## 5 Discussion
The most influential problem of overestimation in CDMC prediction would be the use of the empirical vulnerability function based on the estimated PGVs and the damage ratios from the field survey during the past devastating earthquakes. In Japan, the majority of such data are coming from the 1995 Kobe earthquake [34; 35], which is a typical crustal earthquake. The observed high PGVs in the epicentral areas of this earthquake were primarily controlled by the asperity pulses with a coherent nature in the intermediate period range around 1 s [5; 6]. On the other hand, the high PGVs would be obtained inside a deep basin structure with thick and soft sediments during the mega-thrust events away from the shore, as is the case for the 2011 Tohoku earthquake. As mentioned before, we did not see any emergence of the high PGV regions in the intermediate period range and, subsequently, we did not see any significant structural damage during the Tohoku earthquake [33]. In our prediction of building damage, the Nagato-Kawase model also relies on the strong ground motions and the damage statistics during the 1995 Kobe earthquake; however, [PERSON] and [PERSON] utilized them to construct the nonlinear response models that consider basic dynamic structural behavior from the current building standard and to optimize the realistic yield capacities in order to reproduce observed damage ratios. Thus, the model can be used to predict damage for synthetic ground motions from not only crustal earthquakes but also mega-thrust events. We also need to point out the potential problem of the strength index of the ground motion to be used in the damage prediction. As mentioned above, no matter what we use as the representative strength index of the ground motion at a site, they would be a kind of extracted value from the whole ground motion time history. This means that we cannot have a perfect strength index to be used for damage prediction. By any operation to the time history in order to obtain the strength index, we are losing some valuable information from the whole time history of ground motion. It is not so meaningful to find a better strength index among so many possibilities because of the fundamental nature of the extraction. It would be better to use the whole time history of ground motion when we predict structural damage because the structural damage is a direct consequence of the input ground motion, not the direct consequence of the strength index extracted from the ground motion. For example, among the strength index based on the peak value of the ground motion, PGV would be the best index for damage prediction (e.g., [34; 35]). However, a ground motion with high PGV in a long-period (>2 s) range could not cause any heavy structural damage because ordinary low- and middle-rise buildings would not respond to such a long-period input. As an advantage of using the Nagato-Kawase model, we can evaluate the effectiveness of countermeasures such as seismic retrofitting and increase of seismic demand in the regulations for new construction. Although we would like to report separately, we have conducted two case studies by introducing the policy to retrofit all the buildings to have 1.25 or 1.5 times the current yield capacity. We found that, roughly speaking, we can reduce damage ratios by about 20% for a 1.25 times increased case and by 30% for a 1.5 times increased case with respect to the average damage ratios shown in Figure 18 or Figure 23. It is a kind of significant number, however, if we consider the necessary cost as a whole and the benefit of this retrofitting when the event occurs; it turns out that this kind of countermeasure for all the buildings in the area does not make sense. This means that when we consider countermeasures using earthquake resistance reinforcement against a coming mega-thrust earthquake along the Nankai Trough, such efforts should be focused only on the regions and structures with high damage potential as delineated by our prediction maps (Figures 14-17 and 19-22).