Acoustic field variability induced by time evolving internal wave fields

Effects of nonlinear internal gravity waves on normal-incident reflection measurements of seafloor sediments

Sonar data acquired by sub-bottom profilers and echosounder systems are widely used to estimate geoacoustic properties of marine sediments. However, the uncertainty of the seabed property estimates caused by water-column variability may limit the application. In this paper, the acoustic focusing and defocusing effects of nonlinear internal gravity waves on normal-incident acoustic reflection measurements are studied. The experiment data were collected in the South China Sea from two transceiver moorings located at two different sites, one of which contained strong nonlinear internal waves (NIWs), while another site did not. The observed reflection intensity variation at the internal wave site varied up to 10 dB. On the other hand, the bottom reflections at the other site without internal waves were stable, and a seafloor sediment sample collected there was analyzed to validate the sediment type inferred from bottom loss. Numerical simulations using ray-tracing and parabolic equation models confirmed the cause of this intensity fluctuation by the acoustic focusing and defocusing of NIWs. This study eventually showed that NIWs may induce a significant bias for geoacoustic property estimates from seabed reflection coefficients.

Underwater acoustic energy fluctuations during strong internal wave activity using a three-dimensional parabolic equation model

The three-dimensional Monterey-Miami parabolic equation model is used to simulate a nonlinear internal wave (NIW) crossing the sound field in a shallow water environment. The impetus for this research stems from acoustic measurements taken during the Shallow Water '06 (SW06) field experiment, where a NIW traversed the water column such that soliton wavecrests were nearly parallel to the source-receiver path. Horizontal refraction effects are important in this scenario. A sound speed profile adapted from experimental SW06 data is used to simulate the NIW, assuming variations along the wavecrests (e.g., curvature) are negligible. Broadband and modal energy metrics show acoustic fluctuations due to internal wave activity. Repeated model runs simulate the NIW crossing the parabolic equation (PE) field over space and time. Statistical analysis shows the PE data are best fit by a lognormal distribution but tends to an exponential distribution during certain scenarios. Small angle differences between the acoustic track and the propagating NIW cause substantial differences in energy distribution throughout the PE field. While refraction effects due to the leading edge of the NIW's arrival are important in all cases, the impacts of focusing and defocusing in the perfectly parallel case dominate the field fluctuations. In the non-parallel case, the strong fluctuations introduced by the passage of the NIW are of similar order to the refraction off the leading edge.

Broadband acoustic signal variability induced by internal solitary waves and semidiurnal internal tides in the northeastern East China Sea

The relation between high-frequency broadband acoustic signal variability and two types of internal waves (short-period internal solitary waves; ISWs, and semidiurnal internal tides; ITs) is investigated using data collected during the shallow-water acoustic variability experiment 2015 in the northeastern East China Sea. In this flat (∼100 m depth) region, an underwater sound channel with sound speed profile (SSP) variability observed during the experiment significantly affects the acoustic variability induced by the ISW, and the arrival structure of the channel impulse response (CIR) modeled by ray tracing. To model the range-dependent SSP due to ISW, the location and characteristics of the mode-1 ISW of wavelength (0.5-1 km) are estimated and verified based on the two-layer Korteweq-de Vries theory and by analyzing the observed temperature fluctuations. It is found from comparison between the measured and modeled CIRs that the ISW scatters the arrival structures of refracted rays. Meanwhile, semidiurnal ITs change the channel size modeled as range-independent considering the wavelengths (15-40 km) longer than the model range (3 km). Higher centroid of acoustic arrival time is found with lower isotherm depressions owing to the multimode ITs, indicative of acoustic energy focusing at the lower channel region.

Acoustic mode coupling induced by nonlinear internal waves: evaluation of the mode coupling matrices and applications

This paper applies the mode coupling equation to calculate the mode-coupling matrix for nonlinear internal waves appearing as a train of solitons. The calculation is applied to an individual soliton up to second order expansion in sound speed perturbation in the Dyson series. The expansion is valid so long as the fractional sound speed change due to a single soliton, integrated over range and depth, times the wavenumber is smaller than unity. Scattering between the solitons are included by coupling the mode coupling matrices between the solitons. Acoustic fields calculated using this mode-coupling matrix formulation are compared with that obtained using a parabolic equation (PE) code. The results agree very well in terms of the depth integrated acoustic energy at the receivers for moving solitary internal waves. The advantages of using the proposed approach are: (1) The effects of mode coupling can be studied as a function of range and time as the solitons travel along the propagation path, and (2) it allows speedy calculations of sound propagation through a packet or packets of solitons saving orders of magnitude computations compared with the PE code. The mode coupling theory is applied to at-sea data to illustrate the underlying physics.

