A composite source model has been used to simulate a broadband strong ground motion with an associated fault rupture process. A scenario earthquake fault model has been used to generate 1 000 earthquake events with a magni-tude of Mw8.0. The simulated results show that, for the characteristic event with a strike-slip faulting, the character istics of near fault ground motion is strongly dependent on the rupture directivity. If the distance between the sites and fault was given, the ground motion in the forward direction (Site A) is much larger than that in the backward direction (Site C) and that close to the fault (Site B). The SH waves radiated from the fault, which corresponds to the fault-normal component plays a key role in the ground motion amplification. Corresponding to the sites A, B, and C, the statistical analysis shows that the ratio of their aPG is 2.15:1.5:1 and their standard deviations are about 0.12, 0.11, and 0.13, respectively. If these results are applied in the current probabilistic seismic hazard analysis (PSHA), then, for the lower annual frequency of exceedance of peak ground acceleration, the predicted aPG from the hazard curve could reduce by 30% or more compared with the current PSHA model used in the developing of seismic hazard map in the USA. Therefore, with a consideration of near fault ground motion caused by the rupture directivity, the regression model used in the development of the regional attenuation relation should be modified accordingly.
With co-seismic surface rupture slip displacements provided by the field observation for the 2001 MS8.1 West Kunlun Mountain Pass earthquake, this paper estimates the rupture speed on the main faulting segment with a long straight fault trace on the surface based on a simple slip-weakening rupture model, in which the frictional overshoot or undershoot are involved in consideration of energy partition during the earthquake faulting. In contrast to the study of Bouchon and Vallée, in which the rupture propagation along the main fault could exceed the local shear-wave speed, perhaps reach the P-wave speed on a certain section of fault, our results show that, under a slip-weakening assumption combined with a frictional undershoot (partial stress drop model), average rupture speed should be equal to or less than the Rayleigh wave speed with a high seismic radiation efficiency, which is consistent with the result derived by waveform inversion and the result estimated from source stress field. Associated with the surface rupture mechanism, such as partial stress drop (frictional undershoot) associated with the apparent stress, an alternative rupture mechanism based on the slip-weakening model has also been discussed.
A mature mathematical technique called copula joint function is introduced in this paper, which is commonly used in the financial risk analysis to estimate uncertainty. The joint function is generalized to the n-dimensional Frank's copula. In addition, we adopt two attenuation models proposed by YU and Boore et al, respectively, and construct a two-dimensional copula joint probabilistic function as an example to illustrate the uncertainty treatment at low probability. The results show that copula joint function gives us a better prediction of peak ground motion than that resultant from the simple linear weight technique which is commonly used in the traditional logic-tree treatment of model uncertainties. In light of widespread application in the risk analysis from financial investment to insurance assessment, we believe that the copula-based technique will have a potential application in the seismic hazard analysis.
According to energy partition principle,we have derived a generalized formula used to calculate the radiation effi-ciency.It overcomes the numerical errors involved in the estimation of radiation efficiency caused by the uncer-tainties owe to the different frictional mechanisms which is used to describe the earthquake faulting.Using real seismic data published in the previous studies,we have recalculated the radiation efficiency with associated to the different frictional mechanisms,and compared with previous results lack of consideration of frictional mechanism.The results indicate that,based on the new formula,the radiation efficiency we have estimated is always less than 1,and the unphysical conclusion of radiation efficiency greater than 1 is avoided completely.
Based on the representation theorem of seismic energy radiation,in this study,we have quantitatively investigated the effect of free surface on the radiation energy distribution due to a coupling interaction between free surface and near surface finite fault for the reverse earthquake faulting.Corresponding to the finite faulting,a 2-D pseudostatic-reverse-fault-dislocation solution has been used in the calculation of the work done by the seismic response against free surface.The results indicate that,due to a strong coupling interaction between the free surface and near surface fault,the total radiated seismic energy ER is much larger than that radiated only from the fault itself(EF),especially for the shallow reverse faulting.In convention,EF is commonly used in the estimation of earthquake energy radiation.However,when the fault depth H,the distance between the free surface and top of fault location,increases,the effect of the coupling interaction between the fault and free surface decreases gradually.Therefore,the total radiated energy ER approaches to the EF when the depth H is about 2 times the fault length l.The current study could provide us a partial explanation of the apparent stress discrepancy observed at the far field and near field in the recent large earthquake.Moreover,the current study also has a significant implication of how to quantitatively describe the near fault strong ground motion and associated seismic hazard from the earthquake source energy point of view.
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 values at any time during an earthquake faulting.However,we have noticed that,in recent source parameter inversion scheme for deriving the critical slip-weakening distance,the apparent stress used as a constraint condition on the fault plane could be less than zero or negative value,and the negative part was considered as dissipation energy and incorporated to the fracture energy.Although the mathematical formula in such case has no influence to the final resolution,however,the earthquake dynamic source process violates obviously the basic physical law,which could results in the overestimating of radiated seismic energy.In this study,we have proposed an alternative way to take account of the apparent stress expression based on the earthquake energy partition principle,and at the same time,we have also suggested that an additional constraint regarding to the radiation energy conservation on the fault could be added into the source parameter inversion in order to estimate the critical slip-weakening distance Dc.
