Modal Attenuation Coefficients Research Articles

Relationships between intrinsic sediment attenuation, modal attenuation, and transmission loss in experiments over sandy-silty sediments.

Numerous shallow water acoustic transmission experiments over sandy‐silty bottoms demonstrate that the frequency dependence of intrinsic sediment attenuation at frequencies less than 1 kHz is nonlinear. Computational analyses including modeled geoacoustic profiles have shown that good agreement with experimental data can be obtained for frequencies between 50 Hz and 1 kHz. Upper sediment attenuation values for 1 kHz are in ranges specified by Hamilton [J. Acoust. Soc. Am. 68, 1313–1340 (1980)], and a nonlinear frequency dependent attenuation with power‐law of about 1.8 is necessary. In this presentation, the relationship between the power‐law exponent and modal attenuation coefficients is quantified for several nearly range‐independent experiments in different locations. These include the Gulf of Mexico (1972), the Strait of Korea (ACT III, 1995), the New Jersey Shelf (1995), and Nantucket Sound (2005). The intrinsic sediment attenuation behavior with frequency and depth implies that modal attenuation coe...

Attenuation inversions using broadband acoustic sources.

Low-frequency attenuation data are widely scattered. The spread most likely reflects differences in sediment type, degree of consolidation, layering, as well as other causes of effective attenuation encountered during low-frequency field measurements. Moreover, attenuation varies with depth, and longer wavelengths, i.e., low frequencies, encounter deeper sediments with different properties. The assumption that the attenuation in the sediment is constant with depth often results in interpretations which give sediment attenuations with a frequency dependence different when depth variations are included in the sediment description. Low-frequency attenuation inversions using broadband acoustic data from different field experiments will be presented and compared. Compressional wave attenuation will be estimated using modal amplitude ratios. Variation of modal attenuation coefficients with frequency and depth will be discussed. [Work supported by the Office of Naval Research.]

Environmental effects on frequency behavior of modal attenuation coefficients for sandy bottoms

The modal attenuation coefficients (MACs) can be determined using a recent simplification of Biot theory [A.D. Pierce et al., J. Acoust. Soc. Am. 114, 2345 (2003)]. Numerical calculations use sandy bottom sediments and isospeed, linear, and piecewise linear water profiles, which are simplifications that preserve key features of those obtained in experiments off the New Jersey Shelf. The calculations indicate the importance of downward refracting profiles and the strength of near‐interface gradients for increasing energy loss. Principal characteristics of the MACs that are observed from the calculations include: increases with interface gradient, reordering of least attenuated modes, and variations of the frequency power‐law exponents of the MACs from f‐1 to f1 at frequencies up to 2 kHz. Evidence of the behavior observed in the calculations is in good agreement with previous analysis of results in Gulf of Mexico experiments [F. Ingenito, J. Acoust. Soc. Am. 53, 858‐‐863 (1973)], for profiles that were cla...

Attenuation and scattering of axisymmetrical modes in a fluid-filled round pipe with internally rough walls

The attenuation of axisymmetric eigenmodes in a cylindrical, elastic, fluid-filled waveguide with a statistically rough elastic wall is studied. It is shown that small perturbation theory can be used to relate explicitly the statistical characteristics of the internal wall surface roughness of an elastic pipe to the attenuation and scattering coefficients of the acoustic modes in the filling fluid. Analytical expressions for modal attenuation coefficients are obtained. The analysis of the frequency dependent attenuation coefficients and the ratio between the roughness correlation length and the inner radius of the pipe is made for different correlation functions of the roughness. It is shown that two scale parameters control the overall behavior of the modal attenuation coefficients. These are the ratios of the roughness correlation length and the inner pipe radius to the acoustic wavelength. The numerical results for sound propagation in a pipe and in a borehole with statistically rough, elastic walls are obtained and discussed.

Modal attenuation in metal-clad graded-index slab optical waveguides

The paper presents the influence of refractive profile shape on the distribution of modal attenuation in planar metal-clad optical waveguide structures. A calculation method has been presented in which we applied the Snyder–Love expression on modal attenuation coefficients and matrix method 4 × 4 for the analysis of planar waveguides. The obtained results are almost identical with the exact results for refractive profiles: the parabolic, exponential, Gaussian and linear ones. It has been demonstrated that the applied calculation method can be used in waveguides of any profiles of the refractive index.

