**Abstract**

Contrary to the long period ground motions that can be predicted and estimated, high frequency ground motions have random character and behave stochastically. Stochastic modeling methods are usually used for the modeling of high frequency ground motions where there are not strong ground motion records. Stochastic methods are of two kinds: in the first one, the seismic source is considered as a point source and in the second, modeling is based on the finite fault. Seismic source is considered as a rectangular fault plane divided by some subfaults in its longitudinal and traversal directions.

Stochastic modeling method, using the seismic point source was presented by Boore in 1983. In the Boore stochastic method, the high frequency motions of earthquakes can be presented as the Gaussian noise with limited frequency band having the mean source spectrum w2. In this method a shape function is applied to a time series of white noise with zero mean, bringing it out of the stationary status, then the Fourier transform is applied to the noise and the amplitude spectrum of this time series is substituted by a desired spectrum and the phase spectrum remains unchanged. Transformation back to the time domain results in a time series whose amplitude spectrum is exactly in accordance with a specified spectrum.

In the simulation based on finite fault modeling, each subfault is considered as a point source, using the source model presented by Brune with a corner frequency and a constant stress drop. The target accelerogram is obtained by summation of accelerograms generated by each subfaults and by considering their corresponding delay times. This simulation method is used broadly in the assessment of strong ground motions. The first ground motion simulation program, FINISM, was finite fault modeling, based on the Boore stochastic method. The new version of the FINISM program, which is called EXSIM, has been used in this study.

Three parameters, quality factor, kappa and stress drop which have effects on the high frequency amplitudes, are important parameters in stochastic modeling which are considered in this study. Moreover the effects of shear wave velocity and density on the simulation accelerations are studied as well. In these simulations to distinguish the effect of a specific parameter, the amount of that parameter is changed, while other parameters are kept constant. It is found that the main effect of quality factor is in the high frequencies and variation of this parameter has no significant effect on the spectral accelerations in low frequencies. With increasing quality factor, the spectral accelerations as well as peak ground acceleration (PGA) which correspond to the spectral accelerations in high frequencies, will increase. This increase is greater in high frequencies and smaller in the low ones. The spectral acceleration and PGA reduce when kappa increases but the acceleration reduction is higher in high frequencies. It has been seen that the spectral accelerations increase with the increase in stress drop. Of course, this increment is small in low frequencies, but considerable in high frequencies. Rupture velocity is usually assumed as 80% of shear wave velocity. As shear wave velocity increases, the rupture velocity increases as well and consequently the fault will fracture more rapidly. Therefore, the delay time of subfault pulses reaching the observation point will reduce. This shows that if shear wave velocity increases, the duration of simulated accelerograms reduces slightly.

Finally the density effect on the simulation results is investigated in this study and it is concluded that if the density increases by ? then PGA, spectral accelerations and Fourier amplitude of simulated accelerogram will increases by 1/??

Stochastic modeling method, using the seismic point source was presented by Boore in 1983. In the Boore stochastic method, the high frequency motions of earthquakes can be presented as the Gaussian noise with limited frequency band having the mean source spectrum w2. In this method a shape function is applied to a time series of white noise with zero mean, bringing it out of the stationary status, then the Fourier transform is applied to the noise and the amplitude spectrum of this time series is substituted by a desired spectrum and the phase spectrum remains unchanged. Transformation back to the time domain results in a time series whose amplitude spectrum is exactly in accordance with a specified spectrum.

In the simulation based on finite fault modeling, each subfault is considered as a point source, using the source model presented by Brune with a corner frequency and a constant stress drop. The target accelerogram is obtained by summation of accelerograms generated by each subfaults and by considering their corresponding delay times. This simulation method is used broadly in the assessment of strong ground motions. The first ground motion simulation program, FINISM, was finite fault modeling, based on the Boore stochastic method. The new version of the FINISM program, which is called EXSIM, has been used in this study.

Three parameters, quality factor, kappa and stress drop which have effects on the high frequency amplitudes, are important parameters in stochastic modeling which are considered in this study. Moreover the effects of shear wave velocity and density on the simulation accelerations are studied as well. In these simulations to distinguish the effect of a specific parameter, the amount of that parameter is changed, while other parameters are kept constant. It is found that the main effect of quality factor is in the high frequencies and variation of this parameter has no significant effect on the spectral accelerations in low frequencies. With increasing quality factor, the spectral accelerations as well as peak ground acceleration (PGA) which correspond to the spectral accelerations in high frequencies, will increase. This increase is greater in high frequencies and smaller in the low ones. The spectral acceleration and PGA reduce when kappa increases but the acceleration reduction is higher in high frequencies. It has been seen that the spectral accelerations increase with the increase in stress drop. Of course, this increment is small in low frequencies, but considerable in high frequencies. Rupture velocity is usually assumed as 80% of shear wave velocity. As shear wave velocity increases, the rupture velocity increases as well and consequently the fault will fracture more rapidly. Therefore, the delay time of subfault pulses reaching the observation point will reduce. This shows that if shear wave velocity increases, the duration of simulated accelerograms reduces slightly.

Finally the density effect on the simulation results is investigated in this study and it is concluded that if the density increases by ? then PGA, spectral accelerations and Fourier amplitude of simulated accelerogram will increases by 1/??

**Keywords**