Waveform perturbation of tomographic receptions due to sound-speed variations

A waveform perturbation method is proposed for the calculation of broadband receptions based on normal-mode theory and second-order Taylor expansions of eigenvalues and eigenfunctions with respect to sound-speed variations. Applying perturbation theory to the vertical eigenvalue problem closed-form analytic expressions are derived for the corresponding first and second derivatives of eigenvalues and eigenfunctions at the reference state (background sound-speed profile), at each frequency within the source spectrum. Using the above approximations broadband receptions at perturbed ocean conditions can be calculated efficiently in a straightforward manner bypassing the solution of the vertical eigenvalue problem at the perturbed state. The present derivation is for the range-independent case, but can in principle be extended to address range dependence as well. The waveform perturbation approach can handle cases of narrowband or broadband propagation with the dispersion behaviour ranging from weak/linear to strongly non-linear. Numerical examples demonstrate the efficiency of the method.