Consistency and accuracy of perturbative inversion methods for group travel time data

Perturbation theory for ocean acoustic modal group speed responses to small environmental changes is investigated with regard to its applicability to 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 proof is given for the equivalence of 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 accurate is examined. It is found that the range of validity is determined not only by the amplitude of the perturbations, but also by their vertical scale size.