Direct and inverse problems of wave propagation through a one-dimensional inhomogeneous medium

This paper deals with a wave process induced by an acoustic impulse in a ve rtically inhomogeneous half-space. The solvability of the corresponding dir ect initial boundary value problem is proved. We also consider a class of o ne-dimensional inverse problems including, in particular, the classical inv erse problem of the scattering theory, the transmission and reflection prob lems of seismology, etc. It is shown that all these inverse problems are eq uivalent in a certain sense, and therefore can be solved by identical metho ds, Theoretical results are illustrated by numerical examples.