Empirical dependence of acoustic transmission scintillation statistics on bandwidth, frequency, and range in New Jersey continental shelf

The scintillation statistics of broadband acoustic transmissions are determined as a function of signal bandwidth B, center frequency f(c), and range with experimental data in the New Jersey continental shelf. The received signal intensity is shown to follow the Gamma distribution implying that the central limit theorem has led to a fully saturated field from independent multimodal propagation contributions. The Gamma distribution depends on the mean intensity and the number of independent statistical fluctuations or coherent cells micro of the received signal. The latter is calculated for the matched filter, the Parseval sum, and the bandpassed center frequency, all of which are standard ocean acoustic receivers. The number of fluctuations mu of the received signal is found to be an order of magnitude smaller than the time-bandwidth product TB of the transmitted signal, and to increase monotonically with relative bandwidth Bfc. A computationally efficient numerical approach is developed to predict the mean intensity and the corresponding broadband transmission loss of a fluctuating, range-dependent ocean waveguide by range and depth averaging the output of a time-harmonic stochastic propagation model. This model enables efficient and accurate estimation of transmission loss over wide areas, which has become essential in wide-area sonar imaging applications.

Acoustic propagation under tidally driven, stratified flow

Amplitude and phase variability in acoustic fields are simulated within a canonical shelf-break ocean environment using sound speed distributions computed from hydrodynamics. The submesoscale description of the space and time varying environment is physically consistent with tidal forcing of stratified flows over variable bathymetry and includes the generation, evolution and propagation of internal tides and solibores. For selected time periods, two-dimensional acoustic transmission examples are presented for which signal gain degradation is computed between 200 and 500 Hz on vertical arrays positioned both on the shelf and beyond the shelf break. Decorrelation of the field is dominated by the phase contribution and occurs over 2-3 min, with significant recorrelation often noted for selected frequency subbands. Detection range is also determined in this frequency band. Azimuth-time variations in the acoustic field are illustrated for 100 Hz sources by extending the acoustic simulations to three spatial dimensions. The azimuthal and temporal structure of both the depth-averaged transmission loss and temporal correlation of the acoustic fields under different environmental conditions are considered. Depth-averaged transmission loss varies up to 4 dB, depending on a combination of source depth, location relative to the slope and tidally induced volumetric changes in the sound speed distribution.

Analysis and modeling of broadband airgun data influenced by nonlinear internal waves

To investigate acoustic effects of nonlinear internal waves, the two southwest tracks of the SWARM 95 experiment are considered. An airgun source produced broadband acoustic signals while a packet of large nonlinear internal waves passed between the source and two vertical linear arrays. The broadband data and its frequency range (10-180 Hz) distinguish this study from previous work. Models are developed for the internal wave environment, the geoacoustic parameters, and the airgun source signature. Parabolic equation simulations demonstrate that observed variations in intensity and wavelet time-frequency plots can be attributed to nonlinear internal waves. Empirical tests are provided of the internal wave-acoustic resonance condition that is the apparent theoretical mechanism responsible for the variations. Peaks of the effective internal wave spectrum are shown to coincide with differences in dominant acoustic wavenumbers comprising the airgun signal. The robustness of these relationships is investigated by simulations for a variety of geoacoustic and nonlinear internal wave model parameters.

