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the hudson laboratories ray tracing program, Schemes and Mind Maps of Chemistry

HUDSON LABORATORIES of Columbia University ... Ray path drawn on great circle chart showing Marsden ... Flow chart of the Ray Trace Velocity Data Search.

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HUDSON
LABORATORIES of
Columbia
University
14S
PaNsade
Street.
Dobbs
Ferry.
N.
Y.
10522
TECHNICAL
REPORT
No.
150
THE
HUDSON
LABORATORIES
RAY
TRACING
PROGRAM
by
H.
Davis
H.
Fleming
W.
A.
Hardy
R.
Minlngham
S.
Rosenbaum
June
1968
Document cleared
for
public
release
and
sale;
its
distribution
is
unlimited.
Contract
Nonr-266
(84)
D
C
DEC4
4,
C
3/O
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HUDSON LABORATORIES of Columbia University

14S PaNsade Street. Dobbs Ferry. N. Y. 10522

TECHNICAL REPORT No. 150

THE HUDSON LABORATORIES RAY TRACING PROGRAM

by

H. Davis

H. Fleming

W. A. Hardy

R. Minlngham

S. Rosenbaum

June 1968

Document cleared for public release and sale; its distribution is unlimited.

Contract Nonr-266 (84)

D C

DEC4 4,

C 3/O

CU- 178-68-ONR- 266-^ Phys.

Hudson Laboratories of. Columbia University Dobbs Ferry, New York 10522

Technical Report No. 150

THE IJUDSON LABORATORIES RAY TRACING PROGRAM

by H. Davis, H. Fleming, W. A.^ Hardy, R. Miningham, and S. Rosenbaum

UNC LASSIFIED

June '

Document cleared for^ public^ release^ and^ sale; its^ distribution^ is^ unlimited. This report consists Copy No. V of^363 pages.^ of^145 copies. This work was supported by the Office of Naval Research under^ Contract Nonr-266(84). Reproduction in whole or in part is permitted for any pur- pose of the United States Government.

ii.

CONTENTS

LU

 - 1. 1. Objectives CHAPTER I INTRODUCTION - 1.3. Ray Tracing 1. 2. Data Inputs z I - 1.4. Intensity Calculations - Reference 
  • CHAPTER II DATA INPUTS AND PROGRAM ORGANIZATION - 2. 1. Introduction - 2.2. Data Flow System - 2.3. Program Management - 2.4. Ray Path Specifications - 2.5. Sources of Sound Velocity Profile Data - 2. 6. Selection of Velocity Profile Data - 2.7. Velocity Field Construction Program - 2.8. "Four-Point" Fits - 2.9. Sources of Bottom Data - 2. 10. Inputs to the Ray Trace Program - 2. 11. Outputs of the Ray Trace Program - 2.12. Conclu.ion
    • CHAPTER III RAY TRACING
      • 3.1. Introduction
      • 3.2. Development of Solution
      • 3.3. Adaptive Controls of Iteration Interval
      • 3.4. Error Estimates
      • 3.5. Printouts
      • 3 6. Ray Magnification Function
          1. Ray Depth Distribution Plots
        • References
    • CHAPTER IV TRANSMISSION LOSS
          1. Preliminary Observations
            • 1 ii
      • 4.3. Intensity Calculations 4. Z. Loss and Weighting FunciiunI
        • 4.4. Types of Intensity Distributions - References
  • CHAPTER V PROGRAM ACCURACY - 5.1. Program Control Parameters - 5.3. Hyperbolic Cosine Profile 5.2. Test Procedures ill - 5.4. Bilinear Profile - 5. 5. Real Velocity Profile - 5.6. Reversibility Test in Real Velocity Field - Reference
  • CHAPTER VI BATHMETRY - 6.1. Introduction - 6.2. Specular Reflection - 6.3. Bathymetry with Non-Cylindrical Symmetry - 6.4. Bathymetric Data - References
  • CHAPTER VII PROGRAMMING - Data Input Programs - Ray Trace and Documentation Programs - Ray Trace Analysis Programs
    • CHAPTER VIII CONCLUSIONS AND RECOMMENDATIONS - 8.1. Technical Improvements - 8.2. Program Extension - 8.3. Experimental Programs - References
    • CHAPTER IX ACKNOWLEDGMENTS
    • APPENDIX THE PHASE OF RAY ARRIVALS - A-1. Review of Kirchoff Theory - A-2. Extension to Inhomogeneous Media

