Technical Report No. 215 004860- 1-T A MIMI PROPAGATION STUDY: COHERENT SPECTRA OF WIDEBAND UNDERWATER ACOUSTIC RECEPTIONS IN THE STRAITS OF FLORIDA, 25 NOVEMBER 1970 by Gerald N. Qerquist Approved by__ c__( Theodore G. Birdsall COOLEY ELECTRONICS LABORATORY Department of Electrical and Computer Engineering The University of Michigan Ann Arbor, Michigan for Contract No. N0014-67-A-0181-0035 Office of Naval Research Department of the N'avy Arlington, Va. 22217 THE UNIVERSITY OF MICHIGAN ay19 ENGINEERING LIBRARY Approved for public release; distribution unlilited.

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ABSTRACT In an underwater acoustic propagation experiment conducted in November 1970 a periodic broadband signal, centered about 420 Hz, was transmitted across the Straits of Florida continuously for 19 days. This report presents the preliminary results from spectral analysis of the acoustic reception of this signal at Birnini, Bahamas, during a 7.61-hour period on 25 November 1970. The spectra are noteworthy for their slow rate of change during this period. Plots of the spectral amplitude and phase of the reception are presented for a 50 Hz bandwidth centered about 420 Hz. iii

FOREWORD Underwater acoustic propagation experiments of the past few years have verified that the general features of long-range, single frequency reception are complicated amplitude fluctuations with deep fades, relatively stable phase and frequency, accompanied by surface scattered energy. The next level of experiment should establish how close two frequencies have to be to behave "similarly, " and how far apart two frequencies have to be to behave "independently." The work reported here is at this level. Sixty-one signal frequencies with spacing of 5/6 hertz that were transmitted simultaneously for over seven hours were analyzed and preliminary results are given in this report. T. G. Birdsall iv

TABLE OF CONTENTS Page ABSTRACT iii FOREWORD iv LIST OF ILLUSTRATIONS vi AUTHOR'S PREFACE viii 1. INTRODUCTION 1 2. THE MIMI PROPAGATION EXPERIMENT OF NOVEMBER 1970 3 2.1 The Miami-Bimini Range 3 2.2 The Transmitted Signal 6 2.3 The Quantities Measured 9 3. THE PROCESSING OF THE BIMINI RECEPTION 12 3.1 The Equipment Configuration at Bimini 12 3.2 On-Site Digital Filtering and Recording 12 3.3 Selection of Data for Spectral Analysis 17 3.4 The Spectral Analysis 18 4. PRELIMINARY ANALYSIS AND CONCLUSIONS 21 4.1 The On-Line Power Measurements 21 4.2 Spectral Plots 23 4.3 Preliminary Conclusions 28 APPENDIX A: Constant Time Plots 31 APPENDIX B: Constant Frequency Plots 78 RE FERENCES 110 DISTRIBUTION LIST 111

LIST OF ILLUSTRATIONS Figure Title Page 1 The Miami-Bimini range: (a) physical layout, (b) bottom profile 4 2 Sound speed vs depth, Miami to Cat Cay, 28-29 November 1961 6 3 Sound ray paths along 25044' on 28-29 November 1961 7 4 A complement-phase modulated signal (a) a portion of the modulating waveform (b) the resulting CM transmission 8 5 The RMS spectrum of a complement-phase modulated signal for L = 15 and D = 8 10 6 Equipment configuration at Bimini 13 7 Complex demodulation of the hydrophone reception 14 8 The carrier and sideband filters used on the November 1970 reception 16 9 On-line power measurements for 25 November 1970 22 10 Prototype constant time plot 24 11 Prototype constant frequency plot 27 12 Spectrum at to = 1118 hours, 25 November 1970 29 13 Spectrum at to + 1 minute, 40 seconds 29 14 Spectrum at to + 10 minutes 30 vi

LIST OF ILLUSTRATIONS (Cont.) Figure Title Page 15 Spectrum at t + 1 hour, 3 minutes, 20 seconds 30 vii

AUTHOR'S PRE FACE This report presents preliminary results rather than the polished conclusions of a completed investigation. No attempt has been made to draw conclusions from the data or to analyze it. A more substantial report on spectral analysis of Project MIMI transmissions is planned for a later date. viii

