# A Numerical Model for Simulating Ground Motions for the Korean Peninsula
## 4 Ground Motion Simulation for the 2017 Pohang Earthquake  
Ground motions were generated using the proposed numerical model, consisting of the stochastic point-source model and shaping window model. The procedure is briefly summarized as follows:  
1. White noise is first generated in time domain for a duration time of the ground motion (Equation (12)).
2. The noise is then windowed using the shaping window model (Equation (10)).
3. The windowed noise is transformed into the frequency domain.
4. The \(A(f)\) of the noise is normalized by the square-root of the mean square of \(A(f)\) in all frequencies.
5. The normalized \(A(f)\) is then multiplied by the stochastic simulation model (Equation (2)).
6. The resulting \(A(f)\) is transformed back to the time domain, which is a simulated ground motion.  
Figure 12a,b show two horizontal components' ground motions at station BUS2 during the 2017 Pohang earthquake, whereas Figure 12c presents one ground motion simulated using the proposed  
Figure 11: Estimated shaping window and duration for the 2017 Pohang earthquake: (**a**) Shaping window, (**b**) Duration with considering corner frequency.  
procedure. Figure 12d presents the geomean of \(A(f)\) for recorded ground motions. In this figure, \(A(f)\) calculated using Equation (2) is also included, which shows that the calculated \(A(f)\) matches that obtained from recorded ground motions. Figure 12e shows the geomean of 5% damped-pseudo spectral acceleration \(PSA(T)\) and the median \(PSA(T)\) values of 1000 simulated ground motions. The difference in \(PSA(T)\) between recorded and simulated ground motions is generally small. Similar observations were made for the ground motions for stations CEA and CEJA.  
To verify the accuracy of the proposed numerical model, ground motions were simulated at 111 stations for the 2017 Pohang earthquake and their \(PSA(T)\) values were calculated. Residuals induced by the difference in simulated and recorded \(PSA(T)(PSA(T)_{sim}PSA(T)_{measured})\) were calculated using Equation (13), with a period (\(T\)) range between 0.01 s and 10 s.  
\[\text{Residual}(T)=\log[PSA(T)_{sim}]-\log[PSA(T)_{measured}] \tag{13}\]  
Residuals were calculated for all ground motions of the 111 stations. Figure 13 shows the residuals according to hypocentral distance. As shown in Figure 13a, the mean value of residuals is near zero,  
Figure 12: Recorded and simulated ground motion at sample stations: (**a**) BUS2 station-EW direction, (**b**) BUS2 station-NS direction, (**c**) BUS2 station-simulated, (**d**) BUS2 station-FAS, (**e**) BUS2 station-PSA, (**f**) CEA station-EW direction, (**g**) CEA station-NS direction, (**h**) CEA station-simulated, (**i**) CEA station-FAS, (**j**) CEA station-PSA, (**k**) CEJA station-EW direction, (**l**) CEJA station-NS direction, (**m**) CEJA station-simulated, (**n**) CEJA station-FAS, (**o**) CEJA station-PSA.  
which indicates that the ground motions in the Korean Peninsula can be adequately simulated using the proposed numerical model with the source, path effect, and site amplification functions.  
If the path effect function proposed by [PERSON] (2003) is used in the numerical model, the mean residual deviates from zero, as shown in Figure 13b. The degree of deviation varies according to the period. In the case of using the source function and site amplification function proposed by others when simulating ground motions with the proposed numerical model, similar observations were made, which are not included in the paper.