LIST OF FIGURES

FVia We% Pae

1 Ray trace data flow diagram. 10

2 Ray path drawn on great circle chart showing Marsden 11

squares.

3 Great circle computed along ray path at 25 n.m. 12

increments.

4 References to velocity profiles stored on NODC tapes. 13

5 Velocity profile plotted in a standard format. 14

6 Multiplot of profile differences compared to a standard. 15

7 Ray trace request form for input data search. I

8 Ray trace request form for operating parameters. 17

9 Printouts showing bottom and ray path. 18

10(a-d) Multiplots of ray piths. 19, 20

S11,11a Ray depth distribution plot at a range of 115 n.m. 21,

12(a-c) Ray trace request form for data reduction procedures. 23-Z

13 Type II intensity calculation printout. 26

14 Calculated transmission loss curve from Hudson 27

Laboratories Op. 251.

15 Type III intensity calculation printout. Z

16 Experimental transmission loss curve for Op. 251.?

17 Multiplot of ray paths over a 300-mile range. 30

18 Great Circle computed along ray path at 25 n. m. 42

increments.

19 NODC Velocity Data related to Marsden Squares. 43

z0 Distribution of North Atlantic velocity profiles > 1900 m. 44

21 Distribution of North Atlantic velocity profiles for 45

December.

-vi-

Fig. No. Page

22 Flow chart of the Ray Trace Velocity Data Search 46

Procedure.

23 Sanplp Marsden^ lint firom^ Ra^ Trace^ Veoct^ Data,^ Searc^ by^^47

Squares.

24 Velocity profiles for June along a ray path from data^48

search.

25 Interpolation and extrapolation formulas^ for^ shallow^49

profiles between deep profiles.

26 Wilson's Equation for^ calculating^ velocities.^50

27 Schematic^ representation^ of^ extrapolation^ procedures^51

for deep and shallow profiles.

Z8 Formulas for calculating curvature and^ gradient.^^52

29 Plot of the effects of various data fits.^53

30 Formulas for Lagrange and Bedford Institute^ method^54

of fits,

31 Ray depth distribution plot at^ 225-mile^ range.^74

32 Ray depth distribution plot at 240-mile range. 75

33 Computed transmission losses as a function of^ range^^105

for hypothetical source at 500 m.

34 Computed transmission losses as a function of range 106

for hypothetical source at 5000 mn.

