Acoustic ray tracing on the general-purpose electronic-analog computer

Abstract

A simulation of the trajectory of underwater acoustic rays is implemented on a general-purpose electronic-analog computer. Equations defining the phenomena are sum marized, assumptions are listed, and a preferred form of the equations is developed to provide maximum attain able accuracy of solution. Included are considerations of the velocity of sound as an arbitrary function of both depth and range, and the effects of reflections from both the surface and an arbitrary bottom. A complete computer diagram is presented and special circuits are described. Typical results of depth versus range are shown for vary ing launch depths and launch angles. A method of ob taining the difference in time required for rays leaving a common emitter at various angles to reach a common receiver is also derived. By use of perturbations, Taylor series expansions, and the method of steepest descents to insert the constraint cos θ/c = constant, the overall error in this highly sensitive computation has been reduced to 0.01 per cent or better.