Range-dependent Propagation Model Research Articles

Modeling propagation in shallow water with the range-dependent sea surfaces and fluid seabeds using the equivalent source method.

This paper describes a shallow water range-dependent propagation model (RPM) based on the equivalent source method (ESM). The proposed model allows both the sea surface and fluid seabed to vary with the propagation range. The proposed equivalent source method-based range-dependent propagation model (ESM-RPM) utilizes three sets of equivalent sources, placed above the sea surface, below the seabed, and above the seabed, which replace the sea surface reflection, seabed reflection, and seabed transmission, respectively. The unknown strengths of the equivalent sources can be determined by solving an inverse problem based on the boundary conditions. The capability of the ESM-RPM for propagation in refractive water is demonstrated by evaluating the Green's function using a modal projection method. Numerical simulations are conducted in iso-velocity and refractive shallow water with an underwater canyon and corrugated surface waves, including two-dimensional (2-D) propagation across the canyon and three-dimensional (3-D) propagation along the canyon. Further simulations demonstrate the 2-D across-canyon and 3-D along-canyon propagations with random rough sea surfaces. The results show that the proposed ESM-RPM provides efficient, benchmark-quality numerical solutions that accurately capture the mode coupling associated with the varying cross section of the waveguide. Thus, the model has great potential to be applied in benchmarking propagation in shallow water with the varying sea surface and seabed.

Quantifying the Impacts of Acoustic Target Detections Using a Range-Independent Model Versus Range-Dependent Model

The purpose of this study is to identify and quantify the difference in detections of a subsurface target from a subsurface sensor source between range-independent and range-dependent versions of the same acoustic propagation model. Environmental data were pulled from open source databases to provide an application for the comparison and using novel measures of merit, the authors were able to quantify the difference in detection performance between models. This study suggests that provided multiple types of environments are considered, it is possible to use a range-independent model to give good approximations to the accuracy of detections, one would achieve using a full range-dependent sound propagation model.

An efficient broadband coupled-mode model using the Hamiltonian method for modal solutions

A numerically efficient broadband, range-dependent propagation model is proposed, which incorporates the Hamiltonian method into the coupled-mode model DGMCM. The Hamiltonian method is highly efficient for finding broadband eigenvalues, and DGMCM is an accurate model for range-dependent propagation in the frequency domain. Consequently, the proposed broadband model combining the Hamiltonian method and DGMCM has significant virtue in terms of both efficiency and accuracy. Numerical simulations are also provided. The numerical results indicate that the proposed model has a better performance over the broadband model using the Fourier synthesis and COUPLE, while retaining the same level of accuracy.

A coupled-mode method for sound propagation with multiple sources in range-dependent waveguides

An accurate and efficient coupled-mode method for multiple-sourceproblems is presented. In order to treat multiple-source problems, we modify the linear system ofequations based on the theory of a range-dependent propagation model recently developed byLuo et al. The additional computational effort causedby the modification is negligible, and thus field solutions can be obtained efficiently by solvingthe modified linear system of equations in the presence of multiple sources.Numerical results indicate that the present model is remarkably accurate, and capable of dealingwith multiple-source problems which cannot be treated efficiently by existing models. This model canserve as benchmark in range-dependent propagation modeling for multiple-source problems, and can also be appliedin three-dimensional modeling to treat realistic propagation and backscattering problems of a beam generatedby a source array.

A numerically stable coupled-mode formulation for acoustic propagation in range-dependent waveguides

In this paper, a stepwise coupled-mode model with the use of the direct global matrix approach is proposed. This method is capable of handling two-dimensional problems with either a point source in cylindrical geometry or a line source in plane geometry. With the use of the direct global matrix approach, this method is numerically stable. In addition, by introducing appropriately normalized range solutions, thismodel is free from the numerical overflow problem. Furthermore, we put forward source conditions appropriate for the line-source problem in plane geometry. As a result, this method is capable of addressing the scenario with a line source on top of a sloping bottom. Closed-form expressions for coupling matrices are derived and applied in this paper for handling problems with pressure-release boundaries and a homogeneous water column. The numerical simulations indicate that the proposed model is accurate, efficient, and numerically stable. Consequently, this model can serve as a benchmark model in range-dependent propagation modeling. Although this method is verified by an ideal wedge problem in this paper, the formulation applies to realistic problems as well.

