Limitations on perturbation theory applied to ocean acoustic inversion

Perturbation theory for ocean acoustic modal group speed responses to small environmental changes is investigated with regard to its applicability in ocean acoustic tomography. Assuming adiabaticity, the inverse problem for each vertical eigenmode is an integral equation whose kernel involves the eigenfunction and its frequency derivative. A new proof is given for the so-called ‘‘third term problem’’ which requires equivalence between two dissimilar forms of the integral equation. Numerical examples are given for the inversion kernel for four types of sound speed profiles, and then the parameter range (amplitude and scale size) in which perturbation theory is accurately examined. It is found that the range of validity is set not only by the amplitude of the perturbations, but also by their vertical scale size. [Work supported by ONR and Saclantcen.]