Frequency variability of modal attenuation coefficients

The intrinsic sediment attenuation in adiabatic waveguides affects transmission loss through the modal attenuation coefficients (MACs). For sand-silt bottoms, the non-linear frequency dependence of attenuation in the upper sediment layer significantly affects the frequency variation of the MACs. This variation is shown to depend strongly on the water, and weakly on the upper sediment layer, sound-speed profiles. The MACs are calculated for a layered environmental model that permits good comparisons with values derived from experimental data in the Gulf of Mexico [Ferris, JASA, 82 (1972)]. The comparisons illustrate the dependence on measured water profiles. The rate of increase of transmission loss with range is conveniently measured by an effective attenuation coefficient. The relationship between this quantity and the MACs is known when one propagating mode dominates [Evans and Carey, JOE, 23 (1998)]. We describe the interesting connection for downward refracting profiles at mid-frequencies with multiple propagating modes. [Work partially supported by ONR.]

On the acoustic field in a Pekeris waveguide with attenuation in the bottom half-space

The acoustic field in a Pekeris channel with an attenuating basement is critically examined, based on contour integrations of the wave number integrals for the two domains. In both regions, the field consists of a finite sum of proper (square integrable) normal modes plus a branch line integral around a hyperbolic cut. For low bottom attenuation, only "trapped" modes exist but as the loss increases additional "dissipation" modes contribute to the mode sum. A Newton-Raphson iterative procedure is introduced for finding the complex eigenvalues of the modes and a new expression is derived which shows that the total number of proper (trapped plus dissipation) modes supported by the waveguide increases essentially linearly with rising bottom attenuation. Approximations for the complex shape functions of the modes in the water column and the basement are developed and compared with the exact shape functions determined from the Newton-Raphson procedure. An expression derived for the modal attenuation coefficient scales in proportion to the square of the mode number and inversely with the square of the frequency. Stationary-phase approximations for the branch line integrals for both domains are developed, which serve to illustrate the asymptotic range dependence of the lateral wave but otherwise have little utility.

Nighttime traffic noise in an urban environment

Traffic noise ducted near the ground at night and in the early morning can be represented simply in terms of normal modes. The effects of surface loss and atmospheric absorption, as well as meteorology, are contained in the mode attenuation coefficients. For a long (5–10 km) road section, the average noise levels are a function of the product of the mode attenuation coefficients and the perpendicular distance from the roadway. This paper considers a two-dimensional model for computing the effective mode attenuation coefficients in an urban environment. Modal attenuation is estimated by propagating modes over an irregular surface that approximates typical urban structures. The mode attenuation due to scattering from the urban structures is compared to the attenuation from atmospheric absorption and from a finite ground impedance. Predicted noise levels are compared to available data and the implications for nighttime urban traffic noise are discussed.

Dependence of modal attenuation coefficient frequency variation on upper sediment attenuation

The range-averaged transmission loss increase in shallow water propagation depends critically on the intrinsic attenuation of the upper sediment. The attenuation coefficients of low-frequency (<1 kHz) propagating modes determine the frequency dependence. Ingenito [J. Acoust. Soc. Am. 53, 858–863 (1973)] showed with measurements and theory that while individual mode attenuation coefficients decrease with frequency f, the sediment attenuation coefficient increases proportional to f1.75. When results from many other shallow-water transmission experiments (broadband and narrowband) over sandy-silty sediments are compared to numerical calculations, it is found that a nonlinear-frequency dependent attenuation is required with an exponent between 1.5 and 2. The question considered here is how the intrinsic upper-sediment attenuation produces such behavior. A recent simplification of the Biot model [A. D. Pierce et al., J. Acoust. Soc. Am. 114, 2345 (2003)] has a power-law exponent of two. With this frequency-dependent bottom attenuation, a two-layer Pekeris waveguide yields modal attenuation coefficients that decrease with frequency as observed by Ingenito. However, a depth-dependent attenuation profile or a third near-surface layer with requisite properties can reverse this behavior. This suggests why higher-frequency numerical computations may require nonlinear frequency-dependent sediment profiles to calculate sound transmission accurately. [Work partially supported by ONR.]

Attenuation in the sediment layers in East China Sea

Compressional wave attenuation in the frequency range 50 to 350 Hz is estimated using broadband data collected in the East China Sea. A time-frequency analysis provides amplitudes of individual modes which are used to estimate the modal attenuation coefficients. Different modes are sensitive to sediment properties at different depths and this mode-depth sensitivity is explored in a sensitivity study. Based on this sensitivity study attenuation in different layers of the sediments will be estimated using different modes which are sensitive at these depths. This is a variation of previous studies where different frequencies have been used to invert for different sediment parameters using sub-space approaches. This approach focuses the inversion to various layers (provided by the geophysical surveys at the site) of the sediment and hence presents a tool to describe the depth variations in the sediment. The attenuation versus frequency behavior of the different sediment layers will be discussed. [Work supported by ONR.]

