Download Lec3 sonar_eqn - Ocean Mixing Group

Sonar Equation
Parameters determined by the Medium
• Transmission Loss
TL
• spreading
• absorption
•Reverberation Level
RL (directional, DI can’t improve behaviour)
•Ambient-Noise Level
NL (isotropic, DI improves behaviour)
Parameters determined by the Equipment
• Source Level
SL
• Self-Noise Level
NL
• Receiver Directivity Index
DI
• Detector Threshold
DT (not independent)
Parameters determined by the Target
• Target Strength
• Target Source Level
TS
SL
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Oc679 Acoustical Oceanography
terms are not very universal!
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Units
N = 10 log10 I where I0 is a reference intensity
I0
the unit of N is deciBels
so we might say that I and I0 differ by N dB
in terms of acoustic pressure, (p/p0)2  I/I0
where the oceanographic standard is p0 = 1 Pa in water
we can write this in terms of pressure as 20 log10
p
p0
for comparison:
• atmospheric pressure
is 100 kPa
• pressure increases at
the rate of 10 kPa per
meter of depth from the
surface down
p/p0
dB = 20log10 p/p0
1
√2
2
4
10
20
100
1000
0
3 (double power level)
6
12
compare p/p0=1/√2, I/I0 = ½
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dB = -3
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we might say the -3dB level or ½ power level
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60
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1 Pa is equivalent to 0 dB
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1 Pa is the reference standard for water
20 Pa is the reference standard for air
20 Pa
1 Pa
20log20 = 26 dB
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Scattering
large target
(relative to λ)
small target
(relative to λ)
(Rayleigh scattering)
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Scattering
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  Large Targets
 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  Small Targets
by comparison the sea is transparent to sound - what limits the propagation of 300 kHz
sound is not scattering but absorption
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TL
Absorption
in a homogeneous medium, a plane wave experiences an attenuation of acoustic
pressure  the original pressure and to the distance traveled – this is represented
by a bulk viscosity in the N-S equations which applies only to compressible fluid (this
is distinct from a shear viscosity – M&C sec 3.4.2)
this is due To wave absorption (energy lost to heat)
e is the amplitude decay coefficient
p  p0e -eR
absorption losses are due to ionic dissociation that is alternately activated and
deactivated by sound condensation and rarefaction
• the attenuation by this manner in SW is 30x that in FW
• dominated by magnesium sulphate and boric acid
acoustic absorption
frequency @S=0
3000 kHz
1500 kHz
500 kHz
2.4 dB/m
0.60 dB/m
0.07 dB/m
absorption
@S=35
2.5 dB/m
0.67 dB/m
0.14 dB/m
typical profiling
range
3-6 m
15-25 m
70-110 m
source: Sontek ADCP manual
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Oc679 Acoustical Oceanography
TL
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TL
10
TL
relate spherical spreading & range attenuation due to absorption in terms of sonar
equation
I R02
spherical spreading 
that is
 2
I0 R
log10 I/I0 = log10 R02/R2 = log10R02 – log10R2
1/R2,
but since typically I0 is referred to 1 m range from source, log10R02=0
and 10log10 I/I0 = – 20log10R
range attenuation related by p = p0e-R, or I = I0e-2R
then 10log10 I/I0 = - 20R
and together these represent a transmission loss
TL = -20log10R - 20R
absorption
spherical spreading
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TL
Spreading
cylindrical spreading is an approximation to
propagation through sound channel
analogue is propagation through medium with
plane-parallel upper and lower bounds
this is important for long range transmission
through sound channel – since the loss is now
1/R rather than 1/R2, propagation is more
efficient
this doesn’t happen
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TL
Spreading
• Spreading