35 Distributions of ray arrivals. 107

36 Effect of^ various^ types^ of^ sampling^ functions.^108

37 Deep profile at range 306 miles. 115

38 Deep profile at^ range^305 miles.^132

39 Deep profile at range 0. 0 miles. 149

40-56 Shallow profiles^ at^ ranges^ 50,^2 to^ 286.4^ miles.^ 150-

57 Deep^ profile^ at^ range^ 305.^7 miles.^167

-vii-

CHAPTER 1

INTRODUCTION

1. 1. Objectives The results of a number ot experiments in low-frequency, (^) long- range underwater sound propagation (^) have shown that bottom interactions as well as changes in the velocity (^) profiles with range will play important roles in determining the efficiency of the acoustical (^) transmission between an underwater source (^) and its receiver. To include these effects in the analysis (^) of experimental data, Hudson Laboratories has (^) developed a ray tracing program (^) which is especially adapted to multipath long-range acoustical propagation - oriented toward (^) ranges of several hundred to several thousand (^) miles - with the point of view that the program (^) should be: i) at (^) least semi-quantitative with respect to the prediction of acoustical (^) transmission losses, ii) a flexible research tool that can (^) be used in connection with the analysis of results from specific experiments to choose (^) parameters needed for the prediction of intensity, and iii) as complete as possible in terms (^) of assimilating and organizing for convenience a variety of data inputs (^) and presenting computed (^) results to the scientist for his interpretation. This complete ray tracing program, or, (^) more accurately, the system of programs that has been developed (Fig. (^) 1) is discussed in this (^) report with the motives that led to the selection of (^) certain techniques. The work can be divided in (^) a natural manner into three major groupings: 1.2. Data Inputs

    1. Ray Tracing 1. 4. Intensity (^) Calculations and these groups are also consecutive steps in (^) the data flow. The over- all program can be illustrated (^) in terms of representative outputs for each group above, which will also (^) serve as an introduction to the details of, and a summary of, the present (^) program.

i - I-

iI

1.2. Data Luputs

Figure 2 indicates a great circle path (^) from 30*N, 20"W to 50"N,

,sover * whch- it `,G dc:;ircd to o--'dbta i t^1

mission (^) loss. Coordinates for this track, or for tracks specified by an initial position and bearing, are computed (^) so that the path can be plotted on standard bathymetric (^) charts to obtain a bottom profile. Figure 3 is an example of the track coordinates printed at 25-mile (^) increments. If no special velocimetric data are available for this path, (^) e.g. data from a particular experiment, or if given data are to be checked against standard data for the area, (^) the magnetic tape files of the National Oceanographic Data Center (NODG) can be searched for data of given months for sound (^) velocity profiles that possess depths equal to or greater than a Maximum Depth of Observation (MDO), and which lie within a specified range or zone width from the given track. (^) Figure 4 gives the identification numbers of all velocity profiles (^) catalogued by NODC for the months 10, (^) 11, 12 with an MDO greater than 1500 meters and which lie within 50 miles of the track of Fig. 1. All the velocity profiles selected as pertinent (^) to a given track from any input data source are converted to a standard form for editorial review before insertion into the ray tracing program. Stations given in terms of temperature, salinity, and (^) depth are converted to 1

sound velocity and depth entries by use of Wilson' s equation. Also, if

the MDO of a station is less than a maximum bottom depth for the (^) ray tracing, (^) an inverse solution is made of Wilson' s equation to determine the water temperature at the MDO (^) and the profile is extrapolated to greater depths by assuming that the water temperature is constant and the sound velocity is a function of pressure (^) only. Figure 5 shows the standard form used for the profiles. A four-point fit of entered data points is (^) used to determine the sound velocity at 20-meter intervals to 2000 meters and at 100-meter intervals (^) to the greatest depths. The MDO of the profile of Fig. 5 was 5277 meters (^) and the entered velocity represented (^) a water temperature of 1.8180 for an assumed salinity of 35.0%.,. (^) Insofar as the roughly 1. 8 temperature is typical of deep water in the geographical area of the profile, this velocity profile and its extrapolation were accepted as valid for oiclusion into the ray (^) tracing program. (^1) References are compiled at (^) the end of each chap~ter.

I Fiure 9 indicates a^ printout^ that^ is^ available^ for^ each^ ray^ traced.

Range,on. the boltorn,depth, angle,arnd the'L travelop plot time, deit and height Ile prores above bottomof th.u rayare .printed ......

  • S± .00 'JA LL1L ±

the surfac~e and the bot torn. Printout intras ty"'l 10o.

tntervals,i typically 1. 0 or ?.

miles, are selected and extra printouts are given at each turning point

and surface or bottom hit.

