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ARL The University of Texas at Austin Methods of characterization of seabed physics for a shallow water environment D. P. Knobles Colleagues: P. Wilson, J. Goff S. Joshi, L. Collins, S. Cho 155th Meeting of the Acoustical Society of America

  1. ARL The University of Texas at Austin Methods of characterization of seabed physics for a shallow water environment D. P. Knobles Colleagues: P. Wilson, J. Goff S. Joshi, L. Collins, S. Cho 155th Meeting of the Acoustical Society of America Paris, France June-July 2008 Work supported by ONR Code 321 OA

  2. ARL Outline The University of Texas at Austin • Description of measurements and analysis approach • Inversion and maximum entropy principle • Application to low frequency data taken on the New Jersey continental shelf  Inversion for global minimum  Marginal probability distributions  Sensitivity to signal processing  Transmission loss uncertainty  Comparison to measured uncertainty

  3. ARL Description of measurements and analysis The University of Texas at Austin From limited acoustic measurements in ocean water column • Inverse problem solved for global minimum environmental solution  Better resolution of attenuation is inferred from long range propagation data –Inference of Biot parameter bounds –Scattering parameters inferred from reverberation measurements –Modeling of wind generated ambient noise

  4. ARL Inversion in a nutshell The University of Texas at Austin Consider a space Γ with volume Ω that contains source-receiver positions, kinematical parameters, and ocean waveguide parameters W is a vector in Γ D - Measured data vector M - Modeled data vector An objective of cost function defined C( W ) = C( D , M ( W )) ~ 1 - correlation ( M · D ) Inversion algorithm is used to explore C( W ) Simulated annealing is used to find the global minimum C min = C( W gm )

  5. ARL Description of measurements and analysis The University of Texas at Austin But • Uncertainty of waveguide parameters leads to uncertainty in propagation • How does one quantify the uncertainty? • Under what circumstances does uncertainty obtained from models and inversion methods = true environmental uncertainty? • How does this uncertainty affect inferences of seabed physics from basic measurements? Therefore, one needs a mathematical framework from which to compute probability distributions

  6. ARL Ideas for distribution The University of Texas at Austin • Cost measures error relative to horizontal stratification • Uncertainties arise from small fluctuations relative to horizontal stratification • One does not know the distribution; thus derive the most conservative distribution that only predicts specific constraints

  7. Uncertainty from Maximum ARL Entropy Principle The University of Texas at Austin What is the probability distribution for a specific parameter in W or transmission loss? Following Jaynes (Phys. Rev. 106 1957) Gibbs or Shannon relative Entropy Analogy with statistical mechanics for a closed system in thermodynamic equilibrium with heat reservoir is global minimum determined from simulated annealing average value of cost function space = 1/N ∑ C(W i )

  8. Maximum entropy principle and ARL canonical ensemble The University of Texas at Austin canonical ensemble partition function Average <C> constraint determines T Entropy in terms of Z, T, and <C>

  9. ARL Mean, standard deviations, and marginals The University of Texas at Austin Reduced or marginal distribution

  10. ARL Evaluation of volume integrals The University of Texas at Austin A point in Γ

  11. ARL Volume integrations The University of Texas at Austin • Sampling of Γ by random walks in limit that N becomes large ~ Monte Carlo sampling • Convergence criteria: Marginal distributions remain unchanged when number of samples increased • ~ 2x10 6 samples appears sufficient for problem considered

  12. ARL Hybrid Cost Function The University of Texas at Austin Center Frequency Center Frequency Averaged Source Model Cross Level Spectrum 2 Σ < > D D* | | M* M | | S Center Frequency i j i j f Averaged Σ element pairs, Cross–Spectral sequences Data C = 2 Σ center < > D D* 2 N < > | D RL | 2 Σ | D REF | frequencies / D D* i j D D* = CEN i j i j element pairs, bins sequences Cross Spectrum Normalization for Center Frequency Averaging 2 Σ | D | | D REF | = N BINS | D | 2 / N ELTS i Minimization of Cost Gives SLs elts Cross Spectrum Normalization Σ + c.c. < > D D* for Center Frequency Average RL M* M i j i j 2 Σ | D RL | = element pairs, | D | 2 / N ELTS ( ) N BINS | | = | | sequences S i f bins,elts Σ 2 | | 2 M* M i j element pairs, sequences

  13. ARL The University of Texas at Austin Hybrid Cost Function, cont. 0 ≤ C ≤ 1 Substituting for gives correlation form of cost function: | | | | S f coherent sum over pairs and sequences incoherent sum over center frequency 2 Σ + c.c. < > D D* M* M i j i j Σ element pairs, 2 C = 1 – sequences 2 Σ Σ 2 center | | < > D D* M* M N frequencies i j i j CEN element pairs, element pairs, sequences sequences Includes gain in the coherent sum over pairs and sequences to fit multipath arrivals and source track dependence. Includes amplitude information to fit TL shape. Greater weight for higher RL data. Increases number of unknowns.

