ARL The University of Texas at Austin Methods of characterization - - PowerPoint PPT Presentation

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ARL The University of Texas at Austin Methods of characterization - - PowerPoint PPT Presentation

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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

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SLIDE 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

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SLIDE 2

ARL

The University of Texas at Austin

Outline

  • 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
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SLIDE 3

ARL

The University of Texas at Austin

Description of measurements and analysis

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

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SLIDE 4

ARL

The University of Texas at Austin

Inversion in a nutshell

Consider a space Γ with volume Ω that contains source-receiver positions, kinematical parameters, and ocean waveguide parameters W is a vector in Γ An objective of cost function defined C(W) = C(D, M(W)) ~ 1 - correlation (M·D) D - Measured data vector M - Modeled data vector

Inversion algorithm is used to explore C(W)

Simulated annealing is used to find the global minimum Cmin = C(Wgm)

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SLIDE 5

ARL

The University of Texas at Austin

Description of measurements and analysis

  • 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?

But Therefore, one needs a mathematical framework from which to compute probability distributions

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SLIDE 6

ARL

The University of Texas at Austin

Ideas for distribution

  • 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

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SLIDE 7

ARL

The University of Texas at Austin

Uncertainty from Maximum Entropy Principle

Gibbs or Shannon relative Entropy

is global minimum determined from simulated annealing

average value of cost function space = 1/N ∑ C(Wi) What is the probability distribution for a specific parameter in W or transmission loss? Following Jaynes (Phys. Rev. 106 1957)

Analogy with statistical mechanics for a closed system in thermodynamic equilibrium with heat reservoir

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SLIDE 8

ARL

The University of Texas at Austin

Maximum entropy principle and canonical ensemble canonical ensemble partition function Average <C> constraint determines T Entropy in terms of Z, T, and <C>

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SLIDE 9

ARL

The University of Texas at Austin

Mean, standard deviations, and marginals

Reduced or marginal distribution

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SLIDE 10

ARL

The University of Texas at Austin

Evaluation of volume integrals

A point in Γ

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SLIDE 11

ARL

The University of Texas at Austin

Volume integrations

  • 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

  • ~ 2x106 samples appears sufficient for

problem considered

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SLIDE 12

ARL

The University of Texas at Austin

Hybrid Cost Function Σ

/

bins D D* i j

< > |D RL|

2 = 2

|DREF|

D D* i j

|D RL| =

2 / NELTS

|D |

i

Σ

2

bins,elts

NBINS ( )

Cross Spectrum Normalization for Center Frequency Average RL

Σ |D |

i

|D |

2 / NELTS elts

2

|DREF| = NBINS

Cross Spectrum Normalization for Center Frequency Averaging S

| |

f

| | M* M

i j

Σ

element pairs, sequences D D* i j

< >

2

C =

Σ

element pairs, sequences D D* i j

< >

2

Σ

center frequencies CEN

N

Center Frequency Averaged Cross–Spectral Data Center Frequency Averaged Source Level Center Frequency Model Cross Spectrum S

| |

f

| | = 2

M* M i j 2

| |

Σ

element pairs, sequences M* M i j

Σ

element pairs, sequences D D* i j

< >

+ c.c.

Minimization of Cost Gives SLs

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SLIDE 13

ARL

The University of Texas at AustinHybrid Cost Function, cont.

Σ

element pairs, sequences D D* i j

< >

2

Σ

center frequencies CEN

N

2

M* M i j 2

| |

Σ

element pairs, sequences M* M i j

Σ

element pairs, sequences D D* i j

< >

+ c.c. 2 coherent sum over pairs and sequences incoherent sum

  • ver center frequency

Substituting for gives correlation form of cost function:

S

| |

f

| | 0 ≤ C ≤ 1

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.

C = 1 –

Greater weight for higher RL data. Increases number of unknowns.

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SLIDE 14

ARL

The University of Texas at Austin

Outline

  • 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
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SLIDE 15

ARL

The University of Texas at Austin

Application to New Jersey experiment

  • 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

Experimental goals

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SLIDE 16

ARL

The University of Texas at Austin

Experimental area

August-September 2006 SW06 BTEC measurement September 2003

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SLIDE 17

ARL

The University of Texas at Austin

Array locations during SW06

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SLIDE 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

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SLIDE 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

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ARL

The University of Texas at Austin

Comparison of TL at global minimum

  • f hybrid cost function; Array 2

Transmission loss - dB 53 Hz 103 Hz 203 Hz 253 Hz Measured Global minimum solution

Range - km

1 2 3 4 5

50 60 70 80 50 60 70 80 40 50 60 70 40 50 60 70

Cost function used complex beam data for two subapertures with full HLA divided into two equal lengths HLA aperture = 230 m

