underwater acoustics including - tau111)r.pdfhistorical underwater acoustics range ~1000 miles polar...
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Underwater Acoustics including Signal and Array Processing
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HIERARCHY(OF(UNDERWATER(ACOUSTIC(MODELS((
Coupled(Modes(
(KRAKEN,CSNAP,COUPLE)(
Coupled(Wavenumber?(
IntegraCon(
(RD?OASES)(
Gridding(Aspects(of(RangeAdependent(PropagaCon(Modeling(
Parabolic(EquaCon(
(RAM)(
Finite(Differences(
Finite(Elements(
Wavenumber(IntegraCon(
Wavenumber(IntegraCon(
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Decaying(ExponenCals(
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Lame�(constants(
4(Unknowns(
Homogeneous(ElasCc(Layers(Wave(EquaCons(
1((2((3((2((4(
Number(of(Boundary(CondiCons(
Homogeneous(ElasCc(Layers(Boundary(CondiCons(
Modal(EquaCon(
Boundary(CondiCons(Ideal(Waveguide(
Away(from(Source(
0(
Normal(Modes(MathemaCcal(DerivaCon(
F(r)( G(z)(
Classical(SturmALiouville(Eigenvalue(Problem(• (Modal(equaCon(has(infinite(set(of(soluCons(–(modes(of(vibraCng(string(• (Modes(characterized(by((
• (Mode(shape(Ψ (z) (eigenfuncCon) (• (PropagaCon(constant.(k(((.(k((((real((eigenvalue)(• (mAth(mode(has(m(zeros(in([0,D](• (k < ω / c
• Modes(are(Orthogonal(• (Modes(form(a(Complete(Set(
2(rm rm
rm min
m
From(Mode(EquaCon(
Range(SoluCon(
Modal(Field(SoluCon(
X(
Not(the(Usual(SturmALiouville(Problem!!(
General(StraCfied(Waveguides(
Field(in(boaom(
Field(in(water(
~(
Virtual(Modes(
Normal(Modes(
Normal(and(Virtual(Modes(
Virtual(Modes(Normal(Modes(
Normal(and(Virtual(Modes(
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Modal(EquaCon(
WKB(ApproximaCon(
WKB(ray(theory(ignores(evanescent(field(beyond((turning(points(
Deep(Ocean(PropagaCon(
Finite(Difference(FormulaCon(
Numerical(Approaches((
Modal(EquaCon(
Finite(Difference(FormulaCon((
p!w!=(
VerCcal(Admiaance(
Normalized(Hankel(FuncCons(
Forward(
Backward(
Forward(
Backward(
AsymptoCc(
r(jA1( j(r( r(j+1(
Sector(j(
Normal(Modes(RangeAdependent(Environments(
�Direct(Global(Matrix�(NormalizaCon(
3AD(Modal(Modeling(Framework(
RangeAIndependent(Sectors(3AD(Ocean(Environment(
Full 3-D Mode Coupling Strong Discontinuities 1. Pre-compute modes for all sectors 2. Each source-receiver combination
• Horizontal ray tracing, all mode combinations
• Local single-scattering approximation in plane geometry
• Approximate accounting for geometric spreading r
COMPUTATIONALLY INTENSIVE
A1/2(
2.5AD(Modal(Modeling(Framework(
RangeAIndependent(Sectors(3AD(Ocean(Environment(
In-Plane Mode Coupling Gradual Range-Dependence 1. Pre-compute modes for all sectors 2. Each source-receiver combination
• In-plane mode propagation between sector boundaries
• Local single-scattering – No horizontal diffraction
• Approximate accounting for geometric spreading r
COMPUTATIONALLY EFFICIENT
A1/2(
AdiabaCc(ApproximaCon(
Gulf(Stream(Environment(
WarmACore(Eddy(PropagaCon(RangeAIndependent(
Coupled(Modes(
AdiabaCc(Mode(Theory(
RangeAindependent(cylindrically(symmetric(
RangeAsoluCon(
Slowly(varying(depth(soluCon((envelope)(
Use(Bessel(EquaCon(
Parabolic(EquaCons(
Slowly(varying(envelope:(
