Random Sound-speed Perturbations Research Articles

Temporal Coherence for Sound Transmission Through Fluctuating Deep Water with Adiabatic Perturbed Modes

Adiabatic approximation (AP) combined with perturbation theory gives a fast normal-mode solution of temporal coherence for sound field in a two-dimensional deep water with time-varying random internal waves. Internal waves induced mode changes are deduced using the first-order perturbation theory [C. T. Tindle, L. M. O’Driscoll and C. J. Higham, Coupled mode perturbation theory of range dependence, J. Acoust. Soc. Am. 108(1) (2000) 76–83]. And mode perturbations in amplitude are neglected by the adiabatic method with wavenumber perturbations in phase merely considered. The AP expression of temporal coherence function is theoretically identical to the adiabatic transport equation theory [J. A. Colosi, T. K. Chandrayadula, A. G. Voronovich and V. E. Ostashev, Coupled mode transport theory for sound transmission through an ocean with random sound speed perturbations: Coherence in deep water environments, J. Acoust. Soc. Am. 134(4) (2013) 3119–3133]. Numerical results of the adiabatic temporal coherence function for several low frequencies and ranges up to 1000[Formula: see text]km are calculated. Then the coherence time scales obtained from the calculations are examined by a one-way coupled theory considering forward scattering [A. G. Voronovich, V. E. Ostashev and J. A. Colosi, Temporal coherence of acoustic signals in a fluctuating ocean, J. Acoust. Soc. Am. 129(6) (2011) 3590–3597]. Comparisons demonstrate that the range and frequency dependence of coherence time for both methods are quite close. And this shows good agreement with the well-known inverse frequency and inverse square root range laws. In addition, the internal wave energy dependence of coherence time is also studied.

Entropy rate defined by internal wave scattering in long-range propagation.

The reduction of information capacity of the ocean sound channel due to scattering by internal waves is a potential problem for acoustic communication, navigation, and remote sensing over long ranges. In spite of recent progress in research on acoustic signal scattering by random internal waves and the fact that random internal waves are ubiquitous in the world oceans, there is no clear understanding of how these waves influence data communication performance. The entropy decrease resulting from scattering by internal waves is an important measure of information loss. Here a rigorous calculation of the entropy is carried out using second moment transport theory equations with random sound-speed perturbations obeying the Garrett-Munk internal-wave model. It is shown that full-wave rate of entropy is of the same order of magnitude as the Kolmogorov-Sinai entropy and Lyapunov exponents for the relevant ray trajectories. The correspondence between full-wave and ray entropies suggests a correspondence between full-wave scattering and ray chaos near statistical saturation. The relatively small level of entropy rate during propagation through the random internal-wave field shows that scattering by internal waves is likely not an essential limitation for data rate and channel capacity.

High-frequency normal-mode statistics in shallow water: the combined effect of random surface and internal waves.

In an earlier article, the statistical properties of mode propagation were studied at a frequency of 1 kHz in a shallow water environment with random sound-speed perturbations from linear internal waves, using a hybrid transport theory and Monte Carlo numerical simulations. Here, the analysis is extended to include the effects of random linear surface waves, in isolation and in combination with internal waves. Mode coupling rates for both surface and internal waves are found to be significant, but strongly dependent on mode number. Mode phase randomization by surface waves is found to be dominated by coupling effects, and therefore a full transport theory treatment of the range evolution of the cross mode coherence matrix is needed. The second-moment of mode amplitudes is calculated using transport theory, thereby providing the mean intensity while the fourth-moment is calculated using Monte Carlo simulations, which provides the scintillation index. The transport theory results for second-moment statistics are shown to closely reproduce Monte Carlo simulations. Both surface waves and internal waves strongly influence the acoustic field fluctuations.

High frequency normal mode statistics in a shallow water waveguide: the effect of random linear internal waves.

Using transport theory and Monte Carlo numerical simulation, the statistical properties of mode propagation at a frequency of 1 kHz are studied in a shallow water environment with random sound-speed perturbations from linear internal waves. The environment is typical of summer conditions in the mid-Atlantic bight during the Shallow Water 2006 experiment. Observables of interest include the second and fourth moments of the mode amplitudes, which are relevant to full-field mean intensity and scintillation index. It is found that mode phase randomization has a strong adiabatic component while at the same time mode coupling rates are significant. As a consequence, a computationally efficient transport theory is presented, which models cross-mode correlation adiabatically, but accounts for mode coupling using the mode energy equations of Creamer [(1996). J. Acoust. Soc. Am. 99, 2825-2838]. The theory also has closed-form expressions for the internal wave scattering matrix and a correction for an edge effect. The hybrid transport theory is shown to accurately reproduce many statistical quantities from the Monte Carlo simulations.

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

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.

Statistics of low-frequency normal-mode amplitudes in an ocean with random sound-speed perturbations: Shallow-water environments

Second- and fourth-moment mode-amplitude statistics for low-frequency ocean sound propagation through random sound-speed perturbations in a shallow-water environment are investigated using Monte Carlo simulations and a transport theory for the cross-mode coherence matrix. The acoustic observables of mean and mean square intensity are presented and the importance of adiabatic effects and cross-mode coherence decay are emphasized. Using frequencies of 200 and 400 Hz, transport theory is compared with Monte Carlo simulations in a canonical shallow-water environment representative of the summer Mid-Atlantic Bight. Except for ranges less than a horizontal coherence length of the sound structure, the intensity moments from the two calculations are in good agreement. Corrections for the short range behavior are presented. For these frequencies the computed mode coupling rates are extremely small, and the propagation is strongly adiabatic with a rapid decay of cross-mode coherence. Coupling effects are predicted to be important at kilohertz frequencies. Decay of cross-mode coherence has important implications for acoustic interactions with nonlinear internal waves: For the case in which the acoustic path is not at glancing incidence with a nonlinear internal-wave front, adiabatic phase randomizing effects lead to a significantly reduced influence of the nonlinear waves on both mean and mean square intensity.

