Ray Tracing in a Sectioned and Layered Atmosphere Using a Shifting Coordinate System

Abstract

Acoustical ray tracing in a horizontally layered and vertically sectioned atmosphere is accomplished on a digital computer using a shifting Cartesian coordinate system. The atmosphere is divided into vertical layers. In each of these layers straight line approximations of the variation of the speed-of-sound curve with altitude are used, thereby generating a constant radius of curvature for the acoustic ray path in each layer. Sectioning of the atrnosphere is performed by allowing boundary lines to emanate outward from the earth's center through the atmosphere. Ray points are established whenever the ray path intersects either a layer boundary or a section boundary. The computer program, called RATRACE, prints the X, Y, and Z coordinates of each ray point referenced to a planar coordinate system with origin at the ray path's beginning as well as the time required for the ray to travel to each ray point. Range versus altitude and range versus drift plots are made of the ray path and the effects on these curves of variations of the initial elevation and azimuth angles of the ray are discussed.