On the Calculation of Ray-Acoustic Intensity

A procedure is described by which ray-acoustic intensity due to a point source in a horizontally uniform medium can be calculated with a digital computer. The process includes a curve-fitting technique applied to velocity-of-sound data, the numerical integration of two sets of two simultaneous ordinary differential equations, the imposition of boundary conditions at reflecting surfaces, and the application of recurrence relationships relating partial derivatives within the first ray path cycle to those at ranges beyond the first cycle. For media with horizontal boundaries it is shown how the required numerical integration can be reduced greatly through use of the symmetries of the ray path. It is shown that significant errors can be introduced to the numerical process through discontinuities in derivatives of the sound-velocity profile. Consideration is given to the propagation of such errors. The error-propagating characteristics of recurrence relationships for intensity are considered also. A curve-fitting technique is described which ensures continuity of the third derivative of the sound velocity and which produces profiles without the extraneous undulations so often introduced by other procedures. It is demonstrated how intensity can be affected greatly by small changes in the sound-velocity profile.