On the problem of determining the structure of a layered medium and the shape of an impulse source

For the equation of wave propagation in the half-space $\mathbb{R}^2_+=\{(x,y)\in\mathbb{R}^2\mid y>0\}$ we consider the problem of determining the speed of wave propagation that depends only on the variable $y$ and the shape of a point impulse source on the boundary of the half-space. We show that, under some assumptions on the shape of the source and the structure of the medium, both unknown functions of one variable are uniquely determined by the displacements of boundary points of the medium. We estimate stability of a solution to the problem.