Introduction

Geometrical acoustics provides a useful intuitive view of acoustic propagation through ocean internal waves, but there are necessary diffractive corrections that must be made due to the small-scale part of the internal-wave spectrum. These diffractive corrections are primarily associated with amplitude fluctuations. In this chapter the focus is on the effects of diffraction in the regime in which acoustic fluctuations are small, that is, the unsaturated regime (Chapter 4). Here the physical picture to keep in mind is propagation with no microrays, and the acoustic fluctuations are caused by the unperturbed ray and its ray tube being modulated by the internal-wave variations.

Several closely related perturbative methods have been applied to this situation, including the Born approximation (Born and Wolf, 1999), the method of smooth perturbations (Tatarskii, 1971; Chernov, 1975), the super eikonal method (Munk and Zachariasen, 1976), and the Rytov method (Rytov, 1937). Much of this work originated in the atmospheric optics context, in which line of sight propagation through homogeneous, isotropic turbulence was considered.

The seminal contributions in ocean acoustics were provided by Munk and Zachariasen (1976) and Flatté et al. (1979), in which the effects of waveguide propagation and internal-wave inhomogeneity and anisotropy were integrated into theoretical expressions for several observables. In this book the Born approximation is utilized because it provides the simplest conceptual picture, while maintaining a reasonable level of accuracy. For some time the wave propagation in random media community believed that the Rytov approximation, which gives the same equations as the Born approximation, apply under a set of less restrictive conditions. It is now known that this optimistic perspective is unfounded (Clifford, 1978) and that the results of both Born and Rytov are expected to apply for the variance of log-amplitude less than roughly 0.3. The physics behind this issue is that the Rytov method fails to treat consistently multiple scattering, while the Born approximation assumes single scattering. It has been discovered experimentally, however, that in both atmospheric and ocean cases the Born results for phase statistics appear to have broad application in both weak and strong fluctuations where the phase variance is significantly larger than 1 (Clifford, 1978; Flatté, 1983, and Section 6.4). The more restrictive applicability of the Born results for log-amplitude makes the theory relevant to short-range, low-frequency transmissions or situations in which the internal-wave field is weak, such as the Arctic.