###### Abstract  
The stochastic Green's function method has been widely used in the field of ground motion simulation in recent years. It is generally assumed that the rise time of each subfault is the same in this method. Since the rise time significantly influences the amplitude of simulation results in the intermediate frequency band, to improve the accuracy of stochastic Green's function method for near-fault broadband ground motion simulation, referring to the numerical simulation results of Day, the rise time is assumed to be non-uniformly distributed on the fault, and an improved approximate expression of rise time on a rectangular fault considering that the rupture starting point may be at any position and the aspect ratio may be arbitrary is proposed. Additionally, the contributions of P, SV and SH wave are considered, respectively, and an improved stochastic Green's function method is proposed for 3D broadband ground motion simulation. Taking the 1994 Northridge earthquake in America and 2013 Lushan earthquake in China as examples, under different subfault division numbers, the synthesized source spectra are compared with the omega-squared theoretical source spectra of the large earthquake, and the simulated ground motions at observation points are compared with observed records to verify the effectiveness of the improved method. The results show that when the Northridge earthquake fault and Lushan earthquake fault are divided into 9 \(\times\) 10 subfaults and 11 \(\times\) 7 subfaults, respectively, the simulation results obtained using the improved method are close to the observed records in the broadband frequency range. Therefore, the improved method can effectively simulate the 3D ground motion in near-fault regions. 3D ground motion simulation; stochastic Green's function method; rise time; 1994 Northridge earthquake; 2013 Lushan earthquake  
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ground motion time history of the large earthquake at the observation point caused by the rupture of the entire fault can be obtained. In the stochastic [PERSON]'s function method, the rise time is an important parameter that affects the conversion function between small and large earthquakes. The commonly used formula for calculating the rise time \(\tau\) at present is \(\tau=\alpha_{\tau}W/V_{\text{R}}\), where \(\alpha_{\tau}\) is an empirical coefficient between 0.25 and 0.6, generally taken as 0.5, \(W\) and \(V_{\text{R}}\) represent the width of the fault and the propagation velocity of rupture on the fault plane, respectively. [PERSON] [8] applied the 3D finite difference method to numerically simulate the earthquake slip function and analyzed the distribution of rise time on the rectangular fault with different aspect ratios (fault length/fault width) when the rupture starting point is located at the center of the fault. The results show that the rise time at a point on the fault plane is related to its position on the fault plane. Near the rupture starting point, the rise time is longer, while near the edge of the fault, the rise time is shorter. The commonly used formula mentioned above is approximately valid along the center line of a long, narrow fault; however, its applicability is limited if the aspect ratio of the fault changes and the fault does not belong to a long, narrow fault. In addition, the rise time at different points on the fault plane is different, and the actual earthquake slip cannot be reflected if the ground motion in each subfault is calculated using the same rise time. From the perspective of energy released during earthquakes, when the slip of the fault is constant, the longer the rise time, the slower the slip velocity of the fault, and the slower the energy is released during the earthquake. Therefore, it is necessary to establish a reasonable formula for calculating the rise time to reflect the actual earthquake slip and improve the accuracy of simulating and predicting the ground motion using the stochastic Green's function method.