Introduction

A good starting place for the analysis of sound propagation through the stochastic ocean is to consider the ray picture of acoustic transmission. As described in Chapter 2, rays provide a pleasing intuitive geometrical picture of wave propagation, and as such this theory has played a central role in ocean acoustics since the beginning of the field. But, the use of ray theory is not just based on theoretical niceties. Quite the contrary, there are strong observational reasons that compel us to use ray theory. Since the advent of broadband–controlled electronic sources, acoustically navigated moorings, and wide vertical aperture receiver arrays, deep–water observations of time fronts from ranges of 50–5000 km have been unambiguously identified with specific ray paths through the ocean. This is the basis of ocean acoustic tomography, whose history is intertwined with that of sound propagation through the random ocean. Figure 5.1 shows an observed deep–water time front at a range of 3250 km, as well as the time front or ray ID (Worcester et al., 1999). Although the late part of the arrival pattern is a confused interference pattern, the early part of the arrival pattern is ray–like with its separated branches. Upon closer inspection of the arrival pattern, however (Figure 5.2), it is seen that the fronts themselves have a narrow interference pattern with multiple peaks associated with a given time front branch. The arrival finale is a complex interference pattern (Colosi et al., 2001). This behavior is associated with ray chaos, and in this chapter it will be demonstrated that ray theory can provide important insights into the statistics of the acoustic field.

As has been previously described, rays are an asymptotic construction with an array of idiosyncrasies. Important among these is that ray trajectories and amplitudes depend on gradients of the ocean sound–speed structure, and there is therefore sensitivity to small scales. Because the ray is infinitely thin, there is no natural acoustical scale to separate meaningful small-scale ocean structure from irrelevant structure. Invariably the finite wavelength of the sound will set this natural separation scale, and this notion has been investigated using the Fresnel zone. Another important issue in ray theory is ray chaos, that is, exponential sensitivity to initial conditions and sound-speed perturbations.