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in this study, new prediction equations are proposed to determine the variables of gamma envelope-shape Function. Envelope-shape functions are employed for the simulation of ground motion using a stochastic method in order to form the white noise. A variety of Envelope-shape functions have been already proposed, among which gamma equations are more used in computational programs for the simulation of ground motion, e.g. SMSIM or EXSIM. In addition to the detection of influential variables of gamma envelope-shape function, their relationship with important seismic criteria such as moment magnitude, closest distance to rupture plane, site conditions and mechanism of faulting are determined and suitable models are presented in this study. Limited research has been already undertaken to specify the variables of envelope-shape equations and their relationships with the main seismic criteria. Hence the results of this study can almost demonstrate this relationship with seismic criteria. The new equations are developed using Iran strong ground motion database, which includes 2228 records of 749 earthquakes that covering up to 2018. The proposed equations can be used to determine exponential window function for earthquakes with moment magnitudefrom 4.5 to 7.6 and rupture distance up to 200 km. The proposed model is compared with some existing models and the results suggest that the equations can lead to better and more reasonable results in the ground motion simulation process, particularly for the estimation of response spectrum of velocity and displacement.

New Equations for Determination of Shaping Window in Stochastic Method of Simulating Ground Motion