1. INTRODUCTION In November 1970 an underwater acoustic propagation experiment (Project MIMI) was conducted jointly by the Acoustics Group of the Rosenstiel School of Marine and Atmospheric Sciences at The University of Miama (Florida) and the Signal Processing Group of the Cooley Electronics Laboratory at the University of Michigan. A periodic broadband signal centered about 420 Hz was transmitted continuously across the Straits of Florida for 19 days. In the on-site portion of the experiment, the power and phase angle of the carrier, the power in the signal sidebands, and the noise power in the signal band were measured at two receiving sites. In addition, the total power and the power spectrum in a narrow band about the carrier frequency were computed to measure signal modulation due to forwardscattered surface reverberation. The received signal was also correlated with a pulse compression reference signal to measure the multipath structure of the acoustic channel. During the course of the experiment, approximately 9 million digital words of the reception were recorded for later processing. Portions of these recordings were complex-valued demodulates of a comb-filtered version of the reception. A period of 7.61 hours on 25 November 1970 for which such recorded demodulates were available from Bimini, Bahamas, was selected for spectral analysis.

Chapter 2 presents background information on the acoustic range and equipment configuration used. Chapter 3 details the processing of the reception at Bimini and the methods used to transform the recorded receptions to frequency domain, and Chapter 4 presents plots of the spectra of the reception.

2. THE MIMI PROPAGATION EXPERIMENT OF NOVEMBER 1970 2.1 The Miami-Bimini Range The Miami-Bimini range, illustrated in Fig. 1, is part of the facilities of the Acoustics Group of the Rosenstiel School of Marine and Atmospheric Sciences (RSMAS) of The University of Miami. It extends across the Straits of Florida from Miami to Bimini, Bahamas. The transmitting site is located at Fowey Rocks [point 2, Fig. 1(a)] approximately 12 miles (19 km) from the RSMAS laboratory and is connected to the laboratory by telephone lines (point 1, Fig. 1). At Fowey Rocks a bottom-mounted projector is located in 72 feet (22 m) of water at the focal point of a 24-foot (7.3 m) compliant tube parabolic reflector. It has a maximum source level of 120 dB/ ibar at 1 m with a nominal bandwidth of 100 Hz. The source level for the November test was 110 dB/ gbar/meter. The 300 beamwidth is directed toward Bimini, a distance of 43 nautical miles (78.6 km). Two receiving sites were used in the experiment. At the first, a bottom-mounted hydrophone is located in 1000 ft (305 m) of water (point 4, Fig. 1) approximately 72 nautical miles (12 km) from the source. The reception from this hydrophone is transmitted to the 1The material in this section is taken from Ref. 1. A more complete discussion on the Miami-Bimini range can be found there. 3

~25_.' Depth in ofthomsr 2. 50' 64I VIRGINIA KEY cbF~~~~ 400~~ P~~~~,. eM,/, l:k S. BIM\ I 0s30 1 f 4O A L ANTIC 40 4 H sIM It I? -2,4 CI FO E~YR0~OCKS (30 / 440 CAT CAY 33. 22S. __ __ __ _ __ __ _ __ _. 240 To 2 COE 142 boto poi 2'9 490 447, 9: / 30' I0 800 50 4o' 30, 20' l0' 800' 795 794d 7930 4 9 20' w. 20" 40i 400 4 a. e00 Fig. 1. The Miami-Bimini range: (a) physical layout,

5 RSMAS laboratory by marine cable. The second receiving site is located off Bimini (point 3, Fig. 1). There, two bottom-mounted hydrophones are cable-connected to a laboratory on Bimini. These hydrophones are located at 100 and 1200 feet depth (30 m and 366 m), 1 and 2 miles (1.8 and 3.6 km) off-shore and are referred to as the shallow and deep hydrophones, respectively. The bottom profile of the Miami-Bimini range is illustrated in Fig. l(b). A shelf extends out from Miami about 15 miles (28 km) to a depth of 400 m followed by a sharp drop-off to a depth of 800 m. Thirty miles (56 km) beyond, the Grand Bahamas bank rises abruptly from this depth. A sound speed profile, obtained during November 1961, appears in Fig. 2. This profile is characterized by a mixed layer which extends to the relatively constant depth of 100 m followed by a region of negative velocity gradient. It is noted that the velocity gradient becomes increasingly negative as the Florida shore is approached. The ray diagram corresponding to the sound speed profile of Fig. 2 is shown in Fig. 3. This diagram shows sound being propagated by reflections from surface and bottom, by refraction and reflection from the bottom and by refraction and reflection from the surface. This latter mode of propagation does not appear in ray diagrams calculated from sound-speed profiles obtained in the spring and summer.

