bellhopmunk17degOcean Acoustics is the study of sound in the undersea environment. When an underwater object vibrates, it creates sound-pressure waves that travels throughout the ocean environment alternately compressing and decompressing water molecules. Maritime Way Scientific provides subject matter advice on the tactical and operational analysis of underwater sound. The Maritime Way team has a strong research and development activity in progressing and developing an operational ocean acoustic modeling system and decision aid for military and commercial uses.


Propagation Models: Each propagation model is based on a specific representation of the field that solves the linearized acoustic wave equation. The hierarchy of acoustic models is shown below in the figure below. We present the basic concepts underlying the various “standard” approaches to solving the wave equation. In particular, we focus on:

  • Transform Solutions (wavenumber integration, normal modes, multipath expansion),
  • Ray Solutions (overlap with multipath expansion techniques), and
  • Marching Solutions (parabolic equations).

These solution techniques are representative of the most widely used models in the underwater acoustics community (some representative model acronyms are given in the figure for each solution technique).


Available Acoustic Models.  Maritime Way has access and commonly uses the following acoustic models:

Normal Modes  –  The normal-mode method involves solving a depth-dependent equation which is precisely an unforced version of the equation solved in the wave-number integration technique.  The unforced problem has a set of modes of vibration which are roughly akin to the modes of a vibrating string. The “frequencies” of the vibration give the horizontal wave-numbers associated with the modal propagation.  The complete acoustic field is then constructed by summing the contributions of each of teh modes weighted in accordance to source depth.

POPP – POPP is a range-independent version of the PROLOSS normal-mode propagation model

Parabolic Equation  –  The PE method has now become the most popular wave-theory technique for solving range-dependent propagation problems in ocean-acoustics.  A detailed description of the derivation of the parabolic equation from the wave equation is given together with a description of a marching solution technique based on Fast Fourier Transforms (FFT). One of the advantages of the PE solution is the presentation of the acoustic field solution in range and depth (so called full field) which gives the user a clear and intuitive view of the strength of the propagation paths in range dependent environments.  The advantage of the PE solution (full field answers) is also its biggest disadvantage.  Its full field solution does not easily provide arrival angle intensity for beamforming, nor does it provide travel time information for temporal modeling, pulse propagation and reverberation modeling


Ray Theory  –  Ray methods are used in operational environments where speed is a critical factor and environmental uncertainty poses much more sever constraints on the attainable accuracy. As a rough guide, ray tracing is satisfactory when the wavelength is very much less than any of the length scales in the problem. As well as water depth, these length scales include bottom and surface roughness, the size of focal regions and the distance over which appreciable changes in sound speed occur.


Integral Transform

SAFARI – SAFARI is based on the wavenumber integration techniques (or fast-field program) to solve the wave equation exactly for strictly range-independent environments.