Estimating Underwater
Acoustic Propagation
Ethem Mutlu Sözer
Research Engineer
MIT Sea Grant College Program
2/23/2006
1
Outline
Outline
„
„
„
What is decibel?
Transducers and hydrophones
Underwater acoustic propagation
Ray tracing
„ Delay and signal strength calculations
„ Channel impulse response
„
„
„
Estimating the range of a source
Estimating the direction of a source
source
2/23/2006
2
Deci-bel (dB)
(dB)
„
„
„
„
„
„
A decibel (dB) is a unit for measuring the
relative strength of a signal in logarithmic scale
P(dB) = 10 log10(P/Pr)
= 20 log10(V/Vr)
V(dB) = 10 log10(V/Vr)
= 10 (log10(V) – log10(Vr))
2/23/2006
2/23/2006
3
Transducer and Hydrophone
Hydrophone
Specifications
Specifications
„
„
„
„
Open Circuit Receiving Response (OCRR)
(OCRR)
Transmitting Voltage Response (TVR)
Directionality Pattern
Pre-Amplifier
2/23/2006
4
Transmitting Voltage Response
Response
(TVR)
(TVR)
dB re µPa/V @ 1m
„
150
140
„
130
120
Transmitting Voltage Response
110
2
10
18
26
Frequency in kHz
ITC 1001 Transducer VTR
2/23/2006
34
Figure by MIT OCW.
output SIL generated per 1 V
of input Voltage at 1m range
as a function of frequency
dB re µPa / V
V = 200 V @ fc=22 kHz
SIL (µPa)
Pa = V (V) x TVR (µPa / V)
SIL = 10 log10(V) + TVR(fc)
= 26 + 144 = 170 dB re µPa
5
Open Circuit Receiving Response
Response
(OCRR)
(OCRR)
„
dB re 1V/µPa
-180
-190
-200
„
-210
Open Circuit Receiving Response
-220
2
10
18
26
Frequency in kHz
output voltage (V) generated
by the transducer per µPa of
sound pressure as a function
of frequency
dB re 1V / µPa
SIL = 190 dB re µPa @ fc=22 kHz
V = SIL (V/µPa)
Pa x OCRR (µPa)
34
VdB = SIL + OCRR(fc)
Figure by MIT OCW.
ITC 1001 Transducer OCRR
= 190 + (-190) = 0 dB re 1V
VdB re 1V = 10 log10 ( V / 1 )
( VdB / 10 )
V = 10
2/23/2006
2/23/2006
= 1 V
6
Directionality Pattern
Pattern
330
0
30
330
60
300
60
270
90
270
90
240
120
240
120
180
10dB/div
210
150
Directivity Pattern at 18.0 kHz
„
„
30
300
10dB/div
210
„
„
0
180
150
Directivity Pattern at 2.0 kHz
ITC 1001 spherical transducer
Uniform response over all
angles ( 0 to 2π) on both
horizontal and vertical plane
plane
„
„
ITC 2010 toroidal transducer
More gain over the sides
(horizontal plane) than the
over the top and bottom
bottom
(vertical plane)
plane)
2/23/2006
7
Figures by MIT OCW.