Inversions for attenuation profiles using modal amplitude ratios

Data from the ASIAEX East China Sea (ECS) experiment is used to estimate sediment attenuation coefficients as a function of frequency and depth. Modal amplitude ratios for modes in the frequency range 10 to 300 Hz are used to obtain the attenuation profiles. These inversions use broad-band data from wide band sources (WBSs) deployed in the area. The modes are detected, identified and their amplitudes measured using a time-frequency wavelet analysis. A joint inversion for attenuation coefficient profile, water depth, source and receiver depths, range and empirical orthogonal functions in the water column is performed. This inversion differs from our earlier technique in that instead of modal attenuation coefficients we treat the attenuation coefficient profile as the primary unknown. This enables us to reduce the number of unknowns and hence allows us to use higher modes in the inversion. Data from many WBS charges will be used to estimate an average value for attenuation and its standard deviation. The results will be compared with core data and frequency and depth dependence will be examined. [Work supported by ONR.]

A simple normal-mode model for nighttime traffic noise

At night, traffic noise propagates to long distance via normal modes trapped near the ground in the sound duct created by surface cooling. Consequently, at distances of 500 m or more, traffic noise at any given location is the sum of contributions from many individual vehicles. To predict the band-averaged and time-averaged levels in such situations, one can use an incoherent sum of normal modes. Using an incoherent modal sum, we derive a simple analytic expression for the noise due to traffic on an infinitely long highway. For long highways (10–20 km), it is shown that the controlling factor in the noise propagation is not distance alone, but, instead, the product of the mode attenuation coefficients and the distance from the highway. The predictions for an infinitely long highway are compared with those for a highway of finite length and error bounds are given.

Frequency dependence of modal attenuation coefficients from a simplified Biot sediment model

Determination of the frequency behavior of modal attenuation coefficients is essential for estimation of propagation influences of poro-elastic sediments. A recent simplification of the Biot model [Pierce et al., J. Acoust. Soc. Am. 114, 2345 (2003)] provides an approach for this determination. For plane compressional waves in a homogeneous medium, the simplified theory reproduces the frequency-squared behavior of the full Biot model. However, data from a variety of shallow water locations suggests power-law exponents that are less than two. Inhomogeneities, particularly in the upper sediment layer, influence the frequency behavior. For a normally consolidated sediment (one never subjected to pressures higher than the current overburden pressure), depth profiles of porosity and sound speed can be estimated [Cederberg et al., J. Acoust. Soc. Am. 97, 2754–2766 (1995)]. We use these profiles to investigate the frequency behavior of the modal attenuations. Comparisons are provided with observations as well as previous numerical studies. [Work supported by ONR.]

Acoustic Mode Coupling by Nonlinear Internal Wave Packets in a Shelfbreak Front Area

A computational case study of coupled-mode 400-Hz acoustic propagation over the distance 27 km on the continental shelf is presented. The mode coupling reported here is caused by lateral gradients of sound-speed within packets of nonlinear internal waves, often referred to as solitary wave packets. In a waveguide having unequal attenuation of modes, directional exchange of energy between low- and high-loss modes, via mode coupling, can become time dependent by the movement of waves and can cause temporally variable loss of acoustic energy into the bottom. Here, that bottom interaction effect is shown to be sensitive to stratification conditions, which determine waveguide properties and, in turn, determine modal attenuation coefficients. In particular, time-dependent energy loss due to the presence of moving internal wave packets is compared for waveguides with and without a frontal feature similar to that found at the shelfbreak south of New England. The mean and variability of acoustic energy level 27 km distant from a source are shown to be altered in a first order way by the presence of the frontal feature. The effects of the front are also shown to be functions of source depth.

Attenuation inversions in the East China Sea

Data from the ASIAEX East China Sea (ECS) experiment is used to estimate sediment attenuation coefficients as a function of frequency and depth. The ECS experiment offers a number of independent measures of sediment parameters using seismic and chirp surveys, gravity and piston cores and historic data. Modal amplitude ratios for modes 1 to 3 are used to obtain the modal attenuation coefficient and attenuation profiles. These inversions use broad-band data from Wide Band Sources (WBS) in the frequency range 20–100 Hz. The modes are detected, identified and their amplitudes measured using a time–frequency wavelet analysis. A joint inversion for modal attenuation coefficients, water depth, source and receiver depths, range and Empirical Orthogonal Functions in the water column is performed. The results will be compared with core data and frequency and depth dependence will be examined. [Work supported by ONR.]