NarrowAangle(approximaCon,(valid(for(grazing(angles(less(than(10A15(deg.(
=(0(for(n=n(z),(rangeAindependent(~(0(for(n(r,z)(slowly(varying(in(r((
SoluCon(technique:(Approximate(PseudoAdifferenCal(Operator(Q(
Ignores(backscaaering(
Outgoing( Incoming(
Generalized(DerivaCon(
k
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k z
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Q(=(cos(θ (relates(to(source(angle,(which(–(if(small(–(jusCfies(Taylor(expansion(
0(
RangeAIndependent(Environment(
Local(Plane(Wave(SoluCon(
n = 1
Standard(PE(
Minimizes(phase(errors(0A40(deg(
Standard(and(Wide(Angle(Parabolic(EquaCons(
k 0
θ#
k rm
m
Phase(Errors(and(Angular(LimitaCons(
Exact(Modal(Phase(
Clairbout(PE(Modal(Phase(
PE(Modal(Phases(
“RAM(PE”(
(
Michael(D.(Collins(
Ray methods
• Long history with contributions by Euclid, Ptolemy, Snell (1626), Fermat (1661), Gauss (1846)
• Provides an approximate solution. Ray theory is to wave propagation as classical mechanics is to quantum mechanics
• Provides the language for describing in intuitive terms what occurs
Characteristics of ray models
• Probably still the most widely used method in operational use
• Attractive for – High-frequency – Broadband (e.g. tomography, acoustic
communication, active sonar) – Range-dependent problems – reverberation
The bad news … A robust model is rather difficult to produce
• Eigenrays are roots of a nonlinear equation • Ray paths and transmission loss are extremely
sensitive to volume and boundary interpolation • Tracing must be restarted after each boundary
interaction • Caustics must be detected even if full caustic
corrections are not used As a result, most ray models do not come close to
the �ray theoretic� result
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Rays and wavefronts
Ray coordinates
τ∇= cdsdx
Define(rays(as(curves(perpendicular(to(the(wavefronts(of((
But,(phase(is(sCll(unknown.(
Lots(of(work…(
Rays(are(now(defined(in(terms(of(
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Eikonal(equaCon:(
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Building a Matlab ray code We are solving an IVP (initial value problem) of the form
Where s is arclength Step 1: define a subroutine that calculates the sound speed and its
gradient Step 2: Solve the ray equations for a fan of take-off angles (initial
conditions) (e.g. ODE45)
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Sound speed profile and ray trace in the Balearic Sea
Ray artifacts in shadow zones
Ray artifacts (caustics)
Effect of profile
interpolation
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Review(of(the(2AD(Model(((((((Cerveny,((Popov,(Psencik…)(
• Trace(a(fan(of(the(beams(from(source((“space(filling”)(
• At(any(given(receiver(locaCon(AA>Eliminates(the(need(for(source(to(receiver(eigenrays(
Sum(up(the(influences(of(all(the(beams(
Beam(has(a(Gaussian(crossAsecCon.(
Gaussian beam tracing
Bellhop • “Beam(Tracing”(model(for(predicCng(acousCc(pressure(field(in(the(ocean(
environment.(• Beam(structurOCEAN(ACOUSTICS(LIBRARY:(hTp://oalib.hlsresearch.com(• es(include(Gaussian(and(hatAshaped(beams(with(both(geometric(and(