– Due to divergence
– No loss of energy
– Sound spread over wide area
– Two types:
• Spherical
– Short Range: R < 1000m
– TL (dB) = 20 log R
• Cylindrical
– Long Range: R > 1000m
– TL (dB) = 10 log R + 30 dB
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Spherical component
now consider the reflected signal from a
target with reflection coefficient R12
pR
p  0 0 e  RR12
R
p is the pressure at range R
R12 is the target reflection coefficient
p  SrecV
Srec is the receiver sensitivity [ Pa/V ]
V is the voltage o/p measured at receiver
SrecV 
p0R0  R
e R12
R
0
log Srec  logV  log p0  log R0  log R   R  log R12
RS
RL
SL
TL
TS
this is the voltage
measured at the
receiver – more
commonly this would be
in counts, which is then
converted to volts
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Oc679 Acoustical Oceanography
this is the physical relationship
that we have developed
p0R0 R
SrecV 
e R12
R
logSrec  logV  log p0  log R0  log R   R  log R12
this is how that relationship is represented
logarithmically
terms in the SONAR EQUATION
represent logarithms
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let’s take a step back now that we have seen how the SONAR
EQUATION is formed
the physics is straightforward as is the transformation to a logarithmic
equations – more straightforward than is implied by the large number of
variations to the SONAR EQUATION that appear – these are usually
specific to the application and intended for unambiguous use by operators
we’ll look at a couple of variations
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Passive SONAR EQUATION
passive sonars listen only
purpose – detection, classification and localization of an acoustic source
in turn, a particular source is embedded in a sea of sources
suppose a radiating object of source level SL (decibels) is received at a
hydrophone at a lower signal level S due to transmission loss TL (TL
always > 0)
S = SL – TL
this is the logarithmic representation of p 
p0R0 R
e
R
where we have already defined TL = 20log10R + 20R to be due to the
product of absorption and spreading (which appear additively in this
logarithmic representation)
and we could represent the signal to noise ratio at the hydrophone as
SNR = SL – TL – N
logarithmic representation of
p
Noise
p0R0 R
e
R

Noise
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DI directivity index
SNR can be increased by beam-forming so that sound does not spread spherically
but is more directional
for an omnidirectional source I is proportional to 4πR2
here it is constrained to πr2 where r might be
the piston diameter of a cylindrical source
Define DI = 10log(intensity of acoustic beam
/intensity of omnidirectional source)
r
S
R=1m r
α/2
DI = 10 log ((p/πr2)/(p/4πR2))
with R = 1
DI = 10 log (4/r2)
and tan(α) = r/R = r
DI = 10 log (4/tan2(α/2))
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SNR can be increased by beam-forming produced by an array of
transducers (perhaps in a single head or maybe distributed geographically)
the directivity index DI represents this advantage for a particular array so
that
SNR = SL – TL – N + DI
ideally, detection is possible when the signal is sufficiently close and not
disguised by noise …
that is, when SNR > 0
however, due to the nature of the signal, interference, the sonar operator’s
training and alertness, etc … something more than 0 is necessary
this extra appears as a detection threshold, DT
we now write the SONAR EQUATION in terms of a signal excess SE
SE = SL – TL – N + DI – DT
this is now the difference between the actual received signal at the output of
the beamformed array and minimum signal required for detection
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if DT set to be too high, only targets with high source levels are detected.
Detection may be difficult but the probability of a false alarm is low as well.
On the other hand, if DT is too low, the probability of false alarms increases
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Looking at a single trace on an oscilloscope is a little antiquated.
A time history helps to see what’s going on.
