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

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.

Key Words:

• Underwater acoustics
• ocean acoustic tomography
• canonical sound channel
• adiabatic range dependence