It is shown in any elementary physics course that as electromagnetic waves travel through mediums of varying indices of refraction that the waves are refracted.  Development of this theory follows directly from considerations concerning the wave equation.  It would seem then that the phenomenon is characteristic of any physical system which exhibits travelling wave behavior such that the wave equation represents a viable model.  Specifically, acoustic waves travelling through stratified media are a prime example. 

            Theories of reflection and refraction for sound waves in stratified fluids are readily available.  However, only the simplest models are typically amenable to analytic solutions, and as such discussions of sound wave refraction often end there.  Unfortunately, nature rarely affords the luxury of being well modeled by textbook problems with pretty, closed form solutions.  My goal in creating this page is to produce a realistic ray trace model for relatively shallow ocean water exhibiting a widely varying sound speed profile, and to present my methods in a language that is not exclusive to seasoned acousticians.  To this end I argue that I have had some success.  However, I found that modeling acoustic wave transmission in the ocean is an incredibly rich field of study with encyclopedic volumes devoted to it.  Therefore, I present here my rudimentary model for consideration, well aware of the boundless room for improvement and higher order corrections.  I will discuss a few of these possibilities here, although the interested reader is encouraged to refer to the bibliography for details that lie beyond the scope of this text.