An Earthquake Source Spectrum Model Considering Rupture Directivity and Its Application for Obtaining Green’s Functions

Abstract

ABSTRACTA 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.