Transmission Loss

Review of Passive Sonar Equation

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

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

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).

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

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

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

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

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.

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

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?

Prop Loss CurveProp Loss Curve

Max Range DP

Max Range BB

FOM = 70 dB

Prop Loss CurveProp Loss Curve

Max Range DP

Max Range CZ

FOM = 82 dB

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)

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

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

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

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

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.

Absorption

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

• Constant of Proportionality, a

dI aIdr 2 1a r r2

1

Ie

I

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

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

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

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

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

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

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,

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