Table of Contents
1.0 PERFORMANCE PREDICTION............................................................................................................ 1-2
1.1 Sonar Equation Application.................................................................................................................. 1-2
1.1.1 Source Level (L
S
) ......................................................................................................................... 1-2
1.1.2 Propagation Loss (N
W
) ................................................................................................................ 1-3
1.1.3 System Noise Level (L
N
) ............................................................................................................. 1-9
1.1.4 Recognition Differential (N
RD
)................................................................................................... 1-11
1.1.5 Acoustic Interface Loss (N
D
) ...................................................................................................... 1-11
Table of Tables
TABLE 1 MEASURED VALUES OF BACKSCATTERING COEFFICIENT, S
B
AS A FUNCTION OF BOTTOM
SLOPE........................................................................................................................................................ 1-4
TABLE 2 ATTENUATION COEFFICIENT IN DB/KYD (`
O
)............................................................................. 1-8
TABLE 3 AVERAGE ATTENUATION COEFFICIENT IN DB//KYD (
D
) AS A FUNCTION OF DEPTH USED
FOR DEPTH SOUNDING (T = 40 F).......................................................................................................... 1-8
TABLE 4. SEA STATE ....................................................................................................................... 1-11
Table of Figures
FIGURE 1 AREA ILLUMINATED BY A CONICAL BEAM............................................................................. 1-5
FIGURE 2 FUNCTION OF THE TRANSMITTED BEAMWIDTH, DEPTH, AND PULSE DURATION........... 1-6
FIGURE 3. DEEP WATER AMBIENT NOISE LEVELS ................................................................................ 1-10
2
1.0 PERFORMANCE PREDICTION
1.1 Sonar Equation Application
The sonar equations developed for handling the detection of sonar targets are the basis for
predicting the performance of bathymetric systems. The sonar equation most generally used
expresses the system performance as a measure of signal-to-noise ratio at the transducer for a
specified depth. The applicable equation for bathymetric systems can be written in two forms
and the choice of propagation loss model determines which form is used. The general form of
the sonar equation used is
Equation 1-1: N
E =
L
S -
N
W -
L
N -
N
RD -
N
D
where
N
E
= Signal excess, expressed in decibels (dB) as the ratio of signal to noise at the
system input above that required for reliable performance, and is a measure of detection
reliability.
L
S
= Source level, a sound pressure expressed in dB referred to 1 dyne/ cm
2
at a
distance of 1 yard from the transducer
N
W
= Total propagation loss (dB)
L
N
= System noise level (dB)
N
RD
= Required signal-to-noise ratio for display used (recorder, digitizer) (dB)
N
D
= Two-way transmission loss in dome or other interface between the transducer
and the water (dB).
1.1.1 Source Level (L
S
)
The source level is the sound pressure level (on axis) expressed in dB relative to 1 bar at a
distance of 1 yard from the transducer. The source level is determined by:
n The amount of electrical transmitting power applied to the transducer
n The ability of the transducer to convert electrical energy to acoustical energy in
the water (i.e., transducer efficiency)
n The ability of the transducer to concentrate the energy into a beam (i.e.,
transducer gain).
The above factors can be combined in a logarithmic equation to give the source level
3
2
A 4
log 10
DIT
N
,
_
percent in efficiency n ,
n
100
log 10 E
(Source Level cont.)
Equation 1-2 L
S
= 71.6 + 10 log P
E
+ N
DIT
-E
where
P
E
= Electrical transmitting power in watts (average pulse power).
E = Transducer efficiency expressed in dB
N
DIT
= Transducer transmitting directivity index.
71.6 = Parameter conversion constant.
In addition, the directivity index for a circular piston transducer can be calculated with a good
approximation by
Equation 1-3
where
A = Effective radiating surface area of transducer in square inches
cycle) / (inches in water h Wavelengt
,
_
frequency f in water, sound of velocity C where ,
c
c
1.1.2 Propagation Loss (N
W
)
There are two basic propagation loss models, which can be used in the sonar equation to
calculate the depth capability of a bathymetric system. The difference between the two models is
based on the assumptions concerning the physics of the reflection from the bottom. The first
model considers the bottom echo to be primarily a coherent signal reflection with a bottom loss
factor to account for absorption and scattering losses. This model is sometimes referred to as the
"lossy mirror" or "specula" model.
The second model assumes no specularly reflected component, and the bottom reflected
signal is an incoherent addition of a large number of independent signal components. Each unit
element of the illuminated area contributes a small amount of reflected signal power dependent
on a back-scattering coefficient. In this case, the reflected signal is a function of the illuminated
area. This model is referred to as the target strength or scattering model.
4
0
1.1.2.1 Specular Model
The propagation loss is given by
Equation 1-4
BL
N
000 1
R 2
2R log 20
W
N + +
where
N
W
= Total propagation loss in decibels
R = Depth, yards
N
BL
= Bottom loss caused by absorption and scattering.
Typical values of bottom loss, N
BL
, at an operating frequency of 12 kHz range from 10 to 30
dB, with value of 20 dB used for an average value. For slope angles less than one half the
acoustic beamwidth, there will be a strong specular return and this first model applies.
