Bias in acoustic travel time through an ocean with adiabatic range-dependence

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Abstract
We consider the propagation of acoustic waves in an ocean sound channel C(z, x) with slow dependence on x. The travel time t RD in the range-dependent channel differs from the travel time t RA through the range-averaged sound channel C RA (z) = ±C(z, x)〉 x . The Hamiltonian formulation (Wunsch, in press) takes advan tage of the nearly periodic (in x) paths of the ray loops. The bias t RD - t RA for an adiabatic x-dependence is a function only of the variance in the channel parameters. Generally (but not always) t RD < t RA , thus giving a “warm bias” in the range-averaged ocean for any inversion of the acoustic travel times which ignores the range dependence of the sound channel. We derive bias formulae for three models of x-dependence, corresponding to perturbations of the first and second baroclinic modes, respectively, and to an x-dependent surface warming.

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