Fast Field Program Research Articles

Sound propagation in the Straits of Bab‐el‐Mandeb

The Straits of Bab‐el‐Mandeb is a natural constriction between the highly saline Red Sea and the Gulf of Aden (Indian Ocean). The merging of these two distinct water masses in the Straits results in a highly stratified sound‐speed profile consisting of a high sound‐speed layer overlying a low speed layer. A sound propagation experiment utilizing shots detonated at 18 m was conducted across the Straits along a relatively flat sandy bottom with an average water depth of 60 m. Results are compared with modeling predictions using the Fast Field Program (FFP).

Theoretical low‐frequency transmission loss over an attenuating sediment‐rock bottom

Computations of transmission loss were made for a shallow source (10 m) and a receiver at 550‐m depth in 3600 m of water using the Kutschale Fast Field Program algorithm. The transmission medium consisted of the water column with typical Atlantic sound speed profile; a 200‐m‐thick sediment layer (d = 200 M) with average sound speed, density and attenuation profiles according to Hamilton; and an elastic half‐space with physical properties of rock, including shear attenuation of 5 dB/wavelength as suggested by historical dale [Attewell et al., Geophysics 31, 1049–1056 (1966)] and recent measurements by the authors. For a rock bottom only, shear wave attenuation increased transmission loss dramatically (40 dB at 10 Hz and 500 km). Together with the sediment layer the loss decreased at frequencies where the wavelength λ < d (20 dB at 10 Hz). At sufficiently small wavelengths the process may be viewed as turning rays that avoid interaction with the high‐loss rock interface but suffer attenuation losses along refracting paths within the sediment. Sediment enhanced transmission is thus limited at low frequencies by the layer thickness and high frequencies by the frequency‐dependent sediment attenuation.Computations of transmission loss were made for a shallow source (10 m) and a receiver at 550‐m depth in 3600 m of water using the Kutschale Fast Field Program algorithm. The transmission medium consisted of the water column with typical Atlantic sound speed profile; a 200‐m‐thick sediment layer (d = 200 M) with average sound speed, density and attenuation profiles according to Hamilton; and an elastic half‐space with physical properties of rock, including shear attenuation of 5 dB/wavelength as suggested by historical dale [Attewell et al., Geophysics 31, 1049–1056 (1966)] and recent measurements by the authors. For a rock bottom only, shear wave attenuation increased transmission loss dramatically (40 dB at 10 Hz and 500 km). Together with the sediment layer the loss decreased at frequencies where the wavelength λ < d (20 dB at 10 Hz). At sufficiently small wavelengths the process may be viewed as turning rays that avoid interaction with the high‐loss rock interface but suffer attenuation losses along r...

Pulse propagation in the ocean. II: The parabolic equation method

The Fast Field Program (FFP) is a convenient method to compute the exact integral solution of the wave equation derived from harmonic sources in multilayered media. Solid layers as well as liquid layers may be included in the model. Thus, elastic subbottom layers are included in the model and, for Arctic propagation, an elastic ice sheet is also included. The sound field is computed as a function of range for each detector depth employing the fast Fourier transform (FFT) algorithm. The FFP has been extended to compute waveforms from broadband sources as a function of range and depth by Fourier synthesis employing the FFT algorithm. The input for this synthesis as a function of frequency is computed by the FFP. The computer program has been used to model SOFAR propagation in the central Arctic Ocean. Computed waveforms for the Arctic channel are in excellent agreement with field data. The computations clearly show the evolution in range of the dispersive signals observed in the Arctic channel. At any selected point in range and depth the waveform may be reversed in time and propagated back through the channel, showing the evolution of pulse compression to the range at which the ocean filter is matched and pulse spreading beyond this range.

Quantitative model/measurement comparisons of propagation-loss mean and fluctuating components

In November 1973 a propagation-loss experiment was performed in the Tongue of the Ocean, Bahama Islands, under carefully monitored conditions with regard to environmental parameters and source/receiver geometry. A projector transmitting a 300-H tone was towed at a depth of 76 m in the surface duct and receiver to a range of 9 km. A model, the Fast Field Program, was used to simulate propagation-loss results using a measured sound-speed profile and bottom parameters selected to achieve a good eyeball fit in the region dominated by bottom-reflected energy. The measured and simulated results were then compared in terms of range-dependent mean and range-dependent standard deviation as obtained in moving windows. The mean level of the model oscillated with range in the bottom bounce region as contrasted to the measured data which exhibited an essentially constant mean level. Variability about the mean was greater for the simulated results than that of the measured data by 2–3 dB. This disparity is accounted for by fluctuation mechanisms shown to be present in the measured data besides multipath interference which is the sole cause of variability in the model simulated data. [Work supported by NUSC.]

