Ray Tracing for Ocean Acoustic Tomography

摘要

This report describes a new, flexible computer code in the FORTRAN computer language to make ray calculations for ocean acoustic tomography. The Numerical Recipes software package provided the basis for much of this computer code. The ray equations are reviewed, and ray equations that include the effects of ocean current are derived. Methods are derived for rapidly integrating those equations to obtain time front and eigenray information for long-range, deep- water acoustic transmissions. These methods include a look-up table for sound speed, sound speed gradient, second derivative of sound speed, and range- dependent information. Cubic spline methods are used to interpolate sound speed with depth and to obtain the derivatives of sound speed. The choice of the step size increments used to integrate the equations is a critical aspect of the integration, affecting both the accuracy of the prediction and the speed of computation. A predetermined, user-specified step size appears to allow more efficient calculations than 'adaptive step' methods. 'Adaptive step' methods adjust the step size automatically to maintain a given accuracy in the integration of the ray equations, while user-specified step sizes allow one to use prior knowledge of the integration problem to achieve the desired accuracy with much less computational overhead. Several integration methods were explored, but the classical 4th order Runge-Kutta method appears to be the most efficient and best method for this integration problem. Appendices describe detailed aspects of the computer code, as well as the methods used for deriving eigenray information and for parallelizing the ray calculations. The computer code is designed to be unstable so that the user can easily modify it to his or her own purposes.