``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 021394307
Email: 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
multidimensional 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, rangedependence,
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 nonlinear 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 basinscale 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:

Acoustic data assimilation. As argued above much stands to
be gained by coupling acoustic and oceanographic models. It will
enable concurrent progress in both disciplines. A number of issues
must be resolved before even tackling the assimilation problem. Data
formats and databases must be reconciled, possibly in a distributed
manner in order to preserve issues of data ownsership and
maintenance. The mutual resolution and sensitivities of acoustic and
oceanographic models must be understood. Acoustic models, to take the
simplest example, operate on a smaller scale and can be very sensitive
to the subgrid numerical noise of oceanographic model outputs. In
order to achieve proper model coupling, the transfer of signal and
noise between models and scales must be investigated using an adequate
stochastic framework. Once models are coupled, efficient algorithms
will be required in order to handle the increased computational
complexity as well as the significantly increased amount of data being
assimilated.

Objectoriented computing. All numerical modeling is
currently done on a procedural basis, most often in
Fortran. This separation of data and processing functions, while very
convenient for the direct implementation of relatively simple
numerical algorithms, has major and known defaults [1]. An
objectoriented methodology must be adopted when combining
crossdisciplinary computational modules in order to contain
unavoidable bugs and build reliable and maintainable
multidisciplinary computational systems integrating the different
physical mechanisms at play, as is the case in ocean data
assimilation. The use of objectoriented technique will further
benefit the development of hybrid threedimensional propagation
modeling techniques by facilitating the combination of existing
separate computation modules such as wavenumber integration and
boundary elements. Finally, the use of features such as operator
overloading enables the use of a metamodeling language, whereby the
scientist can optimally merge two data sets by simply ``adding'' them
and is then free to focus on scientific questions.

Distributed computing. Given the increasingly
multidisciplinary nature of ocean sciences including acoustics, future
ocean observing systems will combine a multitude of heterogeneous
assets which are distributed in nature. While acoustic data might be
acquired on a given node of a generalized observation network, a
mobile autonomous underwater vehicle (AUV) might acquire in situ
data at a different location, and oceanographic data might be gathered
at a third location. AUV navigation as well as realtime data
assimilation will entail a large amount of acoustic computations which
some nodes, such as the AUV, might not be able to handle. One can then
envision a distributed system in which a number of modeling
computational tasks are performed on a service basis by the relevant
nodes. This approach is also beneficial to MFP, which is an inherently
parallel approach. Distributed computing will require some measure of
encapsulation readily provided by objectoriented techniques.

Software metadata. In order to facilitate large scale
distributed computing as well as crossdisciplinary interaction among
the various ocean sciences, knowledge about existing numerical
prediction codes is required. It must list and quantify the actual
modeling assets available to the community as well as guide the choice
of a potentially inexperienced user. Software metadata would then
assist in the localization of all existing modeling assets relevant to
a given operational problem, for instance in the course of a realtime
environmental assessment exercise. The appropriate model would then be
used for the assimilation of data into a complete multidisciplinary
ocean model.

BuzziFerraris, G., Scientific C++  Building Numerical
Libraries the ObjectOriented Way, AddisonWesley, 1993.

Jensen, F. B., Kuperman, W. A., Porter, M. B., and Schmidt, H.,
Computational Ocean Acoustics, AIP, 1994.

Munk, W., Worcester, P., and Wunsch, C., Ocean Acoustic
Tomography,Cambridge University Press, 1995.

Tolstoy, A., Matched Field Processing for Underwater
Acoustics, World Scientific, Singapore, 1993.