physicsAbased(spreading.(• Can(produce(a(variety(of(outputs(including(basic(raytracing(plots,(
transmission(loss,(eigenrays,(arrivals,(and(received(Cme(series.((• Allows(for(range(dependence(in(top(and(boaom(boundaries(as(well(as(
sound(speed(profile((with(userAdefined(environmental(files).(• Top(and(boaom(reflecCon(coefficients(can(be(provided.(• Bellhop(is(implemented(in(Fortran,(Matlab,(and(Python(and(works(on(Mac,(
Windows,(and(Linux.((
• hap://hlsresearch.com/personnel/porter/papers/JASA/JASA%20gbt%20bw%20with%20errata.pdf(
(
3D sound speeds and bathymetry
3D(bathymetry(causes(horizontal(refracCon(
Horizontal(waveguide(formed(by(two((syntheCc)(soliCons(limits(spreading(and(provides(beaer(detecCon(opportuniCes(
Focus(range(varies(with(elevaCon(angle(
Horizontal(fan(of(beams(at(0(degrees(
Horizontal(fan(of(beams(at(2.5(degrees(
Paul Hursky, Martin Siderius and Michael B. Porter (HLS)
Ocean(AcousCc(Models(Summary(
Ray(Tracing((
IntuiCve,(computaConally(efficient(RI(and(RD(environments(
HighAfrequency(approximaCon(Does(not(incorporate(diffracCon(Does(not(handle(causCcs(properly(
Wavenumber(IntegraCon((
Exact,(efficient(soluCon(for(RI(waveguides(Full(seismoAacousCcs,(including(poroAelasCcity(Coupled,(twoAway(propagaCon(for(stepwise(RD(
ComputaConally(intensive(for(RD(
Normal(Modes((
Highly(efficient(for(RI(environments(Efficient(coupled(and(adiabaCc(modes(for(stepwise(RD(
Backscaaer(by(twoAway(coupled(modes(HighAfrequency(approximaCon(
PreAcomputaCon(of(modes(and(coupling(coefficients(for(general(3D(environments((
Parabolic(EquaCons((
Highly(efficient,(Inherently(rangeAdependent(ConCnuous,(gradual(rangeAdependence(AdAhoc(approximaCons(for(backAscaaer(
No(preAcomputaCon(gain(for(general(3D(environments(and(sourceAreceiver(configuraCons.((
Underwater Acoustics including Signal and Array Processing
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MOTIVATION:ONE(MAN�S(NOISE(IS(ANOTHER(MAN�S(SIGNAL(
• WHITE(NOISE:(�UNCORRELATED�(sensor(to(sensor(ANONAPROPAGATING(• ISOTROPIC(NOISE:PROPAGATING(IN(ALL(DIRECTIONS(WITH(EQUAL(AMPLITUDE(• CONFUSED(WITH(WHITE(NOISE(BECAUSE(WHEN(SENSED(AT(HALF(WAVE(LENGTHAAsame(a(white(noise(• SEA(SURFACE(NOISE:(PROPAGATING(PARTIALLY(CORRELATEDAHAS(DIRECTIONALITY:((• SHIPPING(NOISE:(PROPAGATING(WHEN(FAR(AWAYAAPPEARS(TO(HAVE(SAME(PROPERTIES(AS(SURFACE(NOISE(• BIOLOGICAL(NOISE(• SEISMIC(NOISE(• THERMAL(NOISE(
___________________________________________________________(• USUALLY(TRY(TO(DETECT(SIGNAL(IN(NOISE(• USE(DIRECTIONALITY/CORRELATION(OF(NOISE(FOR(INVERSION(• ACOUSTIC(DAYLIGHT,INVERSION(• THIS(TALK((WILL(END(WITH(UTILIZING(NOISE:(((((((((((((((((((((((((((((((((((((((((TREATING(NOISE(AS(THE(SIGNAL(((
58
HISTORY (2)
FOG ALERT SYSTEM: 100 HZ TRAVELS FURTHER --BUT 300-400 HZ MORE EASILY HEARD BECAUSE OF “ENVIRONMENTAL NOISE” : FIRST USE OF SIGNAL TO NOISE TERMINOLOGY LASKY, JASA 1977.
USEFUL(Noise(+(TR:Track(of(storm(from(microseisms((0.2(Hz)(
Gerstoft et al., 2008; Zhang et al 2009, see also Wilson,Makris, JASA 2006 (UWA frequencies)
Webb, Rev Geo. 1998
Another(Example(of(Using(SHIP(NOISE(AA(FOR(INVERSION(
Battle, JASA 2004
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)!
