Guy V. Norton

Including dispersion and attenuation directly in the time domain for wave propagation in isotropic media

When sound propagates in a lossy fluid, causality dictates that in most cases the presence of attenuation is accompanied by dispersion. The ability to incorporate attenuation and its causal companion, dispersion, directly in the time domain has received little attention. Szabo [J. Acoust. Soc. Am. 96, 491-500 (1994)] showed that attenuation and dispersion in a linear medium can be accounted for in the linear wave equation by the inclusion of a causal convolutional propagation operator that includes both phenomena. Szabos work was restricted to media with a power-law attenuation. Waters et al. [J. Acoust. Soc. Am. 108, 2114-2119 (2000)] showed that Szabos approach could be used in a broader class of media. Direct application of Szabos formalism is still lacking. To evaluate the concept of the causal convolutional propagation operator as introduced by Szabo, the operator is applied to pulse propagation in an isotropic lossy medium directly in the time domain. The generalized linear wave equation containing the operator is solved via a finite-difference-time-domain scheme. Two functional forms for the attenuation often encountered in acoustics are examined. It is shown that the presence of the operator correctly incorporates both, attenuation and dispersion.

A model for variations in the range and depth dependence of the sound speed and attenuation induced by bubble clouds under wind-driven sea surfaces

When modeling sound propagation through the uppermost layers of the ocean, the presence of bubble clouds cannot be ignored. Their existence can convert a range-independent sound propagation problem into a range-dependent one. Measurements show that strong changes in sound speed and attenuation are produced by the presence of swarms of microbubbles which can be depicted as patchy clouds superimposed on a very weak background layer. While models suitable for use in acoustic calculations are available for the homogeneous bubble layer (which results from long time averages of the total bubble population), no similar parameterizations are available for the more realistic inhomogeneous bubble layer. Based on available information and within the framework of a classification scheme for bubble plumes proposed by Monahan, a model for the range and depth dependence of the bubbly environment is developed to fill this void. This model, which generates a possible realization of the bubbly environment, is then used to calculate the frequency-dependent change in the sound speed and attenuation induced by the presence of the bubble plumes. Time evolution is not addressed in this work.

The impact of the background bubble layer on reverberation‐derived scattering strengths in the low to moderate frequency range

The impact that a near‐surface, range‐independent background or persistent bubble layer may have on the derivation of sea surface backscattering strengths from reverberation measurements is examined. A simple ray model is proposed to account for the refractive and attenuating effects of the bubble layer and is used to calculate the modified insonification of the air–sea interface. This simple approach is validated against a highly accurate numerical solution. Scattering at the interface is handled via first order small perturbation theory. The combined propagation/scattering model is exercised in the low‐ to moderate‐frequency range in order to examine bubble‐induced modifications to sea surface backscatter calculations. Results indicate that the refractive effects due to the background bubble layer significantly enhance scattering levels as a function of wind speed. Furthermore, reasonable variations in the background bubble spectrum are shown to yield scattering levels that compare quite well with explo...

An evaluation of the Kirchhoff approximation in predicting the axial impulse response of hard and soft disks

To test the ability of the Kirchhoff approximation for estimating the various components in the near‐field impulse response of a circular disk, the predictions from a time domain formulation of the Helmholtz–Kirchhoff solution [Trorey, Geophys. 35, 762–864 (1970)] are benchmarked against results obtained via the Fourier synthesis of highly accurate frequency domain solutions [Kristensson and Waterman, J. Acoust. Soc. Am. 72, 1612–1625 (1982)]. In these numerical experiments, a collocated point source and receiver lie on the symmetry axis of an acoustically hard (rigid) or soft (pressure release) disk. A time‐domain analysis is carried out in order to unambiguously evaluate the Kirchhoff approximation for different components of the scattered field. It is found that, while Helmholtz–Kirchhoff predicts the correct reflected component, it fails to accurately predict the strength of the diffracted component. The magnitude of the error depends on whether the disk is soft or hard and on the source/receiver heig...

The effect of sea‐surface roughness on shallow water waveguide propagation: A coherent approach

Standard propagation models in underwater acoustics (e.g., normal modes, PE) are deterministic in nature, i.e., they deal with a single realization of the environment. Additionally, for mathematical reasons, they typically treat the sea surface as a flat pressure‐release surface. Effects of sea surface and bottom roughness are incorporated through a loss mechanism. This is accomplished by including an additional attenuation factor based on coherent loss of the surface‐interacting component of the propagating field. This type of correction presents a mathematically inconsistent model, since usually results from stochastic scattering models are applied to results from single realizations of the stochastic medium. Moreover, scattering kernels are generally derived assuming a homogeneous medium underlying the sea surface, an assumption incompatible with a realistic environment. Using a numerical model [Norton et al., J. Acoust. Soc. Am. 97, 2173–2180 (1995)] that combines a high fidelity Parabolic Equation pr...

