Parabolic approximations for underwater sound propagation

Several alternative parabolic approximations to the reduced wave equation and their numerical solution are investigated for underwater acoustics applications. Parabolic approximations are derived by splitting the wave equation into transmitted and reflected components. An exact splitting operator is found, and further parabolic approximations for the transmitted fields are based on approximations to this operator. For the case of a range-independent environment, the resulting parabolic approximations are compared with normal-mode theory. The efficiency with which numerical results can be obtained is discussed, and an example of propagation from shallow to deep water is given. Subject Classification: 30.20; 20.15, 20.40.