1. Oc679 Acoustical Oceanography
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 TS
Target Source Level SL
Oc679 Acoustical Oceanography

2. terms are not very universal!

3. Oc679 Acoustical Oceanography
Units
N = 10 log where I0 is a reference intensity
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
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
√ (double power level)
4 12
compare p/p0=1/√2, I/I0 = ½
dB = -3
we might say the -3dB level or ½ power level
Oc679 Acoustical Oceanography

4. 1 Pa is equivalent to 0 dB

5. 20 Pa 1 Pa 1 Pa is the reference standard for water
20 Pa is the reference standard for air
20 Pa
1 Pa
20log20 = 26 dB

6. Scattering
large target
(relative to λ)
small target
(relative to λ)
(Rayleigh scattering)

7. 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

8. Oc679 Acoustical OceanographyTL
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
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 absorption typical profiling
frequency @S= @S= range
3000 kHz dB/m dB/m m
1500 kHz dB/m dB/m m
500 kHz dB/m dB/m m
source: Sontek ADCP manual
Oc679 Acoustical Oceanography

9. TL

10. TL

11. Oc679 Acoustical OceanographyTL
relate spherical spreading & range attenuation due to absorption in terms of sonar equation
spherical spreading  1/R2, that is
log10 I/I0 = log10 R02/R2 = log10R02 – log10R2
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
Oc679 Acoustical Oceanography

12. Oc679 Acoustical OceanographyTL
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
Oc679 Acoustical Oceanography

13. Spreading Due to divergence No loss of energyTL
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
A.     SPREADING - spherical and cylindrical
1.       due to divergence.
2.       no loss of energy.
sound spread over wide area
Spherical: TL (dB) = 20 log R Cylindrical: TL (dB) = 10 log R + 30 dB
short range (R < 1000 m) long range (R > 1000 m)
NOTE: When the range is greater than 1000m we assume that the sound initially spreads out spherically to a range of 1000 m. At 1000 m we assume that the sound is now bounded by the surface and the bottom, so it spreads out cylindrically. The difference between 20 log R and 10 log R at 1000m is 30 dB.
Spherical component

14. Oc679 Acoustical Oceanography
now consider the reflected signal from a target with reflection coefficient R12
p is the pressure at range R
R12 is the target reflection coefficient
Srec is the receiver sensitivity [ Pa/V ]
V is the voltage o/p measured at receiver
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
Oc679 Acoustical Oceanography

15. this is the physical relationship that we have developed
this is how that relationship is represented logarithmically
terms in the SONAR EQUATION represent logarithms

16. 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

17. 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
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
this is the logarithmic representation of

18. 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)
DI = 10 log ((p/πr2)/(p/4πR2)) r r S
R = 1 m
α/2
with R = 1 DI = 10 log (4/r2)
and tan(α) = r/R = r
DI = 10 log (4/tan2(α/2))

19. 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

20. 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

21. Looking at a single trace on an oscilloscope is a little antiquated.
A time history helps to see what’s going on.

22. 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

23. three principal differences from passive case
received signal level modified by target strength TS
reverberation is the dominant interference
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

24. Homework 1 – Martin Hoecker-Martinez 18 Jan 2011

25. So, there are essentially two types of background that may mask the signal that we wish to detect:
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.

26. 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

27. Oc679 Acoustical Oceanography
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
Oc679 Acoustical Oceanography

28. 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
Oc679 Acoustical Oceanography

29. sounds in the sea
or N in the SONAR EQUATION
natural physical sounds
natural biological sounds
ships
Oc679 Acoustical Oceanography

30. 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
Oc679 Acoustical Oceanography

31. 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
Oc679 Acoustical Oceanography

32. 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
Oc679 Acoustical Oceanography

33. Homework Assignment 2
assigned: 18 Jan 2010
due: 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.

35. Oc679 Acoustical Oceanography