[1] Using a global set of in situ temperature and salinity profile observations, the sonic layer depth (SLD) and the mixed layer depth (MLD) are analyzed and compared over the annual cycle. The SLD characterizes the potential of the upper ocean to trap acoustic energy in a surface duct while MLD characterizes upper ocean mixing. The SLD is computed from temperature and salinity profile pairs using a new tunable method while MLD is computed using recently developed methods and either temperature only profiles or temperature and salinity profile pairs. Both SLD and MLD estimates provide information on different and important aspects of the upper ocean. The SLD and MLD often coincide because sound speed increases with depth down to the MLD, where (typically) a decrease in temperature occurs, resulting in a local maximum sound speed. The depth of this maximum sound speed is the SLD. The SLD and MLD are not always the same because sound speed is substantially more sensitive to temperature than to salinity compared to density. Since MLD is a commonly known and studied parameter, MLD is often used as a proxy for SLD in scientific and operational applications. In the boreal spring when fresh restratification events occur, the SLD is 10 m deeper (shallower) than the MLD in 39% (7%) of the observed profiles. A parabolic equation acoustic transmission model is used to evaluate the relative skill of the SLD and MLD estimates to predict surface acoustic trapping as measured by a simple metric.Citation: Helber, R. W., C. N. Barron, M. R. Carnes, and R. A. Zingarelli (2008), Evaluating the sonic layer depth relative to the mixed layer depth,

The equivalence of range and frequency averaging of acoustic propagation model results, based on the similarity of their analytic forms in mode calculations, was shown by Harrison [J. Acoust. Soc. Am. 97, 1314–1317 (1995)]. Here it is shown how oceanographic measurement errors and receiver bandwidth can be mapped into uncertainty in the number of modes being propagated. This can be mapped into range boundaries for averaging calculations, thereby giving upper and lower confidence boundaries for frequency-averaged transmission loss calculations. Examples of the application of this technique to synthetic data, where the measurement uncertainties are known and deliberately included, are shown.

The parabolic equation method implemented with the single-scattering correction accurately handles range-dependent environments in elastic layered media. Interfaces between elastic media may be treated efficiently by subdividing into a series of two or more single-scattering problems [Küsel et al., J. Acoust. Soc. Am. 121, 808–813 (2007)]. In addition to environmental waveguide parameters, the procedure uses several computational parameters. The impacts of the number of interfacial scattering problems, an iteration scheme convergence parameter, and the number of iterations for convergence are shown on the accuracy and efficiency of the method. In particular, selection criteria for these parameters are developed. Fourier transforms and syntheses generate time-domain solutions for seismic applications of interest. Examples for model waveguides show features of Rayleigh and Stoneley wave propagation, and comparisons with solutions from other methods are shown. [Work supported by the ONR.]

A finite-difference time-domain (FDTD) solution to the two-dimensional linear acoustic wave equation is utilized in numerical experiments to test the hypothesis that near-surface, bubble-induced refraction can have a significant impact on low to moderate frequency sea-surface reverberation. In order to isolate the effects of bubble-modified propagation on the scattering from the air/sea interface from other possible phenomena such as scattering from bubble clouds, the bubbly environment is assumed to be range independent. Results of the study show that both the strong wind-speed dependence and the enhanced scattering levels of the order found in the reverberation data are obtained when a wind-speed-dependent bubble layer is included in the modeling.

This study presents the theoretical framework for variational data assimilation of acoustic pressure observations into an acoustic propagation model, namely, the range dependent acoustic model (RAM). RAM uses the split-step Padé algorithm to solve the parabolic equation. The assimilation consists of minimizing a weighted least squares cost function that includes discrepancies between the model solution and the observations. The minimization process, which uses the principle of variations, requires the derivation of the tangent linear and adjoint models of the RAM. The mathematical derivations are presented here, and, for the sake of brevity, a companion study presents the numerical implementation and results from the assimilation simulated acoustic pressure observations.