1 Oc679 Acoustical Oceanography Sound scattered by a body (Medwin & Clay Ch 7) scattering is the...

$: 1 Oc679 Acoustical Oceanography Sound scattered by a body (Medwin & Clay Ch 7) scattering is the consequence of the combined processes of reflection, refraction.$
1

Oc679 Acoustical Oceanography

Sound scattered by a body (Medwin & Clay Ch 7)

scattering is the consequence of the combined processes of reflection, refraction and diffraction at surfaces marked by inhomogeneities in , c - these may be external or internal to a scattering volume ( internal inhomogeneities important when considering scattering from fish, for example )

net result of scattering is a redistribution of sound pressure in space – changes in both direction and amplitude

for a monostatic system, we are most interested in the sound reflected back to the source/receiver – this is termed backscatter

scattering is wavelength- (frequency, sort of) dependent

the sum total of scattering contributions from all scatterers is termed reverberation

this is heard as a long, slowly decaying quivering tonal blast following the ping of an active sonar system

to start, we consider simple, hard, individual scatterers

2


reverb following explosive charge

initial surface reverb is sharp, followed by tail due to multiple reflection & scattering

then volume reverb in mid-water column (incl. deep scattering layer)

then bottom reflection, 2nd surface reflection, and long tail of bottom reverb

explosive source at 250 mnearby receiver at 40 mbottom depth 2000 m

3


transmission is a gated sinusoid or ping of duration tp

• sound pressure scattered by a small object – crests of sinusoid indicated as a sequence of wave fronts• in this sketch , dependencies of incident wave are suppressed (this would be due to source beam pattern)• for simplicity wavefronts drawn as if coming from center of object – for a complex object, as shown, there would be many interfering wave fronts spreading from the object• within shadow, interference of incident and scattered waves is destructive as incident and scattered waves arrive at the same time with same amplitude, but out-of-phase• outside of shadow, interference of incident and scattered waves forms a penumbra (partial shadow)• beyond penumbra ( < interfer), incident and scattered waves can be separated (no interference)

4


traces of incident and scattered sound pressures – ping has duration tp

travel time for sound to scatter to receiver is R/c (here R is measured from the scattering object)

this is referred to previous figure

2( ) i ft

inc incp t P e 0

pt t

= 0, otherwise

,

incident sound pressure: scattered sound pressure:

Complex Acoustical Scattering Length, ( , , )L f

consider amplitude and ignore phase/ 20( , , ) 10 /R

scat incP P L f R

/ 20( , , )( , , ) 10 Rscat

inc

P fL f R

P or dimension is length, unrelated to any

length scale of the body

/ /p

R c t R c t

= 0, otherwise

,pscat(t) = Pscat ei2πf(t-R/c)

5


Differential Scattering Cross-section, ( , , )s

f

2 22 /10

2

( , , )( , , ) ( , , ) 10 Rscat

s

inc

P f Rf L f

P dimension area [ m2 ]

here, s, L, and Pscat all depend on the geometry of the measurement and the carrier frequency, f, of the ping (really they depend on wavelength)

above is a bistatic representation in which source and receiver are at different positions

when at same position (monostatic), it is called backscatternow = 0 and = 0, and

2

(0,0, ) ( ) (0,0, )s bs

f f L f

differential backscattering cross-section

6


total scattering cross section

total scattering cross-section is the integral of over total solid angle

( , , )s

f

scat is the total power scattered by the body

note that so far we have only considered the differential (and have used ) – that is we have only considered a differential portion of the total radiated power from the scattering body – this is done by looking at only a portion of the 3D surface with a finite receiver such as shown in the schematic sketch

or

7


target strength

logarithmic measure of differential cross-section

2

2

( , , )( , , ) 10log [ ]

1

( )( ) 10log [ ]

1

( , , )( , , ) 20log [ ]

1

( )( ) 20log [ ]

1

s

bs

bs

fTS f db

m

fTS f db

m

L fTS f db

m

L fTS f db

m

reference area is 1 m2

for backscatter

relative to scattering length

or backscattering length

8


where P0 is referred to R0 (usually 1 m)

travel time source to receiver is R/c

sound spreads spherically from source and then from object

single source/receiver

2( ) i ft

inc incp t P e 0

pt t ,

Pscatei2πft = P0 ei2πf(t-R/c) R0Lbs(f) 10-2αR/20/R2

Pincei2πft = P0 ei2πf(t-R/c) R010-αR/20/R

how do we quantify a single transducer measurement – R now referenced to transducer location

9


Scattering by spheres

• simple shape, well studied

• an acoustically small and compact non-spherical body scatters in about the same way as a sphere of same volume and same average physical characteristics (, c)

• acoustically small ( ka << 1 ) dimensions much less than those of incident sound wavelength