Pulse propagation in the ocean. I: The fast field program method

Long-range propagation experiments are often conducted in range-dependent environments. The prediction of pulse propagation characteristics in such environments is possible with the parabolic equation (PE) method, using the Tappert—Hardin split-step Fourier algorithm. A program has been developed to compute temporal waveforms from broadband sources as a function of range and depth, using Fourier synthesis to coherently add up the frequency response as obtained from the PE code at each range step. The effects of range-dependent ice roughness are modeled by a modified formula of Marsh and Mellen, using as input the rms ice roughness along the propagation path. The computed waveforms have been tested against field data on SOFAR propagation in the central Arctic Ocean, and excellent agreement has been obtained. Numerical simulations of pulse compression in the Arctic channel using predistorted waveforms to match the dispersion of the channel at specified ranges show in detail the possibility of successfully achieving significant signal gain by pulse compression.

Lateral waves and low-frequency negative bottom loss

Many of the recent low-frequency bottom loss experiments, although conducted by different investigators in diverse geographical locations and using different experimental procedures, have resulted in the paradoxical observance of “negative”, bottom loss values. It has been conclusively shown in the previous paper that artifacts of the experimental procedures need not be the explanation for the anomaly. The contention of this paper is that the “negative” loss anomaly results from the application of models which do not account for the time coincident interaction of ocean bottom reflected energy with subbottom energy returning to the water column. This hypothesis will be supported by presenting and discussing a Fast Field Program (FFP) time domain simulation where the lateral wave is the only additional arrival interacting with the arrival of the reflected wave. [This work was sponsored by Naval Sea Systems Command, SEA 06H1-4, A.P. Franceschetti.]

Deconvolution of low-frequency ocean sediment acoustic signals. I. Simulation study

The previous paper described a Fast Field Program propagation model consisting of two contiguous, semi-infinite, constant sound-speed fluids (ocean and sediment). A point source and a receiver were placed in the ocean above the boundary and varied in range to simulate a (real world) relative type bottom loss measurement. A 100-msec, 50-Hz sinusoidal pulse was transmitted through the ocean to study the reflected and lateral acoustic wave interaction at the boundary. To obtain the acoustic impulse response of the simulated sediment, deconvolution was performed by dividing the spectrum of the sediment interacting acoustic signal by the spectrum of a transmitted (direct path) signal and computing the inverse Fast Fourier Transform. Controlled amounts of Gaussian noise were added to simulate ambient noise. Even low noise levels (S/N=20 dB) were found to degrade the process to a point where the deconvoled signal was no longer discernable. The degree of degradation was determined by comparing bottom reflectivity ratios and lateral and reflected waveforms, after deconvolution, obtained in the absence and presence of noise. Applying averaging and stabilization techniques reduced noise degradation significantly. A 16-mm motion picture camera is requested to show a 5-min film of the modeling results. [This work was sponsored by Naval Sea Systems Command, SEA 06H1-4, A.P. Franceschetti.]

Analysis of low‐frequency sound channel propagation in Baffin Bay

The axial arrival pattern at low frequencies (below 100 Hz) and relatively long ranges (200 km) from a sound channel propagation experiment in Baffin Bay shows an extensive series of arrivals after the refracted arrival pattern. Since the bottom at this location was relatively lossless, the hypothesis that these later arrivals represented energy that was diffracted from the sound channel was examined using the Fast Field (Modeling) Program. A comparison of sound‐propagation characteristics was made for the frequency range 1–100 Hz, assuming both high and low loss bottoms. The results show that diffraction does not significantly change the average propagation loss at frequencies above 5 Hz.

Fast field program (FFP)

The archetype model of a stratified ocean leads to an integral (Hankel) transform representation of the underwater sound field of a simple source. For numerical work, the asymptotic (ray) method or a residue (normal mode) series have been widely used to approximate this transform. Both have mathematical limitations, and being eigenvalue problems, can present significant computational difficulties. Current computer technology now permits direct numerical evaluation of the transform. We accomplish this using a fast Fourier transform (whence the title). Development of this technique was initiated in 1967 under the sponsorship of the Acoustics Programs, Office of Naval Research. We have employed it over a wide range of the various parameters involved, and it is now in routine use at our laboratory. Its speed and accuracy make it a viable candidate for large-scale calculations or for use on naval vehicles with limited computer facilities.

