A small earthquake with strong rupture directivity is inappropriate to use as a point source when estimating ground motion. A source spectrum model is proposed to remove the effects of rupture directivity and finite fault size from observed earthquakes. This model is developed by using a kinematic source model of a rectangular fault with bilateral‐bidirectional rupture propagation. Its amplitude spectrum is modeled to decay as ω−2 at high frequency and is approximated by its envelope to make deconvolution a stable operation. The effectiveness of the proposed spectrum model is demonstrated through application to the two aftershocks of Mw 4.0 and Mw 5.5 observed following the 2016 Kumamoto earthquake. These aftershocks had similar focal mechanisms and were located near to each other. A method to estimate the source parameters by using the proposed spectrum model is presented and its effectiveness is demonstrated. The deconvolution of the ground‐motion records using a suitable source spectrum model gives us the Green’s function. The amplitude spectra of the Green’s functions obtained from both observed aftershock events are shown to be consistent. The far‐field ground motions are simulated by using the Green’s functions. The simulated ground motions match well with the observed ones. Simulation of the ground motions by using the Green’s functions obtained from the deconvolution of ground‐motion records by the proposed spectrum model has an advantage compared to the use of small earthquake records as empirical Green’s functions (EGFs). Specifically, this approach reduces the variation in ground‐motion simulation results due to the choice of different EGFs.

中文翻译：

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考虑破裂方向的地震源谱模型及其在格林函数获得中的应用

估计地震动时，破裂方向性强的小地震不适合用作点源。提出了一种源谱模型，以消除地震观测中破裂方向性和有限断层尺寸的影响。该模型是通过使用具有双向双向破裂传播的矩形断层的运动学源模型开发的。它的振幅谱被建模为在高频下以ω-2衰减，并通过其包络线近似以使去卷积成为稳定的操作。通过对2016年熊本地震后观测到的Mw 4.0和Mw 5.5两次余震的应用证明了所提出频谱模型的有效性。这些余震具有类似的震源机制，并且彼此靠近。提出了一种利用提出的频谱模型估计源参数的方法，并证明了其有效性。使用合适的源谱模型对地面运动记录进行反卷积可以为我们提供格林函数。从两个观察到的余震事件获得的格林函数的振幅谱显示是一致的。利用格林函数模拟远场地面运动。模拟的地面运动与观测到的运动非常吻合。与使用小地震记录作为经验格林函数（EGF）相比，通过使用拟议的频谱模型对地面运动记录进行反卷积获得的格林函数对地面运动进行模拟具有优势。特别，