A point source of $SH$ waves in the medium with a vertical boundary in the case of smooth increasing velocity of wave's propagation with the depth

The solution of the equation for $SH$ waves is constructed by the separation of variables method. Here $\alpha(x),g(x)$ are step functions, $\beta(y),d(y)\in C^\infty$, $d'>0$. Its asymptotic expansion, as $\omega\to+\infty$ is found. Bibliography: 6 titles.