Underwater Acoustics including96)r.pdf · Energy, Energy Density,Power and Intensity (plane wave)...
Transcript of Underwater Acoustics including96)r.pdf · Energy, Energy Density,Power and Intensity (plane wave)...
Underwater Acoustics including Signal and Array Processing
William A. Kuperman
Scripps Institution of Oceanography of the University of California, San Diego
OUTLINE
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Underwater Acoustics including Signal and Array Processing
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Helmholtz Equation
Let p(r,t) = p(r)e− iω t
Rectangular Coordinate: Plane Waves
Spherical Symmetry: Spherical Waves
p(x, y, z) ~ e± ik ⋅r
p(r) ~ e± ikr
r
With
And note that
is the equation of a plane and therefore a �surface of constant phase�
k
Energy, Energy Density,Power and Intensity (plane wave) Instantaneous Energy Density: E(t)=P.E. +K.E (Average) Energy Density: E Intensity, I, is average rate of flow of energy through a unit area normal to the direction of propagation Power is energy rate (e.g., watt) I ~ c X E X Area
= ρ0v2 =
p2
ρ0c2 =
pvc
= ρ0vrms2 =
prms2
ρ0c2 =
prmsvrmsc
= ρ0cvrms2 =
prms2
ρ0c= prmsvrms
UNITS DECIBEL (dB re_ ): 10 LOG (Intensity/Intensityref) = 20 LOG (Pressure/Pressureref)
Air: Pressureref = 20 µ Pa ( 1 Atmosphere = 194 dB = 105 Pa)
Water: Pressureref = µ Pa 20 LOG 20 = 26 dB ⇒ Same dB in air is higher pressure !!!!
Units cont�d Where do the intensity numbers come from? Intensity is flow of energy through a unit area = energy/
(time x area) Energy/time = power (e.g. watts) ⇒ Intensity units =>
Watts/m2
INTENSITY (plane wave) = P2
rms/(ρc)
Units cont�d ρcwater= 1.5 x 106 kg/m2s and ρcair = ρcwater/3500
0 dB re µPa in water:
Intensity of µPa plane wave in water is = .67 x 10-18
watts/m2 Int of 20 µPa in air = 10-12 / .67 x 10-18 = 1.5 x 106
Intensity of µPa in water
In dB: 61.7 dB which is (about) the same as 26 +10 Log 3500
Deep Scattering Layer
Fish/Scatterers deeper in the day than at night Day:deeper swim bladders-- smaller--hf scatterers Night: strong scattering within 100 m of surface Sunset/Sunrise: biggest change
b.a.
BUBBLES
• Pop and make noise
• Have Resonances
• Bubbly media attenuate an incoming field by • Absorbtion • Scattering
• Bubbly media have lower sound speeds
Km = µKb + (1− µ)Kw →1Bm
= µ1Bb
+ (1− µ) 1Bw
Void fraction
Example: µ = .0001 and .001→ c = 930m / s and 370m / s
Range ~1000 miles
polar latitudes Mid latitudes
array
Typical mid-latitude sound speed profile
Typical northern sound speed profile
Radiated noise
Sea mountain or continental
shelf
Ray trapped in the Deep Sound Channel
(DSC)
Depth ~10000 ft
Layers of constant sound speed
C (m/s)!
Box 1!
Historical Underwater Acoustics
! Sound Speed Profile!
! Pulse Shape !
! Propagation Model!� Normal Mode Methods " ORCA : Evan Westwood (1996) !
Propagation Modeling
Problems Associated with Undersea Acoustic Communication
5.72 5.73 5.74 5.75 5.76 5.77 5.78 5.79 5.8 5.81 5.82-1
0
1
2.71 2.72 2.73 2.74 2.75 2.76 2.77 2.78 2.79 2.8 2.81-1
0
1
0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2-1
0
1
(a)
(b)
(c)Time (s)
Ampl
itude
(a.
u.)
Ampl
itude
(a.
u.)
Ampl
itude
(a.
u.)
Tranfer Function and Symbol Spread in Shallow Water
Fo=3500, 1 ms,r=10 km Depth 120m
Fo=6500, .5 ms,r=4km Depth 50m
Fo=15000, .1 ms,r=.16km Depth 12m
MUST deal with Intersymbol Interference (�ISI�)
Ocean Tomography
Different rays have
Different group speeds
Therefore have different
Arrival times
Which ray corresponds To which arrival time?
