Abstract
The second-order sensitivity of finite-frequency acoustic travel times to sound speed perturbations in range-independent environments is studied. Using the notion of peak arrivals and the normal-mode representation of the Green's function first- and second-order perturbation expressions are derived for the travel times in terms of the underlying perturbations in the Green's function and finally in the sound speed profile. The resulting theoretical expressions are numerically validated. Assuming small and local perturbations the non-linear effects appear to be strongest for sound speed perturbations taking place close to the lower turning depths of the corresponding eigenrays. At the upper turning depths ― in the case of temperate propagation conditions ― the effects are much weaker due to the larger sound speed gradients. The magnitude of the second-order sensitivity of travel times relative to the first-order sensitivity can be used to obtain an estimate for the limits of linearity.
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