Historical Underwater Acoustics
Range ~1000 miles
polar latitudes
Mid latitudes
array
Typical mid-latitude sound speed profile
Typical northern
sound speed profile
Radiated signal
Sea mountain or continental
shelf
Ray trapped in the Deep Sound Channel
(DSC)
Depth ~10000 ft
Layers of constant sound speed
C (m/s)!
Historical Underwater Acoustics
Noise at Array
AMBIENT NOISE SPECTRA (WENZ)
AMBIENT NOISE SPECTRA (WENZ)
Thermal Noise “FLOOR”
BIOLOGICS
66
NOISE LEVELS AND
SOURCE LEVELS
BRADLEY,STERN NRC 2008
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
68
NOISE LEVELS +PASSING SHIP
BRADLEY,STERN, NRC 2008
Shipping and Wind Noise
Carey,Evans,CTCA 2010
TYPICAL SONAR VIEW OF NOISE: NUISANCE
GOAL OF ARRAYS OR ANTENNAS: 1. ADD UP MORE SIGNAL THAN NOISE 2. LOOK IN A CERTAIN DIRECTION
1. TOWARD A SIGNAL OF INTEREST 2. LOW SIDELOBES
3. ADAPTIVE PROCESSING: USE DATA FOR HIGH RESOLUTION AND MINIMUM
SIDELOBE
ARRAY(GAIN:(Signal(adds(up(faster(than(noise(
Isotropic(noise( is(uncorrelated(at(( λ / 2
AG(=(10(log(m(
Incoherent:(no(correlaCon((between(sensors:(no((XAterms(in(sumA>m(terms(Vs(m2(for(coherent(
GEOMETRY(FOR(SURFACE(DISTRIBUTED(NOISE(MODEL(
TheoreCcal(approach(((discrete,(modal(part)(
B(
A(
t(t(
surface(noise(
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R(
at(frequency(ω,#
( ) ( ) ( )( )RkHRkH21RkJ n0n0n0 −+=with#
Z�(
Z1( Z2(
W.A.(Kuperman(&(F.(Ingenito,(JASA,(1980(
NOISE STRUCTURE IN SHALLOW WATER (mode or spectral model)
(((
GEOMETRY FOR PE NOISE MODEL (March toward array adding random surface sources)
A PE NOISE MODEL RUN
80 C. G. Anderson 1972 NOSC Tech Note 800
Deep Water Noise Notch (Atlantic)
up
81
DOWNSLOPE CONVERSION
WAGSTAFF, JASA 1981
82
Ambient Noise Notch: Model/Data Comparison
-12
-8
-4
0
-30 -20 -10 0 10 20 30
data model
look direction (deg)
-12
-8
-4
0
outp
ut (d
B r
e: m
ax) -12
-8
-4
02 kHz
3 kHz
4 kHz
Model/Data Comparison
Frequency (Hz)
Beam
form
er
look d
irection (
deg)
noise
notch
Result: Good model/data agreement for both width and depth of noise notch.
Compare ECS data and model for
beamformer output at 2, 3, and 4 kHz.
Data
Applied Physics Laboratory • University of Washington
SHALLOW WATER NOISE NOTCH- INT WAVES
ROUSEFF, TANG JASA 2006
QUESTIONS?(
Underwater Acoustics including Signal and Array Processing
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WHAT(PART(OF(THE(WATER(COLUMN(MOST(AFFECT(THE(PROPAGATION?(
• FAF(experiments(– Data(
(• Environmental(perturbaCons(
– RelaCng(∆p(to(∆c((
• AcousCc(SimulaCons(– SensiCvity(maps(
(• Inversion(esCmates(
– Simulated(((
• Future(work(
Focused(AcousCc(Fields((FAF)(
• Pianosa,(near(Elba(Island((Italy)(
• NATO(Undersea(Research(Center((NURC)(
– Formerly,(SACLANT(URC(
• NRV(Alliance(
Map(from(hap://commons.wikimedia.org/wiki/File:Tuscan_archipelago.png(
29(x(32(Sets(of(Greens(funcCons,(recorded(every(20s(Each(represents(the(arrival(structure(due(to(mulCpath(propagaCon(
R = 4 km
SA(29(Elements(~3.5(kHz(
RA(32(Elements(
D =
100
m
Experimental(setup(
RA(SA(
SA element 4
SA element 15
5.75( 5.76( 5.77( 5.78( 5.79( 5.8(
30(
40(
50(
60(
70(
80(
90( -30(
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-15(
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Time (s)
Dep
th (m
) D
epth
(m)
Signals received on RA
Source(signal:(3(kHz(A(4(kHz(LFM(chirp(
Data(example(
Data(A(single(receiver(
23
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c rG r r G r r G r r dV rc r
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Born(approximaCon(to(a(perturbaCon(
sr
rr
r!
