A normal mode method for propagation modeling in acousto-elastic ocean waveguides is described. The compressional (p-) and shear (s-) wave propagation speeds in the multilayer environment may be constant or have a gradient (1/c2 linear) in each layer. Mode eigenvalues are found by analytically computing the downward- and upward-looking plane wave reflection coefficients R1 and R2 at a reference depth in the fluid and searching the complex k plane for points where the product R1R2=1. The complex k-plane search is greatly simplified by following the path along which |R1R2|=1. Modes are found as points on the path where the phase of R1R2 is a multiple of 2π. The direction of the path is found by computing the derivatives d(R1R2)/dk analytically. Leaky modes are found, allowing the mode solution to be accurate at short ranges. Seismic interface modes such as the Scholte and Stonely modes are also found. Multiple ducts in the sound speed profile are handled by employing multiple reference depths. Use of Airy function solutions to the wave equation in each layer when computing R1 and R2 results in computation times that increase only linearly with frequency.

Outgoing solutions of the wave equation, including parabolic equation (PE) and normal-mode solutions, are usually formulated so that pressure is continuous with range for range-dependent problems. The accuracy of normal-mode solutions has been improved by conserving energy rather than maintaining continuity of pressure [Porter et al., “The problem of energy conservation in one-way equations,” J. Acoust. Soc. Am. 89, 1058–1067 (1991)]. This approach is applied to derive a higher-order energy-conserving PE that provides improved accuracy for problems involving large ocean bottom slopes and large range and depth variations in sound speed and density. A special numerical approach and complex Padé coefficients are applied to suppress Gibbs’ oscillations. The back-propagated half-space field, an improved PE starter, is applied to handle wide propagation angles. Reference solutions generated with a complex ray model and with the rotated PE are used for comparison.

A straightforward algorithm for broadband matched-field source localizaton is developed and subsequently applied to experimental data. For the two-receiver case, the algorithm involves correlating modeled and measured cross spectra and summing coherently over frequency. The extension to the multiple-receiver case is to perform the two-receiver algorithm on each pair of hydrophones and sum the complex results coherently. The frequency band over which the summation is made may be chosen to maximize the signal-to-noise ratio. Using an acoustic propagation model based on ray theory to produce modeled cross spectra, the broadband localization scheme is applied to an experimental dataset in which a pseudorandom noise source was towed past a bottom-moored vertical array in a deep-ocean environment. Localization is successful out to the maximum range of 43 km. The effects on the source localization of varying such parameters as the number of phones, bandwidth, and receiver aperture are examined. It is found that matching the autospectra as well as the cross spectra significantly degrades the localization, and that coherent summation over both frequency and phone pairs is superior to incoherent summation.

A method for extracting the normal modes of acoustic propagation in the shallow ocean from sound recorded on a vertical line array (VLA) of hydrophones as a source travels nearby is presented. The mode extraction is accomplished by performing a singular value decomposition (SVD) of individual frequency components of the signal's temporally averaged, spatial cross-spectral density matrix. The SVD produces a matrix containing a mutually orthogonal set of basis functions, which are proportional to the depth-dependent normal modes, and a diagonal matrix containing the singular values, which are proportional to the modal source excitations and mode eigenvalues. The conditions under which the method is expected to work are found to be (1) sufficient depth sampling of the propagating modes by the VLA receivers; (2) sufficient source-VLA range sampling, and (3) sufficient range interval traversed by the source. The mode extraction method is applied to data from the Area Characterization Test II, conducted in September 1993 in the Hudson Canyon Area off the New Jersey coast. Modes are successfully extracted from cw tones recorded while (1) the source traveled along a range-independent track with constant bathymetry and (2) the source traveled up-slope with gradual changes in bathymetry. In addition, modes are successfully extracted at multiple frequencies from ambient noise.

A method for eliminating the branch cuts and branch line integrals from the normal-mode solution to the range-invariant acoustic wave equation has been developed and implemented. In the usual normal-mode formulation, evaluation of the vertical wave number in the ocean waveguide’s lower half space involves a square root operation and gives rise to a branch point at the critical angle. When the Pekeris cut is chosen, energy steeper than the critical angle is represented by leaky modes, and lateral-wave energy near the critical angle is represented by the branch line integral. When a mode lies near the branch cut, the branch line integral can be significant at all ranges. Branch line integrals are cumbersome to compute, and, for range-dependent problems, cannot be included in adiabatic and coupled-mode algorithms. By inserting small attenuation and sound-speed gradients in the lower half space, the plane-wave solution is replaced by an Airy function solution, the branch point is eliminated, the Pekeris branch cut is replaced by a series of modes, and the leaky modes become bounded at infinite depth. Implementation of and example calculations using this approach using the normal-mode model ORCA are given.