## 6 Calculation of the Elastic, Geotechnical, V\({}_{\rm s}\)[30], and Petrophysical Properties
### Elastic Moduli  
Table 3 summarizes the calculated elastic moduli, the petrophysical properties, and geotechnical parameters of the soils/rocks of the investigated site using \(\rm V_{P}\) and \(\rm V_{s}\) values for all 17 seismic profiles. The following is a summary of the elastic moduli findings:  
The densities for the first, second, and third layers ranged from 1.35 to 1.55 g/cm\({}^{3}\), 1.77 to 1.86 g/cm\({}^{3}\), and 2.06 to 2.26 g/cm\({}^{3}\), respectively. According to [PERSON] et al. [44], seismic wave velocities and density are directly related. Accordingly, the density increased with increasing seismic wave velocity, which increased the degree of soil/rock competence. The density results showed that the density gradually increased from the first to the third layer, indicating that the third layer had high density values due to the highly competent materials and greater burial depth. Poisson's ratio values of this site ranged from \(-\)1.29 to 0.29, \(-\)7.67 to \(-\)0.05, and \(-\)0.4 to 0.28 for the first, second, and third layers, respectively. Lowly competent rocks possessed a higher Poisson's ratio and vice versa. The Poisson ratio findings demonstrated that the first layer was made up of less competent materials, whilst the second and third levels comprised fairly to moderately competent materials. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type** & **Parameter** & **The Formula Employed** & **References** \\ \hline \multirow{8}{*}{Stress Ratio (\(\rm S_{i}\))} & Concentration index (\(\rm Ci\)) & \(C_{i}=\left[3-4\left(\frac{V_{i}^{2}}{V_{\rho}^{2}}\right)\right]/\left[1-2 \left(\frac{V_{i}^{2}}{V_{\rho}^{2}}\right)\right]\) & [49] \\ \cline{2-3}  & Stress Ratio (\(\rm S_{i}\)) & \(S_{i}=1-2\left(\frac{V_{i}^{2}}{V_{\rho}^{2}}\right)=\left(C_{i}-2\right)^{-1}\) & [49] \\ \cline{2-3}  & Material Index (\(\rm Mi\)) & \(\rm Mi=(1-4\sigma)\) where \(\sigma\) is Poisson’s ratio & [50] \\ \cline{2-3}  & Liquefaction potentiality (\(\rm N\)-value) & \(V_{s}=89.9*N^{0.341}\) & [51; 52] \\ \cline{2-3}  & Ultimate bearing capacity (qult) & \(q_{ult}\cong\gamma V_{s}(0.1)=\rho V_{s}(\rm kN/m^{2})\) & \\  & Ultimate bearing capacity (qult) & \(q_{ult}=1/100\rho V_{s}(\rm kg/m^{2})\) & [53] \\  & & where \(\gamma\) is the ground’s unit weight, \(\rho\) is the density of the & [53] \\  & & rocks, and \(\rm V_{s}\) is the velocity of the shear waves. & \\ \hline \multirow{8}{*}{Settlement (\(\rm\delta\))} & \(\delta_{Z}=\frac{4\omega}{2}Z\) & \multirow{8}{*}{[54]} \\  & & \(Z^{2}=\frac{3}{4\pi}\frac{\delta_{2}}{0.333}\) & \\ \cline{1-1}  & & \(q_{ult}\) for the load at unit area is the stress value & \\ \cline{1-1}  & & depending on the depth \(\rm z\), \(\rm\delta_{z}\) is the settlement value for & \\ \cline{1-1}  & & the soil column with the depth. & \\ \hline \multirow{8}{*}{V\({}_{\rm s}\)[30]} & \multirow{8}{*}{[55]} \\  & & \(V_{\rm s}\)[30] & \\ \cline{1-1}  & & where \(\rm Vi\) and \(\rm hi\) indicate the thickness (\(\rm m\)) and the \(\rm V_{s}\) of & \\ \cline{1-1}  & & the \(\rm i^{th}\) layer present in the top 30 \(\rm m\), respectively. & \\ \hline \hline \end{tabular}
\end{table}