r!
r!
Temporal(sensiCvity(of(received(pressure(
23
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i tr s sr s
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ωωω ω
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∞−
−∞
∂& &= ⋅ −
& &∂ ∫
r!
sr
rr
r!
SimulaCons(
• PE acoustic propagation model
• Pekeris waveguide – 100m deep x 1km wide
• Broadband source signal – 3kHz to 4kHz
SimulaCons(A(pressure(record(
1(2(
3(4(
5(
SimulaCons(A(kernels(1(
3(2(
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∂c(r ')( )i −Pi (t)∂P (t )∂c(r ')( )r
P(t) 2
Phase(and(amplitude(kernels(
• Amplitude/envelope sensitivity
• Phase sensitivity €
dA per ms−1( )
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dθ(radians) per ms−1( )
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Arrays(of(kernels(
1(
Arrays(of(kernels(
2(
Arrays(of(kernels(
3(
Arrays(of(kernels(
4(
Inversion(for(SoundASpeed(
1 2
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1 2 2
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2 2 22
3 3 33
4 4 4 4
r r R
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P H C
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Δ = Δ
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Δˆ p (t) = ∂p( t)∂c(r ') Δc(r' )dV
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RealisCc(example(
• Mean profiles from FAF�05 CTD measurements – Temperature – Salinity – Sound-speed
Internal(waves(
• Provides(realisCc(perturbaCons(
Internal(waves(
• Helps(constrain(inversion(problem(
Inversion(results(
• Input(perturbaCon(
• Estimated perturbation
LAB(MEASUREMENT(((((((Direct(Path(((((((Surface(Reflected(Path(
RA(SA(
Range ~ 4 km (a) (b)
~120(m(
Mean sound speed (m/s)
Dep
th (m
)
1500( 1520( 1540(
0(
20(
40(
60(
80(
100(
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Eigenray/SensiCvity(Kernel(“Micro?Surgery”(at(Sea( Roux(et(al,(FluctuaCons…,(JASA(2013(
Refer/further/to/Time/Reversal//analysis/in/subsequent/lecture/
QUESTIONS(
Wave(Models(
• Wavenumber(IntegraCon(
• Normal(Modes(
• Parabolic(EquaCon(• Shallow(water(examples(
(
Gradient(Fluid(Layers(
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Ai Bi
n2(linear(profile(
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Fluid(Water(Column(
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ElasCc(Sediment(Layer(
ElasCc(Halfspace(
Boundary(CondiCons(
Wavefield(Unknowns(
Vacuum(0(
4(
2(
2(
4(
2(
2(3(
2(
3(
4(
14(unknowns( 14(equaCons(
Global(EquaCons(and(Unknowns(
Outgoing(waves(only(
Wavenumber(IntegraCon(
