1. Review of Passive Sonar Equation
Transmission Loss
Review of Passive Sonar Equation

2. Terminology LS/N= LS - LN > DT Signal to Noise
Detection Threshold (DT)
The ratio of received echo from target
to background noise produced by everything else.
The measure of return signal required for an operator using installed equipment to detect a target 50% of the time.
1. Signal-to-Noise ratio or SNR is essentially the same as with radar.
- Go over definition.
- A high SNR is good.
2. Detection Threshold (DT).
- What this means is that if a target is out there the detection threshold is
the SNR level when an operator will first detect the target (see the
target’s return over the noise).
- The DT is a function of equipment and the operator.
3. Bottom line:
To achieve a detection with a specified degree of probability, the signal minus the noise must be equal to or greater than the detection threshold.
S - N > DT (all in dB)
This is the foundation for all sonar equations to predict performance.
LS/N= LS - LN > DT

3. Terminology Source Level (SL) Noise Level (NL = NLs  NLA) Self (NLs)
For ACTIVE sonar operations:
The SONAR’s sonic transmission (transducer generated)
For PASSIVE sonar operations:
Noise generated by target
Noise Level (NL = NLs  NLA)
Self (NLs)
Generated by own ship at the frequency of interest.
Ambient (NLA)
Shipping (Ocean Traffic), Wind and Weather - Sea State (Hydrodynamic)
Biologic and Seismic obtained from other methods
A.     OWNSHIP / EQUIPMENT
1.       DETECTION THRESHOLD (DT) - Signal to Noise Ratio (SNR) required to detect target 50% of time ; S - N > DT where S is the Signal and N is the Noise.
2.       SOURCE LEVEL (SL) - for ACTIVE sonar operations - the sonar’s “bang”!!
3.       SELF NOISE LEVEL (NLs) - generated by ship at frequency of interest
DIRECTIVITY INDEX (DI) - a function of a receivers directional sensitivity or the ability of the sonar system to direct it’s hydrophones to avoid unwanted noise; the receiver’s “discrimination” against noise; N = NL - DI

4. Terminology Directivity Index (DI) Transmission Loss (TL)
Receiver directional sensitivity.
LN = NL - DI
Transmission Loss (TL)
Amount the Source Level is reduced due to spreading and attenuation (absorption, scattering).
B.      ACOUSTIC ENVIRONMENT
1.       AMBIENT NOISE LEVEL (NLa) - obtained from Wenz Curves (see appendices - traffic, sea state, etc).
2.       TRANSMISSION LOSS (TL) - amount the active sonar Source Level (SL) is reduced due absorption, spreading, scattering.
REVERBERATION LEVEL (RL) - backscatter noise from own ship’s active sonar transmission.

5. Passive SONAR Equation (Signal Radiated by the Target)
SNR required for detection = DT
To achieve detection > 50% of the time…
SNR > DT
LS – LN > DT
LS = SL – TL (one way)
LN = NL – DI
Remember NL = NLs  NLa
Therefore…
1. The Passive Sonar Equation represents the ability to detect a target without using active sonar. Just listening for the noise generated by the Target itself.
(No echo Returns)
2. From the basic equation of: S - N > DT
a. . The Source noise level (S) is the Source Noise Level (SL) minus the sound losses due to the water environment (reflection, absorption, scattering , etc.). These losses to the environment are called Transmission Losses (TL)
b. The Noise is the self noise (noise from own ship) and the environmental noise. Together they are the noise level (NL)
c. The Noise portion of the equation is further modified by what is call the Directivity Index (DI) . DI comes into play because the sonar can look in specific directions rather than just 360 degrees. If you are looking the direction of the target you have a better chance of seeing it so the DI increases the Detection Threshold. (it is positive)
(1) Note that N = NL - DI and noise is always positive so DI can never
be more than the Ambient Noise Level (NL).
LS/N=SL - TL – (NL – DI) > DT

6. Passive Sonar Equation
LS/N=SL - TL – (NL – DI) > DT
III.    PASSIVE SONAR EQUATION - As you recall from the discussion above, the minimum SNR required for detection is referred to as the Detection Threshold (DT). To achieve detection more than 50 % of the time, the SNR > DT or S - N > DT
where S = SL - TL (one way) and N = NL - DI Note: (remember: NL = NLs + NLa)
Therefore, SL - TL - NL + DI > DT

7. The Passive Sonar Equation

8. Making the Sonar Equations Useful
Passive Example
Known
Can Measure
Function of
Equipment
Can Measure
Experimentally
SL - TL - NL + DI > DT
If we look at the equation that we used to describe our ability to detect a contact by sonar (Passive or Active Sonar Equation) we see
SL (source level) - We know or can calculate
NL (noise level) - Can measure
DI (directivity index) - know since it is a function of the sonar system
DT (detection threshold) - We can determine this through experimentation with
operators using the sonar system.
Only thing we don’t know or can’t predetermine is the Transmission Losses.
If we use algebra to rearrange knowns on one side of the equation and unknowns on the other, we get an equation that says what kind of Transmission losses can we have and still detect a SPECIFIC contact 50% of the time.
Transmission losses are from spreading, absorption, scattering. Spreading losses are mostly a function of range. Absorption is mostly due to bottom type. Can relate the Transmission losses as a function of range.
The equation we developed and shown is called the FIGURE OF MERIT.
ONLY UNKNOWN

9. Figure of Merit
Often a detection threshold is established such that a trained operator should be able to detect targets with that LS/N half of the time he hears them. Called “Recognition Differential.” (RD)
Passive sonar equation is then solved for TL allowable at that threshold. Called “Figure of Merit.” (FOM)
TLallowable = Figure of Merit = SL- LS/N Threshold - (NL-DI)
Since TL logically depends on range, this could provide an estimate of range at which a target is likely to be detected. Called “Range of the Day.” (ROD)
Any LS/N above the Recognition Differential is termed “Signal Excess.” (SE) Signal Excess allows detection of targets beyond the Range of the Day.