Transport equation approach for second order mode statistics in an ocean with random sound speed perturbations: Coherence

A transport equation has been derived to describe the range evolution of the single frequency cross mode coherence matrix so that acoustic field coherence functions with temporal as well as depth and transverse separations can be easily computed. The theory assumes 2-D propagation in the depth range plane, small angle weak multiple forward scattering, and the Markov approximation, and it has been previously shown to accurately predict the observable of mean intensity for both deep and shallow water environments. This talk will address the issues of: the accuracy of the approximations, relative contributions from coupling and adiabatic effects, scaling with range and frequency, and the functional form of the coherence with regards to lag.

Transport equations for cross-frequency transport equations for acoustic intensity moments

The second and fourth moment mode-amplitude statistics for ocean sound propagation through random sound-speed perturbations are investigated using exact transport theory for the cross-frequency cross-mode coherence matrix. These exact equations are derived using the method of successive approximations, originally developed by Klyatskin and Tartarskii. These equations allow the determination of the validity of the usual transport equation (involving the Markov approximation), which is the first order approximation (in a infinite sequence of approximations to the exact equations). The range scales for the approach to the asymptotic behavior of the intensity moments, and the decay of the cross-modal coherence is easily determined at all frequencies.

Statistics of mode amplitudes in an ocean with random sound speed perturbations: Temporal coherence.

A transport equation has been derived to describe the range evolution of the single frequency cross mode coherence matrix including time separations. The theory assumes 2‐D propagation in the depth range plane, small angle, weak multiple forward scattering, and the Markov approximation, and it has been shown to accurately predict the observable of mean intensity for both deep and shallow water (i.e., strongly lossy) situations. This paper will present results for the acoustic observable time coherence and will address the issues of accuracy of the temporal coherence approximations, relative contributions from coupling and adiabatic effects, scaling with range and frequency, and the functional form of the coherence with regards to lag.

Effects of non-adiabaticity in modal propagation through random sound speed perturbations.

Modal propagation through sound speed fluctuations in shelf environments can be modeled adiabatically or fully coupled through polynomial chaos (PC) expansions of the modal amplitudes or complex phase. The importance of modal scattering versus adiabatic effects is explored for random sound speed fields in the mid-frequency regime. It is shown that the importance of inter-modal scattering is related to the interference wavelength between the modes in relation to the horizontal wavelengths of the sound speed fluctuations as well as the vertical structure of the sound speed fluctuations with respect to the shape of the interacting modes. Modal scattering is also highly affected by the relative amplitudes between the modes with strong scattering into weaker modes. While these effects are well known, the coupled mode PC equations give unique insight into the detailed physics of these controlling factors.

Statistics of normal mode amplitudes in an ocean with random sound-speed perturbations: Cross-mode coherence and mean intensity

In this paper Creamer's [(1996). J. Acoust. Soc. Am. 99, 2825-2838] transport equation for the mode amplitude coherence matrix resulting from coupled mode propagation through random fields of internal waves is examined in more detail. It is shown that the mode energy equations are approximately independent of the cross mode coherences, and that cross mode coherences and mode energy can evolve over very similar range scales. The decay of cross mode coherence depends on the relative mode phase randomization caused by coupling and adiabatic effects, each of which can be quantified by the theory. This behavior has a dramatic effect on the acoustic field second moments like mean intensity. Comparing estimates of the coherence matrix and mean intensity from Monte Carlo simulation, and the transport equations, good agreement is demonstrated for a 100-Hz deep-water example.

Matched-field minimum variance beamforming in a random ocean channel

Matched-field source localization methods that employ deterministic full-wave acoustic propagation models can be seriously degraded due to the presence of random inhomogeneities in the ocean channel. In this paper, a minimum variance (MV) matched-field beamformer is presented that achieves greater robustness to random inhomogeneities in the sound-speed profile between the source and receiver. The proposed modification of the MV beamformer consists of employing multiple linear constraints derived from predicted pressure fields obtained using a set of perturbed sound-speed profiles. In order to investigate the nature of wave-front variations due to random sound-speed perturbations, a normal mode model based on adiabatic and first-order perturbation approximations is examined. The signal wave-front spatial correlation implied by this model suggests that the coherence among modes can remain high even in a fluctuating ocean environment. This in turn implies that the dimension of the signal perturbation constraint space for the MV beamformer can be small for typical sound-speed variations at moderate source ranges. Given the signal constraint space, design of the MV beamformer with sound-speed perturbation constraints is achieved by selecting its quiescent response to maximize the average signal-to-noise ratio gain against spatially uncorrelated noise. This leads to a computationally efficient realization of the beamformer that avoids the need to repeatedly compute perturbed pressure fields. Simulation experiments using a realistic deep-water Pacific Ocean environment are presented, which suggest that robust unambiguous low-frequency source location estimates can be achieved in the presence of mesoscale inhomogeneities given only knowledge of the second-order statistics of the random range-dependent sound-speed profile plus a single environmental measurement at the receiving array.