Generalized Coupled-Mode Formulation for Sound Propagation in Range-Dependent Waveguides

An accurate and numerically stable method based on the coupled-mode theory is presented. By applying the direct global matrix approach to obtain the modal expansion coefficients, this method is numerically stable. In addition, appropriately normalized range solutions are introduced, which resolves the overflow problem entirely. Furthermore, we put forward source conditions appropriate for the line-source problem in plane geometry. As a result, this method is capable of dealing with the scenario where a line source is located inside the region of a deformation. Closed-form expressions for coupling matrices are provided for ideal waveguides. Numerical results indicate that the present method is accurate and numerically stable. Consequently, this model can serve as a benchmark in range-dependent propagation modeling.

Mapping the sound field of an erupting submarine volcano using an acoustic glider

An underwater glider with an acoustic data logger flew toward a recently discovered erupting submarine volcano in the northern Lau basin. With the volcano providing a wide-band sound source, recordings from the two-day survey produced a two-dimensional sound level map spanning 1 km (depth) × 40 km(distance). The observed sound field shows depth- and range-dependence, with the first-order spatial pattern being consistent with the predictions of a range-dependent propagation model. The results allow constraining the acoustic source level of the volcanic activity and suggest that the glider provides an effective platform for monitoring natural and anthropogenic ocean sounds.

A computational assessment of the sensitivity of ambient noise level to ocean acidification

Low-frequency sound propagating through the ocean is partly attenuated by the pH-dependent boric acid relaxation process. Thus, the uptake of increased levels of atmospheric CO(2) by seawater, leading to reduced pH, has potential to change ambient noise levels. An important question is: By how much? Here, changes in ambient noise level due to hypothetical changes in seawater pH have been calculated at three receiver locations for years 1960 and 2250. The calculations used a range dependent propagation model that was applied to realistic environments based on climatology. Model results indicate changes in noise levels less than 0.21 dB are anticipated.

English

Fine resolution spatial survey carried out off the west coast of India during June and December 2004 was utilised to study the transmission loss (TL) variability associated with the upwelling and downwelling processes in this region. During June, the upwelling was confined to the upper 80 m. Downsloping of isotherms below this depth towards the coast and the occurrence of low saline waters indicated the presence of undercurrent. Between the periods of upwelling and downwelling, temperature and salinity in the surface layers increased by 1-2 o C and 2 PSU, respectively, while at the sub-surface levels, the corresponding increase was ~8 o C and ~0.5 PSU. A range-dependent acoustic propagation model based on parabolic equation method was utilized to compute TL for these two periods. The model was run with a source frequency of 3 kHz kept at 5m depth for different environmental setup, viz. propagation along the constant-depth contour, range-independent and range-dependent environment, and upslope/downslope propagation. The computations revealed significant variability in the TL characteristics between the upwelling and downwelling scenario, though bathymetry and geo-acoustic properties were the same. The analysis also stressed the need of range-dependent acoustic propagation model for realistic prediction of transmission loss variability. Defence Science Journal, 2010, 60(5), pp.476-482 , DOI:http://dx.doi.org/10.14429/dsj.60.570

Efficient matched processing for localisation of a moving acoustic source

In recent years matched processing techniques have emerged as a solution for the problem of target motion analysis. A target's motion parameters are estimated by determining which of a bank of replica signals best correlates with the signal received from that target. Matched processing methods have been used in low SNR environments such as the underwater acoustic environment because they outperform pseudomeasurement-based target motion analysis. However, matched processing is notoriously computationally demanding, requiring evaluation of complex equations for replica generation, and batch processing via an exhaustive search of a multidimensional parameter space. This study presents a matched processing method for localisation of a slow-moving low-frequency acoustic source by matching Fourier coefficients from a single frequency bin. A simple range-dependent propagation model is assumed, and the Doppler effect is carefully modelled to produce realistic replicas. An efficient matching algorithm is presented which computes cost values in a recursive fashion, discarding poorly scoring replicas before they are fully evaluated. Simulated examples demonstrate the ability of the technique to resolve the locus of low-Doppler targets at extremely low SNR with a fraction of the cost associated with exhaustive search batch processing.

