Far-field analytical solutions of the non-homogeneous Helmholtz and wave equations for spatially non-localized sources.

Non-localized impulsive sources are ubiquitous in underwater acoustic applications. However, analytical expressions of their acoustic field are usually not available. In this work, far-field analytical solutions of the non-homogeneous scalar Helmholtz and wave equations are developed for a class of spatially extended impulsive sources. The derived expressions can serve as benchmarks to verify the accuracy of numerical solvers.

Broadband transmission losses and time dispersion maps from time-domain numerical simulations in ocean acoustics.

In this letter, a procedure for the calculation of transmission loss maps from numerical simulations in the time domain is presented. It can be generalized to arbitrary time sequences and to elastic media and provides an insight into how energy spreads into a complex configuration. In addition, time dispersion maps can be generated. These maps provide additional information on how energy is distributed over time. Transmission loss and time dispersion maps are generated at a negligible additional computational cost. To illustrate the type of transmission loss maps that can be produced by the time-domain method, the problem of the classical two-dimensional upslope wedge with a fluid bottom is addressed. The results obtained are compared to those obtained previously based on a parabolic equation. Then, for the same configuration, maps for an elastic bottom and maps for non-monochromatic signals are computed.

An immersed interface method for the solution of the standard parabolic equation in range-dependent ocean environments.

A numerical approach for the treatment of irregular ocean bottoms within the framework of the standard parabolic equation is proposed. The present technique is based on the immersed interface method originally developed by LeVeque and Li [(1994). SIAM J. Numer. Anal. 31(4), 1019-1044]. The method conserves energy to high order accuracy and naturally handles generic range-dependent bathymetries, without requiring any additional specific numerical procedure. An illustration of its capabilities is provided by solving the well-known wedge problem.

An axisymmetric time-domain spectral-element method for full-wave simulations: Application to ocean acoustics.

The numerical simulation of acoustic waves in complex three-dimensional (3D) media is a key topic in many branches of science, from exploration geophysics to non-destructive testing and medical imaging. With the drastic increase in computing capabilities this field has dramatically grown in the last 20 years. However many 3D computations, especially at high frequency and/or long range, are still far beyond current reach and force researchers to resort to approximations, for example, by working in two dimensions (plane strain) or by using a paraxial approximation. This article presents and validates a numerical technique based on an axisymmetric formulation of a spectral finite-element method in the time domain for heterogeneous fluid-solid media. Taking advantage of axisymmetry enables the study of relevant 3D configurations at a very moderate computational cost. The axisymmetric spectral-element formulation is first introduced, and validation tests are then performed. A typical application of interest in ocean acoustics showing upslope propagation above a dipping viscoelastic ocean bottom is then presented. The method correctly models backscattered waves and explains the transmission losses discrepancies pointed out in F. B. Jensen, P. L. Nielsen, M. Zampolli, M. D. Collins, and W. L. Siegmann, Proceedings of the 8th International Conference on Theoretical and Computational Acoustics (ICTCA) (2007). Finally, a realistic application to a double seamount problem is considered.

A perfectly matched layer for fluid-solid problems: Application to ocean-acoustics simulations with solid ocean bottoms.

A time-domain Legendre spectral-element method is described for full-wave simulation of ocean acoustics models, i.e., coupled fluid-solid problems in unbounded or semi-infinite domains, taking into account shear wave propagation in the ocean bottom. The technique can accommodate range-dependent and depth-dependent wave speed and density, as well as steep ocean floor topography. For truncation of the infinite domain, to efficiently absorb outgoing waves, a fluid-solid complex-frequency-shifted unsplit perfectly matched layer is introduced based on the complex coordinate stretching technique. The complex stretching is rigorously taken into account in the derivation of the fluid-solid matching condition inside the absorbing layer, which has never been done before in the time domain. Two implementations are designed: a convolutional formulation and an auxiliary differential equation formulation because the latter allows for implementation of high-order time schemes, leading to reduced numerical dispersion and dissipation, a topic of importance, in particular, in long-range ocean acoustics simulations. The method is validated for a two dimensional fluid-solid Pekeris waveguide and for a three dimensional seamount model, which shows that the technique is accurate and numerically long-time stable. Compared with widely used paraxial absorbing boundary conditions, the perfectly matched layer is significantly more efficient at absorbing both body waves and interface waves.

Some illustrative examples of the use of a spectral-element method in ocean acoustics.

Some numerical results in the time domain obtained with the spectral-element method are presented in order to illustrate the high potential of this technique for modeling the propagation of acoustic waves in the ocean in complex configurations. A validation for a simple configuration with a known solution is shown, followed by some simulations of the propagation of acoustic waves over different types of ocean bottoms (fluid, elastic, and porous) to emphasize the wide variety of media that can be considered within the framework of this method. Finally, a movie illustrating upslope propagation over a viscoelastic wedge is presented and discussed.

Wavefield extraction using multi-channel chirplet decomposition.

In acoustical and seismic fields, wavefield extraction has always been a crucial issue to solve inverse problem. Depending on the experimental configuration, conventional methods of wavefield decomposition might no longer likely to hold. In this paper, an original approach is proposed based on a multichannel decomposition of the signal into a weighted sum of elementary functions known as chirplets. Each chirplet is described by physical parameters and the collection of chirplets makes up a large adaptable dictionary, so that a chirplet corresponds unambiguously to one wave component.