Modifying the sound-speed profile to improve the accuracy of the parabolic-equation technique.

The parabolic-equation technique has received considerable attention since its introduction to the underwater-sound community by Tappert and Hardin three years ago. The technique relies upon removing the primary radial dependence of the acoustic field from the elliptic wave equation, and approximating the resulting equation with a parabolic (or Schroedinger) equation which may then be rapidly solved on digital computers. The parabolic approximation has been shown for layered media to result in an error in the phase velocity of the normal modes. In underwater-sound propagation the phase-velocity error can cause substantial shifts in the range of convergence zones. A significant reduction in this error appears achievable by a simple modification to the refractive-index profile n (z) which transforms the (n,z) pairs of points into a new set of points (?,?). Within the accuracy of the WKB approximation, the normal modes for this new environment have the same phase velocities as the equivalent wave-equation modes in the original environment. The z to ? mapping indicates the correspondence between field points in the old and new environments. This mapping is designed to approximately map turning point into turning point. Comparisons with normal-mode solutions of the full elliptic wave equation are presented to illustrate the improvement in accuracy of the parabolic results under this transformation. A ray comparison is also given. Problems associated with extending the technique to a range-dependent environment are discussed and in limited testing have been found to be minimal. [ABSTRACT FROM AUTHOR]