## 3 Strong Ground Motion Prediction of the Nankai-Trough Earthquake
### Waveform Synthesis and Its Validation  
A statistical Green's function was generated using the source, path, and site characteristics for each target site, as estimated in Section 2. Strong ground motion waveforms of the hypothesized Tonankai earthquake (Figure 3), a hypothesized Tokai earthquake, and a hypothesized Nankai earthquake were generated by the summation method of Irikura [13]. Then, a hypothesized consecutive rupture scenario of all the three segments (Tokai, Tonankai, and Nankai) along the Nankai Trough were evaluated by adding these three earthquake waveforms with proper time differences. Figure 4 shows a comparison between the peak ground acceleration (PGA) or peak ground velocity (PGV) calculated in this work for the hypothesized Tonankai earthquake and the attenuation relation (ground motion prediction equation, GMPE) by [PERSON] and [PERSON] [10]. The synthetic PGAs from the Green's function summation method agree quite well with the attenuation relation. The synthetic PGVs also correspond well to the  
GMPE; however, we need to consider the difference in the assumed average velocity for site amplification. When we plot the velocity GMPE by [PERSON] and [PERSON] [10], we assume that the average S-wave velocity in the top 30 m (Vs30) to be 600 m/s, whereas the overall average Vs30 of K-NET and KiK-net is around 400 m/s. A comparison of the PGV of the elementary source and the velocity GMPE for the same magnitude shows that the synthetic values are underestimated to the same extent as shown in Figure 4, and thus the PGV of the elementary source based on the assumed source spectrum is confirmed to be slightly smaller than the average of previously observed events. One issue that we should consider is that the time-varying characteristics are determined from the acceleration envelope when generating our statistical Green's function, thus the envelope is mostly governed by short-period components so that PGV would not be directly regulated. Therefore, data should be added in the future to increase the stability of separation properties and improve modeling of long-period phase characteristics that may govern PGV. Note that the maximum magnitude in the database used to derive the empirical attenuation relation in Si and Midorikawa [10] was 8.0, and thus the comparison shown here is a small extrapolation. Figure 5 shows a comparison of seismic intensity scale according to the converted seismic intensity from the synthesized strong ground motions of the hypothesized Tonankai earthquake in this study and the contour map from the damage survey of the 1944 Tonankai earthquake according to the publicly available information from HERP [28]. The seismic intensity scale of VI lower and VI upper in red circles in this study corresponds to the maximum rank of VI lower equivalent or higher in HERP, also marked in red. The seismic intensity scale of V in orange circles also corresponds to the same class marked in yellow. The strong ground motion of the hypothesized Tonankai earthquake in this work does not consider a saturation phenomenon near the fault and non-linearity of the underground structure. As described in the figures by HERP, there is uncertainty in the source characteristics and some fluctuation of the designated underground structure within the same municipality is inevitable. The overall seismic intensity scale distributions of these two results match well, as seismic intensity may easily change by one between these two results for the reasons mentioned above. Please note that the converted seismic intensity was calculated as shown in [22; 29], whereas the intensity estimated from the damage survey was based on the table by JMA [30]. Figure 4: Peak ground acceleration and velocity from a hypothesized Tonankai earthquake by the statistical Green’s function summation method of this study (symbols) and by the GMPE of [PERSON] and [PERSON] [10] as a function of the shortest distance to the fault.