NAUTICAL MILES 0 10 20 30 40 /;Xta~~~~~ / g /!c,~~~~~100 1, 4so / / IIn~~~~~~~~~~~~~~ " 1I VSTATION POSITION / / Fig. 2. Sound speed vs. depth, Miami to Cat Cay, 28-29 November 1961 2.2 The Transmitted Signal The transmitted signal, complement-phase modulate (CM), consisted of a carrier wave at 420 Hz modulated by a linear-maximal, pseudorandom sequence. The phase of the carrier was shifted to either + 45 or -45~ depending on the value of the binary digit in the modulating sequence. A portion of such a CM signal is shown in Fig. 4 where fc = carrier frequency in hertz c~~

z 800Fig. 3. Sound ray paths along 250 44? on 28-29 Nov. 1961.

8 d = duration of the sequence digit in seconds D = number of cycles of carrier per sequence digit. For all MIMI experiments, the number of cycles of carrier per digit D is chosen to be integer-valued; thus the CM signal is periodic with period T Id I D/ f where L is the number of digits in one period of the modulating sequence. +1 d = D/fc -1 (a) (b) Fig. 4. A complement-phase modulated signial (a) a portion of the modulating waveform (b) the resulting CM transmission

9 The RMS power spectrum of a typical periodic signal of CM type is shown in Fig. 5. For all such signals, the spectrum has a sin(x)/x envelope except at the carrier frequency. Approximately half of the total power is contained in the carrier line with the other half contained in the sideband lines. The signal used in the November experiment had f = 420 Hz c D = 8 cycles/digit and L = 63 digits with the result that the digit duration and the period were d = 0.019 seconds and T = 1.2 seconds The spacing Af between adjacent lines in the transmitted spectrum is Af = 1/T = 5/6 Hz Finally, there are 127 spectral lines lying within the nominal transducer bandwidth of about 105 Hz. The bandwidth of the main lobe of the transmitted spectrum is also 105 Hz. 2.3 The Quantities Measured The quantities measured on site during the November 1970

10 1 I 0 1 1 1~~~IL AC.. \ f - f /D Af f + fc/D f C C C C C Fig. 5. The RMS spectrum of a complement-phase modulated signal for L = 15 and D = 8

11 experiment can be grouped into three categories: (1) signal power, noise power and carrier angle measurements, (2) forward-scattered surface reverberation measurements, and (3) multipath structure measurements. These measurements were obtained using digital processing techniques implemented by a digital computer located at each receiving site. Each of the measurements was computed and recorded every 100 sec on the basis of 80 sec of reception. (The remaining 20 sec were used solely for computations.) As each 80 sec of reception was digitized, it was effectively passed through a combfilter before being stored in the memory of the computer. This filtered reception was recorded on magnetic tape for later processing at Cooley Laboratory, and the spectra contained in this report are derived from this reception. A discussion relating the spectra and the simultaneous measurements from categories (1) and (2) above is given in Chapter 4. For a detailed discussion of the on-site measurements, the reader is referred to Ref. 2.

