Roger M. Oba

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.

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.

Global boundary flattening transforms for acoustic propagation under rough sea surfaces

This paper introduces a conformal transform of an acoustic domain under a one-dimensional, rough sea surface onto a domain with a flat top. This non-perturbative transform can include many hundreds of wavelengths of the surface variation. The resulting two-dimensional, flat-topped domain allows direct application of any existing, acoustic propagation model of the Helmholtz or wave equation using transformed sound speeds. Such a transform-model combination applies where the surface particle velocity is much slower than sound speed, such that the boundary motion can be neglected. Once the acoustic field is computed, the bijective (one-to-one and onto) mapping permits the field interpolation in terms of the original coordinates. The Bergstrom method for inverse Riemann maps determines the transform by iterated solution of an integral equation for a surface matching term. Rough sea surface forward scatter test cases provide verification of the method using a particular parabolic equation model of the Helmholtz equation.

Convergence of polynomial chaos expansion based estimates of acoustic field and array beam response probability density functions.

The polynomial chaos expansion (PCE) method has been applied recently to the computation of acoustic field uncertainties arising from uncertainties of the acoustic propagation environment [Finette, J. Acoust. Soc. Am. 120(5)]. The present work investigates, through computational studies, the properties of acoustic field probability density functions (PDFs) and the rate and manner of convergence of PCE based approximations to those PDFs. The studies assume a stratified ocean waveguide, with uncertainties of sound speed and attenuation represented by joint PDFs. Numerically accurate computations of the field and beam response PDFs are first computed from the parameter PDFs using the normal‐mode expansion and the change in variables’ theorem of probability theory. The resulting field and beam power PDFs exhibit irregular functional behavior and singularities associated with features of the mapping from the parameter space to the field or beam power space. The singularities have implications for the choice of...

Acoustic field propagation through a time‐evolving buoyant jet

Previous theoretical work regarding internal wave/acoustic wave interaction has shown that in the case of soliton (i.e., nonoverturning) propagation, significant effects on acoustic propagation occur via both amplitude and phase components. Acoustic flow visualization data obtained recently in the South China Sea [Orr and Mignerey, J. Geophys. Res. 108 (2003)] indicate the presence of internal bores with associated Kelvin–Helmholtz instabilities at the base of the mixed layer. These overturning bores are examples of nonhydrostatic dynamics associated with significant vertical acceleration of the fluid. In order to explore the effect of overturning on acoustic field propagation, we have used a nonhydrostatic hydrodynamic model to simulate the temporal evolution of internal bores. The initial condition is a stationary front separating two regions characterized by slightly different but homogeneous densities. The front is released at t=0 and the gravity‐induced flow evolves into an internal bore with associated Kelvin–Helmholtz instabilities, or rotors, behind the leading edge of the bore. Results for transmission loss and signal gain degradation over a frequency range of 200–500 Hz will be presented. [Research sponsored by ONR.]

Beamforming through an anisotropic, time‐varying internal wave field

Shallow‐water environments commonly exhibit complex spatial and temporal variations in temperature and salinity caused by internal wave activity. These quantities map into a sound‐speed distribution that can significantly distort both the amplitude and phase of an acoustic field propagating through the environment. This presentation describes computer simulation results on the effect of an anisotropic, time‐varying internal wave field on plane wave beamforming of a point source within a shallow‐water waveguide. The (azimuthal) anisotropy is described by a solitary wave packet propagating through the region. A 3D parabolic equation code was used to propagate a 400‐Hz signal through this space and time‐evolving environment. Beamformed power, parametrized by receiver depth and an azimuthal angle, is illustrated for horizontal arrays and presented in terms of beam space, time, and range from the source. When the packet enters the region between source and receiving array, significant periodic beam wander and ...