1.1.2.2 Scattering Model
The propagation loss for this model is
Equation 1-5
B
S - A log 10
000 1
R 2
R log 40
W
N +
where
S
B
= Bottom back scattering strength per unit area, a function of bottom slope.
A = Effective illuminated area in square yards.
Measured values of back scattering coefficient S
B
are listed in Table 1.
Table 1 Measured Values of Backscattering Coefficient, S
B
as a function of Bottom Slope
S
B
5 -10
10 -12
15 -15
There are two methods in calculating the ensonified or illuminated area, depending on the depth.
The first area (A) is a function of the transmitted beamwidth and depth. For a flat bottom,
and the area illuminated by a conical beam is determined by the geometry below.
db/kyd t, coefficien n Attenuatio
5
Figure 1 Area illuminated by a conical beam
Then
Where
R = depth below transducer.
2
)
2
L
( A
2
tan R
2
L
2
tan
2
R A
6
The second area (A) is a function of the transmitted beamwidth, depth, and pulse duration.
Figure 2 Function of the transmitted beamwidth, depth, and pulse duration
2
r
2
A
2
R -
2
2
Tc
R
1
]
1
+
r
2
2
Tc
RTc
1
]
1
+
r
2
2
Tc
RTc
1
]
1
>>
RTc r
RTc
2
A
Sound of Speed c
Width Pulse T
Transducer Below Depth R
Beamwidth Acoustic
7
db/kyd
f
T
Bf
2
2
2
f
f
T
f
2
Sf
T
A
o
,
_
+
+
,
_
+ 273 T
1520
- 6
where
A
1
= A
2
occurs at the cross-over depth.
R
c
is the cross-over depth.
area. d illuminate as
1
A use , R R depths For
c
area. d illuminate as A2 use , R R depths For
c
>
For a sloping bottom, the calculation of the ensonified area becomes more complex and
requires an analysis of the bathymetric geometry, including bottom slope and transmitted pulse
duration.
1.1.2.3 Attenuation Coefficient (
o
)
The final consideration in determining the propagation loss is the determination of the
attenuation coefficient (
o
) in Equation 1-4. The attenuation coefficient becomes a limiting
factor in the propagation of acoustic signals as the frequency increases. The attenuation
coefficient becomes significant for frequencies above 10 kHz and is a parameter whose value has
been determined by a combination of theory and experimental measurements.
The equation most often used is that fitted by Schulkin and Marsh
5
to some 30,000
measurements made at sea.
Equation 1-6
where
S = Salinity in parts per thousand (typically = 35)
A = Constant = 1.86 x 10
-2
B = Constant = 2.68 x 10
-2
f = frequency in kHz
f
T
= temperature dependent relaxation frequency = 21.9 x 10
T is in degrees centigrade (f
T
= 72.7 at 40 F).
Some values for are given in
Table 2 for typical frequencies used in bathymetric systems.
RTc
2
2
tan
2
R
2
2
tan
Tc
c
R
8
Table 2 Attenuation Coefficient in dB/kyd (
o
)
Frequency ( kHz)
Temperature 3.5 7 12 15 20 40 100 200
40 F 0.1141 0.4534 1.310 2.018 3.481 11.60 34.64 56.53
50 F 0.0889 0.3544 1.031 1.597 2.786 9.898 35.34 61.35
60 F 0.0700 0.2794 0.8158 1.268 2.227 8.254 35.35 66.14
70 F 0.0558 0.2230 0.6526 1.016 1.793 6.823 31.95 69.55
80 F 0.0447 0.1786 0.5236 0.8163 1.444 5.592 28.62 70.69
90 F 0.0362 0.1448 0.4248 0.6628 1.175 4.598 25.03 69.18
The effect of pressure or depth on the attenuation coefficient is to modify it by
d
=
o
(1 - 0.965 x 10
-5
d) where
d
= Average attenuation coefficient used in bathymetric equation for depth sounding at depth
(d)
d = Depth of water between transducer and bottom in feet
o
= Value of attenuation coefficient before being corrected for depth.
Some values of
d
for an average water temperature of 40 F are given in Table 3
Table 3 Average Attenuation Coefficient in dB//kyd (
d
) as a Function of Depth Used for Depth Sounding (T =
40 F)
Frequency (kHz)
Depth (ft) 3.5 7 12 15 20 40 100 200
35,000 0.076 0.299 0.867 2.33 2.30 7.68 22.9 37.4
30,000 0.81 0.322 0.930 1.43 2.47 8.24 24.6 40.1
25,000 0.087 0.244 0.994 1.53 2.64 8.80 26.3 42.9
20,000 0.092 0.365 1.05 1.62 2.81 9.36 27.9 45.6
18,000 0.094 0.374 1.08 1.67 2.87 9.58 28.6 46.7
15,000 0.097 0.387 1.12 1.72 2.98 9.92 29.6 48.3
12,000 0.101 0.400 1.16 1.78 3.08 10.2 30.6 50.0
10,000 0.103 0.409 1.18 1.82 3.14 10.5 31.3 51.0
8,000 0.105 0.418 1.21 1.86 3.21 10.7 32.0 52.2
5,000 0.109 0.431 1.25 1.92 3.31 11.0 33.0 53.8
2,000 0.112 0.444 1.28 1.98 3.41 11.4 34.0 55.4
1,000 0.113 0.448 1.30 2.00 3.45 11.5 334.3 56.0
500 0.114 0.451 1.30 2.01 3.46 11.5 34.5 56.2
0 0.114 0.453 1.31 2.02 3.48 11.6 34.6 56.5
9
1.1.3 System Noise Level (L
N
)
System-noise level includes self noise generated by the vessel, ambient noise that exists
in the water, and reverberation noise which is a function of the propagation paths and
configuration of the acoustic system.