3. THE PROCESSING OF THE BIMINI RECEPTION 3.1 The Equipment Configuration at Bimini The equipment configuration at Bimini is shown in Fig. 6. A frequency standard accurate to 1 part in 1010 provides a reference signal that is converted to a 1680 Hz (equal to 4 times carrier frequency) clock signal by a frequency synthesizer. After passing through an isolation amplifier, the clock signal controls the analogto-digital conversion circuitry on the computer. The receptions from both the shallow and the deep hydrophones are passed through signal conditioning bandpass filters and amplifiers and brought to a patch panel. There the operator selects which hydrophone signal is to be connected into the A/D converter on the computer. Because of an equipment failure on the deep hydrophone link, the shallow hydrophone reception was used for the data covered in this report. (Recall that the shallow hydrophone is in 100 ft of water 1 mile offshore.) 3.2 On-Site Digital Processing and Recording The computer is programmed to demodulate the input at the A/D converter from a real-valued, bandpass signal centered at 420 Hz to a complex-valued, lowpass signal centered about dc (i. e., zero Hz). The processing is effectively shown in Fig. 7. The input signal 12

Ba ndpas s Patc h Deep Amp Terminal Amplifier Isolation Amplifier Rydrophones Marine Cable Attenuator and Prpea 1/3 octave Filter qimn 1 ~~~~~~~~~~~~~Bandpass A Shallow Amp Terminal Amplifier ilaeion Isolation Amplifier Frequency Frequency Standard i — ll~ Olge) Synthesizer 1680 Hz Clock Signal Fig. 6. Equipment co'figuration at Bimini

Low Pass Samples of Filter Real Part ~t —- cosine phase Input 420 Hz I I I Low Pass Signal Oscillator Sampler, 210 samples/sec Complex Signal ~ —-sine phase Low Pass Samples of Filter Imaginary Part Fig. 7. Complex demodulation of the hydrophone reception

15 is demodulated by multiplication with both sine and cosine phase of a 420-Hz reference signal. A lowpass filter on the output of each multiplier passes only the difference-frequency components to the samplers, which provide 210 samples/sec of each channel. If the output from the cosine phase channel is called the real-part of the demodulated signal and the output of the sine channel is called the imaginary-part, then this real-imaginary pair can be thought of as a complex-valued representation of the input bancpass waveform. In point of fact, no information is lost in this process, and each signal processing operation that can be performed on the bandpass signal can also be performed on the lowpass complex signal to yield the same results (Ref. 3). An advantage of the complex representation in this case is that the number of samples per second which must be dealt with depends only upon the bandwidth of the signal and not upon its center frequency. Inside the computer, the complex samples are passed through a number of digital filters to perform the on-line measurements described in Section 2.3. The spectral characteristics of the filters germane to this current investigation are shown in Fig. 8. These filters separate the line spectrum of the transmission into two disjoint pieces: the carrier alone, and the sidebands excluding the carrier. Of course, both filter outputs contain those noise components that are immediately adjacent to the signal lines. The sideband filter

Carrier Filter -~ |-.013 Hz f = 420 Hz f c Sideband Filter 1 - *t-.013 Hz H f.833 Iz= f - sid-f fc f +af ft C C Fig. 8. The carrier and sideband filters used on the November 1970 reception

17 produces a time series of 252 complex points every 80 sec, and the carrier filter produces one complex point every 80 sec. The outputs of these filters are written onto magnetic tape after each 80-sec segment of reception is collected. 3.3 Selection of Data for Spectral Analysis The record data from the Bimini receiving site span a period of 19 days. The data from the period from -1130 hours to -1900 hours local time, 25 November 1970, were selected for spectral analysis for the following reasons: (1) Recordings of sideband filter and carrier filter outputs are available for that period from the 7-mile hydrophone cabled back to RSMAS (point 4 on Fig. 1). (2) The receiving and transmitting frequency standards were closely matched in frequency during that period. (Inadvertently for some parts of the experiment, they were approximately 2 millihertz apart, which is enough to compromise the phase structure of the wideband spectra.) (3) The wideband, sideband power shows two distinct modes of behavior during the period, one of lower, constant power and another of higher, varying power. This behavior had been observed in past years on the carrier power measurement at the end of November, and a more thorough investigation was sought.