• Slow(evanescent(decay(if(receiver(depth(close(to(source(depth(• Homogeneous(soluCon(decay(slowly(if(source(close(to(interfaces(• Short(range(–(slow(exp()(oscillaCon(A>(Evanescent(contribuCon(significant(• Long(range(–(fast(exp()(oscillaCon(A>(Evanescent(contribuCon(insignificant(
+( A(
TruncaCon(of(IntegraCon(Interval(
Integral(TruncaCon(
FFP(IntegraCon(
Example(Pekeris(Waveguide(
FFP(IntegraCon(
AaenuaCon(in(Seawater((Jkps(Eq.(1.34)((α(=(3.3eA3(+(0.11*f^2/(1+f^2)((α:( (AaenuaCon((dB/km)(f:( (Frequency((kHz)((
Pekeris(Waveguide(DepthAdependence(clear(
D=100;(z0=D;(c1=1500;(c2=1800;(rho1=1000;(rho2=1800;(f=20;(omega=2*pi*f;(alpha2=0.0;(delta2=alpha2/54.58;(k1=omega/c1;(k2=omega/c2*(1+i*delta2)(((((((zs=36;(nk=2^10;(km=2*real(k1);(dkr=km/(nkA1)(kr=[0:dkr:km];(nkr=length(kr);(eps=3/(2*pi*log10(exp(1)))(*dkr;(kr=kr(A(i*eps;((nzw=41;(dz=D/(nzwA1);(z=[0:dz:D*1.2];(nz=length(z);((pk=pek_kernel(kr,z,zs,D,z0,k1,k2,rho1,rho2);((figure(1)(subplot(2,1,1);(hold(off(wavei(dba(pk),real(kr),DAz,A60,40);(h=Ctle('Wavenumber(Kernel');(set(h,'Fontsize',16);(h=xlabel('Horizontal(Wavenumber((m^{A1})');(set(h,'Fontsize',14);(h=ylabel('Depth((m)');(set(h,'Fontsize',14);(hold(on;(h=plot([0(real(kr(nkr))],([0(0],'m');(set(h,'Linewidth',2);((%(Transmission(loss([pr,r]=ffp(pk,kr,z);((subplot(2,1,2);(hold(off;(wavei(dba(pr(:,1:nkr/2)),1eA3*r(1:nkr/2),DAz,A120,A20)(h=Ctle('Transmission(Loss');(set(h,'Fontsize',16);(h=xlabel('Range((m)');(set(h,'Fontsize',14);(h=ylabel('Depth((m)');(set(h,'Fontsize',14);(hold(on(h=plot([0(1eA3*r(nkr/2)],([0(0],'m');(set(h,'Linewidth',2);(axis([0(3(DAz(nz)(DAz(1)]);((
pekeris_c.m(
r(jA1( j(r( r(j+1(
Sector(j(
Sector(Interface(Coupling(ConCnuity(of(Pressure(
r(jA1( j(r( r(j+1(
Sector(j(
Sector(Interface(Coupling(ConCnuity(of(ParCcle(Velocity(
r(jA1( j(r( r(j+1(
Sector(j(
Interface(Coupling(EquaCons(
�ReflecCon�(
r(jA1( j(r( r(j+1(
Sector(j( Source(
RadiaCon(CondiCon(b(((=(0(N(
IniCal(and(RadiaCon(CondiCons(
r(jA1( j(r( r(j+1(
Sector(j(
RadiaCon(CondiCon(b(((=(0(N(
Mean(of(pressure(and(velocity(coupling((Other:(p/(ρc)(((conCnuous(1/2(
OneAway(Coupled(Modes(
Split(Step(Parabolic(EquaCons(
Environment( PropagaCon(
θ#
0(
n = 1
=(k rm#
Range-Independent Environment
2# ψ#=(A(k rm#
2# (Φ� � 2ik Φ) #
Phase(Errors(and(Angular(LimitaCons(
0#
PE(Propagates(Normal(Modes(Undistorted(
PE(Modal(Phase(
Phase(Errors(and(Angular(LimitaCons(
Exact(Modal((Phase(
PE(Modal(Pressure(Field(
Phase(Errors(and(Angular(LimitaCons(
c(((=(1590(m/s(ρ((((=(1200(kg/m( 3(2(2(
PE(Workshop(Case(3B(
OUTLINE • OVERVIEW OF NOISE
– OCEAN ENVIRONMENT – PROPAGATION – DIFFERENT TYPES OF NOISE – SIGNAL PROCESSING: From NOISE AS A
NUISANCE • EXTRACTING COHERENT
INFORMATION FROM NOISE – THERMAL NOISE – SHIPPING/BIOLOGICAL NOISE – NATURAL: SEISMIC AND SURFACE
131