  14. ARL Outline The University of Texas at Austin • Description of measurements and analysis approach • Inversion and maximum entropy principle • Application to low frequency data taken on the New Jersey continental shelf  Inversion for global minimum  Marginal probability distributions  Sensitivity to signal processing  Transmission loss uncertainty  Comparison to measured uncertainty

  15. ARL Application to New Jersey experiment The University of Texas at Austin Experimental goals • Infer frequency dispersion of seabed attenuation • Test various theories of seabed physics that predict attenuation • Effects of seabed variability on propagation • Sensitivity of ambient noise and reverberation on seabed physics

  16. ARL Experimental area The University of Texas at Austin August-September 2006 SW06 BTEC measurement September 2003

  17. ARL Array locations during SW06 The University of Texas at Austin

  18. ARL The University of Texas at Austin Sub-bottom layering along dip-line Design of experiment was to place L-array on uniform sand sheet Chirp reflection image provided by John Goff

  19. ARL The University of Texas at Austin Sub-bottom between two L-arrays ? Image provided by John Goff Chirp reflection image provided by John Goff

  20. Comparison of TL at global minimum ARL of hybrid cost function; Array 2 The University of Texas at Austin Measured Global minimum solution 50 60 53 Hz 70 80 Transmission loss - dB 40 Cost function used 50 complex beam data 103 Hz 60 for two subapertures 70 with full HLA divided into 40 two equal lengths 50 203 Hz 60 HLA aperture = 230 m 70 50 253 Hz 60 70 80 1 2 3 4 5 Range - km

  21. Methodology to extract frequency ARL dependence The University of Texas at Austin Horizontal variability is small enough on range scales of 20 km to extract attenuation structure over large bandwidth • Use coherent Full Field Inversion (FFI) technique on low-frequency tow data and impulsive sources at two array locations to invert for – Sound speed structure in sediment • Include range-variability with PE RAM to extract attenuation • Extend to higher frequencies at Array 1 location

  22. Inferred attenuation and comparison to Biot ARL model The University of Texas at Austin Biot parameters bounds determined from basic measurements by Goff

  23. ARL Comparison to Zhou study The University of Texas at Austin

  24. ARL Example of use of global minimum solution: Modeling measured reverberation time series with Lamberts law The University of Texas at Austin Nautreverb µ =-37.0 dB

  25. Example of use of global minimum solution: Extracted µ ARL values assuming Lamberts law The University of Texas at Austin 0 -5 -10 10 log ( µ ) - dB -15 -20 -25 -30 -35 -40 -45 -50 0 200 400 600 800 1000 1200 1400 1600 1800 Frequency - Hz

  26. ARL Measured wind noise during TS Ernesto The University of Texas at Austin a b

  27. ARL Wind noise relative to deep water location The University of Texas at Austin 12 10 8 Δ - dB 6 4 Measured Modeled using global minimum solution 2 Modeled using NJCS geo-acoustic profile but with linear frequency dependence of attenuation 0 0 500 1000 1500 2000 2500 3000 3500 Frequency - Hz

  28. ARL The University of Texas at Austin CSS time series comparison Range = 4.7 km SD=26.2 m RD=69.5 m BW=10-3000 Hz Measured 2500 Modeled 1250 Amplitude 0 -1250 Sensitive to outer shelf layer properties -2500 -3750 0.125 0.250 0.375 0.500 0.625 Time - sec

  29. ARL Cost envelopes for CSS inversions near Array 1 The University of Texas at Austin 1st layer Thin hard sand 2nd layer over thicker softer layer 2nd layer

  30. ARL Marginal probability distributions of position and kinematical parameters at Array 2 The University of Texas at Austin Range @ t 0 - m Bearing @ t0 - deg Source depth - m Mean = 1029 m Mean = 29.8 m Mean = 85.6 deg σ = 141 m σ = 1.05 m σ = 1.77 deg Speed - m/s Course - deg Mean = 2.54 m/s Mean = 98.1 deg σ = 0.21 m/s σ = 3.74 deg

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