Normal-mode program with N2 linear layers

Normal-mode expansions provide a low-frequency complement to the high-frequency ray theoretic methods. These methods are useful in environments where the sound speed and density profiles are essentially stratified, i.e., these parameters have a weak dependence on range. They also provide a means of confirming the validity of other approximate methods for which a direct error analysis is not possible. The theory of such expansions is well established, but their implementation is sometimes difficult. In the present program, the sound speed and density profiles in the ocean and the bottom are approximated and the resulting approximation is solved exactly. The nature of the profile approximation is as follows: The depth coordinate is partitioned into N layers such that in each layer the square of the index of refraction may be approximated by a straight line and the density by a constant. The Z-dependent portion of the pressure field can then be expressed in terms of Airy functions. The results are compared with a modified NRL program [A. V. Newman and F. Ingenito, “A Normal Mode Computer Program for Calculating Propagation in Water with an Arbitrary Velocity Profile,” NRL Rep. 2381 (Jan. 1972)] and with the FFP program [F. DiNapoli, “Fast Field Program for Multilayered Media,” NUSC Rep. No. 4103 (1971)] for a set of examples presented at the recent ONR Non-Ray Tracing Workshop, May 1973. In addition, the effects of the continuous spectrum are considered. [Supported by Naval Ordnance Systems Command.]

Some Effects of a Solid Bottom on Propagation Loss at Low Frequencies

The fast field program (FFP) is a fast, convenient method employing the fast Fourier transform to compute propagation loss as a function of range. The FFP integrates directly the exact integral solution of the wave equation derived from point harmonic sources in multilayered media. In the past, the bottom has been represented by a layered liquid, but here the FFP is used to investigate some effects at low frequencies of a layered solid bottom on propagation loss as a function of range. Computations of propagation loss are compared between bottoms with the same layer thicknesses, compressional-wave velocity, and density but with and without rigidity. In deep water, the main effect in the band 8–30 Hz on propagation loss of a solid bottom is to alter the detailed fluctuations of loss with range in response to the multipath interference of the waves, but the smoothed loss with range commonly measured from explosive sources is not significantly different for the test cases over the range intervals up to 200 km. In shallow water, however, propagation loss as a function of range at frequencies below cutoff for the all-liquid guide may be significantly less when the rigidity of the bottom is included.

Nomograms of Low-Frequency Transmission Loss

In the design or operation of sonar systems it is required to know under what conditions optimum performance can be achieved. The subject of this paper is a technique which should be useful in dealing with one term in the sonar equation, namely, transmission loss. Since the amount of energy lost depends on many parameters (e.g., the sound-speed profile, source and receiver depths, frequency, bottom loss, etc.), the process of determining the optimum mix of these parameters is cumbersome even if a validated transmission loss model is available. The approach utilizes the Fast Field Program (FFP) to generate transmission loss values for typical sound-speed profiles of the major ocean areas. It is assumed that at a sufficiently large range the mean propagation loss is represented by A+10 logr+αr where r is horizontal range and α is Thorp's attenuation coefficient. The constant A is then determined from a linear least-squares fit between this expression and the FFP values. The FFP is rerun for various combinations of the input parameters and the value of A are then combined to form a collection of nomograms which display the dependence of the mean transmission loss upon the input parameters. This work supported by the Chief of Naval Material.]

A Study of Very Low-Frequency Attenuation in the Deep Ocean Sound Channel

The fast field program (FFP) is used to study sound propagationin a deep ocean sound channel for the frequency range 1–200Hz. Typical sound velocity profiles from the Atlantic and Pacific Oceans are used. Both the velocity profile and bottom depth are assumed to be invariant with range. The channel cutoff frequency is determined and the bottom loss contributionto the measured values of attenuation is estimated. Comparison is made with recent experiments.

Project Hiawatha Revisited: Application of FFP to Lake Superior Attenuation Experiment

Owing to the pressure dependence of the temperature of maximum density in fresh water, the sound channel in Lake Superior is extremely weak. The fast field program (FFP) is applied to determine if the bottom loss is significant for sound channel propagation in the kilohertz region. The values of attenuation are computed for the frequency range 500–10 000 Hz and compared to values obtained from the Lake Tanganyika experiment.