Inversion for sediment geoacoustic properties at the New England Bight

This article discusses inversions for bottom geoacoustic properties using broadband acoustic signals obtained from explosive sources. Two different inversion schemes for estimating the compressional wave speeds and attenuation are presented in this paper. In addition to these sediment parameters, source-receiver range is also estimated using the arrival time data. The experimental data used for the inversions are SUS charge explosions acquired on a vertical hydrophone array during the Shelf Break Primer Experiment conducted south of New England in the Middle Atlantic Bight in August 1996. The modal arrival times are extracted using a wavelet analysis. In the first inversion scheme, arrival times corresponding to various modes and frequencies from 10 to 200 Hz are used for the inversion of compressional wave speeds. A hybrid inversion scheme based on a genetic algorithm (GA) is used for the inversion. In an earlier study, Potty et al. [J. Acoust. Soc. Am. 108(3), 973-986 (2000)] have used this hybrid scheme in a range-independent environment. In the present study results of range-dependent inversions are presented. The sound speeds in the water column and bathymetry are assumed range dependent, whereas the sediment compressional wave speeds are assumed range independent. The variations in the sound speeds in the water column are represented using empirical orthogonal functions (EOFs). The replica fields corresponding to the unknown parameters were constructed using adiabatic theory. In the second inversion scheme, modal attenuation coefficients are calculated using modal amplitude ratios. The ratios of the modal amplitudes are also calculated using time-frequency diagrams. A GA-based inversion scheme is used for this search. Finally, as a cross check, the computed compressional wave speeds along with the modal arrival times were used to estimate the source-receiver range. The inverted sediment properties and ranges are seen to compare well with in situ measurements and historical data.

Analytic expressions for time-domain forward propagation through a waveguide with random inhomogeneities including causality and dispersion relations

Analytic expressions in the time domain are derived for the mean forward field propagated through a waveguide containing random volume and surface inhomogeneities. The results are expressed in terms of the modal attenuation and dispersion coefficients in a waveguide [P. Ratilal and N. C. Makris, 112, 2403 (2002)]. Simulations in a shallow-water waveguide containing bubbles for a finite-time duration pulse show that the scattering leads to additional time delay and distortion of the signal waveform. Stationary phase approximations are also applied to represent the time-domain field in terms of the modal group velocities that are smaller than those in a waveguide without inhomogeneities. We show that the dispersion and attentuation effects cannot be explained by heuristic results based on an effective medium sound speed computed using bulk moduli and volume fractions since it does not account for scattering from inhomogeneities in the medium. The time-domain expressions for the forward propagated field obey causality and are consistent with Kramer–Kronig relations when used in their range of validity.

Covariance of the forward propagated field through a waveguide containing random inhomogeneities

Analytic expressions are derived for the spatial covariance of the field from a point source after forward propagation though a waveguide containing random surface and volume inhomogeneities. It is shown that the depth-averaged second moment and expected power of the forward propagated field can be obtained analytically. The mean forward propagated field has also been obtained analytically in terms of modal attenuation and dispersion coefficients in a waveguide [P. Ratilal and N. C. Makris 112, 2403 (2002)]. The covariance between two receiver depths of the forward propagated field through the entire random medium can then be determined by invoking the equi-partition of modal energy after significant multiple scattering. It is expressible as a sum of modal covariance terms. Each term depends on (1) the modal extinction cross-section [P. Ratilal and N. C. Makris, 110, 2924–2945 (2001)] of an expected elemental inhomogeneity of the medium, and (2) the scatter function variance of an elemental inhomogeneity which couples each mode to all the other modes.

Propagation through a stratified ocean wave guide with random volume and surface inhomogeneities, Part I. Theory: Attenuation, dispersion, and acoustic mirages

Analytic expressions for the mean field propagated through a stratified ocean with random volume or sufrace inhomogeneities of arbitrary size compared to the wavelength are derived from a wave guide scattering model stemming from Green’s theorem. It is found that multiple scattering through inhomogeneities in the forward direction can be succinctly expressed in terms of modal attenuation and dispersion coefficients under widely satisfied conditions. The inhomogeneities can have an arbitrary distribution in depth so that the model can realistically apply to scattering from internal waves, bubbles, fish, seafloor and seasurface roughness as well as sub-bottom anomalies. An understanding of the coherence of the forward scattered field can be gained by analogy with the formation of optical mirages in low-grazing angle forward scatter from random surfaces.

Application of Davidenko's method to a lossy nonlinear waveguide

Davidenko's method is implemented for determining the complex propagation constants (Modal index and attenuation coefficient) of nonlinear TE waves guided by an asymmetrical lossy nonlinear dielectric wave-guide. The waveguide structure has a generalized nonlinear substrate with a permittivity of the form ɛ ∼ | E |δand an absorbing cover making the propagation constant to be complex. Davidenko's method shows to be a fast and accurate analysis in finding the complex propagation constants. The effects of initial condition parameter on the propagation characteristics are investigated, analyzed and discussed.