Table 4 The correlations used by each code for V_P, density, and damping ratio

KRD, SLS, SPZ

V_P (m/s)

\(\left\{\begin{array}{cc}(1.9{V}_{S}+371.57)(1.81-6.48\times {10}^{-4}{V}_{S})& depth\le 25 m\\ (1.42{V}_{S}+1162.9)(1.26-7.10\times {10}^{-5}{V}_{S})& depth >25 m\end{array}\right.\)

\(\left\{\begin{array}{cc}(1.06{V}_{S}+436.7)& {V}_{S}\le 400 m/s\\ (1.39{V}_{S}+1189.4)& {V}_{S} >400 m/s\end{array}\right.\)

Density (kg/m³)

\(1000(1.4+0.67\sqrt{\frac{{V}_{S}}{1000}})\)

\(\left\{\begin{array}{cc}1000+\frac{1530{({V}_{S}/1000)}^{0.85}}{\left(0.35+1.889{({V}_{S}/1000)}^{1.70}\right)}& {V}_{S}\le 300 m/s\\ (1740{{v}_{p}}^{0.25})& {V}_{S} >300 m/s\end{array}\right.\)

\({v}_{p}=0.9409+2.0947({V}_{S}/1000)-0.8206{({V}_{S}/1000)}^{2}+0.2683{({V}_{S}/1000)}^{3}-0.0251{({V}_{S}/1000)}^{4}\)

Damping ratio (D)

\(\frac{5}{{V}_{S}\times f} where f is frequency in Hz\)

\(\frac{5}{{V}_{S}\times f} where f is frequency in Hz\)

IBRH11

V_P (m/s)

\(\left\{\begin{array}{cc}(1.9{V}_{S}+371.57)(1.81-6.48\times {10}^{-4}{V}_{S})& depth\le 10 m\\ (1.42{V}_{S}+1162.9)(1.26-7.10\times {10}^{-5}{V}_{S})& depth >10 m\end{array}\right.\)

\(\left\{\begin{array}{cc}(1.9{V}_{S}+371.57)& {V}_{S}\le 200 m/s\\ (1.42{V}_{S}+1162.9)& {V}_{S} >200 m/s\end{array}\right.\)

Density (kg/m³)

\(1000(1.4+0.67\sqrt{\frac{{V}_{S}}{1000}})\)

\(\left\{\begin{array}{cc}1000+\frac{1530{({V}_{S}/1000)}^{0.85}}{\left(0.35+1.889{({V}_{S}/1000)}^{1.70}\right)}& {V}_{S}\le 200 m/s\\ (1740{{v}_{p}}^{0.25})& {V}_{S} >200 m/s\end{array}\right.\)

\({v}_{p}=0.9409+2.0947({V}_{S}/1000)-0.8206{({V}_{S}/1000)}^{2}+0.2683{({V}_{S}/1000)}^{3}-0.0251{({V}_{S}/1000)}^{4}\)

Damping ratio (D)

\(\frac{5}{{V}_{S}}\)

\(\frac{5}{{V}_{S}}\)