An appropriate value of self noise generated by the vessel should be determined for the
installation considered. It is usually the self-noise level that limits bathymetric system
performance. Self noise is expressed as a spectrum level and specified in dB// bar in a 1Hz
band. It then becomes necessary to increase the spectrum level by a bandwidth correction factor
(N
BW
) determined by the bandwidth of the receiving system. The bandwidth correction factor is
expressed in dB as:
Equation 1-7
Hz 1
BW
log 10
BW
N
where
N
BW
= bandwidth correction factor
BW = bandwidth of receiving system in Hz.
Self-noise levels are generally assumed as isotropic sources. This assumes that noise
received at the hydrophone has no directional characteristics, and consequently, the directivity of
the transducer will act to reduce the self noise that passes into the receiving system. The total
noise term in the sonar equation is then expressed by:
Equation 1-8 L
N
= L
a
+ N
BW
- N
DIR
where
L
N
= Total self noise in the receiver bandwidth
L
a
= Spectrum level of self noise in a 1 Hz bandwidth
N
BW
= Bandwidth correction factor
N
DIR
= Directivity index of receiving transducer.
It should be remembered that self noise, like ambient noise, is not always isotropic in its
directional characteristics. Consequently, the use of the directivity index as an exact reduction of
the noise level entering the receiving system is not always satisfactory. For example, if a highly
directional noise source exists within the beamwidth of the receiving system, then the directivity
index will be almost meaningless as a measure of discrimination against noise.
Contributions of the electronics in a bathymetric system to the self-noise level usually
occurs only at high frequencies; potential electrical noise sources in the receiving system should
be reduced to a value well below the limiting ambient acoustic noise level.
10
Ambient noise is that background noise level that exists in the ocean due mainly to
marine life and man-made noise. Man-made noise will vary in its origin e.g., for surveys in a
harbor, man-made noise may be predominately originated on land. Whereas, for bathymetric
operations near shipping lanes, man-made noise will be the aggregate of nearby and distant
shipping noise.
The lower limit of ambient noise is that generated by the movement of the water itself.
Water noise may be generated in a number of ways, again depending on where the bathymetric
operations are being performed. Measurements of water noise in a wide variety of locations, and
under varying conditions, have yielded statistical estimates as to its magnitude. As might be
expected, the resulting averages have been found to vary with the state of the sea. Values for the
spectrum level of water noise as a function of frequency and sea state
6
are shown in Figure 1.
The significance of the noise levels shown in Figure 1 is that the dominant noise level (self
noise) that is present during bathymetric operations is often given relative to the spectrum levels
shown. Table 4-4 presents the sea-state numbers, and a description of the conditions they
represent.
Another source of noise in bathymetric systems is that caused by reverberation.
Reverberation can be defined as the re-radiations of sound by the sum of all the unwanted
scattering contributions from all scatterers not pertinent to the bathymetric measurement. The
reverberation that occurs can come from the water surface, re-radiation from a body of marine
life scatterers (volume reverberation) in the sea, or from the bottom. Bottom reverberation is a
significant noise source consideration in active sonar systems. For bathymetric applications,
bottom reverberation is considered only when the application is to discriminate some feature that
extends above or is buried in the bottom and might be obscured.
Figure 3. Deep Water Ambient Noise Levels
11
Table 4. State of the Sea
Sea State Number Description Height of Waves (ft)
0
1
2
3
4
5
6
7
8
9
Calm Sea
Smooth Sea
Slight Waves
Moderate Sea
Rough Sea
Very Rough Sea
High Sea
Very High Sea
Precipitous Sea
Confused Sea
0-1
1-2
2-3
3-5
5-8
8-12
12-20
20-40
40+
---
1.1.4 Recognition Differential (N
RD
)
An acceptable value of recognition differential has been arrived at empirically by many
observers using various types of displays in bathymetric applications. The two principal display
techniques for bathymetric systems are the dry paper precision recorder and digital. Current
design practice dictates that when a signal-to-noise ratio of 10 dB is used for the recognition
differential for a dry paper recorder, and a signal-to-noise ratio of 14 dB is used for digital
systems, reliable data recognition is achieved by the system.
1.1.5 Acoustic Interface Loss (N
D
)
When the transducer transmits in any manner other than directly into the sea, or final
propagation medium, then an acoustic interface loss (two-way transmission loss) must be
considered when using the general form of the sonar equation. The technique for calculating this
loss is explained in detail in Section 3.2.3.