Fast Field Program (FFP) and Attenuation Loss in Hudson Bay

In August of 1970, shallow-water attenuation measurements were conducted in Hudson Bay [“Sound Propagation and Reverberation Measurements in Hudson Bay,” paper N13 presented at 81st meeting of the Acoustical Society of America, J. Acoust. Sac. Amer. 50, 103 (A) (1971)]. The experimental results indicated that below 1 kHz, values for the attenuation coeffecient were considerably higher than those which would be predicted from Thorp's formula. One possible explanation for this anomaly was that the experimental values were affected by a significant bottom loss in addition to the attenuation loss in the water column. In order to obtain a better understanding of the governing factors, theoretical propagation loss predictions were made with the FFP. The model incorporates both a layered bottom and a complex wavenumber and the influence of each can be determined parametrically. It was found that at the frequencies of interest the bottom was not a significant factor and that the values of the theoretical attenuation coefficient, needed to match the FFP and experimental propagation-loss results, were in good agreement with the values determined experimentally.

Fast Field Program (FFP) for Surface Duct Propagation

The FFP is a numerical method, due to H. W. Marsh, of evaluating accurately and efficiently the solution of the acoustics wave equation. Presented here is a form of the FFP, due to W. S. Liggett, in which by proper choice of an integration contour the wave solution is expressed as a sum of residues plus a branch cut integral. By appropriate approximation, these can be evaluated using the FFT or Chirp Fourier Transform algorithms. A general numerical integration scheme, which allows arbitrary sound-velocity profiles that need not be approximated by analytic functions nor divided into layers, and which permits propagation loss computation as a function of both range and depth, is used to evaluate the kernel of the FFT. Although the FFP is more generally applicable, to illustrate the procedure, the propagation loss is computed for a surface duct case with no bottom returns. Our results are compared to those in the literature for this case, which were found by normal mode and ray trace computations and from empirical data. [This research was supported by the Office of Naval Research.]

Fast Field Program

The hydrodynamical field equations yield to three methods of solution. Two of these, the method of characteristics and that of separation of variables, have been widely used for both analytical and numerical investigation, but usually with either physical or mathematical approximations. The third, direct integration of the partial differential equations has always existed in principle but not until the advent of the fast Fourier transform could this approach be exploited in a systematic and economical manner. H. W. Marsh recognized this fact and introduced the concept of the fast field program (FFP). Several examples are presented and discussed which demonstrate that the FFP is not only feasible but a highly efficient algorithm for providing propagation estimations rapidly without undue approximations to the basic field equations. The results are compared with those predicted by both ray theory and normal-mode theory. [This research was supported by the U. S. Underwater Sound Laboratory.]

A Fast Ray-tracing Technique For SoundPropagation In A Stratified Moving Medium

A new method is suggested for the evaluation of sound field in a moving stratified atmosphere above an absorbing ground. The new method stems from a recent development on a high-frequency approximation of sound propagation outdoors in the presence of wind and temperature gradients[K M Li, J. Acoust. Soc. Am. 95, 1840-1852]. The present work attempts to implement the new method numerically with vertical variations in temperature and vectorial wind velocity as input parameters. Although the algorithm is applied to atmospheric sound propagation, the general idea can be applied to other branches of wave propagation such as the transmission of sound in an ocean environment. The determination of the ray path is simplified by the introduction of an apparent index of refraction that has included the Doppler effect due to the motion of the medium. Instead of using a 'hit-and-miss' approach, we use an iterative scheme that would find all eigenrays. The search of eigenrays is based on a fourth-order Runge-Kutta algorithm with adjustable step sizes. We also remark that the leading term of the high-frequency solution is identical to that derived by the classical ray theory but the new method is based on a rigorous estimation of a Fourier integral. Furthermore, a close examination of the new solution reveals that the total sound field is composed of three terms, namely, a direct wave, a (geometrically) reflected wave and a ground wave, respectively. However, the classical ray theory does not predict the existence of the ground wave component. Numerical results from the new ray-tracing methods are presented and compared with other numerical schemes such as the Fast Field Program (FFP). Transactions on the Built Environment vol 10, © 1995 WIT Press, www.witpress.com, ISSN 1743-3509 278 Computational Acoustics