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Transmission Loss Review of Passive Sonar Equation

Transmission Loss

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Transmission Loss. Review of Passive Sonar Equation. L S/N = L S - L N > DT. Terminology. Signal to Noise Detection Threshold ( DT ). The ratio of received echo from target to background noise produced by everything else. - PowerPoint PPT Presentation

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Page 1: Transmission Loss

Transmission Loss

Review of Passive Sonar Equation

Page 2: Transmission Loss

Terminology

• 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

Terminology• 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

Terminology

• 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

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

Passive Sonar EquationLS/N=SL - TL – (NL – DI) > DT

Page 7: Transmission Loss

The Passive Sonar Equation

S/ NL SL TL NL DI

S

0

ISL 10logI

S

R

ITL 10logI

N

0

INL 10logI

DI 10log d

Page 8: Transmission Loss

Making the Sonar Equations UsefulMaking the Sonar Equations UsefulPassive ExamplePassive Example

SL - TL - NL + DI > DT

Known

Can Measure

Function ofEquipment

Can MeasureExperimentally

ONLY UNKNOWN

Page 9: Transmission Loss

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

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

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

Prop Loss Curve

Max Range DP

Max Range BB

FOM = 70 dB

Page 13: Transmission Loss

Prop Loss Curve

Max Range DPMax Range CZ

FOM = 82 dB

Page 14: Transmission Loss

Transmission Loss

• Sound energy in water suffers two types of losses:–Spreading–Attenuation

Combination of these 2 losses:

TRANSMISSION LOSS (TL)

Page 15: Transmission Loss

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 componento

o

rrTL 10log 20logr 1

TL 20log r

Page 16: Transmission Loss

Spherical Spreading

S

R

ITL 10logI

r1

r2r3

2

1

22

1

22

2

1

222

211

21

44

44

rr

rr

II

rIrI

PP

2

1

r rTL 20log 20log 20log rr 1

Page 17: Transmission Loss

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

rII

rII

TL 0

0

log10yd 1

log10yd 1

log10

00 log10log20

rrrTL

r4r5

spherical cylindrical

ro

Page 18: Transmission Loss

Spherical to Cylindrical Transition Range in a Mixed Layer

dHHRHr

80

ray sound of curvature of radiuscos

source theofdepth knesslayer thic mixed

n

n

gcR

dH

Page 19: Transmission Loss

Attenuation• 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

Absorption

• Decrease in intensity, proportional to:– Intensity– Distance the wave travels

• Constant of Proportionality, a

dI aIdr 2 1a r r2

1

I eI

Page 21: Transmission Loss

Absorption Coefficient

2 1a r r1

2

ITL 10log 10log eI

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

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 x10r

Page 23: Transmission Loss

General Form of the Absorption Coefficient

2r

2 2r

Af ff 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

Aff

Page 24: Transmission Loss

Estimating Absorption Coefficient

• Viscosity – Classical Absorption - Stokes2

23

16 f3 c

s v34

Shear and volume viscosity

4 22.75x10 f For seawater, dB/m, f in kHz

Page 25: Transmission Loss

Chemical Equilibrium

3 24 2 4 2MgSO H O Mg SO H O

2

2

40f4100 f

Magnesium Sulfate:

Boric Acid:

3 4B OH OH B OH

2

2

.1f1 f

f in kHz

f in kHz

Page 26: Transmission Loss

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

Attenuation Summary

kyddB 1075.2

410040

11.0003.0

wheredB 10

242

2

2

2

3

ff

fff

rTL

Note that below 10000Hz, attenuation coefficient is extremely small and can be neglected,

Page 28: Transmission Loss

Transmission 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