transmission loss review of passive sonar equation
TRANSCRIPT
![Page 1: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/1.jpg)
Transmission Loss
Review of Passive Sonar Equation
![Page 2: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/2.jpg)
TerminologyTerminology
• Signal to Noise
• Detection Threshold (DT)
The ratio of received echo from targetto 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.
LS/N= LS - LN > DT
![Page 3: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/3.jpg)
TerminologyTerminology• Source Level (SL)
– 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
![Page 4: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/4.jpg)
TerminologyTerminology
• Directivity Index (DI)– Receiver directional sensitivity.
– LN = NL - DI
• Transmission Loss (TL)– Amount the Source Level is reduced due to
spreading and attenuation (absorption, scattering).
![Page 5: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/5.jpg)
Passive SONAR Equation(Signal Radiated by the Target)
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…
LS/N=SL - TL – (NL – DI) > DT
![Page 6: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/6.jpg)
Passive Sonar EquationPassive Sonar EquationLS/N=SL - TL – (NL – DI) > DT
![Page 7: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/7.jpg)
The Passive Sonar Equation
S/ NL SL TL NL DI
S
0
ISL 10log
I
S
R
ITL 10log
I
N
0
INL 10log
I
DI 10log d
![Page 8: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/8.jpg)
Making the Sonar Equations UsefulMaking the Sonar Equations UsefulPassive ExamplePassive Example
Making the Sonar Equations UsefulMaking the Sonar Equations UsefulPassive ExamplePassive Example
SL - TL - NL + DI > DTSL - TL - NL + DI > DT
KnownKnown
Can MeasureCan Measure
Function ofEquipmentFunction ofEquipment
Can MeasureExperimentallyCan MeasureExperimentally
ONLY UNKNOWN
![Page 9: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/9.jpg)
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.
![Page 10: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/10.jpg)
Range ???Range ???• FOM helps to predict RANGE.
– 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
![Page 11: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/11.jpg)
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?
![Page 12: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/12.jpg)
Prop Loss CurveProp Loss Curve
Max Range DP
Max Range BB
FOM = 70 dB
![Page 13: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/13.jpg)
Prop Loss CurveProp Loss Curve
Max Range DP
Max Range CZ
FOM = 82 dB
![Page 14: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/14.jpg)
Transmission LossTransmission Loss
• Sound energy in water suffers two types of losses:–Spreading
–AttenuationCombination of these 2 losses:Combination of these 2 losses:
TRANSMISSION LOSS (TL)TRANSMISSION LOSS (TL)
![Page 15: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/15.jpg)
SpreadingSpreading• 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
Spherical component
o
o
rrTL 10log 20log
r 1
TL 20log r
![Page 16: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/16.jpg)
Spherical Spreading
S
R
ITL 10log
I
r1
r2r3
2
1
22
1
22
2
1
222
211
21
4
4
44
r
r
r
r
I
I
rIrI
PP
2
1
r rTL 20log 20log 20log r
r 1
![Page 17: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/17.jpg)
r1
r2r3
Can be approximated as the sides of a cylinder with a surface area of 2r5H
H
transition range
r4
r5
Cylindrical Spreading
rIrI
rI
I
rI
ITL 0
0
log10yd 1
log10yd 1
log10
00 log10log20
r
rrTL
r4r5
spherical cylindrical
ro
![Page 18: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/18.jpg)
Spherical to Cylindrical Transition Range in a Mixed Layer
dH
HRHr
80
ray sound of curvature of radiuscos
source theofdepth
knesslayer thic mixed
n
n
g
cR
d
H
![Page 19: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/19.jpg)
AttenuationAttenuation• 2 Types• Absorption
– 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.
![Page 20: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/20.jpg)
Absorption
• Decrease in intensity, proportional to:– Intensity– Distance the wave travels
• Constant of Proportionality, a
dI aIdr 2 1a r r2
1
Ie
I
![Page 21: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/21.jpg)
Absorption Coefficient
2 1a r r1
2
ITL 10log 10log e
I
2 1 2 1TL a r r 10log e 4.343a r r
2 1TL r r
4.343a Has units of dB/yard
32 1TL r r x10 Has units of dB/kiloyard
![Page 22: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/22.jpg)
Example
• Spherical Spreading• Absorption coefficient, = 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
322 1
1
rTL 20log r r x10
r
![Page 23: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/23.jpg)
General Form of the Absorption Coefficient
2r
2 2r
Af f
f f
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,
2
r
Af
f
![Page 24: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/24.jpg)
Estimating Absorption Coefficient
• Viscosity – Classical Absorption - Stokes
22
3
16f
3 c
s v
3
4 Shear and volume viscosity
4 22.75x10 f For seawater, dB/m, f in kHz
![Page 25: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/25.jpg)
Chemical Equilibrium
3 24 2 4 2MgSO H O Mg SO H O
2
2
40f
4100 f
Magnesium Sulfate:
Boric Acid:
3 4B OH OH B OH
2
2
.1f
1 f
f in kHz
f in kHz
![Page 26: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/26.jpg)
Scattering• Scattering from inhomogeneities in seawater
• Other scattering from other sources must be independently estimated
0.003dB / kyd
All lumped together as Transmission Loss Anomaly
![Page 27: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/27.jpg)
Attenuation Summary
kyddB 1075.2
4100
40
1
1.0003.0
where
dB 10
242
2
2
2
3
ff
f
f
f
rTL
Note that below 10000Hz, attenuation coefficient is extremely small and can be neglected,
![Page 28: Transmission Loss Review of Passive Sonar Equation](https://reader031.vdocument.in/reader031/viewer/2022012313/56649e245503460f94b11f06/html5/thumbnails/28.jpg)
Transmission Loss EquationsTransmission Loss Equations
TL = 10 log R + 30 + R + A
Range 1000 meters
TL = 20 log R + R + A
Range < 1000 meters
Cylindrical Spreading
Absorption
Transmission Loss Anomaly
Spherical Spreading
Absorption
TLA