Second-order perturbations of peak-arrival times due to sound-speed variations

The concept of peak arrivals is used to study the second-order arrival-time behavior of broadband tomographic signals due to sound-speed variations. Peak arrivals, defined as the local maxima of the pressure amplitude at the receiver in the time domain, are the exact theoretical counterparts of the experimental observables in ocean acoustic tomography, and they offer a uniform description of all the peaks in the arrival pattern, independent of whether they can be resolved as ray/modal arrivals or not. Closed-form expressions for the first and second sound-speed derivatives of peak-arrival times are derived in terms of sound-speed derivatives of the Green’s function. Using normal-mode theory the sound-speed derivatives of the Green’s function are analytically expressed for the case of a range-independent medium in terms of eigenvalues and eigenfunctions at the reference state. Numerical examples are given for range-independent environments motivated from the Thetis-2 experiment, showing different kinds of nonlinear behavior of the arrival times in the large and the fine scale and demonstrating the performance of the second-order approach.