Spectral inversion method of wave equations

The statements of inverse problems of two types are considered within the framework of the scalar wave equation. The inverse problems include the reconstruction of sources of the wave field (the right-hand side of the equation) and the determination of the unknown coefficient (wave velocity). In spite of some difference in the statements of these problems, they are closely interrelated: the solution of one of the problems follows from the solvability of the other problem, and vice versa.