The subject of underwater acoustic modeling deals with the translation of our physical understanding of sound in the sea into mathematical formulas solvable by computers. This book divides the subject of underwater acoustic modeling into three fundamental aspects: the physical principles used to formulate underwater acoustic models; the mathematical techniques used to translate these principles into computer models; and modeling applications in sonar technology and oceanographic research. The material presented here emphasizes aspects of the ocean as an acoustic medium. It shows mathematicians and physical scientists how to use this information to model the behavior of sound in a spatially complex and temporally variable ocean. This approach diminishes the need for discussions of engineering issues such as transducers, arrays and targets. Aspects of hardware design and modeling in underwater acoustics are discussed in other excellent texts. Recent developments in underwater acoustic modeling have been influenced by changes in global geopolitics. These changes are evidenced by strategic shifts in military priorities as well as by efforts to transfer defense technologies to non-defense applications.