Inverse Problems of Wave Processes

This monograph covers dynamical inverse problems, that is problems whose data are the values of wave fields. It deals with the problem of determination of one or more coefficients of a hyperbolic equation or a system of hyperbolic equations. The desired coefficients are functions of point. Most attention is given to the case where the required functions depend only on one coordinate.

The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

Part 1 One-dimensional inverse problems: setting of a problem for string equation; peculiarities of solution - formulation of the direct problem; the first method of solution of inverse problem; method of linear integral equations; the case of discontinuous s(y) the Gel'fand-Levitan equation for second-order hyperbolic equations; some cases of explicit solution; on connection of inverse problems with nonlinear ordinary differential equations; the case of more general system of equations. Part 2 Theory of inverse problems for wave processes in layered media: inverse problems of acoustics; general second-order hyperbolic equations; the scattering problem for the general hyperbolic equation. Part 3 Inverse problems for vector wave processes: inverse problem for elasticity equation; inverse problem of sound propagation in a moving layered medium; the case of one-dimensional sound propagation; inverse problems for hyperbolic systems; second-order hyperbolic system.