The Biquaternionic acoustic wave equation

Equations for irrotational, linearized Euler fluid, where the mass continuity equation incorporates a linear equation of state, define linear acoustics that can be recast in terms of complexified quaternions, the biquaternions, which satisfy Cauchy-Fueter regularity equations. This gives first order partial differential equations from the four space-time dimensions to the four (complex) dimensional velocity-pressure space, with time and pressure in the biquaternionic scalar parts. The biquaternionic planar exponential provides the basis to elementary solutions as biquaternionic functions of a single biquaternionic variable. Analysis of this form shows significant geometrical algebraic properties including imaginary units for time distinct from those for space. The single biquaternion acoustic field at each point of space-time allows the propagation four complex coefficients in a single geometric algebraic structure, suitable for three or four dimensional Fourier analysis. (Work supported by the U.S. Office of Naval Research.) Equations for irrotational, linearized Euler fluid, where the mass continuity equation incorporates a linear equation of state, define linear acoustics that can be recast in terms of complexified quaternions, the biquaternions, which satisfy Cauchy-Fueter regularity equations. This gives first order partial differential equations from the four space-time dimensions to the four (complex) dimensional velocity-pressure space, with time and pressure in the biquaternionic scalar parts. The biquaternionic planar exponential provides the basis to elementary solutions as biquaternionic functions of a single biquaternionic variable. Analysis of this form shows significant geometrical algebraic properties including imaginary units for time distinct from those for space. The single biquaternion acoustic field at each point of space-time allows the propagation four complex coefficients in a single geometric algebraic structure, suitable for three or four dimensional Fourier analysis. (Work supported by the U.S. Offic...

Stochastic matched-field processing using polynomial chaos expansions to model environmental uncertainty

A stochastic generalization of matched-field processing (MFP) is presented that incorporates stochastic steering matrices rather than steering vectors. This provides a natural framework for including environmental uncertainty associated with incompletely known environmental knowledge. Parametric probabilities allow use of polynomial chaos (PC) expansions to describe environmental uncertainty in a rigorous manner, yielding efficient representations of the stochastic steering matrices through the application of sparse sampling methods. In particular, PC methods apply to the uncertainty of sediment variability that can be modeled via horizontal spectral methods. With moderate variability over scales justified by data in the New Jersey shelf region, the sediment uncertainty can be modeled with relatively few PC expansion coefficients, which depend only on the mean amplitude of spectral components. The coefficients express the nonlinear dependence of the acoustic field on the sediment variability, essentially orthonormalizing higher moments. The coefficients lead immediately to stochastic steering matrices, which are then compared via various MFP processors against acoustic data for MFP source localization. [Work supported by the U.S. Office of Naval Research.]A stochastic generalization of matched-field processing (MFP) is presented that incorporates stochastic steering matrices rather than steering vectors. This provides a natural framework for including environmental uncertainty associated with incompletely known environmental knowledge. Parametric probabilities allow use of polynomial chaos (PC) expansions to describe environmental uncertainty in a rigorous manner, yielding efficient representations of the stochastic steering matrices through the application of sparse sampling methods. In particular, PC methods apply to the uncertainty of sediment variability that can be modeled via horizontal spectral methods. With moderate variability over scales justified by data in the New Jersey shelf region, the sediment uncertainty can be modeled with relatively few PC expansion coefficients, which depend only on the mean amplitude of spectral components. The coefficients express the nonlinear dependence of the acoustic field on the sediment variability, essentially ...

Stochastic-basis matched-field processing

Matched-field processing (MFP) suffers serious degradation due to environmental mismatch between received acoustic-field vectors and modeled replica vectors. Physical reasons for degradation include uncertainty caused by incomplete descriptions of the parameters and fields necessary for correct specification of the acoustic waveguide (i.e., environmental uncertainty), and system uncertainty associated with incomplete knowledge of the array configuration, source depth, etc. Recent research in the theory of stochastic-basis expansions (polynomial chaos) provides a mathematically consistent way of incorporating both types of uncertainty into MFP. Such expansions are used efficiently to construct replica matrices that steer high-rank subspaces capable of capturing signals with uncertain wavefronts. When combined with cross-spectral density matrices, stochastic-basis steering matrices enable the design of new processors with properties not previously evaluated in a MFP context. A maximum likelihood processor i...

Empirical and quadrature approximation of acoustic field and array response probability density functions

Numerical methods are presented for approximating the probability density functions (pdfs) of acoustic fields and receiver-array responses induced by a given joint pdf of a set of acoustic environmental parameters. An approximation to the characteristic function of the random acoustic field (the inverse Fourier transform of the field pdf) is first obtained either by construction of the empirical characteristic function (ECF) from a random sample of the acoustic parameters, or by application of generalized Gaussian quadrature to approximate the integral defining the characteristic function. The Fourier transform is then applied to obtain an approximation of the pdf by a continuous function of the field variables. Application of both the ECF and generalized Gaussian quadrature is demonstrated in an example of a shallow-water ocean waveguide with two-dimensional uncertainty of sound speed and attenuation coefficient in the ocean bottom. Both approximations lead to a smoother estimate of the field pdf than that provided by a histogram, with generalized Gaussian quadrature providing a smoother estimate at the tails of the pdf. Potential applications to acoustic system performance quantification and to nonparametric acoustic signal processing are discussed.