10. Range ??? FOM helps to predict RANGE. Probability of Detection
The higher the FOM, the higher the signal loss that can be suffered and, therefore, the greater the expected detection range.
Probability of Detection
Passive
If FOM > TL then > 50% prob det
If FOM < TL then < 50% prob det
Use Daily Transmission Loss (Prop Loss/FOM) curve provided by Sonar Technicians
V.      FIGURE OF MERIT (FOM) - a measure of a sonar’s capability.
A.     FOM - The total amount of TL a signal can suffer and still maintain a 50% probability of detection.
B.      Solve the Sonar Equation for TL and set = FOM:
FOMP = SL - NL +DI - DT (Passive)
FOMA = SL + TS - NL + DI - DT (Active - Noise Limited)
FOMA = SL + TS - RL - DT (Active - Reverberation Limited)
C.      The higher the FOM, the higher the signal loss that can be suffered and, therefore, the greater the expected detection range.
D.      FOM is increased by increasing the SL (active transmissions)
E.       Probability of Detection:
Passive Active
if FOM > TL then > 50% prob det if FOM > 2TL then > 50% prob det if FOM < TL then < 50% prob det if FOM < 2TL then < 50% prob det

11. HW Example
A submarine is conducting a passive barrier patrol against a transiting enemy submarine. The friendly sub has a directivity index of 15 dB and a detection threshold of 8 dB. The enemy sub has a source of 140 dB. Environmental conditions are such that the transmission loss is 60 dB and the equivalent isotropic noise level is 65 dB.
What is the received signal level?
What is the signal to noise ratio in dB?
What is the figure of merit?
Can the sub be detected? Why?

12. Prop Loss Curve
Max Range DP
Max Range BB
FOM = 70 dB

13. Prop Loss Curve
Max Range DP
Max Range CZ
FOM = 82 dB

14. Sound energy in water suffers two types of losses:
Transmission Loss
Sound energy in water suffers two types of losses:
Spreading
Attenuation
Combination of these 2 losses:
A.     Sound energy in water suffers 2 types losses:
1.       Spreading & Attenuation
- Combination of these 2 losses = Transmission Loss (TL)
TRANSMISSION LOSS (TL)

15. Spreading Spreading Due to divergence No loss of energy
Sound spread over wide area
Two types:
Spherical
Short Range: ro < 1000 m
Cylindrical
Long Range: ro> 1000 m
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

16. Spherical Spreading r1 r2 r3

17. Cylindrical Spreading
spherical
cylindrical r5 r4
Can be approximated as the sides of a cylinder with a surface area of 2r5H H r1 r2 r3 r4 r5 ro
transition range

18. Spherical to Cylindrical Transition Range in a Mixed Layer

19. Attenuation 2 Types Absorption Scattering and Reverberation
Process of converting acoustic energy into heat.
Viscosity
Change in Molecular Structure
Heat Conduction
Increases with higher frequency.
Scattering and Reverberation
All components lumped into Transmission Loss Anomaly (A).
Components:
Volume: Marine life, bubbles, etc.
Surface: Function of wind speed.
Bottom Loss.
Not a problem in deep water.
Significant problem in shallow water; combined with refraction and absorption into bottom.
      Absorption - any process involving conversion of acoustic energy into heat  acoustic lost to the environment. Caused by repeated pressure fluctuations in medium as sound propagated. Absorption coefficient ( a ) - Varies with frequency. Normally ignored at frequencies less than 3 kHz.
2.       Scattering - sound energy reflects off suspended foreign bodies in direction different than what is desired. Sound energy can also be lost in interactions with the surface of the bottom of the ocean. Finally, but possibly most importantly, the direction of propagation changes because of velocity changes. All of these effects are lumped together in a term called Transmission Loss Anomaly ( A ).
·         Volume Reverb - reflections from suspended bubbles, solids, fish/marine life
·         Surface Reverb - other than smooth surface; affected by wind
·         Bottom Reverb - sound reflected off rocky bottom; energy lost to bottom (mud)
SVP effects - all of the bending and concentrating discussed in the last lecture are modeled in computer generated transmission loss curves and are accounted for in this term.

20. Absorption Decrease in intensity, proportional to:
Distance the wave travels
Constant of Proportionality, a

21. Absorption Coefficient
Has units of dB/yard
a Has units of dB/kiloyard

22. Example Spherical Spreading Absorption coefficient, a = 2.5 dB/kyd
Find the TL from a source to 10,000 yards
Find the TL from 10,000 yards to 20,000 yards

23. General Form of the Absorption Coefficient
fr = relaxation frequency. It is the reciprocal of the relaxation time. This is the time for a pressure shifted equilibrium to return to 1/e of the final position when pressure is released
f = frequency of the sound
When f << fr,

24. Estimating Absorption Coefficient
Viscosity – Classical Absorption - Stokes
Shear and volume viscosity
For seawater, dB/m, f in kHz

25. Chemical Equilibrium
Magnesium Sulfate:
f in kHz
Boric Acid:
f in kHz

26. Scattering Scattering from inhomogeneities in seawater
Other scattering from other sources must be independently estimated
All lumped together as Transmission Loss Anomaly

27. Attenuation Summary
Note that below 10000Hz, attenuation coefficient is extremely small and can be neglected,

28. Transmission Loss Equations
TL = 10 log R a R + A
Range  1000 meters
Transmission Loss Anomaly
Absorption
Cylindrical Spreading
TL = 20 log R + a R + A
Range < 1000 meters
Spherical Spreading
Absorption
TLA