Study On The Two-stage Stochastic Empirical Green’s Function Method For Ground Motion Simulation

The ground-motion prediction at a specific site in the future earthquake is the major task in the seismic hazard assessment.The two-step stochastic empirical Green’s function(EGF)method,proposed in recent years have been widely used and have succeed in simulating ground motions in some eartqhaukes.However,some problems still existed in this method.In this paper,we made some efforts to solve these problems,including the appropriate representation of earthquake stress drop,the quantitative uncertainty of simulated ground motion,modeling the rupture directivity,and exploring soluation for the absence of EGF.The following was the main work in this paper.(1)A model for representing the earthquake stress drop was proposed,and the validation of the simulation was tested.We proposed that the stress drop should be represented as the determined probabilic distribution.Based on the computed stress drops for large numbers of earthquakes in global,it should follow the lognormal distribution with the standard deviation approximately from 0.2 to 0.6,related to the seismogenic area.We suggested that the average stress drop was estimated by the relationship between the average slip and the size of the rupture plane.Ground motions produced by the 2013 Mw 6.6 Lushan earthquake,the 2008 Mw 6.9 Iwate-Miyagi Nairiku earthquake,and the 2016 Mw 7.1 Kumamoto earthquake were simulated based on the two-step stochastic EGF method.Only asperity with high stress drop on the rupture plane was considered.The short-period(<2.0s)ground motions were well reproduced.However,the long-period(>2.0s)ground motions were significantly underestimated,which may be ascribed to EGFs from small earthquakes that lack long-period signals.We also confirmed that rupture areas with low stress drop made few contributions to the simulated ground motions.(2)Uncertainty of the simulated ground motion was quantitatively analyzed.Ground motions produced by the Lushan,Iwate-Miyagi Nairiku,and Kumamoto earthquakes were simulated with different stress drop ratios ranging from 0.5 to 8.0 at an interval of 1.5.The simulated ground motion increased with the increasing stress drop ratio.The linear correlation between the residual of the simulated ground motion and the natural logarithm of the stress drop ratio was obviously observed.A relationship between the simulated ground motion and the stress drop ratio was developed.Furthermore,stress drops were randomly generated through the Monte Carlo sampling technique,which followed the lognormal distribution with the standard deviation varying from 0.2 to 0.6 at an interval of 0.1(log10 units).A quantitative relationship between the standard deviation of the simulated ground motion and the standard deviation of the stress drop was developed.The simulated ground motions at the longer period show the much smaller variability.The standard deviations of simulated ground motion at periods from 0.05 to 5.0 s were equal to 0.11-0.37,when the standard deviation of the stress drop varied from 0.2 to 0.6.Finally,we also investigated the quantitative uncertainty from the stochastic rupture processes.The simulated ground motions from stochastic rupture processes followed the lognormal distribution verified by K-S test.The standard deviation of the simulated ground motions in 200 realizations was 0.05-0.15,which increased with the increasing period.(3)The rupture directivity was effectively simulated based on the improved two-step stochastic EGF method.Strong-motion recordings from Lushan aftershocks(EQII and EQIII)with significant rupture directivity were regarded as EGFs to simulate ground motions produced by the Lushan earthquake.The simulated ground motions showed significant directivity effects,which was coincident with the rupture directivity effects from the EGF event.Therefore,the rupture directivity of the EGF event should also be considered.The two-step stochastic EGF method was improved to represent the rupture directivity,in which the apparent corner frequency was substituted for the corner frequency.Ground motions were simulated again with EQIII as EGF event based on the improved method.The simulated ground motions did not show directivity,and were in good agreement with the observed ground motions.Furthermore,ground motions produced by a series of Lushan-like earthquakes with various rupture directivities assumed were simulated based on the improved method.The simulated ground motions showed significant directivity effects,which correspond to the assumed directivity characteristics.(4)The concept of the generalized EGF was proposed for exporlation the soluation of the absence of EGF.The generalized EGF was selected without the hypocenter location between the large and EGF events considered.The path differences on ground motions with epicenter distance less than 150 km between China and Japan can be approximately ignored according to the intra-event residual analyses.Strong motion recordings from the K-NET stations and the KiK-net borehole stations on bedrock were used to simulated ground motion produced by the Lushan earthquake.Generally,the observed ground motions fell in the average simulation plus or minus one standard deviation.The simulated ground motions well represented the observed recordings.Furthermore,strong motion recordings from KiK-net borehole stations on bedrock were used to simulate ground motions produced by the 1976 Ms 7.8 Tangshan earthquake.The simulated ground motions at short periods(0.1-3.0 s)had good agreements with the predicted values of ground motion prediction equation.The simulated PGA contours were in good agreement with the isoseismals of the macro-intensity map.