Improvement of Source Spectrum Fall-Off for Simulating Ground Motion Using Stochastic Green’s Function Method

The stochastic Green's function method (SGFM), which simulates the source spectra of small earthquakes based on the ω⁻² model and follows the scaling law of earthquakes to synthesize into a large earthquake, is a practical ground motion simulation method in areas lacking suitable small earthquake records. However, one of the problems in the application of the SGFM is that the source spectrum synthesized from small earthquakes shows a fall-off in the mid-frequency band, as the number of fault divisions of the large earthquake increases. To solve this problem, this study proposes an improved method, which introduces a correction coefficient for the source spectrum according to the ω⁻² model and considers the variation of subfault rise time with the rupture process. Taking the 1994 Northridge earthquake as an example, the ground motion simulation results of the improved method are compared with observed records. The results show that only introducing the correction coefficient causes larger amplitude of simulation results than observed records. Only considering the variation of subfault rise time can improve the fall-off problem to some extent, but the accuracy of ground motion simulation at observation points has no significant improvement. By simultaneously introducing the correction coefficient and considering the variation of subfault rise time, the simulation results are in good agreement with observed records and are able to reproduce the directivity effect at the forward observation points. Therefore, the improved SGFM proposed in this study is an effective and reliable tool for ground motion simulation.