18 The data for analysis consisted of (1) 274 time series, each containing 252 complex points, and being the lowpass representation of an average (i.e., comb-filtered) period of the reception with the carrier removed. (2) 274 complex points yielding carrier amplitude and phase. Each (time series, carrier) pair was produced on the basis of 80 sec of data taken over a 100-sec time span. Thus the data spans 274 x 100 sec = 456 + 2/3 min = 7.61 hrs. 3.4 The Spectral Analysis The spectral analysis proceeded in the steps outlined below. (1) Fourier Transformation of the Time Series Each 252-point time series Z(i) was discrete-Fourier-transformed according to the following definition: 251 252 (k) (i) e k = 0,..., 251 i=0 where j = -i-. As expected, the frequency spectrum H(k) had an extremely low carrier value. (That the carrier value was not zero is attributed to the round-off errors in the computation.) (2) Reinsertion of the Carrier The large amplitude of the carrier in relation to the sideband lines H(k) called for some scaling of the carrier prior to its

19 reinsertion into H(k) and subsequent display. The scale factor chosen was such as to transform the transmitted spectrum of Section 2.2 into a pure sin(x)/x curve; i.e., the carrier was attenuated exactly enough to fit into the smooth sin(x)/x curve of the other lines. The ratio of transmitted carrier power for the CM signal used to the carrier power in the equivalent [ sin(x)/x] power spectrum is P, where P 1 + L L - j L- + L+1 For the L = 63 digit sequence used in the experiment, P= 62 1 = 62.03125 = (7.875992)2 Since the spectra are in volts and not power, each carrier line was attenuated by 1/7.875992 and reinserted into its corresponding spectrum H(k) as H(0). (3) Removal of Phase Bias The relative phase of each of the frequency lines in the transmitted signal is determined by the pseudorandom modulating sequence. In general, the phase angles of adjacent lines are not at all close, making visual determination of phase behavior for even closely spaced lines rather difficult. Consequently, the phase of each line in all 274 received spectra was modified by subtracting from it the phase of the same line in the transmitted spectrum. This allowed phase

20 plots for adjacent lines to reflect oceanic influences rather than the phase structure of the transmitted signal. (4) Selection of Lines for Further Analysis Inspection of the on-line sideband power measurements for the data under investigation indicates that the wideband signal plus noiseto-noise ratio from the sideband filter varied from a minimum of 10 dB to a maximum of 25 dB. The centermost lines of the transmitted spectrum contain the most power. Subject to cancellation due to interference phenomena, the signal plus noise-to-noise ratio of the centermost lines is greater than or equal to that of the sideband filter output. Thirty lines to each side of the carrier, as well as the carrier itself, were selected for further analysis and display. The power transmitted in these lines varies from 1.008 to 2.166 times the average line power in the main lobe of transmission. The effective length of the time series that were transformed was 1.2 sec, yielding an eigenfrequency spacing in the spectrum of 5/ 6 Hz. Since 61 lines were selected, the spectra spanned 50 Hz, i.e., 25 Hz either side of the carrier.

4. PRELIMINARY ANALYSIS AND CONCLUSIONS 4.1 The On-Line Power Measurements The results of the on-line signal power measurements are shown in Fig. 9, which is drawn from Ref. 2. The sideband filter output, labeled S, and the carrier filter output, labeled C, clearly show the two distinct modes of behavior mentioned in Section 3.3. Before 1440 hours the S-output is lower and relatively constant; after that time it rises rapidly and is much more variable. In general the carrier level tends to follow the sideband level. The substantial fluctuations in carrier level are probably caused by cancellation of the carrier due to interference phenomena occurring within the relatively narrow (13 millihertz) carrier tooth. The trace on Fig. 9 labeled R is the output of a surface reverberation measurement filter and is the energy in a 5/ 6-Hz band about the carrier. The signal plus noise-to-noise ratio in dB of any of the C, S, or R outputs is simply the difference between it and the trace labeled N, which is a wideband noise measurement. For further information on the measurements shown on Fig. 9, refer to Ref. 2. The numeric labels on various features of the carrier level in Fig. 8 refer to the spectral plots and will be discussed in the next sections. 21

Relative Power (decibels) c 0 0 0 0 0 0 0 C> CD CD CD C> Z -102 -155 _______ 1 266 70 CI~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C 562 745 -1100 1175H,1313 402 - 0 O 1~1535" 49 ~'~~~~~~~1~~~ "-1757..................2134 - -2311 ~-,, 244..' )~~-I. 25412660' 3027 co 3065 31 54 -304 32456 c, ~~~~~~ 3~5 --

