Linear Sound Speed Profile Research Articles

Localisation for underwater acoustic networks with a piece-wise linear sound speed profile

ABSTRACT Underwater agent localisation is a precondition for plenty of ocean applications. The variation of the underwater sound speed (USS) is one of the main factors that constrain the performance of underwater localisation. In this paper, a scheme is designed to reduce the agent localisation error arising from the USS variation in deep water and an agent localisation algorithm named ‘localisation with a piecewise linear USS' (LPL) is proposed. According to the characteristics of a real USS in deep water, a piecewise linear USS model is introduced to approximate the real USS. The agent above under the ‘sound fixing and ranging’ (SOFAR) channel are both considered. The LPL algorithm consists of three parts: initial value estimation, horizontal distance estimation and localisation. Considering the piecewise linear USS profile, the proposed LPL algorithm improves the performance for localisation with 60% more precision than the state-of-the-art methods.

On plane-wave reflection from a two-layer marine sediment: A surficial layer with linear sound speed profile overlying an iso-speed basement.

An analysis of plane wave reflection is developed for a two-layer sediment, the top layer consisting of a fine-grained material (mud) with an upward refracting linear sound speed profile. Beneath is a homogeneous basement, and above is homogeneous seawater. A rather curious, exact analytical expression for the reflection coefficient is derived, involving easy to evaluate integrals over finite limits, of the modified Bessel functions of low-integer order. The expression is generally valid for any linear profile with positive gradient in the surficial mud layer and for any sound speed in the basement, either greater than or less than that in the seawater. For "fast" basements, a critical angle always exists that is independent of the sound speed in the mud layer. With a "slow" basement, a quasi-angle of intromission may exist, which depends only weakly on both frequency and the gradient of the profile in the mud, a conclusion that may be relevant to the conditions of the Seabed Characterization Experiment (2017) performed over the New England Mud Patch. With both types of basement, fast and slow, the reflection coefficient, as a function of grazing angle, exhibits fluctuations that are strongly frequency dependent, associated with resonances and anti-resonances in the mud layer.

A three-dimensional bistatic reverberation model of underwater explosion by interface scattering at variable sound speeds

Underwater reverberation is a main limitation of the sonar performance and thereby the reverberation level estimation becomes crucial. In this study, based on the Lambert law and ray theory, a model for predicting 3D bistatic reverberation performance by interface scattering at linear sound speed profile is established and then verified through the underwater explosion experiments. The Influences of source and receiver positions, and relative sound speed gradient on reverberation performance are further investigated. The results indicate that: (1) the proposed model can predict the short-range mean reverberation level effectively, with the deviation 2–4 dB and describe the whole reverberation level distribution in some details; (2) at the early reverberation phase, the interference effects between the interface scattering sounds are considerable and a dominating interface exists; the counterbalance between the losses by scattering, spreading and medium absorption results in the local high-intensity zones close to corresponding interfaces, respectively; (3) as the sound source moves towards some interface, associated local high-intensity zone gradually expands, while the other one shrinks; if the sound speed approaches are constant, an extra local high-intensity zone will appear between the previous two but with a lower magnitude.

Source motion modeling for high-speed aircraft noise propagation

A continuous source motion model has been developed to represent a cruising aircraft traveling at high altitudes. The numerical implementation is based on the Lorentz transform (LT) and a Fast Field Program (FFP) formulation, which is used to compute the sound fields due to a monopole point source traversing in a horizontally stratified atmosphere parallel to a ground surface. To reduce the computational expenses, a one-dimensional LT-FFP is performed to obtain the pressure time-history for overhead flight conditions. The continuous source motion model is compared against a heuristic model which applies a Doppler shift to the stationary source sound field. A linear sound speed profile was selected to simplify the ray model implementation. A parametric study involving the source Mach number and source emission frequency has been performed in a variety of environmental conditions. The differences in the predicted maximum sound pressure levels between the two models can be as large as 9 dB under certain cond...

