Practical Spreading Laws: the Snakes and Ladders of Shallow Water Acoustics

  • Michael A. Ainsliea, Peter H. Dahlb, Christ A. F. de Jonga, Robert M. Lawsc, Michael A. Ainslie
  • Published 2014


Geometrical spreading laws are widely used in underwater acoustics because they provide if chosen carefully an accuracy that is sufficient for many applications (source characterisation, impact assessment, sound mapping, regulation) for negligible computation time. The simplest and most widely used form is that corresponding to spherical spreading, with propagation loss, PL(R) = 20log10R dB, which can provide a suitable approximation for deep water. In shallow water, propagation is influenced by multiple reflections from the seabed and sea surface, and a modification is then needed. The resulting effect depends on the kind of source (e.g., continuous or transient) and its directivity (e.g., monopole or dipole). The result often simplifies to the form PL(R) = (A + Blog10R) dB, where the values of A and B depend on the conditions. If the source level is known, the received SPL can then be calculated for a continuous source using sound pressure level, SPL(R) = SL – PL(R) = SL – (A + Blog10R) dB, but the expected behaviour depends on source directivity, so the values of A and B need to be adjusted accordingly. For a transient source, there are no simple expressions for sound pressure level, but the sound exposure level can be related in a similar way to the energy source level. Guidance is provided for the choice of A and B in shallow water for different activities, including seismic surveys, shipping, explosions, pile driving and use of active sonar. Guidance is also offered on where not to use these simple rules, such as for the calculation of SPL for short transient sources and the pitfalls associated with applying far-field concepts such as source level to distributed sources such as pile drivers.

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Cite this paper

@inproceedings{Ainsliea2014PracticalSL, title={Practical Spreading Laws: the Snakes and Ladders of Shallow Water Acoustics}, author={Michael A. Ainsliea and Peter H. Dahlb and Christ A. F. de Jonga and Robert M. Lawsc and Michael A. Ainslie}, year={2014} }