Horizontal Refraction Angle Research Articles

Horizontal refraction of acoustic signals retrieved from North Pacific Acoustic Laboratory billboard array data

In 1998–1999, a comprehensive low-frequency long-range sound propagation experiment was carried out by the North Pacific Acoustic Laboratory (NPAL). In this paper, the data recorded during the experiment by a billboard acoustic array were used to compute the horizontal refraction of the arriving acoustic signals using both ray- and mode-based approaches. The results obtained by these two approaches are consistent. The acoustic signals exhibited weak (if any) regular horizontal refraction throughut most of the experiment. However, it increased up to 0.4 deg (the sound rays were bent towards the south) at the beginning and the end of the experiment. These increases occurred during midspring to midsummer time and seemed to reflect seasonal trends in the horizontal gradients of the sound speed. The measured standard deviation of the horizontal refraction angles was about 0.37 deg, which is close to an estimate of this standard deviation calculated using 3D modal theory of low-frequency sound propagation through internal gravity waves.

Studies of horizontal refraction and scattering of low-frequency acoustic signals using a modal approach in signal processing of NPAL data

In our previous paper [J. Acoust. Soc. Am. 112, 2232], we obtained a time dependence of the horizontal refraction angle (HRA) of acoustic signals propagating over a range of about 4000 km in the ocean. This dependence was computed by processing of acoustic signals recorded during the North Pacific Acoustic Laboratory (NPAL) experiment using a ray-type approach. In the present paper, we consider the results obtained in signal processing of the same data using a modal approach. In this approach, the acoustic field is represented as a sum of local acoustic modes with amplitudes depending on a frequency and arrival angle. We obtained a time dependence of HRA for a time interval of about a year. Time evolution of HRA exhibits long-period variations which could be associated with seasonal trends in the sound speed profiles. The results are consistent with those obtained by the ray approach. Different horizontal angles within arrivals were impossible to resolve due to sound scattering by internal waves. A theoretical estimate of the angular width of the acoustic signals in a horizontal plane was obtained. It appears to be consistent with the observed variance of HRA data. [Work supported by ONR.] a)J. A. Colosi, B. D. Cornuelle, B. D. Dushaw, M. A. Dzieciuch, B. M. Howe, J. A. Mercer, R. C. Spindel, and P. F. Worcester.

Horizontal refraction and coherence of acoustic signals propagating over a long-range in the ocean

The paper is devoted to experimental and theoretical studies of horizontal refraction and coherence of acoustic signals recorded during the NPAL experiment with the use of the billboard acoustic array [The NPAL Group, J. Acoust. Soc. Am. 109, 2384 (2001)]. Both ray- and mode representations of the acoustic field are used for signal-processing. In the first approach, signals at different pairs of hydrophones located at approximately the same depth are cross-correlated. This allows us to obtain the mean horizontal refraction angle, its time-dependence and variance, and the coherence radius of the sound wavefront. The variance and the coherence radius are also estimated using a theory developed. In this theory, the energy of the sound field scattered by internal waves spreads in horizontal directions according to a diffusion law. The diffusion coefficient is evaluated numerically for the Garret–Munk spectrum and canonical Munk profile. It is shown that the variance of the horizontal refraction angle and the coherence radius of the wavefront calculated theoretically agree qualitatively with their values obtained using the NPAL data. [Work supported by ONR.] a)J. A. Colosi, B. D. Cornuelle, B. D. Dushaw, M. A. Dzieciuch, B. M. Howe, J. A. Mercer, R. C. Spindel, and P. F. Worcester.

Horizontal refraction of acoustic signals retrieved from NPAL billboard array data

A comprehensive, long-range sound propagation experiment was carried out with the use of the billboard acoustic array of the North Pacific Acoustic Laboratory (NPAL) in 1999. The antenna consisting of five vertical line arrays was deployed near a California coast and received broadband acoustic signals transmitted from Hawaii over a distance of about 4000 km. Acoustic signals propagating over such a long distance might exhibit noticeable horizontal refraction. The paper will present results of processing the NPAL data to infer horizontal refraction angle (HRA) as a function of time. Different methods were used for determining HRA. The first approach employed cross correlation of the acoustic signals at different VLAs. Time delay corresponding to maximum of cross correlation is related to HRA assuming the angle is approximately the same for all rays (or modes). The second method used modal representation of the arriving broadband signals. The dependency of the amplitudes of acoustic modes on mode number, frequency, and arrival angle was determined independently within narrow frequency bins, and then the results were averaged over whole frequency range. This method allowed, in particular, to evaluate angular width of the arrived signal, which appeared to be of the order of a few milliradians.

