Ocean acoustic tomography inversion in the adiabatic-invariant approximation

We discuss inversion of vertical-slice, ocean acoustic tomography (traveltime) measurements, in which we use the adiabatic-invariant approximation to convert multi-loop measurements to single-loop ray properties before using an Abel transform. For a range-dependent sound channel, the method yields a range average of the symmetric part of the sound channel and the antisymmetric part of the sound channel at the source and receiver if the symmetric part of the sound channel at the source and receiver can be determined. For a uniform sound channel, the inversion recovers both the symmetric and antisymmetric parts of the sound channel, including the vertical displacement of the sound-channel axis. We demonstrate the inversion by applying it to a simulated pulse-arrival sequence for a uniform sound channel (generated by ray tracing), and compare the recovered sound-speed profile with that used for the simulation.