Acoustic tomography by Hamiltonian methods including the adiabatic approximation

Abstract

Long‐range acoustic propagation for ocean tomography is elegantly described by invoking a Hamiltonian formulation. Many results previously derived in an ad hoc manner emerge naturally from the use of the Hamiltonian. The cycling between the upper and lower ocean that is characteristic of oceanic sound propagation is treatable as a libration phenomenon. General perturbation methods, highly developed in astronomy and quantum mechanics, are immediately available for understanding both range independent and range dependent disturbances to a reference profile. The tomographic two‐point boundary value problem leads, in an analogy to the old Bohr quantum mechanics, to quantization of the action, although the more naturally quantized variable is the canonical angle. An adiabatic approximation merges naturally from the formalism. In the adiabatic approximation the range dependent bias problem in tomography can be fully understood and accounted for as long as the source and the receiver remain axial.