Benchmarking Range-Dependent Propagation Modeling in Matched-Field Inversion

This paper considers how the accuracy of range-dependent propagation modeling affects the results of matched-field inversion (MFI) for seabed geoacoustic parameters. In MFI, the forward problem of computing the acoustic fields associated with candidate geoacoustic models is solved a large number of times. Given significant mismatch due to measurement and theory errors, together with the computationally intensive nature of MFI, the appropriate tradeoff between modeling accuracy and computational speed is not obvious. This tradeoff is considered here in terms of the degradation in information content for the geoacoustic parameters that results from inaccurate propagation modeling. The information content is quantified using the marginal posterior probability distributions of the geoacoustic parameters, as computed from a fast Gibbs sampling approach to Bayesian inversion. A synthetic example of this analysis is presented in which the parabolic equation is used to model acoustic fields for a shallow-water, upslope environment, with different levels of modeling accuracy/speed controlled by the range and depth step sizes of the computational grid.

BENCHMARKING RANGE-DEPENDENT PROPAGATION MODELING IN MATCHED-FIELD INVERSION

This paper considers how the accuracy of range-dependent propagation modeling affects the results of matched-field inversion (MFI) for seabed geoacoustic parameters. In MFI, the forward problem of computing the acoustic fields associated with candidate geoacoustic models is solved a large number of times. Given significant mismatch due to measurement and theory errors, together with the computationally intensive nature of MFI, the appropriate tradeoff between modeling accuracy and computational speed is not obvious. This tradeoff is considered here in terms of the degradation in information content for the geoacoustic parameters that results from inaccurate propagation modeling. The information content is quantified using the marginal posterior probability distributions of the geoacoustic parameters, as computed from a fast Gibbs sampling approach to Bayesian inversion. A synthetic example of this analysis is presented in which the parabolic equation is used to model acoustic fields for a shallow-water, upslope environment, with different levels of modeling accuracy/speed controlled by the range and depth step sizes of the computational grid.

The SWAM'99 Workshop - An Overview

The SWAM'99 (Shallow Water Acoustic Modeling, 1999) workshop on the topic of benchmarking shallow water range-dependent propagation modeling was held in Monterey CA in September No specific benchmarks were generated. Rather, each participant offered his (her) Transmission Loss curves for comparison with other results. This overview article will: • discuss the six (6) test cases; • discuss each individual's contribution to this benchmarking effort (see the associated articles in this Special issue for full details); • conclude with suggestions for future efforts.

THE SWAM'99 WORKSHOP — AN OVERVIEW

The SWAM'99 (Shallow Water Acoustic Modeling, 1999) workshop on the topic of benchmarking shallow water range-dependent propagation modeling was held in Monterey CA in September No specific benchmarks were generated. Rather, each participant offered his (her) Transmission Loss curves for comparison with other results. This overview article will: • discuss the six (6) test cases; • discuss each individual's contribution to this benchmarking effort (see the associated articles in this Special issue for full details); • conclude with suggestions for future efforts.

Objective Functions for Ocean Acoustic Inversion Derived by Likelihood Methods

Selection of a suitable objective function is an integral part of the inverse problem, and poor selection can have a strong influence on the inverse result. Objective functions are here derived for many practical occasions such as for single frequency and broadband, with and without knowledge of source strength, and with and without the received signal phase. These objective functions are all derived from a unified approach based on maximum likelihood and additive Gaussian noise models. The assumptions for the objective function are thus clear and the resulting estimator has good properties. From a Bayesian point of view, the solution to the inverse problem is the a posteriori probability distribution of the unknown parameters, which can be found from the likelihood function. Thus using objective functions based on likelihood functions facilitates computing the a posteriori distributions.