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ARL

The University of Texas at Austin

Methodology to extract frequency dependence

  • Use coherent Full Field Inversion (FFI) technique
  • n 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

Horizontal variability is small enough on range scales of 20 km to extract attenuation structure over large bandwidth

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SLIDE 22

ARL

The University of Texas at Austin

Inferred attenuation and comparison to Biot model

Biot parameters bounds determined from basic measurements by Goff

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SLIDE 23

ARL

The University of Texas at Austin

Comparison to Zhou study

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SLIDE 24

ARL

The University of Texas at Austin

Example of use of global minimum solution: Modeling measured reverberation time series with Lamberts law

Nautreverb

µ=-37.0 dB

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SLIDE 25

ARL

The University of Texas at Austin

Example of use of global minimum solution: Extracted µ values assuming Lamberts law 10 log (µ) - dB

Frequency - Hz

  • 50
  • 45
  • 40
  • 35
  • 30
  • 25
  • 20
  • 15
  • 10
  • 5

200 400 600 800 1000 1200 1400 1600 1800

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SLIDE 26

ARL

The University of Texas at Austin

Measured wind noise during TS Ernesto

a b

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SLIDE 27

ARL

The University of Texas at Austin

Wind noise relative to deep water location

2 4 6 8 10 12

Frequency - Hz Δ - dB

Measured Modeled using global minimum solution Modeled using NJCS geo-acoustic profile but with linear frequency dependence of attenuation 500 1000 1500 2000 2500 3000 3500

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SLIDE 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

  • 3750
  • 2500
  • 1250

1250 2500

Amplitude Modeled Measured

0.125 0.250 0.375 0.500 0.625

Time - sec

Sensitive to outer shelf layer properties

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SLIDE 29

ARL

The University of Texas at Austin

Cost envelopes for CSS inversions near Array 1

1st layer 2nd layer 2nd layer Thin hard sand

  • ver thicker

softer layer

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SLIDE 30

ARL

The University of Texas at Austin

Marginal probability distributions of position and kinematical parameters at Array 2

Range @ t0 - m Bearing @ t0 - deg Source depth - m Speed - m/s Course - deg

Mean = 1029 m σ = 141 m Mean = 85.6 deg σ = 1.77 deg Mean = 29.8 m σ = 1.05 m Mean = 2.54 m/s σ = 0.21 m/s Mean = 98.1 deg σ = 3.74 deg

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SLIDE 31

ARL

The University of Texas at Austin

Marginal probability distributions of selected environmental parameters

~1715 m/s Water depth - m Ratio(layer 1) ~1630 m/s ± 26 m/s Measured Thickness(layer1) - m Density (layer 1) - g/cc Ratio(layer 2) Thickness(layer2) - m No information on this parameter

Mean = 70 m σ = 0.57 m Mean = 1.09 σ = 0.0178 Mean = 13.9 m σ= 8.5 m, long

tail influence

Mean = 1.83 g/cc σ = 0.1 g/cc

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SLIDE 32

ARL

The University of Texas at Austin

Global minimum solution and <TL>± σ solutions compared to measured TL

53 Hz 103 Hz 203 Hz 253 Hz gm solution mean Mean ± σ

1 2 3 4 5

Range - km

40 60 80 40 60 80 40 60 80 40 60 80

TL - dB

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SLIDE 33

ARL

The University of Texas at Austin

Measurement of variability along propagation track: Single J-15-1 tow

2 4 6 8 10 12 14 16 18 20

Range - km

30 50 70 90

Transmission loss - dB

53 Hz 103 Hz 203 Hz 253 Hz 503 Hz

30 50 70 90 30 50 70 90 30 50 70 90 30 50 70 90

SWAMI-32 SWAMI-52 Range variability is small between two arrays “Average” Uncertainty ~ 5 dB Expect greater variability along dip-line

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SLIDE 34

ARL

The University of Texas at Austin

Computed TL s from maximum entropy principle versus range

Standard deviation of TL - dB Range - km 2 4 6 8 10 12 14 16 18 20

8 6 4 2

53 Hz 103 Hz 203 Hz 253 Hz

Computed standard deviations appear consistent with measured values

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SLIDE 35

ARL

The University of Texas at Austin

Long range TL uncertainty

Range - km TL - dB gm solution short range mean Mean ± σ

0 2 4 6 8 10 12 14 16 18 20 53 Hz 103 Hz 203 Hz 253 Hz

Range - km

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SLIDE 36

ARL

The University of Texas at Austin

Summary

  • Current inferences of attenuation based on

global minimum solutions

  • Maximum entropy principle applied to quantify

statistics of environmental parameters and propagation

  • Computed and measured TL uncertainty consistent
  • Environmental parameter marginals

– Sensitive to signal processing – Dependent on volume and sensitivity

  • Uncertainty of Biot parameters is ongoing

research