Starting Fields and Far Fields in Ocean Acoustics

摘要

In Section II the authors continue with their use of transmutation theory to show how these ideas may be implemented to use with the parallel approximations to the Helmholtz equation for a stratified media. In Section III a parabolic approximation to the fundamental singularity is derived and this used to obtain an integral representation for the solution in an exterior region. Such representations are useful for constructing starting fields. The integral representation is then used to construct a parametrix for the finite, variable index ocean. Section IV treats the far field in a uniform ocean of finite depth. In a finite ocean it is well-known that certain modes propagate, whereas the others attenuate. Hence, it is not surprising that an expression for the far field pattern is obtained which depends on just propagating modes.