The ray trace equations provide a powerful tool for tracking the direction of propagation of high frequency acoustic waves in water.  The refraction and reflection diagrams generated by my model are in good keeping with previous models such as those presented by Jensen et al.  In general, however, the ray trace method provides only a skeletal frame of the acoustic field for a point source [5].  A more complete model should take into account amplitude attenuation, the trajectories of low frequency waves, transmission at boundary interfaces, etc.  However, numerical integration of the ray equations provides a great deal of insight into the behavior of acoustic waves in a continuously stratified  fluid that it usually not available through analytic expressions.  Furthermore, because the sound speed and any other continuously varying parameters must be continually updated throughout the integration, and since frequent checks must be made to determine if the trajectory has reached a boundary, the number of computations to produce a more complete model quickly becomes prohibitive.  Therefore, even in much more comprehensive models considerable simplifications are often made to the pertinent equations [5].  As a closing remark, I encourage the interested reader to consider improvements that might be made upon the model presented here and compare with the algorithms discussed by Jensen et al, Etter, and the myriad other excellent resources on the subject [5][8].  There are plenty of open questions in oceanographic acoustics to entertain any scholar or hobbyist.