Snell’s law of refraction and sound rays for a moving medium

Fermat’s principle of least time is used to calculate a new law of refraction for a stratified medium moving horizontally with different temperatures in each layer. This new law of refraction includes velocity of sound, wind speed, and the angle between the vectorial sum of sound velocity and the wind speed. This new equation is compared with the usual approximations for the different refraction laws of a moving medium occasionally mentioned in literature as ‘‘Snell’s law for a moving media.’’ The sound rays in a moving thermically stratified medium are refracted more or less (dependent on either upwind or downwind sound propagation), then calculated according to the ‘‘Snell’s law.’’ For upward-oriented sound rays and a moderate thermical stratification with high wind speeds, the difference in the angle of refraction between the new refraction law and the usual approximation is roughly 3 degrees and neglectable for grazing incidence. The sound ray trajectories expressed as analytical equations for a constant sound velocity combined with a wind speed profile proportional to height; the results are shown in a figure. Furthermore, the sound ray trajectories for a linear sound speed profile combined with a linear height-dependent wind speed profile are calculated and shown graphically.

Influence of ground effect and refraction on road traffic noise

Ground effect and refraction modify geometrical spreading. In the present study a simplified model of ground effect is applied. Refraction is analyzed for the motionless atmosphere with a linear sound speed profile. Noise generated by constant speed road traffic is assessed by the time-average sound level, L AeqT -. The model of L AeqT prediction contains free parameters that are estimated from noise measurements at the site in question. The model makes possible the prediction of L AeqT at an altitude of a few tens of meters above the ground surface, within the range of a few hundred meters from the road. Contours of L AeqT = constant in the vertical plane represent the radiation pattern of road traffic noise.

Analytical solutions for outdoor sound propagation in the presence of wind

A theoretical analysis for the sound field due to a point monopole source in a fluid, layered atmospheric environment is described. The analysis has included explicitly the effect of fluid motion in the three-dimensional wave equation. The atmospheric environment is assumed to have sound-speed and vector wind-velocity profiles that either increase or decrease monotonically with height. In addition, the atmosphere is assumed to be vertically stratified. In such an environment, the solution can be expressed analytically in terms of Airy functions but the forms of solution are different for the situations of upward and downward refraction. Some sound-speed and wind-velocity profiles are amenable to exact analyses. Two notable examples are (i) a windless environment with a linear sound-speed profile; and (ii) a medium with a linear wind shear layer and a constant sound speed. These two profiles are studied analytically and compared numerically with other computational schemes. The validity of a heuristic approximation, which replaces the vector wind-velocity profile with an effective sound-speed profile, is also investigated numerically.

Using matched-field processing to estimate shallow-water bottom properties from shot data taken in the Mediterranean Sea

It is extremely difficult to determine shallow ocean bottom properties (such as sediment layer thicknesses, densities, and sound speeds). However, when acoustic propagation is affected by such environmental parameters, it becomes possible to use acoustic energy as a probe to estimate them. Matched-field processing (MFP) which relies on both field amplitude and phase can be used as a basis for the inversion of experimental data to estimate bottom properties. Recent inversion efforts applied to a data set collected in October 1993 in the Mediterranean Sea north of Elba produce major improvements in MFP power, i.e., in matching the measured field by means of a model using environmental parameters as inputs, even using the high-resolution minimum variance (MV) processor that is notoriously sensitive and usually results in very low values. The inversion method applied to this data set estimates water depth, sediment thickness, density, and a linear sound-speed profile for the first layer, density and a linear sound-speed profile for a second layer, constant sound speed for the underlying half space, array depth, and source range and depth. When the inversion technique allows for the array deformations in range as additional parameters (to be estimated within fractions of a wavelength, e.g., 0.1 m), the MFP MV peak value for the Med data at 100 Hz can increase from 0.48 (using improved estimates of environmental parameters and assuming a vertical line array) to 0.68 (using improved estimates of environmental parameters PLUS improved phone coordinates). The ideal maximum value would be 1.00 (which is achieved for the less sensitive Linear processor). However, many questions remain concerning the reliability of these inversion results and of inversion methods in general.

