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