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Acoustic wave propagation in the ocean

The acoustic wave propagation in the ocean detailed modelled in the book of Ahluwalia D., Keller J. (1977) Wave propagation and Underwater Acoustics Lecture Notes in Physics, vol 70, Springer, Berlin . We have to consider the Helmholtz equation
\begin{eqnarray*}(\Delta +k_0^2n^2(x))u(x)=0\end{eqnarray*}
in the strip $\R^3_H:=\{x\in \R^3\; with\; 0<x_3<H\}$. Here denotes $k_0=\omega/c_0$ where $\omega$ is the frequency (assumed to be fixed) $c_0$ the reference sound velocity. The refraction index $n=c_0/c(x), c(x)$ being the sound velocity, which is esentially bounded in the strip. Consider a bounded domain $G$ with Lipschitz boundary $\Gamma $ which consists of $\Gamma _0, \Gamma _H$ and $\Gamma $ such that
\begin{eqnarray*}&&\Gamma _0:=\{\overline {G}\}\cap\{x_3=0\}\\&&\Gamma _H:=\{......x_3=H\}\\&&\Gamma _c:=\Gamma \setminus(\Gamma _0\cup\Gamma _H)\end{eqnarray*}
Consider the problem with homogeneous Neumann boundary condition on $\Gamma _0$ (hard bottom), a homogeneous Dirichlet condition on $\Gamma _H$ (pressure release) and an inhomogenous Dirichlet condition on $\Gamma _c$ with $f\in H^{1/2}$.

A late reference: M. Ikehata, G.N. Makrakis and G. Nakamura (2001) Inverse boundary value problem for ocean acoustics MMAS 24, 1-8

collected and worked out by Wolfgang Sprößig, TU-Bergakademie Freiberg