Wave scattering from a ground with a Gaussian bump or trough in an inhomogeneous medium

A closed-form solution of the Helmholtz equation is obtained for the case of a time-harmonic line source embedded in a medium with the linear sound-speed profile. Substituting the closed-form expression of the Green’s function into the Helmholtz–Kirchhoff integral equation, the exact solution of the scattered fields from a ground with a Gaussian shaped bump or trough in such a medium is obtained. An extension of the method of moments, which can solve the Helmholtz–Kirchhoff integral equation for sound scattering in the inhomogeneous medium, has been developed. Using these new tools, the effects of scattering in the region beyond a bump or trough are studied for situations when the background medium is upward refracting. Numerical results show that a soft ground with a bump or a hard ground with a trough in the upward refracting medium may cause some enhanced field regions beyond the bump or trough. The phenomenon is not observed when the background medium is homogeneous. Numerical results also show that a hard ground with a bump or a soft ground with a trough in the inhomogeneous medium may not cause any major difference when compared with results from the case using the homogeneous medium as the background medium.

Sound propagation with a linear sound-speed profile over a rough surface

The distribution of an acoustic field propagating at grazing angles over a hard rough surface is described by an integral equation that results from the Helmholz integral in the parabolic approximation. The Green’s function corresponding to the case when the sound speed varies linearly with distance from the surface is found. The integral equation is solved analytically for the case of a flat surface. The field distribution in the space above the surface, obtained by numerical methods, is presented for a flat surface and for a rough surface. In both cases, the sound speed varies linearly with distance from the surface.

Heuristic model for outdoor sound propagation based on an extension of the geometrical ray theory in the case of a linear sound speed profile

In the case of outdoor sound propagation at relatively short ranges, it is reasonable to assume that sound follows straight ray paths. At longer ranges, refraction due to temperature and wind gradients results in ray paths that are curved, and calculations using straight rays are no longer valid and lead to erroneous results. In addition, atmospheric turbulence plays an ever-increasing role by degrading the coherence of the sound field. In this paper, the theory valid for propagation from a point source above an impedance plane is extended to include the effects of curved rays and the loss of coherence due to atmospheric turbulence. The model assumes a sound speed gradient that varies linearly with height above the ground. This assumption allows an analytical determination of the travel times of the curved rays and the modified angle of incidence of the ground-reflected paths. The additional reflected rays that may appear in the presence of a positive gradient are included in the calculation. The assumption also permits the determination of the position of the shadow zone in the presence of a negative gradient. The total sound pressure level is computed by summing the contribution from all the rays. In this summation, a fluctuating index of refraction is used to take into account the partial coherence between the rays caused by the effects of atmospheric turbulence. If the receiver is in the shadow zone, a diffraction theory based on a residue series solution is used to compute the sound levels. The results of calculations using the model are compared with experimental results.

A fast and accurate bistatic bottom reverberation model

A simple bistatic reverberation model has been developed to model low‐frequency, wideband, bottom, or surface reverberation. The model allows for arbitrary separation of source and receiver in both range and depth, and accommodates both source and receiver beam patterns. Total reverberation is computed by the incoherent summation of the incremental contributions from each three‐dimensional ray path connecting the source, scattering element, and receiver. Simplified ray path calculations are made with either a constant or a linear sound speed profile, assuming spherical spreading along each ray, and specular reflection from the flat, horizontal boundary interfaces. Acoustic characteristics of the surface and bottom are assumed to be completely represented by the reflection loss and scattering strength functions. A realistic representation of generalized bistatic scattering [D. D. Ellis and D. R. Haller, J. Acoust. Soc. Am. Suppl. 182, S124 (1987)] has been successfully used to model reverberation from expl...

Inversion of shallow water reciprocal transmission data to determine current profiles

Acoustic reciprocal transmission geometries have been used to remotely measure fluctuations of ocean current and temperature. Usually, the travel time of a pulse is used as a measure of the integrated sound speed or current along a ray path. Reciprocal transmission experiments in the Florida Straits are characterized by refracted, bottom reflected rays making multiple bottom reflections resulting in a continuum of multipath arrivals. Owing to interference, distinct arrivals cannot be identified and used for travel time measurements. As an alternate method, we are comparing the phase differences for the upstream and downstream pulse arrival patterns. Modeling the sound channel with a linear sound speed profile, sloping bottom, we find that arrival time is linearly related to the average height of the rays above the bottom. Thus phase differences for upstream and downstream transmissions are proportional to depth average currents making possible a simplified inversion to obtain current profiles. At the time...