During large crustal earthquakes, strong ground motions with a significant amount of residual displacement are observed if the rupture of the fault approaches very close to or reaches the earth’s surface. Those ground motions are often called ‘fling steps’. Fling steps are mainly due to the rupture of shallower parts of the fault. During the mainshock of the 2016 Kumamoto earthquake, significant fling steps were observed because the rupture reached the surface. On the other hand, during the 1995 Kobe earthquake, the rupture did not reach the surface in the Kobe side and the devastating ground motions were mainly associated with the rupture of deeper asperities. This was the reason why the conventional studies related to design ground motions were mainly focused on the rupture of deeper asperities and less attention was paid to fling steps. In this study, we propose a composite source model which can consider fling steps in addition to strong ground motions from deeper asperities. The source model comprises of Domain A representing deeper asperities and Domain B which reaches the surface and generates fling steps. The ground motions from Domain A are calculated by the corrected Empirical Green’s function method, while the ground motions from Domain B are calculated by the discrete wavenumber method because the reflection coefficients at the free surface should rigorously be considered for the calculation of the fling steps. In this study, first, the results of the discrete wavenumber method were compared with analytical results including Okada’s analytical solutions for static crustal deformations to understand the criteria for accurately calculating fling steps with the discrete wavenumber method. Then a composite source model was actually developed for the mainshock of the 2016 Kumamoto earthquake. The authors’ intention was to develop a simple model which can be easily handled by engineers. For this reason, the geodetic fault model by the GSI was used as a starting point and parameters related to the temporal evolution of the slip were added to form Domain B. Then it was combined with Domain A representing asperities to form a composite source model. The simulation results showed that the composite source model can well reproduce near-source displacement and velocity waveforms including fling steps, although the model was a relatively simple one in a sense that the slip-velocity function and the rise time were uniform for each of the faults in Domain B.

Key Words: Fling step, source model, fault, earthquake ground motion, discrete wavenumber method