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