由能量分配原理探讨滑移弱化与视应力的关系
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摘要
按照震源地震波能量辐射原理,在断层面上任意一点由破裂或滑动而产生的地震波能量ES、地震矩M0及相应的视应力σa都应大于零.在近期研究中发现Poldo等在震源参数反演求取断层面上临界滑动弱化距离Dc所采用的视应力约束方程出现了"视应力取值小于零"的情形,其负值被解释为对地震波辐射能无贡献的耗散能,可合并至破裂能部分.数学上的表述并未影响到反演结果,但从能量守恒观点上讲,这样的表述是不准确的.进一步讲,由此表述所求得的辐射能量ES大于由能量分配原理所得结果.根据能量分配准则,指出出现负值视应力是不合适的,并给出了表述视应力随断层滑移过程变化的替代方法,同时提供了求解临界滑动弱化距离Dc的正确途径.
According to the representation theorem of seismic energy radiation,we know that,at any point on the fault,the instantaneous seismic radiation energy ES,the seismic moment M0,and the apparent stress σa=μES/M0(μ is the shear modulus on the fault plane)should be positive at any time during an earthquake faulting.However,we have noticed that,in recent source parameter study in deriving the critical slip-weakening distance,the apparent stress used as a constrained condition on the fault plane could be less than zero,and the negative value was considered as the dissipation energy and incorporated to the fracture energy.Although the mathematical formula in such case has no influence to the final resolution,the source process violates the basic physical law,resulting in the overestimate of radiated seismic energy.In this study,we have proposed an alternative way to take account of the apparent stress expression based on the energy partition principle,and at the same time,we have suggested that an additional constraint including the radiation energy conservation on the fault could add to the inversion for source parameters in order to estimate the critical slip-weakening distance Dc.
According to the representation theorem of seismic energy radiation,we know that,at any point on the fault,the instantaneous seismic radiation energy ES,the seismic moment M0,and the apparent stress σa=μES/M0(μ is the shear modulus on the fault plane)should be positive at any time during an earthquake faulting.However,we have noticed that,in recent source parameter study in deriving the critical slip-weakening distance,the apparent stress used as a constrained condition on the fault plane could be less than zero,and the negative value was considered as the dissipation energy and incorporated to the fracture energy.Although the mathematical formula in such case has no influence to the final resolution,the source process violates the basic physical law,resulting in the overestimate of radiated seismic energy.In this study,we have proposed an alternative way to take account of the apparent stress expression based on the energy partition principle,and at the same time,we have suggested that an additional constraint including the radiation energy conservation on the fault could add to the inversion for source parameters in order to estimate the critical slip-weakening distance Dc.
引文
Dahlen F A.1977.The balance of energy in earthquake faulting[J].Geophys J R astr Soc,48:239-261.
Kostrov B.1974.Seismic moment and energy of earthquakes,and seismic flow of rock[J].Izv Earth Physics,1:23-40.
Madariaga R.1977.Implications of stress drop models of earthquakes for theinversion of stress dropfromseismic obser-vations[J].Pure Appl Geophys,115:301-315.
Pulido N,Irikura K.2000.Estimation of dynamic rupture parameters from the radiated seismic energy and apparentstress[J].Geophys Res Lett,27:3945-3948.
Rivera L,Kanamori H.2005.Representations of the radiated energyin earthquakes[J].Geophys J Int,162:148-155.
Rudnicki J W,Freund L B.1981.On energy radiation fromseismic sources[J].Bull Seism Soc Amer,71:583-595.
Wyss M,Brune J N.1968.Seismic moment,stress,and source dimensions for earthquakes in the California-Nevada re-gion[J].J Geophys Res,73:4681-4694.
Kostrov B.1974.Seismic moment and energy of earthquakes,and seismic flow of rock[J].Izv Earth Physics,1:23-40.
Madariaga R.1977.Implications of stress drop models of earthquakes for theinversion of stress dropfromseismic obser-vations[J].Pure Appl Geophys,115:301-315.
Pulido N,Irikura K.2000.Estimation of dynamic rupture parameters from the radiated seismic energy and apparentstress[J].Geophys Res Lett,27:3945-3948.
Rivera L,Kanamori H.2005.Representations of the radiated energyin earthquakes[J].Geophys J Int,162:148-155.
Rudnicki J W,Freund L B.1981.On energy radiation fromseismic sources[J].Bull Seism Soc Amer,71:583-595.
Wyss M,Brune J N.1968.Seismic moment,stress,and source dimensions for earthquakes in the California-Nevada re-gion[J].J Geophys Res,73:4681-4694.
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