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2011
Skarsoulis, EK, Cornuelle BD, Dzieciuch MA.  2011.  Second-Order Sensitivity of Acoustic Travel Times to Sound Speed Perturbations. Acta Acustica United with Acustica. 97:533-543.   10.3813/aaa.918434   AbstractWebsite

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.

1993
Cornuelle, BD, Worcester PF, Hildebrand JA, Hodgkiss WS, Duda TF, Boyd J, Howe BM, Mercer JA, Spindel RC.  1993.  Ocean Acoustic Tomography at 1000-Km Range Using Wave-Fronts Measured with a Large-Aperture Vertical Array. Journal of Geophysical Research-Oceans. 98:16365-16377.   10.1029/93jc01246   AbstractWebsite

Broadband acoustic signals transmitted from a moored 250-Hz source to a 3-km-long vertical line array of hydrophones 1000 km distant in the north central Pacific Ocean were used to determine the amount of information available from tomographic techniques used in the vertical plane connecting a source-receiver pair. A range-independent, pure acoustic inverse to obtain the sound speed field using travel time data from the array is shown to be possible by iterating from climatological data without using any information from concurrent environmental measurements. Range-dependent inversions indicate resolution of components of oceanic variability with horizontal wavelengths shorter than 50 km, although the limited spatial resolution of concurrent direct measurements does not provide a strong cross-validation, since the typical cast spacing of 20-25 km gives a Nyquist wavelength of 40-50 km. The small travel time signals associated with high-wavenumber ocean variability place stringent but achievable requirements on travel time measurement precision. The forward problem for the high-wavenumber components of the model is found to be subject to relatively large linearization errors, however, unless the sound speed field at wavelengths greater than about 50 km is known from other measurements or from a two-dimensional tomographic array. The high-ocean-wavenumber resolution that is in principle available from tomographic measurements is therefore achievable only under restricted conditions.