Transmission Loss

Transmission Loss

Review of Passive Sonar Equation

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

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

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).

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

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

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

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 ???• 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 Curve

Max Range DP

Max Range BB

FOM = 70 dB

Prop Loss Curve

Max Range DPMax Range CZ

FOM = 82 dB

Transmission Loss

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

Combination of these 2 losses:

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 componento

o

rrTL 10log 20logr 1

TL 20log r

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

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

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

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.

Absorption

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

• Constant of Proportionality, a

dI aIdr 2 1a r r2

1

I eI

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

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

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

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

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

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

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,

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