Modeling of Sound Wave Propagation in the Random Deep Ocean

Transcription

1 Modeling of Sound Wave Propagation in the Random Deep Ocean Jin Shan Xu MIT/WHOI Joint Program in Applied Ocean Science and Engineering John Colosi Naval Postgraduate School Tim Duda Woods Hole Oceanographic Institution

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3 OUTLINE Introduction Observations: Ocean Environmental Measurements Sound Wave Fluctuation Measurements Modeling of Acoustic Wave Propagating through Random Deep Ocean Garret & Munk Internal Wave Spectrum Rytov Theory Monte Carlo Numerical Simulations Comparison: Observations, Theory and Monte Carlo Simulations Summary

4 Hubble Ultra Deep Field Introduction It is an Image of a small region of space composited from Hubble Space Telescope. It is the deepest image of the universe ever taken in visible light, looking back in time more than 13 billion years. It is contains an estimated 1, galaxies.

5 Introduction (continued) We know quite a lot about out space, but how much we know about our ocean? Why do we need a space-based observatory rather than a ground-based telescopes? it remains a fact that human beings crossed a quarter million miles of space to visit our nearest celestial neighbor before penetrating just two miles deep into the earth's own waters to explore the Midocean Ridge. The Eternal Darkness: A Personal History of Deep-Sea Exploration, Robert D. Ballard We know a lot more about moon surface than our deep ocean.

6 Introduction (continued) The angular resolution of the ground-based telescope is limited by the turbulence in the atmosphere, which causes stars to twinkle. Acoustic waves are today the only practical way to carry information underwater, and it is has analogical limitations imposed by the random fluctuating medium in the ocean as electromagnetic wave put by the turbulence in the atmosphere. Motivation and Application Quantitatively understand the limits that randomness imposes on the practical uses of wave propagation Global underwater navigation and communication Global Ocean temperature monitoring

7 Review 197 s and 198 s, ocean acoustic WPRM focused on high acoustic frequency and short-range experiments. There were successful finding based on weak fluctuations theory and internal wave models, but it is limited in the short-range, high acoustic frequency, narrowband. [Munk et al., 1976]. From late 198 s to present, low-frequency basin scale experiments were motivated to measure ocean climate change, which requests the low frequency, broadband and long range acoustic transmission. Some puzzles were found that, such as : Acoustic fluctuations were much stronger than previously predicted, especially for acoustic energy which traveled within a few hundred meters vertically from the sound-channel axis in SLICE89 [Duda et al, 1992] In ATOC AET94, It showed surprising vertical and temporal coherence for the early ray-like arrivals which were far in excess of the currently predicted values pulse time spreading to be far lower than predictions; intensity fluctuations were slightly larger tan predicted. Shadow zone arrivals recorded in the NAVY SOSUS extended significantly in depth and in time. [Colosi 1996,1999; Dushaw,1999] It is a twofold problem, which includes two interrelated topics: Sound Propagation and Random Media. It is fair to say that essentially no progress has been made by anyone attempting a direct attack on the general theory without a deep physical understanding of a particular medium.- Stanley M. Flatte, 1983

8 Objectives First is quantification of ocean sound speed space-time scales due to internal waves continuum, near inertial waves, internal tides and sub-inertial motions from the North Pacific Acoustic Laboratory(NPAL)98-99 environmental data. To understand how low frequency sound wave propagates through the random deep water environment, considering that internal-wave-induced sound-speed fluctuations are the dominant source of high-frequency variability of the acoustic wave field in the ocean.

9 Random fluctuating medium in the Deep Ocean Quantification of ocean sound speed space-time scales due to internal waves, mesoscale eddies, internal tides NPAL Environmental Mooring East 125 m (Buoy) m MicroCAT MicroTemp ADCP 516 m 66 m 696 m 53 m (Anchor)

10 Time series of Temperature and salinity at different depths 16 Temperature measurement from Eastern Mooring 14 Temperature ( o C) Salinity measurement from East Mooring 34 Depth :159 m Salinity ( PSU ) Depth :31 m Depth :46 m Yearday, 1998

11 Frequency Spectrum of the sound speed at depth 49m 1 1 Frequency Spectrum of the Sound Speed in the East Mooring: Depth: 49M Cutoff Frequency Inertial Frequency f 1 Semidiurnal Tide Power Spectral Density : (m/s) 2 /(CPD) Sub inertial Band Statistical Tide Super inertial Band Deterministic Tide 95% Frequency (CPD)

12 Garrett-Munk universal internal wave spectrum In the lower and main thermocline of ocean, the GM spectrum provides a zeroth order description of internal waves. The introduction of the GM model was a critical breakthrough in the 197s to predicting observed acoustic fluctuations. There is a standard method to connect the sound speed fluctuation with displacement of internal waves. Internal-wave-induced sound-speed perturbations are proportional to the product internal-wave-induced vertical displacements and potential sound-speed gradient.