An objective of the program is to^ determine^ the^ principal^ arrival

structure that constitutcs far field illumination. The angular increments

are chosen small enough so^ that,^ insojar^ as^ possible,^ each^ arrival^ is^ well

defined. In practical situations this usually requires from one hundred to

two hundred rays or more. Sunitynr7 informatiun of the total field is ob-

tained by comrniiiog the data from the individual ray tracings on an output

tape to produce multiplot data or data for the intensity calculations^ dis-

cussed in Chapter IV. Figures 10a through^ 10d^ indicate^ the^ build-up^ of

the total field by^ the^ variovs^ ,^ ays^ tYom^ the^ source.^ To^ reduce^ confusion

in this representation of the field patterns, aich plot is limited to a maxi-

mum number of 30 rays.

More specific data^ are^ given^ in^ the^ Ray^ Depth^ Distribution^ Plot^ of

Fig. 11. These plots can be obtained at every range that is also a print-

out interval of the ray trace progranm. The sequence of the plot is^ in

ternms of the angular increments used in the ray trace and the asterisks

show the depth of that ray at the selected range. A ray will be oscillating

in depth about that range (Fig.^ 9)^ and^ the^ maximum.^ and^ minimum^ depth

of the oscillations that occur about the printout range ape indicated by the

plus and minus signs in Fig. 1 Ia. The extreme right-hand side of the

figure plots the travel time for each ray.

It is clear that if a vertical line is drawn in Fig. 11, representing

a given depth between the surface and the bottom, the line will intersect

certain families of rays and^ each^ intersection^ will^ give^ a^ differk-nt^ arrival

that can contribute^ to^ the^ acoustic^ field.^ In^ this^ figure^ the^ shallower

angles correspond to sound duct propagation and^ the^ steeper^ angles^ repre-

sent RSR and bottom bounce propagation.

1.4. Intensity Calculations Figure 12 is the control form for the "Ray Trace Intensity Calculations" and indicates a number of parameters that are^ included the callcullation, ruc as .- ateution~ LA UC~I.JnciLoa, aio andu receiver directivity functions, etc. These are described in^ Chapter^ IV. It i3 a feature of the calculations that intensity is determined^ as^ a probability distribution that is obtained by mapping the arrival structure depicted in Fig. 11 across the ocean depth at a given range. This per- mits a calculation of the intensity at a given range and depth, and there- fore the transmission loss. It also determines the distribution of in- tensity in depth as the sound propagates between the confining sea surface and bottom planes of the ocean. All such calculations are subject to uncertainties in the input data and must be interpreted as averages over "representative" data. Addi- tional averaging is necessary to account for the fluctuations that are due to multipath structure. In a coarse differentiation corresponding to limiting physical situations, the intensity calculations have been classified into three types, only two of which, types II and III, are considered for long-range propagation. The ILtne II intensity calculation is applicable where the depth distribution of acoustical intensity (^) will change with range. Figure 13 shows a printout that gives the transmission loss calculated at twelve depths and for nineteen equally spaced range intervals, usually two-mile increments, that are centered on a given range. These data could be used, for example, to construct the predicted transmission loss to a given re- ceiver from a source that is towed in range at a specified depth. Suc- cessive outputs of the type of Fig. 13 can be continuously plotted to give the transmission loss as a function of range in the form of Fig. 14. When the input data becomes uncertain, and at very long ranges such that convergence zone structure is "washed out, ", it becomes preferable not to predict the range-dependent Type II transmission losses but instead to (^) average these over a large range interval that would cor- respond to a convergence zone. For this limit of averaging a Type III transmission loss is calculated with the printout shown in Fig. l5. The