23 4.2 Spectral Plots Plots of the spectra are bound into the rear of this report. They are presented in polar coordinate r-O form to correspond to the amplitude-phase intuition of the electrical engineer (Appendixes A and B). The spectra may be viewed as 274 samples of 61 complex-time series. They are denoted as S(f, t), f = 1,..., 61; t = 1,..., 274 4.2.1 Constant Time Plots. Plots of S(f, t) holding t constant for each plot are shown in Appendix A. These correspond to 50-Hz wide spectra separated in time by 100 sec. A sample page is shown in Fig. 10. Six spectra spanning ten minutes in time are plotted on each page. Their time order is: 1 3 5 2 4 6 At each plot position, the amplitude IS(f, t)l is plotted above the phase angle arg[ S(f, t)] with frequency increasing to the right. The carrier frequency is marked with a tick. The phase is plotted between two horizontal lines, the top one of which also serves as the zero line for the amplitude plot. The range of the angle plot is one revolution (i. e., 3 60 degrees or 27r radians). The phase angles to be plotted were modified by the following transformation.

Cross Reference Third Plot Position Label ~4- II1S ~'~',?!: ~i,!!i::::Amplitude Plot Fir st Plot' Posit'ion.:-:: ii~-:rt i: i:"- ~ ~ ~ /~- Phas Plt Second Plot._ 1 -I':r -i -~C t-...~~~~~~~-J, 4 Position Fig. 10. Prototype constant time plot

25 arg[ S(f, t)] plot = arg[ S(f, t)] data- (af - b) where the constants a and b were chosen empirically to be a = 0.45507 revolution/frequency step b = 0. 58593 revolution This transformation is equivalent to shifting the time origin 0. 54608 sec and the phase origin 0. 58593 revolutions. (The original time and phase origins were arbitrary since they were established by the instant-of-time at which the receiving processor began operating.) The constants a and b were chosen to make the largest portions of all the 274 angle plots as flat (or alternately, as smoothly connected) as possible. In those cases where the phase angle does cross the phase reference (zero revolution) axis, no attempt is made to draw a smooth line connecting adjacent angles. Rather the "offending" angle is plotted as a point instead of as a member of a line. At the upper left of each page in Appendix A is a numeric label. This label is a computer data access code for the original recorded data that produced the spectrum in the upper left corner of the page, i.e., plot position 1. The second number in this label is the same as the numeric label on the C-power line of Fig. 9 and can be used to establish a time correspondence between power levels and spectral displays. The time duration of one page of spectra —ten minutes —is indicated on Fig. 9. (Hopefully these limited capabilities

26 for cross-referencing Fig. 9 and the plots in Appendix A will prove sufficient; the macroscopic rather than microscopic features are of interest here. ) 4.2.2 Constant Frequency Plots. Plots of S(f, t) holding f constant for each plot are shown in Appendix B. These correspond to time series of signal amplitude and phase for each signal line in the 61-frequency ensemble selected in Section 3.4. Two r-O time series, each spanning 7.61 hours, are plotted on a page, one in the top half and the other in the lower half of the page. A sample page is shown in Fig. 11 with IS(f, t)l plotted above arg[ S(f, t)] with time increasing to the right. The vertical scaling is not the same as that of the constant time plots. The angles portrayed in the constant frequency plots are computed directly via arg[ S(f, t)] and undergo no transformation. Again, as with the constant time case, angles which cross the phase reference axis are plotted as points instead of as members of a smooth line. At the upper left of each time series plot is a number indicating the f value for the time series shown. To convert the f value into a frequency in hertz, use the following relation: 5(integer f value - 31) Frequency in hertz = 420 + Accordingly, the carrier plot is labeled 31. Note that the C-power trace in Fig. 9 corresponds to time-series 31 when allowance is made for dB vs linear scales on amplitude.

f value:17-71Amplitude lo ": ti-,~~~~~~~~~~ - ------- -71 7N. 7~~~r- 7f- -: -- - -;. _. _7- 7 Ir7::: First Plot.I -:::~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~F Second Plot.t; Pas Po Position:: t'::4Fig. 11. Prototype constant frequency plot:

28 4.3 Preliminary Conclusion The most striking feature of the S(f, t) function is that it seems to change slowly both in frequency f and time t. Figures 12 to 15 show a sequence of spectra spanning over one hour. At the end of this time, the gross amplitude structure, especially the frequencies of the predominant nulls, has not changed appreciably. The frequency boundaries of the areas of linear phase angle behavior have also not shifted to an appreciable extent. Future work will consist of attempts to exploit the relative stationarity of the spectrum exhibited here, with some emphasis on better methods of display.

