Uncertainty of low frequency sound attenuation estimate in marine - - PowerPoint PPT Presentation

SLIDE 1

Uncertainty of low frequency sound attenuation estimate in marine sediment

Yong-Min Jiang and N. Ross Chapman University of Victoria Victoria BC Canada University of Victoria, Victoria, BC, Canada Work supported by ONR

Jiang and Chapman ASA157, Portland, Oregon, 18 - 22 May 2009

SLIDE 2

Objective:

• Measurement of marine sediment attenuation at frequencies

lower than 5 kHz

• Evaluation of the uncertainty of the attenuation estimate

Outline: Outline:

• Experimental geometry

S di t tt ti ti ti th d

• Sediment attenuation estimation method
• Factors that affect the uncertainty of attenuation estimates
• fluctuation of the signals
• fluctuation of the signals
• uncertainties of sediment sound speed and layer thickness
• The results

Jiang and Chapman ASA157, Portland, Oregon, 18 - 22 May 2009

• Summary and acknowledgements

SLIDE 3

Methods of estimating sound attenuation in marine sediment :

• For attenuation at high frequencies (f > 10 kHz):
• For attenuation at high frequencies (f > 10 kHz):

In situ measurements by using two embedded probes

• For attenuation at low frequencies (f < 1 kHz):

Inferences from different kinds of inversions of sound Inferences from different kinds of inversions of sound propagation data

• An alternate way of estimating the sediment attenuation:

The signal used in this study is LFM pulse with frequency

Jiang and Chapman ASA157, Portland, Oregon, 18 - 22 May 2009

bandwidth of 1.5 kHz to 4.5 kHz

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Experimental geometry:

Jiang and Chapman ASA157, Portland, Oregon, 18 - 22 May 2009

Sound travel path in the sediment

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Example of the received signal:

• m

Direct arrival Surface reflection Bottom reflection

Sub-botto Direct Surface Bottom BRSR SRBR

Bottom reflection Sub-bottom reflection Bottom reflection surface reflection Surface reflection bottom reflection Surface reflection bottom reflection

Jiang and Chapman ASA157, Portland, Oregon, 18 - 22 May 2009

SLIDE 6

Method of estimating sediment attenuation:

) ( 2 1 Re

2 1 ) (

) , , ( ) , , ( ) (

r r b c b Src b b

neper w

e r r f D f D V p f p

+ −

⋅ + =

α

η φ ξ θ

Signal from bottom reflection:

Src

D

• Directional

response of

6 5 4 3 Re

) , , ( ) , , ( ) (

sb c sb Src sb sw ws sb

r r r r f D f D V T T p f p + + + = η φ ξ θ

Signal from sub bottom reflection: source

c

DRe - Directional

f

) ( ) ( ) (

6 5 ) ( 4 3 ) (

r r f r r

neper sb neper w

e e

+ ⋅ − + −

⋅ ⋅

α α

The ratio of reflections from bottom to sub bottom (dB): response of receiver

) ( ) ( ) ( log 20 ) ( log 20 ) (

6 5 10 10

r r f B f p f p f P

sb sb b

+ ⋅ + = − = Δ α

Linear frequency dependence: or Nonlinear frequency dependence:

B f r r f P

f sb

+ ⋅ ⋅ + = Δ

) ( 6 5

) ( ) ( α B f f r r f P

f sb

+ ⋅ ⋅ + = Δ

β

α ) ( ) ( ) (

6 5 ) ( f sb

α

is in dB/m•kHz

f sb

α

is in dB/m @1 kHz, fo is 1 kHz

Jiang and Chapman ASA157, Portland, Oregon, 18 - 22 May 2009

1000 /

) ( ) ( sb f sb sb

c ⋅ = α α λ

in dB/λ

SLIDE 7

The uncertainty of attenuation estimate:

B f r r f P

f b

+ ⋅ ⋅ + = Δ

) ( 6 5

) ( ) ( α

Linear frequency dependence: or Nonlinear frequency dependence:

B f f r r f P

f b

+ ⋅ ⋅ + = Δ

β

α ) ( ) ( ) (

6 5

B f r r f P

sb

+ + Δ

6 5

) ( ) ( α B f f r r f P

sb

+ + Δ α ) ( ) ( ) (

6 5

in dB/m•kHz in dB/λ is in dB/m @1 kHz, fo is 1 kHz

B f f P

sb c r r

sb

+ ⋅ ⋅ = Δ

+ ⋅ ) ( ) ( 1000

6 5

) (

λ

α

The uncertainty of the attenuation estimate:

in dB/λ

The uncertainty of the attenuation estimate:

the measurement

signal amplitude fluctuation signal amplitude fluctuation

the uncertainty of sound speed and layer thickness estimates

Bayesian travel time inversion

Jiang and Chapman ASA157, Portland, Oregon, 18 - 22 May 2009

Bayesian travel time inversion

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Estimate attenuation from bottom and b b fl i sub-bottom reflections:

Jiang and Chapman ASA157, Portland, Oregon, 18 - 22 May 2009

Matched filtered waveforms ∆P(f) at different frequencies

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Example of uncertainty due to signal fluctuation

Determine the frequency dependence of the attenuation in terms of:

• the width of 95% of the credibility interval
• the consistency of the estimates from different source-receiver pairs

Monte Carlo approach, linear fitting

Jiang and Chapman ASA157, Portland, Oregon, 18 - 22 May 2009

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Linear fitting for data from four source-receiver pairs Linear fitting for data from four source-receiver pairs

Jiang and Chapman ASA157, Portland, Oregon, 18 - 22 May 2009

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The uncertainty of sediment sound speed and L thi k ti t Layer thickness estimates:

Optimization: p

Water column SSP, source & receiver geometry: Range, Water depth, Array tilt Source depth, Receiver depth

Bayesian inversion: Bayesian inversion:

Uncertainty of sediment sound speed and layer thickness

Jiang and Chapman ASA157, Portland, Oregon, 18 - 22 May 2009

and layer thickness

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Uncertainty of sediment sound speed and layer Uncertainty of sediment sound speed and layer thickness estimates from Bayesian travel time inversion: inversion:

Sound speed Layer thickness grazing angle 1550 1600 1650 10 20 30 10 20 30 40

Jiang and Chapman ASA157, Portland, Oregon, 18 - 22 May 2009

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Example of uncertainty of attenuation estimate:

Sound path length Sound path length/sound speed 0.06 0.08 0.1 distribution 70 80 90 100 110 0 04 0 05 0 06 0 07 6 8 10 12 0.02 0.04

(f)

Probability d

) (

6 5

r r +

) ( 6 5

) (

f sb

r r α ⋅ +

70 80 90 100 110 0.04 0.05 0.06 0.07

sb

c r r / ) (

6 5 +

(r5 + r6) × α(f)

sb

1.4 1.4 0 6 0.8 1 1.2 0 6 0.8 1 1.2 0 0 0 08 0 08 0 09 0 09 0 1 0 10 0 11 0.2 0.4 0.6 0 1 0 12 0 14 0 16 0 18 0 2 0.2 0.4 0.6

Jiang and Chapman ASA157, Portland, Oregon, 18 - 22 May 2009

) ( f sb

α

in dB/m•kHz in dB/λ

) (λ

αsb

0.075 0.08 0.085 0.09 0.095 0.1 0.105 0.11 0.1 0.12 0.14 0.16 0.18 0.2

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Summary:

• Marine sediment sound attenuation at low frequency is estimated

from single bounce sub-bottom reflections

• Frequency dependence of the attenuation is determined by the

Frequency dependence of the attenuation is determined by the measured data

• The uncertainty of the attenuation estimate is mapped from the

fluctuation of measured signal and the uncertainty of the fluctuation of measured signal and the uncertainty of the sediment property estimates from Bayesian travel time inversion

• VLA and source at different depths experimental geometry

Offi f N l R h f i th h

Acknowledgements:

• Office of Naval Research: for sponsoring the research
• Drs. William Hodgkiss and Peter Gerstoft from MPL (acoustic data)
• Dr. David Knobles from ARL (navigation and source depth data)

Jiang and Chapman ASA157, Portland, Oregon, 18 - 22 May 2009

• Dr. John Goff from IG, Univ. of Texas at Austin (seismic reflection )