Pre-Amplifier
„
„
Amplifies the signals generated at the receiving element
(hydrophone or transducer)
Gain defined in dB
mV
V
amplifier
Vin = 1 mV, Gain = 20 dB
mV
pre-amplifier
2/23/2006
Vout(dB) = Vin(dB) + Gain(dB)
Vin(dB) = 10 log10(Vin) = 10 log(10e-3) = -30 dB
Vout(dB) = -30 + 20 = 0 dB
Vout = 10(-10/10) = 0.1 Volt
8
Shallow Water Propagation
Propagation
„
Assumptions:
Constant sound speed (c = 1500 m/s)
„ Surface and bottom are smooth
„
d=20m
θ1
source
θ1
r=100m
destination
h=80m
θ2
2/23/2006
θ2
9
Length of propagation paths
paths
Direct path => d0 = 100m
Surface reflection => d1 = 2d/cos(θ1) = 107.7 m
θ1 = atan(r/2d)
Bottom reflection => d2 = 2h/cos(q2) = 188.7 m
θ2 = atan(r/2h)
SBS reflection =>
d3 = 2(2d/cos(θ3)+ h/cos(θ3)) = 260 m
BSB reflection =>
d4 = (2d/cos(θ4)+ 2(h/cos(θ4))) = 399.5 m
d=20m
θ1
source
θ1
r=100m
destination
h=80m
θ2
2/23/2006
θ2
10
Time of arrival to the receiver
„
τi = di/c
„
„
„
„
„
τ0 = 66.7 msec
τ1 = 71.8 msec
τ2 = 125.8 msec
τ3 = 173.3 msec
τ4 = 266.3 msec
2/23/2006
11
Transmission loss
loss
„
„
„
„
„
fc=22kHz
T = 15 ˚C (fm=100 kcycles/sec, A=6e-4, B=2.4e-7)
a = (A fm f2)/(f2+fm2)+Bf2 dB/m
Surface reflection loss (RLs) = 1 dB
Bottom reflection loss (RLb) = 3 dB
TL = TLs + TLa + RLs + RLb
TLi = 20log(di) + adi + RLs + RLb
TL0
TL1
TL2
TL3
TL4
2/23/2006
=
=
=
=
=
40.3
42.0
49.1
54.0
60.2
dB
dB
dB
dB
dB
12
12
Impulse Response
„
output of a system to an
excitation with a unit impulse
n =1
⎧1
δ (n) = ⎨
⎩0 otherwise
d=20m
θ2
source
θ2
r=100m
destination
h=80m
θ1
2/23/2006
θ1
13
Transmitted and Received SIL
SIL
„
„
ITC1001, fc=22kHz, V=100 V
„ SILs = 144 + 10 log(100) = 170 dB re mPa at 1m
SILri = SILs – TLi
„ SILr0 = 129.7 dB
„ SILr1 = 128.0 dB
„ SILr2 = 120.9 dB
„ SILr3 = 116.0 dB
„ SILr4 = 109.8 dB
2/23/2006
14
14
Received Voltage
Voltage
„
„
„
„
OCRR = -162 dB re V / µPA
Pre-amplifier gain, G = 40 dB
VdB = SILri -162 + 40
40
V = 10(VdB/10)
„ V0 = 5.9 V
V
„ V1 = 4.0 V
V
„ V2 = 0.8 V
V
„ V3 = 0.2 V
V
„ V4 = 0.1 V
V
2/23/2006
15
15
Results for 1000m
2/23/2006
16
Determining the Range of a Source
Source
„
„
„
„
Tracker sends a pulse, p(t) = A sin(2πfc1t), 0<t<Ts
Target replies, p1(t) = A sin(2πfc2(t-τp-τt))
Tracker receives, p2(t) = A sin(2πfc2(t-τp-τt-τp))
How can we measure τp+τt+τp ?
2/23/2006
17
17
Correlation
„
Definition:
R (a,b) (λ ) =
∞
∫ a(t)b(t − λ)dt
−∞
„
Autocorrelation:
R (a,a) (λ ) =
∞
∫ a(t)a(t − λ)dt
−∞
autocorrelation
2/23/2006
18
Estimating the Range
Range
„
„
„
„
„
Correlate p(t) with p(t-τp-τt-τp)
Find the peak of the correlation, λ
λ = 2τp-τt
τp is the propagation delay
Range is, d=c τp = 1500 τp
2/23/2006
19
19
Correlation Results
100m, delay estimate is 66.7 msec
2/23/2006
100m, delay estimate is 666.7 msec
20
Determining the Direction of the
the
Target
Target
Four hydrophones
hydrophones
„
„ Measure delay at
each hydrophone
„
„ Compare delay pairs
(τ1, τ2), (τ2, τ3),
(τ3, τ4), (τ4, τ1) to find
which quadrant
„
„ Estimate the angle
„
„
Quadrant 1
Quadrant 4
θ
Η4
Η3
Quadrant 3
r1-r4
d
θ
Η1
Η2
Quadrant 2
θ = sign(r1-r4)acos( |r1-r4| / d)
2/23/2006
2/23/2006
21
21