An improved Gaussian beam caustic correction for Bellhop at low frequencies

Abstract

Gaussian beams are commonly used in ray-tracing to mitigate the effects of caustics and shadow zones. The problem is how to determine the width of these “fuzzy” beams. Porter and Bucker [J. Acoust. Soc. Am. 82, 1349–1359, 1987] proposed a method that expressed the beamwidth and curvature in terms of p and q of the dynamic ray equations. We call q the beamwidth factor. In the Gaussian beam implementation caustics are not caused by the crossing of two rays; rather they occur when the beamwidth factor, which appears in the denominator of the amplitude, becomes small. In practice, this is generally not a problem at high frequencies, but as the frequency gets lower the problem gets more severe. The widely used Bellhop model has a procedure, which “caps” the beamwidth when q becomes too small, but the procedure eventually breaks down at low frequencies. Here, we propose a different cap based on a cylindrical wave front converging to the focal point of a caustic. The various caps are compared with the “exact” normal mode solution for a shallow-water upward refracting environment, illustrating how the new cap provides better reduction of the caustic anomalies.