An inverse problem for harmonic acoustics in stratified oceans
The inverse problem of determining the refraction index function \(n(z)\) for acoustic waves in a stratified ocean is under consideration. Thereby it is assumed that the refraction property as well as the propagating sound field, produced by a line source are to be recovered simultaneously. The initial-boundary value problem associated with this applied problem is formulated. Moreover, an equivalent representation of the problem as a nonlinear Volterra integral equation is given. Studying the properties of this integral equation it can be shown that the identification of both unknown functions \(n(z)\) and \(u(r,x)\) (sound pressure) is possible in a unique manner when some additional assumptions on measurement functions are imposed. It would be interesting to make assertions on the stability in order to discuss the well-posedness or ill-posedness in all its aspects.
scientific article; zbMATH DE number 399056