Coupling scattering from the sea surface to a one‐way marching propagation model via conformal mapping: Validation

Propagation models in underwater acoustics usually incorporate sea surface scattering effects in an ad hoc manner which in most cases requires making severe approximations. In particular, to include in a coherent manner in a marching acoustic propagation model the scattering that occurs at a rough sea surface poses a serious problem. Dozier [J. Acoust. Soc. Am. 75, 1415–1432 (1984)] introduced a rigorous approach in the framework of the split‐step parabolic equation model, which used a sequence of conformal mappings to flatten segments of the sea surface locally. Each conformal mapping preserved the elliptic form of the wave equation. In each transformed space the parabolic approximation is made and the solution advanced one range step. The method has the attractive feature of handling surface roughness within a propagation model in a mathematically consistent manner, including refraction and multiple surface interactions when and where they occur. In this work the technique developed by Dozier is impleme...

On the relative role of sea-surface roughness and bubble plumes in shallow-water propagation in the low-kilohertz region

In the low-kilohertz frequency range, acoustic transmission in shallow water deteriorates as wind speed increases. Although the losses can be attributed to two environmental factors, the rough sea surface and the bubbles produced when breaking- or spilling waves are present, the relative role of each is still uncertain. For simplicity, in terms of an average bubble population, the time- and space-varying assemblage of microbubbles is usually assumed to be uniform in range and referred to as “the subsurface bubble layer.” However the bubble population is range- and depth-dependent. In this article, results of an experiment [Weston et al., Philos. Trans. R. Soc. London, Ser. A 265, 507–606 (1969)] involving fixed source and receivers, and observations during an extended period of time under varying weather conditions are re-examined by exercising a numerical model that allows for the dissection of the problem. Calculations are made at 2- and 4-kHz. It is shown that at these frequencies and at wind speeds ca...

The impulse response of an aperture: Numerical calculations within the framework of the wedge assemblage method

A numerical calculation technique applicable to arbitrary aperture shapes on which Dirichlet (soft) or Neumann (hard) boundary conditions exist is described. The method is based on a generalization of the wedge assemblage (WA) method to fully two‐dimensional surfaces and yields the impulse response directly. Benchmark tests of the technique are conducted for the case of a circular aperture. The results are in near perfect agreement with the reference solution (provided by a T‐matrix code). In addition to a solid validation of the extended WA method, it is shown in this paper that multiple scattering effects can be accurately included. Finally, the physical insight that the WA method offers is demonstrated through its ability to completely and accurately dissect the scattered field into reflected, diffracted, and multiple diffracted components.

INCLUDING DISPERSION AND ATTENUATION IN TIME DOMAIN MODELING OF PULSE PROPAGATION IN SPATIALLY-VARYING MEDIA

Modeling of acoustic pulse propagation in nonideal fluids requires the inclusion of attenuation and its causal companion, dispersion. For the case of propagation in a linear, unbounded medium Szabo developed a convolutional propagation operator which, when introduced into the linear wave equation, accounts for attenuation and causal dispersion for any medium whose attenuation possesses a generalized Fourier transform. Utilizing a one dimensional Finite Difference Time Domain (FDTD) model Norton and Novarini showed that for an unbounded isotropic medium, the inclusion of this unique form of the convolutional propagation operator into the wave equation correctly carries the information of attenuation and dispersion into the time domain. This paper addresses the question whether or not the operator can be used as a basic building block for pulse propagation in a spatially dependent dispersive environment. The operator is therefore used to model 2-D pulse propagation in the presence of an interface separating two dispersive media. This represents the simplest description of a spatially dependent dispersive media. It was found that the transmitted and backscattered fields are in excellent agreement with theoretical expectations demonstrating the effectiveness of the local operator to model the field in spatially dependent dispersive media. [Work supported by ONR/NRL.]

Finite-difference time-domain simulation of acoustic propagation in dispersive medium: An application to bubble clouds in the ocean

Abstract Accurate modeling of pulse propagation and scattering is a problem in many disciplines (i.e. electromagnetics and acoustics). For the case of an acoustic wave propagating in a two-dimensional non-dispersive medium, a routine 2nd order in time and space Finite-Difference Time-Domain (FDTD) scheme representation of the linear wave equation can be used to solve for the acoustic pressure. However when the medium is dispersive, one is required to take into account the frequency dependent attenuation and phase speed. Until recently to include the dispersive effects one typically solved the problem in the frequency domain and not in the time domain. The frequency domain solutions were Fourier transformed into the time domain. However by using a theory first proposed by Blackstock [D.T. Blackstock, J. Acoust. Soc. Am. 77 (1985) 2050. [1] ], the linear wave equation has been modified by adding an additional term (the derivative of the convolution between the causal time-domain propagation factor and the acoustic pressure) that takes into account the dispersive nature of the medium. In the case of acoustic propagation through water, the water environment becomes strongly dispersive due to the presence of air bubbles that are present below the air–water interface.