Coupled mode transport theory for sound transmission through an ocean with random sound speed perturbations: Coherence in deep water environments

Abstract

Second moments of mode amplitudes at fixed frequency as a function of separations in mode number, time, and horizontal distance are investigated using mode-based transport equations and Monte Carlo simulation. These second moments are used to study full-field acoustic coherence, including depth separations. Calculations for low-order modes between 50 and 250 Hz are presented using a deep-water Philippine Sea environment. Comparisons between Monte Carlo simulations and transport theory for time and depth coherence at frequencies of 75 and 250 Hz and for ranges up to 500 km show good agreement. The theory is used to examine the accuracy of the adiabatic and quadratic lag approximations, and the range and frequency scaling of coherence. It is found that while temporal coherence has a dominant adiabatic component, horizontal and vertical coherence have more equal contributions from coupling and adiabatic effects. In addition, the quadratic lag approximation is shown to be most accurate at higher frequencies and longer ranges. Last the range and frequency scalings are found to be sensitive to the functional form of the exponential decay of coherence with lag, but temporal and horizontal coherence show scalings that fall quite close to the well-known inverse frequency and inverse square root range laws.

On horizontal coherence estimates from path integral theory for sound propagation through random ocean sound-speed perturbations

“…The inverse square-root scaling for y 0 is in fact the same as the scaling for the other path integral derived coherences, namely, those for depth and time separations. There is no compelling evidence to suggest that transverse coherence should behave differently from the depth and time coherences, and there is significant theoretical evidence that all three of these coherences should scale very nearly as R À1/2 (Voronovich and Ostashev, 2009;Voronovich et al, 2011;Colosi et al, 2013). In addition observational results show that time coherence does indeed scale very closely as one over the square-root of range (Yang, 2008).…”

Observations and transport theory analysis of low frequency, acoustic mode propagation in the Eastern North Pacific Ocean

“…A more recent article by Colosi et al (2013) has extended the transport theory approach to also predict mode time coherences. The transport theory equations for the cross mode coherences with time separation, s, are given by…”

Modeling and Forecasting Ocean Acoustic Conditions

“…Example sound statistics are intensity and phase variances, and field correlation scales. The necessary statistics of the environment can be obtained by analyzing output of dynamical models, and may include RMS sound-speed variations, correlation scales of those variations, or mode coupling matrices (Colosi and Morozov 2009;Colosi et al 2012bColosi et al , 2013Raghukumar and Colosi 2014). One aspect of this approach is that one can treat the ocean as non-stationary and examine the evolution of statistical quantities.…”

“…Ensembles of dynamical ocean models that are properly formulated for specific dynamical processes can also be used to define the statistics of those processes. Statistics of the acoustic field can be computed and then examined by feeding the ocean statistics (model-or data-derived) into statistical acoustic models (Flatté et al 1979;Colosi and Morozov 2009;Colosi et al 2012bColosi et al , 2013Gong et al 2013;White et al 2013;Raghukumar and Colosi 2014;Rouseff and Lunkov 2015;Colosi 2016).…”