Ships Underway Broadband Source Level (dB re 1 Pa at 1 m)
Tug and Barge (18 km/hour) 171 Supply Ship (example: Kigoriak) 181
Large Tanker 186 Icebreaking 193
Seismic Survey Broadband Source Level (dB re 1 Pa at 1 m )
Air gun array (32 guns) 259 (peak) Military Sonars Broadband Source Level
(dB re 1 Pa at 1 m ) AN/SQS-53C
(U. S. Navy tactical mid-frequency sonar, center frequencies 2.6 and 3.3 kHz)
235
AN/SQS-56 (U. S. Navy tactical mid-frequency sonar, center
frequencies 6.8 to 8.2 kHz)
223
SURTASS-LFA (100-500 Hz) 215 dB per projector, with up to 18 projectors in a vertical array operating
simultaneously Ocean Acoustic Studies Broadband Source Level
(dB re 1 Pa at 1 m ) Heard Island Feasibility Test (HIFT)
(Center frequency 57 Hz 206 dB for a single projector, with up to 5
projectors in a vertical array operating simultaneously
Acoustic Thermometry of Ocean Climate (ATOC)/North Pacific Acoustic Laboratory
(NPAL) (Center frequency 75 Hz)
195
Source Broadband Source Level (dB re 1 Pa at 1 m )
Sperm Whale Clicks 163-223 Beluga Whale Echolocation Click 206-225 (peak-to-peak) White-beaked Dolphin Echolocation Clicks 194-219 (peak-to-peak) Spinner Dolphin Pulse Bursts 108-115 Bottlenose Dolphin Whistles 125-173 Fin Whale Moans 155-186 Blue Whate Moans 155-188 Gray Whale Moans 142-185 Bowhead Whale Tonals, Moans and Song 128-189 Humpback Whale Song 144-174 Humpback Whale Fluke and Flipper Slap 183-192 Southern Right Whale Pulsive Call 172-187 Snapping Shrimp 183-189 (peak-to peak)
Man Made Sounds
Animal Sounds
Underwater Acoustics including Signal and Array Processing
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Utilizing First Order Baseline Properties of Waveguide
Propagation
Group vs Phase Speed and Waveguide Invariant
Reminder: Phase and Group Speeds
• Our waveguide speeds are horizontal velocities • Phase speed is related to ray or mode angle
– Horizontal ray has phase speed of medium – Vertical Ray has infinite phase speed
• Refracting ray has phase speed of SSP at turning point • Group Speed of horizontal path is ~ speed of medium • Group Speed of Vertical path is zero • Group Speeds of rays are horizontal range/time • Group Speeds of modes are related to mode weighted
SSP slowness
k=ω/c(z) c
krm= ω/vmp
kzm(z)
θm
vmg=c cos θm
Remember triangles for Range Independent Env.:
• Modal wavenumbers • Modal phase speeds: vmp • Modal group speeds: vmg
Prop down the waveguide
SHALLOW WATER ARRIVALS (Bottom Reflected Paths) Lowest Mode-most direct Arrival comes in first. DEEP WATER ARRIVALS (Refracted Paths) Deep Refracted Arrivals come In before Deep Sounds Channel Axis Arrivals
€
I(ω,r) = c ⇒ ΔI = 0∂I∂rΔr +
∂I∂ω
Δω = 0
∴ΔωΔr
= −∂I /∂r∂I /∂ω
= βωr
Waveguide Invariant:
Lines of Constant Intensity
β
Simple Ranging in shallow water
Range along track
or array Δr
Δω
r
ω
ΔωΔr
= βωr
Note: a single receiver spectrogram has (t,f) not (r,f) axes One solution: use long, horizontal array that provides a measurement of Δr
1+=β
3−=β
Waveguide Invariant: ββ changes sign depending on the
environment
Burenkov, Sov. Phys. Ac., 1989
I(ω, r) = const ⇒ ΔI = 0∂I∂rΔr + ∂I
∂ωΔω = 0
∴ΔωΔr
= −∂I /∂r∂I /∂ω
= βωr
β −1 = −∂Sg∂Sp
= −vpvg
&
'((
)
*++
2∂vg∂vp
MACRO Properties of the Sound Field
Lines of Constant Intensity
βWaveguide Invariant: (Chuprov…)
REFLECTION Dominated
GENERALIZED Waveguide Invariant Theory Pressure / Intensity Field
Waveguide Invariant Theory: Chuprov (1982), Grachev (1993), Weston (1971,1979),D’Spain & Kuperman (1999)
Stationary Phase Condition (Constant Intensity Lines : striation)
,)exp()( ∑=m
mm rikArP
,)cos()(,∑=nm
mnnm rkAArI Δ
,rkmnΔΦ ≡ 0=Δ
Δδ+
δ=Φδ
mn
mnkk
rr
0hh1
rr
=+−δ
βγ
ωδω
βδ
nmmn kk)c,h,(k −=ωΔ
21 −== γβ ,
Group Speed vs Phase Speed
1480 1500 1520 1540 1560 1580 16001380
1400
1420
1440
1460
1480
1500
Phase Speed (m/s)
Gro
up S
peed
(m/s
)
20 m
40 m
100 m1480 1500 m/s
1600 m/s
Idealized Summer Profile
CAN WE OVERCOME SINGLE SENSOR INVARIANT RESTRICTION
…THAT WE MEASURE A TIME DIFFERENCE
BUT NEED A RANGE DIFFERENCE