Broadband strong motion simulation in layered half-space using stochastic Green’s function technique

The stochastic Green’s function method, which simulates one component of the far-field S-waves from an extended fault plane at high frequencies (Kamae et al., J Struct Constr Eng Trans AIJ, 430:1–9, 1991), is extended to simulate the three components of the full waveform in layered half-spaces for broadband frequency range. The method firstly computes ground motions from small earthquakes, which correspond to the ruptures of sub-faults on a fault plane of a large earthquake, and secondly constructs the strong motions of the large earthquake by superposing the small ground motions using the empirical Green’s function technique (e.g., Irikura, Proc 7th Japan Earthq Eng Symp, 151–156, 1986). The broadband stochastic omega-square model is proposed as the moment rate functions of the small earthquakes, in which random and zero phases are used at higher and lower frequencies, respectively. The zero phases are introduced to simulate a smooth ramp function of the moment function with the duration of 1/fc s (fc: the corner frequency) and to reproduce coherent strong motions at low frequencies (i.e., the directivity pulse). As for the radiation coefficients, the theoretical values of double couple sources for lower frequencies and the theoretical isotropic values for the P-, SV-, and SH-waves (Onishi and Horike, J Struct Constr Eng Trans AIJ, 586:37–44, 2004) for high frequencies are used. The proposed method uses the theoretical Green’s functions of layered half-spaces instead of the far-field S-waves, which reproduce the complete waves including the direct and reflected P- and S-waves and surface waves at broadband frequencies. Finally, the proposed method is applied to the 1994 Northridge earthquake, and results show excellent agreement with the observation records at broadband frequencies. At the same time, the method still needs improvements especially because it underestimates the high-frequency vertical components in the near fault range. Nonetheless, the method will be useful for modeling high frequency contributions in the hybrid methods, which use stochastic and deterministic methods for high and low frequencies, respectively (e.g., the stochastic Green’s function method + finite difference methods; Kamae et al., Bull Seism Soc Am, 88:357–367, 1998; Pitarka et al., Bull Seism Soc Am 90:566–586, 2000), because it reproduces the full waveforms in layered media including not only random characteristics at higher frequencies but also theoretical and deterministic coherencies at lower frequencies.