Horizontal refraction modal tomography (HRMT) for ocean front and ocean current monitoring

It has been pointed out by Voronovich and Shang [IEEE J. Ocean. Eng. 24, 224–231 (1999)], that the HRMT has the ability of reducing the mode-coupling effect. In this paper, two examples of the application of HRMT in strong mode-coupling environment are discussed: (1) Polar front, and (2) transverse current in Fram Strait. In both cases, strong mode coupling takes place for the used frequency and mode number. Due to the modal phase difference is measured by two close paths, the mode-coupling effect can be significantly reduced. The results of the retrieved frontal parameters and the transverse component of the current based on adiabatic theory are pretty good even without any iteration. For the Polar front, the horizontal refraction angle is estimated. The parameters that can be retrieved by using HRMT are: the normal direction of the front, the center location of the front, and the sound speed profile difference of the two water masses. The interaction of those acoustically estimated parameters with satellite remote sensing is discussed. [Work supported by NOAA and ONR.]

Horizontal refraction modal tomography of the ocean with mode interactions

The acoustical tomography scheme for inferring a three-dimensional sound-speed field within some area based on the measurements of horizontal refraction angles is reviewed. The numerical simulations made so far were based on the assumption of the adiabaticity of low-frequency mode propagation. In this paper, an inversion scheme is presented that accounts for the acoustic mode interaction. We found that, generally, the interaction weakly affects the horizontal refraction angle, and it can be accounted for by iterations. Numerical simulations for the case of an Atlantic meddy corresponding to a strong double channel stratification are presented. Only three iterations were required to retrieve the exact strong sound-speed-field inhomogeneity within an area of 500 km/spl times/500 km.

Numerical simulations with horizontal-refraction-modal tomography. Part I. Adiabatic propagation

Numerical simulations on retrieving the 3-D structure of the sound-speed inhomogeneities based on data on the horizontal refraction angle (HRA) of acoustic modes have been performed. The inversion proceeds in two stages. At the first stage the values of propagation constants of different acoustic modes at the nodes of a horizontal grid are calculated. The corresponding procedure represents a linear 2-D problem which is solved for different modes independently. At the second stage the coefficients of the expansion of the variation of the sound-speed profile with respect to some set of empirical orthogonal functions are calculated based on already determined values of propagation constants. This stage represents a 1-D nonlinear problem which is solved for different nodes of the horizontal grid independently. When error-free HRA data were used in the numerical simulations, the 3-D sound-speed field was retrieved perfectly. Then the HRA data were artificially distorted with random errors. It was found that the relative error of the retrieved values of the propagation constant of modes is proportional to the error in HRA (expressed in radians). Corresponding relative error in retrieved values of sound speed is in its turn proportional to the relative error in propagation constants. When the level of HRA error has been chosen according to the level arising from distortions caused by internal waves, the rms error in the retrieved sound-speed values for the situation considered appeared to be about 0.7 m/s.

Ocean current effects on a low-frequency acoustic field and the feasibility of their use to monitor ocean dynamics

Ray-travel-time nonreciprocity has been used in most tomography experiments to determine current velocity in the ocean by acoustic means at distances large compared to ocean depth. Although very successful in deep water, this approach is not applicable in the coastal ocean where ray arrivals are not separable and/or identifiable due to multiple bottom interactions. In this paper, other parameters of the acoustic field, including normal mode travel time, ray and mode horizontal refraction angles, and full field phase, are treated as possible data for the current velocity field. Some qualitative differences between acoustic fields in moving and motionless fluid are indicated and their importance for acoustic monitoring of ocean currents is emphasized. Existing mathematical models of low-frequency underwater sound propagation in a moving ocean are discussed. It is demonstrated that nonreciprocity of various acoustic field variables possess quite a different sensitivity to the flow velocity field and robustness with respect to unavoidable uncertainties in our knowledge of system and environmental parameters. Full-field inversion, based on an appropriate acoustic field variable, is concluded to be a promising technique for current velocity remote sensing in the coastal ocean environments. [Work supported by NSERC and RBRF.]

Horizontal refraction tomography with mode interaction

Measurements of horizontal refraction angles associated with horizontal refraction of different acoustic modes can be used for inferring 3-D ocean inner structure [A. G. Voronovich and E. C. Shang, J. Acoust. Soc. Am. 98, 2708–2716 (1995)]. Numerical simulations demonstrated that the corresponding inversion scheme works very well for adiabatic propagation. It was also shown that the nonadiabatic case can be incorporated into the inversion scheme when mode interactions can be approximately accounted for by modifying local values of propagation constants of modes. In the present investigation, mode interaction is taken into account in a much more realistic ‘‘N×2-D’’ approximation (only relatively weak azimuth coupling is neglected). A new exact algorithm was used for the calculation of mode interactions in the plane of propagation. Numerical simulations showed that in many cases, the effect of mode interactions on horizontal refraction is rather weak and can be taken into account by rapidly converging iterative procedure. The results of tomography reconstruction of mesoscale inhomogeneities typical for the Pacific are demonstrated. [Work supported by ONR.]

