Corrections to “Ground-Return Parameters of Submarine Cables Buried in the Seabed”

Abstract

In [1], (5b) has a typo; the correct formula is as follows: \begin{equation*} \Delta _{6}^{\mathrm{QT}} = \int \nolimits _{0}^{\infty } \frac{{\mathrm{e}}^{-2 \alpha _{2} h_{ij}}}{\alpha _{1}+\alpha _{2}}\frac{1}{\alpha _{2}^{2}} \cos \left(q_{ij}\lambda \right) \,{\mathrm{{d}}}\lambda \;. \tag{1} \end{equation*} In (34), the term $G_{\mathrm{b}} (\lambda)$ is missing of the denominator; the correct formula is as follows: \begin{equation*} \begin{aligned} G_{\mathrm{b}} \left(\lambda \right) = &\\ =& \frac{2 \mu _{1} \mu _{2} \alpha _{2} {\mathrm{e}}^{-\alpha _{2} \left(h_{1}+h_{2}-2h_{\mathrm{s}} \right) }}{ \left(A_{10}A_{21}+\Delta _{10}\Delta _{21}{\mathrm{e}}^{-2\alpha _{1}h_{\mathrm{s}}} \right) \left(s_{10}s_{21}-d_{10}d_{21}{\mathrm{e}}^{-2\alpha _{1} h_{\mathrm{s}}} \right) } \cdot \\ & \!\!\! \left\lbrace \phantom{\int }{\kern-10.0pt} \left(\gamma _{2}^{2} \!-\ \gamma _{1}^{2} \right) \left( s_{10} A_{10} \!-\! d_{10}\Delta _{10} {\mathrm{e}}^{-4 \alpha _{1} h_{\mathrm{s}}} \right) \!-\! 2 \mu _{0} \mu _{1} {\mathrm{e}}^{-2 \alpha _{1} h_{\mathrm{s}}} \right. \cdot \\ & \!\!\! \left. \left[ \alpha _{0}^{2} \gamma _{1}^{2} \left(\gamma _{2}^{2} - \gamma _{1}^{2} \right) + \alpha _{1}^{2} \gamma _{0}^{2} \left(\gamma _{2}^{2} + \gamma _{1}^{2} \right) - 2 \alpha _{1}^{2} \gamma _{1}^{2} \gamma _{2}^{2} \right] \phantom{\int }{\kern-10.0pt} \right\rbrace \, \end{aligned} \tag{2} \end{equation*}