1) rigid sphere ka >> 1 reflection dominates, geometrical or specular scattering

2) rigid sphere ka << 1 diffraction dominates, Rayleigh scattering

3) fluid sphere – includes transmission through medium

10


geometrical scatter from a rigid sphere ( ka >> 1 ) specular (mirrorlike) reflection

in the Kirchoff approximation ( discussed in text) plane waves reflect from an area as if the local, curved surface is a plane

scatter consists of a spray of reflected waves each obeying simple reflection law – that is, angle of reflection = angle of incidence – we will employ a ray solution

diffraction effects are ignored - these would come from edge of shadow and behind sphere

we will calculate the scattering from a fixed, rigid, perfectly reflecting sphere at very high frequencies ( ka >> 1 )

incident sound is a plane wave of intensity Iinc

no energy absorption in medium

no energy penetrates surface of sphere

short wavelengths ka >> 1 or big objects

11


a

dSi

adi

i

2asini

dSicosi

di is a ring increment about the sphere

1st we need to know the incoming power at angle i

2

2

2 ( sin )

cos

2 sin cos

,

sin(2 )

i i i

i i

inc inc inc i i

inc inc i

dS a ad

dS dS

d I dS I a d

or

d I a d

surface area increment (corresponding to grey shaded area)

component in direction of incident wave

input power to ring

short wavelengths ka >> 1 short wavelengths ka >> 1 or big objects

12


now, calculate scattered power incident rays within angular increment di at angle i are scattered within increment ds=2di at angle s=2i

the geometrically-scattered power measured at range R is

2

2 ( sin )

2 sin2 2

gs gs s s

gs gs i i

d I R Rd

or

d I R d

assume all incident power is scattered [ no power loss ]then

and

in terms of scattering length

gs incd d

2

2,

4 2gs gs

inc inc

I Pa aor

I R P R

2

2

10.28

2

gsgs

gs

inc

gs

LP awhere L

P R

or

L

a

[ we will get back to this later ]

result:scattered intensity is independent of angle of incidence – which should be the case by symmetry of the sphere, but is not the case in general

in the case of the sphere, this means that all differential geometrical scattering cross-sections, including backscattering cross-sections, are equal

short wavelengths ka >> 1 short wavelengths ka >> 1 or big objects

13


the differential scattering cross-section is:

and the total geometrical scattering cross-section is

22

, 14gs gs

aL for ka

24 , 1gs gs a for ka , where a2 is the cross-sectional area

gs does not include the effects of diffraction, so is not the total scattering cross-section

the ray solution is deceptively simple: is accurate in the backscatter direction 0-90but it ignores the complicated interference patterns beyond 90

more complete calculations using wave theory indicate that the total scattering cross-section approaches twice its geometrical cross-section (2a2) for large ka

short wavelengths ka >> 1

>>

>>

short wavelengths ka >> 1 or big objects

14


Rayleigh scatter from a sphere ka << 1

long wavelengths ka << 1or small objects

when the wavelength is large compared to the sphere radius, scatter is due solely to diffraction. 2 simple conditions cause scatter:

1. monopole radiation – in the case that the bulk elasticity (E1) of the sphere (recall E = pA/ = compressibility-1) is less than that of water (E0), the incident condensations and rarefactions compress and expand the body, thereby reradiating a spherical wave – phase reversed if E1>E0

2. dipole radiation – if the sphere’s density (1) is much greater than that of the medium (0), the body’s inertia will cause it to lag behind as the plane wave oscillates (sloshes back and forth). This motion is equivalent to the water being at rest and the body being in oscillation. This motion generates a dipole reradiation. When 1< 0, the effect is the same but the phase is reversed. In general, when 1 0, the scattered pressure is proportional to cos, where is the angle between scattered and incident directions.

15


long wavelengths ka << 1

M&C develop a solution for the monopole and dipole radiation independently and then sum them

the scattered pressure is:22( ) 3

1 cos3 2 2

ikR

incscat m d

P eka aP P P

R

scattering length and cross-sections determined by referencing R to 1 m

2

242

( ) 3( , ) 1 cos

3 2

( ) 3( , ) 1 cos

9 2s

kaL f a

kaf a

backscatter determined by setting = 02

42

5( )

625( )

36

bs

bs

kaL a

kaa

Rayleigh scattering

geometrical scattering

peaks, troughs at ka>1 due to interference between diffracted wave around periphery and wave reflected at front surface of sphere

relative scattering cross-section is obtained by /a2 and is (ka)4

result: the acoustical scattering cross-section for Rayleigh scatter is much less than for geometrical scatter because sound waves bend around and are almost unaffected by acoustically small, non-resonant bodies

long wavelengths ka << 1or small objects

16


fluid sphere, Rayleigh scattering ( ka << 1)

more general case, when sphere is an elastic fluid2

4 21 1( , ) ( ) cos , 1

3 2 1s

e gf ka a ka

e g

• g = 1/0, ratio of sphere’s density to medium density

• h = c1/c0

• e = E1/E0

= angle between incident and scatter directions[ backscatter determined for = 0 ]

monopole component dipole component

most bodies in the sea have values of e and g close to unity and both terms are of similar importance

bubbles have e << 1 and g << 1 - in this case the monopole term dominates

- highly compressible bodies such as bubbles are capable of resonating when ka << 1

- resonant bubbles produce scattering cross-sections several orders of magnitude greater than geometrical

17

small target compared to λka << 1

Rayleigh scattering

large target compared to λka << 1

geometrical scattering

18


scattering of light follows essentially the same scattering laws as sound

but light wavelengths are much smaller than sound - O(100s of nm)

almost all scattering bodies in seawater are large compared to optical wavelengths and have optical cross-sections equal to their geometrical cross-sections

the sea is turbid to light

on the other hand, acoustic wavelengths are typically large compared to scattering bodies found in seawater (at 300 kHz, 5 mm, 4 orders of magnitude larger) - acoustic scattering is dominated by Rayleigh scattering

by comparison the sea is transparent to sound - what limits the propagation of 300 kHz sound is not scattering but absorption

19


why is the sky blue?