The coupled mode parabolic equation

The coupled mode parabolic equation (PE) is a generalization of the adiabatic mode PE that includes mode coupling terms. It is practical to apply this approach to large-scale problems involving coupling of energy between both modes and azimuths. The solution is expressed in terms of the normal modes and mode coefficients, which satisfy coupled horizontal wave equations. The coupled mode PE may be solved efficiently with the splitting method. The first step is equivalent to solving the adiabatic mode PE over one range step. The second step involves the integration of the coupling term. The coupling mode PE solution conserves energy, which is an important aspect of a range-dependent propagation model. The derivation of the coupled mode PE, which involves completing the square of an operator, is related to the derivation of an adiabatic mode PE that accounts for ambient flow. Examples are presented to illustrate the accuracy of the coupled mode PE.

Gaussian ray bundles for simulating shallow-water torpedo reverberation

A range-dependent propagation model was developed to simulate shallow-water torpedo reverberation. The model is based on Gaussian ray bundles in the form ‖P(r,z)‖2=[β/√2πσ(r)prr]exp(−0.5[(z−zr)/ σ(r)]2), where r is the horizontal range from the source to the field point, z is the vertical depth of the field point, zr is the vertical depth along a central ray, pr is the horizontal slowness along a central ray, β depends on the source, and σ(r) is an effective standard deviation given by σ(r)=(1/2)max(Δzr,8λ). Here, Δzr is the vertical distance between two adjacent rays and λ is the wavelength at the field point. [Work supported by the Naval Sea Systems Command (PMS-402 and PMS-406) and the Office of Naval Research (ONR-321).]

Deterministic reverberation from ocean ridges

The deterministic relationship between low-frequency reverberation and detailed geomorphology is documented for wide-area insonifications of the western Mid-Atlantic Ridge. Charted reverberation registers precisely with extended ridges and has a high correlation with negative transmission loss, confirming previous analysis with lower resolution data [J. Acoust. Soc. Am. 95, 1865–1881 (1993)]. For a given ridge, prominent returns come from steep escarpments and cliffs that face the bistatic source and receiving arrays. This was hypothesized in the above reference, but could not be proven without the higher resolution waveforms and more sophisticated charting procedures of the present analysis. Monostatic and bistatic returns from the same lineated ridge at 1/2, 11/2, and 21/2 convergence-zone ranges are used to thoroughly document the registration with steep scarps. A decrease in resolution of the scattering site is also documented for increasing measurement range. Ambiguity from the horizontal receiving array is resolved by two independent methods that show close agreement for prominent returns. The first is an environmental symmetry breaking (ESB) technique that requires detailed knowledge of bathymetry to be incorporated into a range-dependent propagation model. The second is a global inversion of reverberation charts obtained from differing receiving-array locations and orientations. The global inversion requires no a priori environmental information and has not been previously applied to field data.

The Lorentz reciprocity theorem and range-dependent propagation modeling

Modeling of electromagnetic propagation in the troposphere has been advanced in the last decade to the point where both the vertical and horizontal variation of refractivity can be accommodated readily. A hybrid ray-optics/parabolic equation model is utilized to predict propagation loss for a range-varying refractive structure to demonstrate the model obeys the Sommerfeld-Pfrang statement of the Lorentz reciprocity theorem. >

Inverting, imaging, and mapping ocean-basin reverberation onto high-resolution bathymetry

The objective of this paper is to determine the relationship between low-frequency ocean-basin reverberation and bathymetry. Long-range reverberation data acquired on the western flank of the Mid-Atlantic Ridge (MAR) are mapped onto high-resolution bathymetry. Since reverberation was measured via horizontally towed line array, there is a ‘‘right–left’’ ambiguity about the array’s axis and a decrease in resolution for off broadside beams and more distant returns. These ambiguities make an objective correlation between reverberation and bathymetry difficult. Therefore, an optimization procedure has been applied for eliminating the right–left ambiguity and maximizing resolution by simultaneously inverting data taken with differing array locations and orientations. Combined with range-dependent propagation modeling, the images show that distant reverberation is significant when the intermediate propagation path is free from bottom interaction. Since the experiment site is primarily bottom-limited, such paths are not abundant, and a sparse azimuthal distribution of strong returns at convergence zone intervals is often found. In general, strong returns coincide with prominent bathymetric features, such as abyssal hillsides. However, such correlations must be made judiciously because the azimuthal resolution of distant returns is often on the order of the width and separation between ridges in the MAR’s continuously rugged bathymetry.