13 Frequency Spectrum of the Sound Speed Fluctuation in Super-inertial band at different depths / GM Spectrum East Mooring 16 m 4 m 64 m 95% Frequency (cph)

14 XBT measurements of Temperature in space scale. Cruise 1998 : Temperture Fluctuation ( C) Depth [m] o Cruise 1999 : Temperture Fluctuation ( C) o ( C) Depth [m] Depth [m] 1 ( C) Depth [m] Longitude (ow)

15 Vertical/Horizontal Wavenumber Spectrum of the Temperature 1 2 Vertical Wavenumber Spectrum XBT GM Horizontal Wavenumber Spectrum XBT GM ( o C) 2 /CPM 1 1 ( o C) 2 /CPM % % Cycle per Meter Cycle per Meter

16 What We Found The frequency spectra in the internal wave band are very GMlike. Similar observations show GM-like characteristics in the vertical/horizontal wavenumber Spectrum Internal wave induced sound-speed fluctuations are the dominant source of high-frequency variability of acoustic wave field in the deep ocean. In general, the comparison result shows GM internal wave model is a well set-up model under certain conditions (like in the North Pacific)

17 Space-time scales of Acoustic fluctuations for 75-Hz, broadband transmissions to 87-km range in the eastern North Pacific Ocean Depth (m) Sound Speed (m/s) Depth (m) Buoyancy Frequency (cph) North Pacific, November, 1994 Over 6 day period Broadband 75 Hz@ 65 m depth, 2-element, 7-m long distant, spanning the depth 9-16m 7 transmission, 4 pulses 2 minute

18 yearday, Pulse: 2 Depth ( m ) Examples of Observed Wavefronts yearday, Pulse: 2 Depth ( m ) Travel Time ( s ) 4 Ray Traces for NVLA W avefronts : ID-3,+4-6 Time Front with index number -5 ID = -3 ID = +4-8 Index -3 Index Depth ( m ) Range ( km ) Travel Time ( s )

19 Procedure of Processing Data 15 Depth (m) Time (second) 4 Depth ( m ) Depth ( m ) ψ 2 (db re max) φ w (rad) φ u (rad) ψ 2 (db re max) φ w (rad) φ u (rad) Good transmission 4 pulse per transmission 2 Hydrophone Depth ( m ) φ c (rad) φ c (rad) 5 5 3X4X2= 24 Depth ( m ) τ (min) Index τ (min) Index 4 1 1

20 Observed Intensity Time Series from Different Hydrophones Phone # 1 25 Index 3 Index 4 3 I (db) 35 4 Phone # 1 25 Index 3 Index 4 3 I (db) 35 4 Phone # 2 25 Index 3 Index 4 3 I (db) Yearday

21 Three different time scales: 2, 4 minute and 6 day. 2 Mins 4 Mins 6 Days ID -3 ID4 ID -3 ID4 ID -3 ID4 <Phi 2 > 1/2 (rad) <I 2 > 1/2 (db) SI Log-amplitude 95% -- 6 days ID -3, 6 days ID 4, 6 days ID -3, 4min ID 4, 4min ID -3, 2min ID 4, 2min Phase ID -3, 4min ID 4, 4min ID -3, 2min ID 4, 2min S χ (1/CPH) S φ (1/CPH) % -- 4 Min 95% -- 2 Min % -- 4 Min 95% -- 2 Min Frequency (CPH) Frequency (CPH)

22 Rytov theory (Munk& Zachariasen, 1976, JASA) Why there is such big difference between arrivals in the low frequency region? Ray Traces for NVLA W avefronts : ID-3,+4-1 Depth ( m ) Depth ( m ) -2-3 ID = -3 ID = Resonance condition between ray and internal waves -5-6 ID = -3 ID = Range ( km ) Rays with high grazing angles do not acquire scattering contribution due to low frequency internal waves