Rayleigh scattering α 1/λ4

λblue << λred

reds pass through atmosphere without scattering but blues are scattered from O2 molecules and enters our eyes from a range of angles

violet scattered even better but our eyes are less sensitive to this

sunrise/sunset

at low azimuth, light passes through extended range of atmosphereblue completely scattered out and sun appears red

green flash

occurs at the very end of the sunset (beginning of sunrise, when sun has passed below horizonshorter wavelengths refracted more effectively than longer wavelengthsblue has been scattered out, reds are not effectively refractedwhat’s left if green (sometimes very bright and pops up above horizon for < 1s)

20

scattering from microstructure

hints of scattering from internal waves and microstructure in 60s, 70s but confusing because of bio-scattering

alternatively, bio-scattering may be confused with microstructure scattering leading to errors in estimating plankton populations

scattering cross-sections were computed based on Tatarski’s computations for atmospheric radar (Proni & Apel 1975)these were based on turbulence structure functions

note: these included the effects of velocity fluctuations as well as T (or c) fluctuations

but uair/cair >> uwater/cwater

21

1st experimental evidence from controlled experiments in Wellington reservoir, W. Australia (Thorpe & Brubaker, 1983)“Observations of sound reflection by temperature microstructure” L&O

Known sourcesTowed cylinder and weights at fixed depths from vessel 1Measured using 102 kHz sounder from vessel 2

results

1.no signal when towed in mixed layer – thus velocity fluctuations do not contribute

2.clear signal of cylinder and weight wakes in stratified regions

3.estimates of energy dissipated by towed cylinder permitted estimates of turbulence quantities, to which scattering theory could be compared

a-a, b-b, c-c are natural scatterers

22

theories employ the use of robust statistical models of turbulence spectra

Batchelor, 1957(“wave scattering due to turbulence” Proc.Symp.Nav.Hydro.)

Goodman, 1990 (considers the bistatic or multistatic problem, not just backscatter)

Ross etal 2004

23

Ross etal 2004

24

High-frequency acoustics – this is an important tool to help detect instabilities that lead to turbulence

scattering from small-scale sound speed fluctuations caused by T and S microstructure sound speed c=c(T,p)

Ross and Lueck 2003

26

but here’s the problem

27

Andone Lavery WHOI

Lavery etal 2009

28

Lavery etal 2009

29

Lavery etal 2009

30

Lavery etal 2009

31

Lavery etal 2010

32

here all scattering is bio.note difference in low k spectra which tend to decrease toward low k compared to turbulence spectra

33

34

35

36


coordinate systems

rectangular cylindrical spherical

37


an object is effectively insonified by plane waves when its dimensions are smaller than the 1st Fresnel zone – within the 1st Fresnel zone, a spherical wavefront can be approximated as a plane wave

38

Urick


definition of volume scattering strength (or backscattering strength if referred to same source and receiver

10log scatv

inc

IS

I

in term of surface scattering can define a surface scattering strength

10log scats

inc

IS

I

note: the distinction in the definitions – the volume scattering strength Sv is defined by the ratio Iscat/Iinc, each referenced to 1 m (or 1 yd) from the objectin M&C terms (that we have so far), Iscat is referenced to the receiver at range R from the object while Iinc referred to 1 m from object– the inclusion of attenuation and spherical spreading (1/R2) gives the length scale unit

39


Urick fig 8.3

a more complete schematic of the problem includes beam pattern of single transducer as both source (b) and receiver (b’) ( here absorption ignored )

• I0 is the axial intensity at unit distance (source level SL = 10 logI0)• intensity at 1 m in direction (, ) is I0b(, ) • incident intensity at dV is I0b(, )/r2 • intensity backscattered at P 1 m back toward source is (I0b(, )/r2)SvdV • scattered intensity at source is (I0b(, )/r4)SvdV, where it is assumed that sound spreads spherically from both source and object dV• receiver will produce voltage (rms) R2(I0b(, )b’(, )/r4)SvdV where R is the receiver sensitivity• total receiver output is V[(R2I0SV /r4) b(, )b’(, )] dV

1 Oc679 Acoustical Oceanography Sound scattered by a body (Medwin & Clay Ch 7) scattering is the...

Documents

Transcript of 1 Oc679 Acoustical Oceanography Sound scattered by a body (Medwin & Clay Ch 7) scattering is the...