The waveguide invariant principle is used to estimate the range to a broadband acoustic source in a shallow-water waveguide using a single acoustic receiver towed along a path directly toward the acoustic source. A relationship between the signal processing parameters and the ocean-acoustic environmental parameters is used to increase the effective signal-to-noise ratio without requiring detailed knowledge of the environment. Heuristics are developed to estimate the minimum source bandwidth and minimum horizontal aperture required for range estimation. A range estimation algorithm is tested on experimental and simulated data for source ranges of 500-2200 m and frequencies from 350 to 700 Hz. The algorithm is accurate to within approximately 25% for the cases tested and requires only a minimal amount of a priori environmental knowledge.

Much of the recent research in ocean acoustics has focused on developing methods to exploit the effects that the sea surface and seafloor have on acoustic propagation. Many of those methods require detailed knowledge of the acoustic properties of the seafloor and the sound speed profile (SSP), which limits their applicability. The range-frequency waveguide invariant describes striations that often appear in plots of acoustic intensity versus range and frequency. These range-frequency striations have properties that depend strongly on the frequency of the acoustic source and on distance between the acoustic source and receiver, but that depend mildly on the SSP and seafloor properties. Because of this dependence, the waveguide invariant can be utilized for applications such as passive and active sonar, time-reversal mirrors, and array processing, even when the SSP or the seafloor properties are not well known. This thesis develops a framework for understanding and calculating the waveguide invariant, and uses that framework to develop signal processing techniques for the waveguide invariant.A method for passively estimating the range from an acoustic source to a receiver is developed, and tested on experimental data. Heuristics are developed to estimate the minimum source bandwidth and minimum horizontal aperture required for range estimation.A semi-analytic formula for the waveguide invariant is derived using WKB approximation along with a normal mode description of the acoustic field in a rangeindependent waveguide. This formula is applicable to waveguides with arbitrary SSPs, and reveals precisely how the SSP and the seafloor reflection coefficient affect the value of the waveguide invariant.Previous research has shown that the waveguide invariant range-frequency striations can be observed using a single hydrophone or a horizontal line array (HLA) of hydrophones. This thesis shows that traditional array processing techniques are sometimes inadequate for the purpose of observing range-frequency striations using a HLA. Array processing techniques designed specifically for observing range-3 frequency striations are developed and demonstrated.Finally, a relationship between the waveguide invariant and wavenumber integrations is derived, which may be useful for studying range-frequency striations in elastic environments such as ice-covered waveguides.

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The frequency dependence of a waveguide's Green's function can be summarized by a single parameter known as the waveguide invariant, β. Although it has been shown analytically that β≈1 for ideal waveguides, numerical and experimental results have shown that β≈1 for many realistic shallow water waveguides as well. There is not much prior work explaining why the non-uniformities present in realistic sound speed profiles sometimes have such a small effect on the value of β. This paper presents a method for calculating β using a modal Wentzel-Kramers-Brillouin (WKB) description of the acoustic field, which reveals a straightforward relationship between the sound speed profile and β. That relationship is used to illustrate why non-uniformities in the sound speed profile sometimes have such a small effect on β and under what circumstances the non-uniformities will have a large effect on β. The method uses implicit differentiation and thus does not explicitly solve for the horizontal wavenumbers of the modes, making it applicable to waveguides with arbitrary sound speed profiles and fluid bottom halfspaces. Several examples are given, including an analytic estimate of β in a Pekeris waveguide.

The waveguide invariant describes striations in a range versus frequency plot of a waveguide’s Green’s function. Analytic expressions for the waveguide invariant only exist for a few select waveguides, but experiments and simulations have shown that the waveguide invariant is approximately equal to unity for almost all realistic shallow-water waveguides. A quasi-analytic method will be presented for estimating the value of the waveguide invariant in waveguides with arbitrary sound speed profiles, including the effects of a bottom fluid halfspace. The method is approximate but allows for an intuitive understanding of why the value of the waveguide invariant does not strongly depend on the details of the sound speed profile.