23 Rytov theory - Acoustic Filer and its cutoff frequency ID -3 ID +4 Depth (m) 1 2 Depth (m) Range (km) Range (km) ω L (cph).4 ω L (cph) Range (km) Range (km) 1 ID 4 (Green), σ lni = (db), ID 3 (Blue), σ lni = (db) 1 2 ID 4 (Green), <φ 2 > = ID 3 (Blue), <φ 2 > = S χ (1/cph) 1 4 S φ (1/cph) Frequency (cph) Frequency (cph)

24 Log-amplitude 95% -- 6 days ID -3, 6 days ID 4, 6 days ID -3, 4min ID 4, 4min ID -3, 2min ID 4, 2min Phase ID -3, 4min ID 4, 4min ID -3, 2min ID 4, 2min S χ (1/CPH) S φ (1/CPH) % -- 4 Min 95% -- 2 Min % -- 4 Min 95% -- 2 Min Frequency (CPH) Frequency (CPH)

25 Comparison Between AET experiment and Rytov theory of Frequency spectrum 1 1 Log-am plitude 1 4 Phase % -- 6 days 1 2 S χ (1/CPH) S φ (1/CPH) % -- 4 Min 95% -- 2 Min % -- 4 Min 95% -- 2 Min Frequency (CPH) Frequency (CPH)

26 Comparison Between AET experiment and Rytov theory of Vertical Wavenumber spectrum 1 4 Log Amplitude ID 3 ID Phase ID 3 ID % 1 95% Wavenumber CPM Wavenumber CPM

27 Monte Carlo Simulation Monte Carlo simulations are carried out by propagating the sound through the time evolved Internal wave field, which follows the internal wave dispersion relationship. Two Types of Monte Carlo simulation are implemented: Narrow Band and Broad Band. Narrow band simulation is implemented by sending out two narrow beams with different beam tilt to simulate the multipath effect of AET experiment. Broad band simulation is implemented by Fourier synthesis of CW results, which is composed of 6 different frequencies (from 45 to 15Hz).

28 Internal wave field simulations depth km Range (km) depth km Time (Day)

29 Spectra of Simulated Internal Wave 1 3 Vertical Spectrum GM VSP Simulation GM Power Spectral Density (m) 2 /cph Cycle per Meter 1 4 Horizontal wavenumber spectrum Simulation GM Frequency (cph) m 2 /CPM CPM

30 Narrow Band Beam Simulations Index Depth (km) Range ( km ) Index Depth (km) Range ( km ) 4

31 Comparison Between MZ theory and Monte Carlo Simulation 1 MZ Broad Band Narrow Band 1 ID 4: S χ (1/CPH) 1-5 ID 4: S φ (1/CPH) Frequency (CPH) Frequency (CPH) 1 1 ID -3: S χ (1/CPH) 1-5 ID -3: S φ (1/CPH) Frequency (cph) Frequency (cph)

32 Comparison Between Rytov theory and Monte Carlo Simulation of vertical wavenumber spectra MZ Broad Band Narrow Band ID 4: S χ (1/CPM) ID 4: S φ (1/CPM) Wavenumber CPM Wavenumber CPM ID 3: S χ (1/CPM) ID 3: S φ (1/CPM) Wavenumber CPM Wavenumber CPM

33 Summary and future direction Ocean Environmental Observations show the GM internal wave model is a well setup model under certain conditions. The Rytov theory model and numerical model based on GM internal wave ocean model successfully describe the statistical variability of the acoustic fluctuations after 87 km range transmission in the deep ocean. Importantly the comparisons show that a resonance condition exists between the local acoustic ray and the internal wave field such that only the internal waves whose crests are parallel to the local ray path will contribute to acoustic scattering. This effect leads to an important filtering of the acoustic spectra relative to the internal wave spectra, such that rays with high grazing angles do not acquire scattering contribution due to low frequency internal waves. We believe that this is the first observational evidence for the acoustic ray and internal wave resonance. We have solved the acoustic scattering case after a one and two upper turning points. For long range acoustic propagation of order 1-km involves order 1 or 2 scattering events, so can we push this theory prediction to further range? Improve ocean sound speed fluctuation model. GM internal wave model is still dominant, but we know there are some other processes other than internal waves. Broadband modeling of acoustic wave propagation.