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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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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
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.
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- 1. 1. Objectives CHAPTER I INTRODUCTION - 1.3. Ray Tracing 1. 2. Data Inputs z I - 1.4. Intensity Calculations - Reference FVia We% Pae
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Z8 Formulas for calculating curvature and^ gradient.^^52
30 Formulas for Lagrange and Bedford Institute^ method^54
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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
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Figure 2 indicates a great circle path (^) from 30*N, 20"W to 50"N,
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
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.
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
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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
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.
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Fig. 1. Ray trace data flow diagram.
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