Horizontal array beamforming in an azimuthally anisotropic internal wave field

A numerical study of beamforming on a horizontal array is performed in a shallow water waveguide where a summer thermocline is perturbed by a time evolving realization of an internal wave field. The components of the internal wave field consist of a horizontally (azimuthally) isotropic, spatially homogeneous contribution, and a horizontally anisotropic, spatially inhomogeneous component. These terms represent a diffuse ("background") internal wave field and a localized solitary wave packet, respectively. Conventional beamforming is performed as a function of time while the internal wave field evolves throughout a computational volume containing the source-receiver paths. Source-receiver orientation with respect to the azimuthally anisotropic component has a significant effect on the beamformed output. When the source-receiver configuration is oriented approximately parallel to the solitary wave crests, beam wander, fading, beam splitting and coherence length degradation occurs in a time-dependent manner as the solitary wave packet passes through the environment. Both horizontal refraction of energy and a time-dependent modal source excitation distribution are responsible for these beamforming effects. In cases where source-receiver orientation is not approximately parallel to the wave crests, these effects are substantially reduced or eliminated, indicating that an azimuthally selective perturbation of the acoustic field can be attributed to the wave packet. Modal decomposition of the acoustic field and single mode starting fields are used to infer that, for the source-receiver orientation along the wave crests and troughs, acoustic propagation is predominantly adiabatic. A modal phase speed analysis explains several features associated with the beamformed power.

Coupled perturbed modes and internal solitary waves

Coupled perturbed mode theory combines conventional coupled modes and perturbation theory. The theory is used to directly calculate mode coupling in a range-dependent shallow water problem involving propagation through continental shelf internal solitary waves. The solitary waves considered are thermocline depressions, separating well-mixed upper and lower layers. The method is fast and accurate. Results highlight mode coupling associated with internal solitary waves, and mode capture or loss to and from the discrete mode spectrum.

Coherence of acoustic modes propagating through shallow water internal waves

The 1995 Shallow Water Acoustics in a Random Medium (SWARM) experiment [Apel et al., IEEE J. Ocean. Eng. 22, 445-464 (1997)] was conducted off the New Jersey coast. The experiment featured two well-populated vertical receiving arrays, which permitted the measured acoustic field to be decomposed into its normal modes. The decomposition was repeated for successive transmissions allowing the amplitude of each mode to be tracked. The modal amplitudes were observed to decorrelate with time scales on the order of 100 s [Headrick et al., J. Acoust. Soc. Am. 107(1), 201-220 (2000)]. In the present work, a theoretical model is proposed to explain the observed decorrelation. Packets of intense internal waves are modeled as coherent structures moving along the acoustic propagation path without changing shape. The packets cause mode coupling and their motion results in a changing acoustic interference pattern. The model is consistent with the rapid decorrelation observed in SWARM. The model also predicts the observed partial recorrelation of the field at longer time scales. The model is first tested in simple continuous-wave simulations using canonical representations for the internal waves. More detailed time-domain simulations are presented mimicking the situation in SWARM. Modeling results are compared to experimental data.

Acoustic propagation through anisotropic internal wave fields: transmission loss, cross-range coherence, and horizontal refraction

Results of a computer simulation study are presented for acoustic propagation in a shallow water, anisotropic ocean environment. The water column is characterized by random volume fluctuations in the sound speed field that are induced by internal gravity waves, and this variability is superimposed on a dominant summer thermocline. Both the internal wave field and resulting sound speed perturbations are represented in three-dimensional (3D) space and evolve in time. The isopycnal displacements consist of two components: a spatially diffuse, horizontally isotropic component and a spatially localized contribution from an undular bore (i.e., a solitary wave packet or solibore) that exhibits horizontal (azimuthal) anisotropy. An acoustic field is propagated through this waveguide using a 3D parabolic equation code based on differential operators representing wide-angle coverage in elevation and narrow-angle coverage in azimuth. Transmission loss is evaluated both for fixed time snapshots of the environment and as a function of time over an ordered set of snapshots which represent the time-evolving sound speed distribution. Horizontal acoustic coherence, also known as transverse or cross-range coherence, is estimated for horizontally separated points in the direction normal to the source-receiver orientation. Both transmission loss and spatial coherence are computed at acoustic frequencies 200 and 400 Hz for ranges extending to 10 km, a cross-range of 1 km, and a water depth of 68 m. Azimuthal filtering of the propagated field occurs for this environment, with the strongest variations appearing when propagation is parallel to the solitary wave depressions of the thermocline. A large anisotropic degradation in horizontal coherence occurs under the same conditions. Horizontal refraction of the acoustic wave front is responsible for the degradation, as demonstrated by an energy gradient analysis of in-plane and out-of-plane energy transfer. The solitary wave packet is interpreted as a nonstationary oceanographic waveguide within the water column, preferentially funneling acoustic energy between the thermocline depressions.