Horizontal refraction tomography for nonadiabatic propagation

A scheme of acoustical tomography of the ocean based on measurements of horizontal refraction angles associated with different acoustic modes has been developed recently [A. G. Voronovich and E. C. Shang, J. Acoust. Soc. Am. (to be published)]. Retrieving the 3-D structure of meso- scale inhomogeneities of sound speed proceeds in this case in two steps: (1) determining propagation constants of different modes in the horizontal plane (2-D linear tomography), and (2) retrieving sound-speed profiles basing on a known set of propagation constants at each horizontal point (1-D nonlinear tomography). This tomography scheme was successfully tested in a numerical simulation based on an assumption of adiabaticity of acoustic propagation. ‘‘Splitting’’ of the inverse problem into two stages appeared to be very effective computationally. The present investigation extends this tomography scheme for the situations when the mode’s interaction should be taken into account. Now, retrieving the set of propagation constants proceeds iteratively and includes data on sound-speed profiles found at the previous step. For a relatively weak mode interaction which can be considered in a perturbative manner iterations converge after a few steps and the inversion scheme remains very effective. Typical parameters of mesoscale inhomogeneities which can be handled by this iterative approach are estimated. [Work supported by ONR.]

A note on horizontal‐refraction‐modal tomography

The use of horizontal antennas composed of long, mode‐resolving, vertical arrays is potentially useful in ocean acoustics. A scheme for acoustic tomography of the ocean based on measurements of the horizontal refraction of horizontal rays, which are related to different acoustic modes, is discussed. The horizontal refraction angle of a given mode is equal to the transverse gradient of the refraction index averaged over the depth interval embraced by this mode and integrated over the acoustic path. The effect of internal waves is estimated. It is shown that internal waves do not significantly blur the angular distribution of the received field. An experiment that involves two pairs of long, vertical arrays and a towed tonal source is proposed for the reconstruction of a 3‐D picture of the ocean’s inner structure over a 1000‐×1000‐km area.

Ocean structure inversion by horizontal refraction tomography

Numerical simulations for the horizontal refraction tomography (HRT) proposed previously [A. G. Voronovich and E. C. Shang, 2851(A) (1994)] were conducted. HRT is based on measurements of horizontal refraction angles (HRA) related to different acoustic modes. HRA are measured with the help of two distant ocean interferometers (each one consists of a pair of long mode resolving vertical arrays separated about 10 km apart). The signal is produced by tonal towed acoustic source. Both model eddy and real oceanic eddy of 100 km×100 km scale measured in Canary Basin were used for simulations. The 3‐D tomography inversion proceeded in two stages: (1) retrieving the values of propagation constants in the knots of a horizontal rectangular greed (linear 2‐D problem) and (2) reconstruction of the sound‐speed profile (SSP) in each knot (1‐D nonlinear problem). Up to 81 values of propagation constants for each mode were retrieved in both cases. Then SSP were calculated in each knot with the help of a special invariant‐imbedding based procedure. With error‐free simulated HRA data, SSPs were exactly reconstructed. The effect of errors on tomography inversion and requirements to the accuracy of phase measurements were also estimated. [Work supported by ONR.]

A new scheme of the acoustic tomography of the ocean

Using horizontal antennas composed out of mode resolving long vertical arrays has powerful potentials in the study of ocean acoustics. The new scheme for acoustic tomography of the ocean is presented based on the measurements of horizontal refraction of horizontal rays related to different acoustic modes. The horizontal refraction angle (HRA) of a given mode equals the transverse gradient of the refraction index averaged over the depth interval embraced by this mode and integrated over the acoustic path. Using HRA offers the following advantages. (a) Only simple tonal signals are involved. (b) There is no need for exact positioning of the source. (c) As rays are straight lines with great accuracy, the linear procedures of inversion are adequate in the 2-D stage. (d) Since tomography reconstruction is two dimensional for any given mode number, the processing and interpretation of the data are greatly simplified; a precise 3-D picture of inhomogeneities is calculated as the next stage after 2-D reconstruction. An experiment involving two pairs of LVA and a towed tonal source which allowed the reconstruction of a 3-D picture of the ocean inner structure in the area of 1000 nm×1000 nm for about 2 weeks, is discussed. [Work partly supported by NRC and ARPA.]