29 R(f) ae'\ 395 Hz 445 Hz Fig, 12. Spectrum at t0o 1118 hrs, 25 November 1970 R(f) _ *0 i i __ 395 Hz 445 Hz Fig. 13. Spectrum at t0 + 1 minute, 40 seconds

30 R(f) 0 (f) 395 Hz 445 Hz Fig. 14. Spectrum at to + 10 minutes R(f) 8 (f) 395 Hz 445 Hz Fig. 15. Spectrum at tO + 1 hour, 3 minutes, 20 seconds

APPENDIX A Constant Time Plots Section 4.2.1 explains how to interpret the constant time plots that follow.

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APPENDIX B Constant Frequency Plots Section 4.3.2 explains how to interpret the constant frequency plots that follow. 78

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REFERENCES 1. J. C. Steinberg and T. G. Birdsall, "Underwater Sound Propagation in the Straits of Florida, " Acoust. Soc. Am., Vol. 39, No. 2, February 1966, pp. 301-315. 2. R. M. Heitmeyer, Underwater Sound Propagation in the Straits of Florida: The Preliminary Analysis of the MIMI Experiment of 1970, Technical Report No. 213, Cooley Electronics Laboratory, The University of Michigan, Ann Arbor, June 1971. 3. A. Papoulis, Probability, Random Variables, and Stochastic Processes, McGraw-Hill Inc., 1965, pp. 373-377. 110

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DOCUMENT CONTROL DATA. R & D''.tr1,lt, riseI lir ^ ation Ci titk, hodr oP aihlifrnt attd lnd.kndn annointiortft r f b n, antrod whe, iho overall repor( i, cta lied) 1. TIQIMNV AC IIVI TV (CorporFIe rIbhor) 2a. REPQORiT SECUTY CLASSIFICATION Cooley Electronics Laboratory Unclassified University of Michigan l. I10 Ann Arbor, Michigan 48105; nwtrowr tITLt A MIMI Propagation Study: Coherent Spectra of Wideband Underwater Acoustic Receptions in the Straits of Florida, 25 November 1970 4. at"L *" c T' Vt1EO.t tSM 00 orf-por and IncatJ" ve dat*) Technical Report May 1973; 7 d AU I0SI teFlI Fet, MFiddle InM al, iat naome ) Gerald N. Cederquist I. lREPORT DATE 741. TOTAL NO. OF PAGES lib. NO. OF REFS May 1973 128 3 4.. CNTRAC t or GRANt A,, T, NO. S,. ORIGINATOR'S REPORT NUMBE.RI.S N00014- 67- A-0181-0035 TR 215 b. PROJECT NO. C. 9b. OTHER REPORT NO(s) (Any other numbers that may be Aeaignnd thle report) d. 004860-1-T I0. ODISTRIUTION STATEU.ENT Approved for public release; distribution unlimited. tI. SUPPLtMEWnTARY NOtES 12. SPONSORING MILITARY ACTIVITY Office of Naval Research Department of the Navy | Arlington, Virginia 22217 I). LAstOSRCt In an underwater acoustic propagation experiment conducted in November 1970 a periodic broadband signal, centered about 420 Hz, was transmitted across the Straits of Florida continuously for 19 days. This report presents the prelimin results from spectral analysis of the acoustic reception of this signal at Bimini, Bahamas, during a 7.61-hour period on 25 November 1970. The spectra are noteworthy for their slow rate of change during this period. Plots of the spectral amplitude and phase of the reception are presented for a 50 Hz bandwidth centered about 420 Hz. DD.'~"no'. 1473 S,_curty Cleaitkdion

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