Appropriate starting fields for different PE approximations

Abstract

The suite of parabolic wave equations available today for solving range-dependent propagation problems in ocean acoustics encompasses forms ranging from the standard narrow-angle PE originally introduced by Tappert to very wide-angle PEs based on Padé series expansions. Each PE form has inherent phase errors that increase with increasing angle away from the main propagation direction (horizontal). These phase errors also affect the angular energy distribution in space so that a given initial field leads to different farfield radiation patterns in different PE's. This is explicitly illustrated by solving the classical Lloyd mirror problem for a point source near the free surface in a homogeneous half-space. The results clearly show the importance of selecting a starting field compatible with the particular PE being solved. Thus it is seen that the use of a wide-angle source with a narrow-angle PE may result in an amplitude over-shoot of 3–4 dB for propagation directions around 30° off the main propagation direction.