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Active SONAR EQUATION
now the transducer transmits a signal that is reflected or scattered from
an object – the modified signal is sensed at the receiver (which may be
the same as the source, in monostatic mode)
this modified signal must be extracted from the background interference
which is not only the sonar noise and ambient noise, but also the
reverberation generated by the original signal
simple example – travel-time measurement of the echo to estimate the
distance to an object (such as a fathometer which measures water depth
by listening to the echo of a ping off the sea floor)
we can simply say that the sound pressure level SPL at range R is
SPL = SL - TL
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three principal differences from passive case
1. received signal level modified by target strength TS
2. reverberation is the dominant interference
3. transmission loss results from 2 paths
transmitter to target + target to receiver
monostatic - transmission loss is 2TL
bistatic - transmission loss is TL1 + TL2
Reverberation Level RL
results primarily from scattering of the transmitted
signal from things other than the target of interest
boundary scattering may be due to waves, ice bottom features
volume scattering may be due to zooplankton, fish, microstructure, …
this means that the total interference term is due to the sum of the noise
and the reverberation N + RL – these act to diminish our ability to
detect TS
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Homework 1 – Martin Hoecker-Martinez
18 Jan 2011
http://wart.coas.oregonstate.edu/Documents/for%20others/jim/150W.gif
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So, there are essentially two types of background that may mask the
signal that we wish to detect:
1) Noise background or Noise Level (NL). This is an essentially a steady
state, isotropic (equal in all directions) sound which is generated by
amongst other things wind, waves, biological activity and shipping. This
is in addition to transducer system self-noise. (Wenz curves)
2) Reverberation background or reverberation level (RL). This is the
slowly decaying portion of the back-scattered sound from one's own
acoustic input. Excellent reflectors in the form of the sea surface and
floor bound the ocean. Additionally, sound may be scattered by
particulate matter (e.g. plankton) within the water column. You will have
experienced reverberation for yourself. For example if you shout loudly
in a cave you are likely to here a series of echoes reverberating due to
sound reflections from the hard rock surfaces. These reverberations
decay rapidly with time.
Although both types of background are generally present simultaneously it
is common for either one or the other to be dominant.
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we could define SONAR EQUATION for a monostatic system as
SE = SL – 2TL + TS – (RL + N) + DI – DT
And for a bistatic system
SE = SL – TL1 + TS – TL2 – (RL + N) + DI – DT
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Sound scattered by a body
- RL in SONAR EQUATION
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
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
consideration usually begins by considering scattering from spheres
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Oc679 Acoustical Oceanography
direct signal
explosive source at 250 m
nearby receiver at 40 m
bottom depth 2000 m
reverberation 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
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Oc679 Acoustical Oceanography
sounds in the sea
or N in the SONAR EQUATION
natural physical sounds
natural biological sounds
ships
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Oc679 Acoustical Oceanography
Wenz curves used to determine ambient noise
thick black line – empirical minimum
A - seismic noise
B – ship noise (shallow water)
C – ship noise (deep water)
H – hail
W – sea surface sound at 5 wind speeds
R1 – drizzle (1 mm/h) 0.6 m/s wind over lake
R2 – drizzle, 2.6 m/s wind over lake
R3 – heavy rain (15 mm/h) at sea
R4 – v. heavy rain (100 mm/h) at sea
F – thermal noise (f1) - molecular
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Oc679 Acoustical Oceanography
on-axis source level spectra of cargo ship at 8 & 16 kts measured
directly below ship – this represents the details of what we saw in the
compilation slides
B – propeller Blade rate
F – diesel engine Firing rate
G – ship’s service Generator rate
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Oc679 Acoustical Oceanography
propagation of coastal shipping noise into deep sound channel
c(z)
this is due to c(z) profile over the shelf, causing a progression of sound down the
slope until the axis of the deep sound channel is reached
after that, a reversal of refraction occurs, and signal trapped in sound channel
coastal shipping noise can be propagated long distances
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Homework Assignment 2
assigned:
due:
18 Jan 2010
27 Jan 2010
A yellow submarine is conducting a passive search against blue
submarines. Yellow submarines have a sonar with directivity index
of 15 dB and detection threshold 8 dB. Blue submarines have
known source level 140 dB. Environmental conditions yield an
isotropic noise level of 65 dB. You can assume an absorption
decay coefficient 0.02 dB/km.
At what range can the blue submarine be detected by the yellow
submarine? Show your answer graphically.
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