Ray Tracing for Ocean Acoustic Tomography
Technical Memorandum
APL-UW TM 3-98
December 1998
Applied Physics Laboratory University of Washington
1013 NE 40th Street Seattle, Washington 98105-6698
Approved for public release; distribution is unlimited.
DARPA Grant MDA 972-93-1-003
ONR Grant N00014-97-1-0259
by Brian D. Dushaw and John A. Colosi
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UNIVERSITY OF WASHINGTON • APPLIED PHYSICS LABORATORY
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ACKNOWLEDGEMENTS
This work is conducted as part of the Acoustic Thermometry of Ocean Climate
(ATOC) and North Pacific Acoustic Laboratory (NPAL) projects supported by DARPA
(Grant MDA 972-93-1-0003) and ONR (Grant N00014-97-1-0259), respectively. John
Colosi is grateful for a Young Investigator Award from the Office of Naval Research.
Matthew Dzieciuch made several constructive comments on this technical report and on
the development of the code. Bruce Cornuelle urged the inclusion of the effects of ocean
currents in the ray calculations. Bob Odom provided most of the discussion of finite-fre-
quency effects on rays passing near the ocean surface.
Questions concerning this report and its associated FORTRAN code may be
addressed to:
Brian Dushaw
Applied Physics Laboratory
College of Ocean and Fisheries Sciences
University of Washington
1013 N.E. 40th Street
Seattle, WA 98105-6698
(206) 543-1300
[email protected]ashington.edu
John Colosi
Applied Ocean Physics and Engineering Department
Woods Hole Oceanographic Institution
MS #11
Woods Hole, MA 02543
(508) 289-2317
ii TM 3-98
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UNIVERSITY OF WASHINGTON • APPLIED PHYSICS LABORATORY
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ABSTRACT
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 meth-
ods 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 inter-
polate 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 inte-
gration, 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 informa-
tion 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 porpoises.
TM 3-98 iii
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UNIVERSITY OF WASHINGTON • APPLIED PHYSICS LABORATORY
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TABLE OF CONTENTS
Page
Motivation .................................................................................................................. 1
Ray Equations, or Equations of Motion..................................................................... 2
Look-Up Tables and Sound Speed Interpolation....................................................... 4
Integration of the Differential Equations ................................................................... 6
Surface and Bottom Reflections .............................................................................. 8
Benchmarking vs Accuracy....................................................................................... 9
Conclusions ................................................................................................................ 10
Appendix A. A Technical Summary and a Flow Chart of the Computer Code........ 12
Appendix B. Calculation of Eigenrays ..................................................................... 14
Appendix C. Modifying the Code for Computations in Parallel .............................. 17
Appendix D. Input and Output Files and Other Operational Information................ 18
Appendix E. The Ray Equations in Terms of Sound Slowness ................................ 21
Appendix F. The Ray Equations with Current.......................................................... 22
References .................................................................................................................. 26
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LIST OF FIGURES
Page
Figure 1. Step sizes determined by an adaptive ray trace and the predetermined
step size presently implemented in the code............................................ 28
Figure 2. Time front predictions associated with various step size scalings .......... 29
Figure 3. Flow chart of ray trace code .................................................................... 30
Figure 4. Ray path increments and sound speed..................................................... 31
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UNIVERSITY OF WASHINGTON • APPLIED PHYSICS LABORATORY
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