Sediment Properties and the Acoustic Field in a Three-layer Waveguide

David Barclay

AOS seminar

June 1st, 2006

Overview

• Motivation

• Acoustic field in a three layer wave guide

• The Makai experiment

• Data and model comparison

• Sediment properties

A simple thought experiment…

V

€

f (θ) =fo

1−V

ccos(θ)

€

θ

€

Δf = f (0) − f (π ) ≈2Vfo

c

Sound speed in the medium can then be found:

Furthermore:

€

cosθ1

c1

=cosθ2

c2

A three layer wave guide witha moving source

€

∇2φ1 −1

c12

∂ 2φ1

∂t 2= −Qδ(x − x '−Vt)δ(y)δ(z − z')e iΩt

€

∇2φ2 −1

c22

∂ 2φ2

∂t 2= 0

€

∇2φ3 −1

c32

∂ 2φ3

∂t 2= 0

x

y

z

hydrophonesea bed

seasurface

bender

microphone

hydrophonevertical array

Z’

h

c - Sediment

c - Ocean

c - Air

BCs ii jj and i’j’

A few transforms and manipulationslater…

€

φ1(x,z, t) =Qe iΩt

16π 3ie ip(x−x '−Vt )e isyF1(η1,η 2,η 3)dpds

−∞

∞

∫−∞

∞

∫

€

φ2(x,z, t) =Qb12e

iΩt

8π 3ie ip(x−x '−Vt )e isyF2(η1,η 2,η 3)dpds

−∞

∞

∫−∞

∞

∫

€

φ3(x,z, t) =Qb13e

iΩt

8π 3ie ip(x−x '−Vt )e isyF3(η1,η 2,η 3)dpds

−∞

∞

∫−∞

∞

∫

€

ηi = η i(c i, p,s)where

€

bij =ρ i

ρ j

Evaluating the integral

• Avoid poles in F2 (located in II and IV quadrants) using a hyperbolic tangent contour.

€

φ2(x,z, t) =Qb12e

iΩt

16π 3ie ip(x−x '−Vt )e isyF2(η1,η 2,η 3)dpds

−∞

∞

∫−∞

∞

∫

Locate receiver at (0, 0, h).

- p’

+ p’

complex p plane

Evaluating the integral

• Avoid poles in F2 (located in II and IV quadrants) using a hyperbolic tangent contour.

€

φ2(x,z, t) =Qb12e

iΩt

16π 3ie ip(x−x '−Vt )e isyF2(η1,η 2,η 3)dpds

−∞

∞

∫−∞

∞

∫

Locate receiver at (0, 0, h).

- p’

+ p’

complex p plane

The Makai Experiment

Locations of SIO’s Fly-By arrayin the MAKAI experiment

SIO shallow site a) array horizontal, anchored on sea bed parallel to shoreline SIGNALS RECORDED

i) Aircraft overflights (50 Hz to 5 kHz) ii) Ambient noise (50 Hz to 5 kHz) b) array vertical, free drifting SIGNALS RECORDED

i) Aircraft overflights (50 Hz to 5 kHz) ii) Ambient noise (50 Hz to 5 kHz)

R/V Kilo Moana site a) array vertical, free drifting SIGNALS RECORDED

i) Aircraft overflights (50 Hz to 5 kHz) ii) Broadband ambient noise (50 Hz to 50 kHz) iii) Comms signals from R/V Kilo Moana

R/V Kilo Moana(water depth ≈ 100m)

SIO shallow site(water depth ≈ 15m)

The Flyby Array

ITC6050C

Tilt/compasssensor

100 lbs maxweight

12 m

0.325 m

11 elements

16 Ch. Data Acquisition

High Bandwidth (> 50 kHz)

Photo by Paul Roberts

RF capability

Putting the array on the bottom

Other parameters and instruments

V, z’, h, c1, c2, 1, 2, 3

Aeroplane Track

Dis

tan

ce to

b

ouy

(m

)A

ltitu

de

(ft)

Airs

pe

ed

(m

/s)

Aircraft

Maule MXT7-180 STO

Dataand

Model Comparison

Spectrogram Comparison

Model Data

Colour bars [Pa]

Pressure time series comparison

Data and Model Spectra comparison

Departure frequency

Approach frequency

Model optimization

Ratio of amplitudes vs. Peak location

c = 1640 m/s c = 1519 m/s

RMS of measured ratios of amplitudes - modeled

c = 1519 m/s

SedimentProperties

Sediment Properties• Wet density = 1685 kg/m3

• Grain density = 2407 kg/m3

• Sound Speed ~ 1540 m/s

Data by Hamilton (o), Richardson and Briggs (x) and curve according to Buckingham

Physical grain parameters

Mean effective radius

Perimeter

RMS roughness

Major/minor axis

Original image

Image w/ background removed

Processed Image

What description of size and shape relates to intergranular friction?

Validity of grains as spheres?

Fourier Roughness

€

R = ro + α n sin(nθ)

n=1

n=2

n=3

Thank you:

Prof. Mike Buckingham

Fernando Simonet

Eric Giddens

Paul Roberts

Yuri Platoshyn

Sediment Properties and the Acoustic Field in a Three-layer Waveguide

David Barclay

AOS seminar

June 1st, 2006