-- 5-

features of the input data, e. g., horizontal gradients and certain types of bottom features, and that these must be included (^) in any realistic predictive model. The examples of Figs. 1 through 15 serve as an (^) introduction to he -- - T- h ey- - - - --........ ,-a the-idr- n-vItl-t-n on a- 1 ,---e that (^) is requred to obtain a reasonably complete description of (^) a sound field that may contain twenty to thirty arrivals or more, and also to estimate (^) the distri- bution (^) of these arrivals with depth at given ranges. With the GE- computer available (^) to the Laboratories, a program extending to a 1000- mile range that computes 200 rays will require about (^10) to 15 hours for the ray tracing itself plus about (^) two hours for associated plots and in- tensity (^) calculations. With a modern higher speed computer and, admittedly, (^) with technical improvements in programming it is estimated that the computational time could be cut to (^) one-fiftieth to one-hundredth of the present running time. Features (^) of the present program that are discussed in (^) detail in subsequent chapters of this report include- i) a capacity for the (^) inclusion of mixtures of all types of velocity (^) profiles, e.g., surface BT casts, deep Nans,.mn casts, etc., to obtain as precise a construction (^) of th: velocity field as (^) the data permits, ii) the (^) inclusion of horizontal gradients, earth' s curvature corrections, and available bottom data in a straight- forward manner, iii) a capability (^) for "trading-off" computational accuracy in terms of shorter computer running times according (^) to the (^) nature and reliability of the input data and the type of calculation desired. Separate experimental studies (^) in long-range acoustical propaga- tion (not reported here) have shown that the horizontal gracients and at least a limited number of bottom interactions must (^) be included to obtain agreement between predictive (^) models for the sound transmission and experimental data, (^) especially at low acoustical frequencies. As a generalization, (^) the bottom interactions that are most important for long- range propagation are (^) of three types:

i) the terrain local to a source that can either augment the ray field by slope-aided rays that propagate to the

"lax LLCIU LC LO %JUDLA UL LLAL8 AAJAhiY

rays that could otherwise propagate, ii) prominent rises, e.g., seamounxts or ridges, at inter- mediate ranges that obstruct the ducting of the sound energy, and iii) terrain at the farthest ranges that can obstruct the sound by additional terrain shadowing or, conversely, can create "hot spots" due to favorable slopes, The sound^ paths^ and^ bottom^ interactions^ shown^ in^ Fig.^17 are typical of physical conditions that prevail in the real ocean and represent the type of propagation toward^ which^ the^ present^ program^ is^ directed. The source is located on a bank at range zero. The^ sound^ energy^ spreads hemispherically, neglecting bottom propaqation, to a near range, R (^1) but during this propagation the steep rays interact strongly with the^ bottom so that only a fraction rl of the source power radiates^ outwardly^ beyond R and the fraction (1-ij)^ is^ lost^ to^ the^ bottom.^ The^ propagation^ to range R 1 acts like a^ filter^ that^ eliminates^ all^ but^ the^ shallow^ angles. If the bottom is deep between ranges RI and a further range R I almost all^ of^ the^ tj^ fraction^ of^ the^ source^ power^ propagates^ as^ cylindrical spreading with very^ little^ decrease^ in^ the value^ of^ i^.^ An^ intervening obstruction at range R^2 will^ cause^ a^ further^ filtering^ of^ the ducted^ energy and will produce a distinct decrease in vi to a value i' after which the power will again spread cylindrically with a nearly constant fraction 'i' Finally, if there is an interaction with the bottom at range R 3 , there will be a further attenuation in the power; however, low-angle reflections from a slope at R can give an increase in the intensity observed at certain depths at the range of R The frequent observations of nearly ideal cylindrical spreading from intermediate to long ranges give such a model a^ strong^ empiric^ basis as, at least, a good approximation for cylindrically spreading waves. Also, the fractions^ q^ can^ be^ measured^ in^ given^ ocean^ regions^ if^ the^ total^ in- tensity that propagates throughout the full^ depth^ of^ the^ ocean^ can be^ measured.

-8-

4o

444 - -% -- - n6"t. s. S.,

f 4S .iV-to flS**^ **t t.^5551 V^ *S

---------- -- -- -- -- -------------

Fig. 1. Ray trace data flow diagram.

I.. to-

1 2 L. Al DD

Fig. 2. The ray path between 30N, 20 W and 50N, 25W drawn Oil a great

circle chart. Marsden squares were computed by program A-173-F1.