Accession Number:



Reciprocity in Vector Acoustics

Descriptive Note:

[Technical Report, Master's Thesis]

Corporate Author:

Naval Postgraduate School

Personal Author(s):

Report Date:


Pagination or Media Count:



The scalar reciprocity equation commonly stated in underwater acoustics relates pressure fields and monopole sources. It is often used to predict the pressure measured by a hydrophone for multiple source locations by placing a source at the hydrophone location and calculating the field everywhere for that source. That method, however, does not work when calculating the orthogonal components of the velocity field measured by a fixed receiver. This thesis derives a vector-scalar reciprocity equation that accounts for both monopole and dipole sources. This equation can be used to calculate individual components of the received vector field by altering the source type used in the propagation calculation. This enables a propagation model to calculate the received vector field components for an arbitrary number of source locations with a single model run for each received field component instead of requiring one model run for each source location. Application of the vector-scalar reciprocity principle is demonstrated with analytic solutions for a range-independent environment and with numerical solutions for a range-independent and a range-dependent environment using a parabolic equation model.


Subject Categories:

  • Numerical Mathematics

Distribution Statement:

[A, Approved For Public Release]