When a large crustal earthquake accompanies either a large slip near the earth's surface or a surface fault trace, ground motions arise that contain permanent displacements in the near-source regions. Ground motions containing such permanent displacements are often referred to as "fling steps." When the 1995 Hyogo-ken Nanbu Earthquake occurred, the ground motions observed in Kobe City did not contain significant fling-step components. However, during the 2016 Kumamoto Earthquake, the rupture of the fault reached the earth's surface, and significant fling-step components were observed in Komori, Nishiharamura, etc. near the fault. For those fling steps observed during the 2016 Kumamoto Earthquake, the rise time was as small as 2 s and they could have caused a significant response to structures. This highlighted the importance of fling steps once again.

When calculating ground motions containing fling-step components, it is necessary to use a method that can precisely handle the boundary conditions at the free surface in order to accurately consider the difference in permanent displacement between the hanging wall and foot wall sides. The discrete wavenumber method is one such method: it allows precise calculation of ground motions for a halfspace or a layered half-space. However, when applying the discrete wavenumber method to near-fault ground motions, various factors that affect the calculation result must be considered, one of which is the subfault size.

In some of previous studies to verify the applicability of the discrete wavenumber method to near-fault ground motions containing flingstep components, the results of the discrete wavenumber method were compared with analytical solutions for the permanent displacement. However, there have been few cases where analytical solutions were obtained for displacement waveforms including the process that leads to permanent displacements. Hence, such verification by comparison with analytical solutions for displacement waveforms themselves has been little studied.

Therefore, in this study, we used the analytical solution obtained by Masuda and Hikima, which is one of the few analytical solutions available as described above, to verify the effectiveness of the discrete wavenumber method for calculating near-fault ground motions. During this study, we examined the required subfault size among other conditions in order to achieve high-precision results. The aforementioned analytical solution pertains to ground motions for an elastic full space when a simultaneous slip occurs on a circular fault; it pertains to displacement components parallel to the slip direction at receivers along the central axis of the circle.

This study revealed that using subfaults as small as 0.5 times the fault distance would yield sufficiently precise results. The figures below indicate the results of calculating displacement waveforms at distances of 10,000 m, 1,000 m, and 100 m from a circular fault with a radius of 1,000 m, using a subfault size of 50 m. Black traces indicate the analytical solutions and red traces indicate the results obtained using the discrete wavenumber method; they agree to each other quite well, indicating good calculation accuracy with these conditions.