Optimization of Gaussian Beam Widths in Acoustic Propagation

The use of Gaussian beams to compute wave propagation phenomena is a field of current interest and activity. Porter and Bucker 1987 supply an extensive list of references. More recent references can be found in Benites and Aki 1989. Gaussian beams can be traced as rays in range-dependent media providing not only propagation loss, but travel times, multipath structure, and frequency dependence. The well-known ray theory problems of caustics and shadow zones are treated automatically. This report outlines a beam width minimization technique applied to a Gaussian beam model developed by Dr. H. P. Bucker. Porter and Bucker 1987 gives the formulation upon which the techniques is built. A free parameter E is usually determined in a heuristic manner. Here, it is shown that the minimization of beam width assigns a precise value to E. Examples are given showing that the minimized beams give good propagation losses in some cases. A case is also shown in the standard Gaussian beams give poor results and the minimized beams give even worse results. The problem appears to arise in beams that pass near boundaries. This problem will have to be corrected before a final judgment can be made on the validity of minimum-width beams. rrh