# Seismic Ground Response Estimation Based on Convolutional Neural Networks (CNN)
## 4 Analytical Procedure
### Conventional Model  
The equivalent linear ground response analyses were performed with the analysis program, SHAKE2000, computing the response in a system of homogenous, visco-elastic layers of infinite horizontal extent. The seismic response was calculated by an iterative process in which the shear modulus and damping ratio are updated in each step for the corresponding value of effective shear strain. The effective shear strain was taken as 65% of the maximum shear strain obtained from the calculated strain history. The thin layers are recommended to capture the highly non-uniform variation in strain vs. depth. Therefore, the layers were divided into more than one sublayer, which meets the criteria as Equation (6) [24]:  
\[\textit{Thickness of sublayers}<\frac{V_{S}}{4*f_{max}} \tag{6}\]  
where \(V_{S}\) is the shear wave velocity of layers, and \(f_{max}\) is maximum frequency. Widely used soil properties were employed from the previous works of literature. According to the material type of layers, they were classified as rock, gravel, and sand, as shown in Table 2. For the rock, the mean values of normalized shear modulus and damping ratio curves by [PERSON] (1973) were taken. For the gravel, the properties by [PERSON] et al. (1986) were taken, and for the sand, those by [PERSON] and [PERSON] (1970) were taken [25; 26; 27; 28]. Figure 9 shows the adopted mean values of normalized shear modulus and damping ratio curves. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Material Type** & **Classification** & **Reference** \\ \hline Argillite & & \\ Breccia & & \\ Granite & Rock (Mean) & [PERSON] (1973) \\ Sandstone & & \\ Tonalite & & \\ \hline Sandy gravel & & \\ Clayey gravel & & \\ \hline Top soil & Sand (Mean) & [PERSON] and [PERSON] (1970) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Classification and reference according to the material type. Figure 9: Dynamic soil properties: (a) Normalized shear modulus reduction curves; (b) damping ratio curves. Figure 12: The six samples of acceleration response spectra measurements and predictions at site FKSH19. (a) FKSH191611240623.EW. (b) FKSH191611240623.NS. (c) FKSH191908041923.EW. (d) FKSH192004200539.NS. (e) FKSH192102132308.EW. (f) FKSH192102132308.NS. Figure 13: The six samples of acceleration response spectra measurements and predictions at site IBRH13. (a) IBRH131412201830.EW. (b) IBRH131412201830.NS. (c) IBRH131611240623.NS. (d) IBRH131908041923.EW. (e) IBRH131611220559.NS. (f) IBRH132006250447.NS. Figure 14: The six samples of acceleration response spectra measurements and predictions at site IWTH02. (a) IWTH021809060308.EW. (b) IWTH021906182222.EW. (c) IWTH021908041923.EW. (d) IWTH021908041923.NS. (e) IWTH022004200539.EW. (f) IWTH022105011027.EW. Figure 15: The six samples of acceleration response spectra measurements and predictions at site IWTH05. (a) IWTH051502170806.EW. (b) IWTH051505130613.EW. (c) IWTH052009121144.EW. (d) IWTH052102132308.NS. (e) IWTH052105140858.EW. (f) IWTH052105140858.NS. Figure 16: The six samples of acceleration response spectra measurements and predictions at site IWTH12. (a) IWTH121801241951.EW. (b) IWTH121908290846.NS. (c) IWTH122002131934.EW. (d) IWTH122004200539.NS. (e) IWTH122012210223.EW. (f) IWTH122102132308.EW. Figure 17: The six samples of acceleration response spectra measurements and predictions at site IWTH14. (a) IWTH141601141225.EW. (b) IWTH141709270522.NS. (c) IWTH141908041923.NS. (d) IWTH142004200539.NS. (e) IWTH142009121144.NS. (f) IWTH142102132308.EW. Figure 19: The six samples of acceleration response spectra measurements and predictions at site IWTH22. (a) IWTH221611220559.EW. (b) IWTH221709270522.NS. (c) IWTH222004200539.EW. (d) IWTH222004200539.NS. (e) IWTH22201221023.NS. (f) IWTH22105140858.NS. Figure 18: The six samples of acceleration response spectra measurements and predictions at site IWTH21. (a) IWTH211310260210.EW. (b) IWTH211601141225.EW. (c) IWTH211611220559.NS. (d) IWTH211801241951.NS. (e) IWTH211908041923.NS. (f) IWTH212004200539.EW.