``Computational Challenges in Ocean Acoustics''
Dr. Pierre Elisseeff, Prof. Nicholas M. Patrikalakis, and Prof. Henrik Schmidt
Massachusetts Institute of Technology, Department of Ocean Engineering
Cambridge, MA 02139-4307
E-mail: elisseef@mit.edu, nmp@mit.edu, henrik@keel.mit.edu
URL: http://dipole.mit.edu:8001/, http://deslab.mit.edu/DesignLab/poseidon/

The past two decades have provided an extremely fertile ground for computational ocean acoustics. Thanks to unprecedented developments in the availability of affordable computer power, the field has evolved from being a mere analytical branch of wave propagation physics to being a mature numerical discipline with original contributions of its own. The current computational techniques can be sorted, for the sake of simplicity, into three main branches: propagation models, scattering models, and inversion methods. A brief review of the more numerically mature techniques, namely propagation models and to some extent inversion methods, follows. Pending and upcoming computational challenges are then discussed.

Acoustic propagation numerical models rely on the same underlying multi-dimensional Fourier transform approach to the wave equation. Once the implicit analytical solution to the wave equation is put in integral form, the numerical scheme chosen to perform the integration will determine the type of propagation code: the stationary phase method yields the ray approach, the method of residues yields the normal mode approach, the direct trapezoidal integration rule yields the wavenumber integration approach. The parabolic equation approach stands aside, being based on a factorization of the wave equation differential operator. The reader is referred to [2] for a full discussion. All four classes of codes correspond to specific, partially overlapping regimes determined by parameters such as frequency, range-dependence, elasticity. Provided accurate environmental information is supplied, the appropriate numerical model will predict the acoustic field within a fraction of a decibel. Inversion techniques aim at measuring environmental or source parameters given some acoustic measurements. They can be viewed as a special class of data assimilation algorithms. The first inversion technique, Ocean Acoustic Tomography, is an adaptation of medical and seismic imaging schemes; it relies on a perturbational approach and assumes a good a priori knowledge of the environment [3]. It is the acoustic equivalent of objective analysis techniques used by oceanographers. The other inversion technique, Matched -Field Processing (MFP), leverages the accuracy of modern propagation models by computing a large number of simulated signals assuming different environmental parameters [4]. It then identifies the synthetic signal most closely correlated with the measured one, therefore inferring what the true environment is. MFP has proven to be a very fertile research ground, providing a truly original approach to non-linear inversion problems such as source localization and environmental estimation.

Computational ocean acoustics now stands at a threshold in the history of the discipline. Having to a large extent solved the forward (prediction) problem for a given deterministic environment, it is now severely limited in its ability to accurately represent, store and use complex environmental information for increasingly relevant scenarios such as coastal and basin-scale operations. Further computational bottlenecks include MFP and scattering studies. Environmental uncertainty is dealt with through the use of stochastic formulations, which require significant computational resources. On the other hand, acoustic waves are the only means of remotely sensing the depths of the ocean, and can provide oceanographers and students of the ocean in general with significantly more field data than what is currently available. Much stands to be gained by coupling acoustic and oceanographic models across disciplinary boundaries. The latter will gain access to vast amounts of untapped data and improve current ocean forecasts. The former will gain the much need environmental information necessary to understand and quantify propagation mechanisms and ultimately improve signal processing performance. Some of the computational challenges ocean acoustics will face in order to achieve this multidisciplinary convergence are:

  1. Buzzi-Ferraris, G., Scientific C++ -- Building Numerical Libraries the Object-Oriented Way, Addison-Wesley, 1993.
  2. Jensen, F. B., Kuperman, W. A., Porter, M. B., and Schmidt, H., Computational Ocean Acoustics, AIP, 1994.
  3. Munk, W., Worcester, P., and Wunsch, C., Ocean Acoustic Tomography,Cambridge University Press, 1995.
  4. Tolstoy, A., Matched Field Processing for Underwater Acoustics, World Scientific, Singapore, 1993.