrospective[G].Risk Management Solutions,Inc:3.
Rivera L,Kanamori H.2005.Representations of the radiated energy in earthquakes[J].Geophys J Int,162:148-155.
Robinson R,Zhou S Y.2005.Stress interactions within the Tangshan,China,earthquake sequence of 1976[J].Bull Seism Soc Amer,95(6):2501-2505.
Rudnicki J W,Freund L B.1981.On energy radiation from seismic sources[J].Bull Seism Soc Amer,71(3):583-595.
Savage J C,Wood M D.1971.The relation between apparent stress and stress drop[J].Bull Seism Soc Amer,61(5):1381-1338.
Scholz C H.2002.The Mechanics of Earthquakes and Faulting[M].2nd.Cambridge:Cambridge University Press:194.
Tumarkin G,Archuleta J,Madariaga R.1994.Scaling relations for composite earthquake models[J].Bull Seism Soc A-mer,84(4):1279-1283.
Wald D J,Quitoriano V,Thomas H H,Kanamori H,Scrivner C W,Worden C B.1999.Relations between peak ground acceleration,peak ground velocity,and Modified Mercalli intensity in California[J].Earthquake Spectra,15(3):557-564.
Wyss M,Brune J N.1968.Seismic moment,stress,and source dimensions for earthquakes in the California-Nevada region[J].J Geophys Res,73(14):4681-4694.
Xie L L,Zhang M Z,Qu C J.1994.Simulation of strong seismic motions for the Tangshan earthquake[J].Earthquake Engineering and Engineering Vibration,14(3):1-10.
Zeng Y,Anderson J G,Yu G.1994.A composite source model for computing realistic synthetic strong ground motions[J].Geophys Res Lett,21(8):725-728.
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