What data for the parabolic equation?

Abstract

The usual reasoning is that: (a) we seek the sound field, therefore the ideal data are sound fields at a specific range, or (b) we seek the Green's function, therefore the ideal data are delta functions centered on the source. Both of the above arguments are irrelevant if we demand that the solution of the parabolic equation should correspond at long ranges to the solution of the Helmboltz equation—at least when the environment does not change with range. Comparisons using different types of initial data will be presented. We recommend that a mode sum ∑ φn(z)φn(zs)be used for initial data. Three criteria are used to eliminate unnecessary terms from the above sum. First, it is particularly important to eliminate the “non‐propagating” modes. These modes are a serious source of error in the solution of the parabolic equation because their relative effects do not decrease with range. Second, it is helpful to eliminate those modes that do not contribute at the depths of interest. Third, why include those modes which are rendered meaningless by phase errors? [Work supported by NUSC.]