Waveguide invariant analysis for modeling time frequency striations in a range dependent environment.

Transcription

1 Waveguide invariant analysis for modeling time frequency striations in a range dependent environment. Alexander Sell Graduate Program in Acoustics Penn State University Work supported by ONR Undersea Signal Processing

2 Overview Modal Interference Patterns Spectral striation patterns Waveguide Invariant formulations Application to CALOPS dataset Performance Improvements Conclusions

3 Mode 2 Mode 4 Mode 2 Modal Interference λ k n nm rn prop = k rn 2π k rm = ω ωn c 2D 1 = + λ 2 The number of propagating modes is proportional to the water 3 depth. The closer the interfering modes are in frequency, the longer the interference Length.

4 Accounting for Range Dependence Mode 2 Mode 4 Mode 2 Mode 4 4

5 Interference from two modes propagating over constant bathymetry and sloped bathymetry Constant water column depth Linearly decreasing water column depth 5

6 What do these interference patterns look like? Time [minutes] Frequency [Hz]

7 A better way to understand striations Modal interference can be understood in terms of phase and group speed = S S = v v f pm pn pm pn 0λ nm 1 1 ( ) 1 ω = ω S S = Ω c c gm gn vgm vgn r0 c At fixed frequency, the separation of our striations is based on phase speed. At fixed range, the separation of our striations is based on group speed.

8 The Waveguide Invariant Parameter Phase and group speed differences describe the horizontal and vertical spacing of our striations. We develop the invariant parameter β S = S The invariant parameter is not the slope of our spectral striations, but contains information necessary to describe them. p g

9 What assumptions must we make? To excite enough modes to create a striation pattern, our source must radiate a broadband signal In order for the invariant to be useful in range and depth classification, our waveguide must be range and depth dependent. Further, we must know the bathymetry and sound speed profile between source and receiver

10 Depth (meters) 10

11 Beamformed signal from 125 element horizontal line array located 9 nm east of Port of the Everglades, FL. 11

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13 Model Spectrogram Time [minutes] Frequency [Hz]

14 Accounting for Range Dependence Recall = S S = v v f pm pn pm pn 0λ nm 1 1 ( ) 1 ω = ω S S = Ω c c gm gn vgm vgn r0 c To get a range dependent invariant, we must average the depth dependent group speeds at points between the source and receiver n ( ) r S p recr n 1 n β( r) =, Sg( r) Sg( x) dx n S () r r g These equations were taken from a 1999 paper by Gerald D Spain and W. A. Kuperman 0

15 Depth (meters) 15

16 Time varying bathymetry between APL Turquoise and receiver 16

17 Relationship between striation slope and the invariant parameter For changing source water column depth, but constant source/receiver range we have ω t) β( t) ω ( = 0 β0 For constant source water column depth, but changing source/receiver range we have β recv ω() t rt () = ω0 r0 β ( t) To account for changes in both parameters, we have ω() t β( t) β rt () β( t) ω = 0 r0 β0 These equations were taken from a 1999 paper by Gerald D Spain and W. A. Kuperman recv 17

18 Applying the Invariant with starting frequencies of 70, 105, and 140 Hz 18

19 How can we improve this? We still need to include range varying bathymetry, but we also need to Include contributions from all propagating modes Weight the modal contributions based upon source and receiver depth Include a depth varying sound speed profile

20 Eβ () r = Lω mid βlm()/ r β Blm [ FC + FS ] 2 lm S p ( recr ) S ( ) l p recr m βlm, ( r) = r 1 ( S ( ) ( )) g x S l g x dx m r FC = C( γ+ ) + C( γ ) F = S( γ ) + S( γ ) S 0 1/2 r 1 ( ( ) ( )) 1 1 midr mid Sg x S / ( ( ( )) l g x dx Q m lm r r 2 0 γ ± = ω βπ ) ± β β ω This formulation was an adaptation of a range independent mid Q = waveguide invariant distribution by Dan Rouseff and Robert Spindel ( ω ω ) max We now have the RaDWID + min

21 Advantages of RaDWID Includes the following: Source depth/receiver depth (modal weighting) Bathymetry between source and receiver Sound speed profile between source and receiver Output is a distribution, which makes for efficient inclusion of the above parameters into Bayesian localization framework

22 RaDWID for APL Turquoise

23 Applying RaDWID to Modeled Spectrogram of Ship Track 23

24 Improving RaDWID Performance RaDWID is sensitive to changes in environmental parameters. Source location (range and depth) Bathymetry along propagation path Sound speed profile along propagation path Better understanding of parameter (environmental) uncertainty will help us sharpen the peaks of the distribution.

25 Invariant Distribution for Massachusetts downward refracting profile D = 70, RD = Normalized E Beta source depth [m]

26 Conclusions The RaDWID is a synthesis of two waveguide invariant models. RaDWID connects spectral striations with acoustically important environmental parameters. We need to better understand environmental uncertainty to improve performance.

27 References and Acknowledgements A. B. Baggeroer, Estimation of the Distribution of the Interference Invariant with Seismic Streamers, AIP Conference Proceedings, vol. 621, pp , G. L. D Spain and W. A. Kuperman, Application of waveguide invariants to analysis of spectrograms from shallow water environments that vary in range and azimuth, J. Acoust. Soc. Am., vol. 106, no. 5, pp , C. W. Jemmott, Model-based recursive Bayesian state estimation for single hydrophone passive sonar localization, PhD. Thesis, The Pennsylvania State University, D. Rouseff and R. C. Spindel, Modeling the Waveguide Invariant as a Distribution, AIP Conference Proceedings, vol. 621, pp , [Work supported by ONR Undersea Signal Processing]