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{\textquoteright}s function first- and second-order perturbation expressions are derived for the travel times in terms of the underlying perturbations in the Green{\textquoteright}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.

}, keywords = {arrival times, biases, kernels, ocean, pacific, propagation, random-media, tomographic receptions, water, waves}, isbn = {1610-1928}, doi = {10.3813/aaa.918434}, url = {