RAPID GEOACOUSTIC CHARACTERIZATION
FOR LIMITING ENVIRONMENTAL UNCERTAINTY
FOR SONAR SYSTEM PERFORMANCE PREDICTION
KEVIN D. HEANEY AND HENRY COX
ORINCON Defense, 4350 N. Fairfax Dr. Suite 400, Arlington VA 22203, USA
E-mail: [email protected]
Ocean acoustic propagation and sonar performance in shallow water environments are
dominated by interactions with the seafloor and is therefore sensitive to the geo-acoustic
properties of the sediment. The goal of this research is improve sonar performance
prediction by estimating the environment and determining the sensitivity to uncertainty.
An approach is presented that links the observed acoustic signals of a sonar system to
the environmental characterization and then, via simulation, to the environmental
sensitivity. Relevant observables are extracted from data taken from a tactical sonar
system (passive towed array, bi-static active, etc). These observables are taken from the
striation patterns (time spread, slope) and the received level vs. range curves for surface
ships of opportunity. The geo-acoustic parameters are estimated using the Rapid Geoacoustic Characterization (RGC) algorithm that matches the observables to a parametric
model of the sediment based upon Hamilton’s equations. Once a baseline geo-acoustic
model is determined, simulation studies are used to examine the sensitivity of the
acoustic observables to variations in the environment. The resulting performance
prediction curves can then computed with relevant confidence intervals. The approach
reduces the mismatch by estimating the geo-acoustic environment and captures and
communicates the uncertainty in performance prediction to the end user.
1
Introduction
The difficulty in predicting sonar performance is that acoustic propagation is sensitive to
environmental variables and these variables generally are not well sampled in standard
navy databases. To restore confidence in, and the utility of, sonar performance
algorithms, a method for determining the environmental parameters in situ must be
developed. Experience in the ocean acoustics research community has shown that
accurate geo-acoustic inversions are possible in controlled experiments. The technical
challenge addressed in this paper is to determine whether a surface ship of opportunity
could be used as a source for covert environmental acoustic calibration. The robust
Rapid Geo-acoustic Characterization (RGC) algorithm was developed and applied to a
data set from a surface ship in the Gulf of Mexico. The algorithm successfully
determines a geo-acoustic profile that permits the reproduction of the relevant acoustic
propagation. We present here the signal processing, parameter extraction, and inversion
algorithm used to extract a geo-acoustic profile that reproduces the key features of the
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N.G. Pace and F.B. Jensen (eds.), Impact of Littoral Environmental Variability on Acoustic Predictions and
Sonar Performance, 163-170.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
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KEVIN D. HEANEY AND HENRY COX
acoustic propagation. We stress that the RGC algorithm is seeking to rapidly match the
acoustic propagation and is not primarily concerned with an accurate representation of
the geo-acoustic profile. Accurate geo-acoustic inversions can subsequently be
performed using Full Search algorithms based upon simulated annealing [1].
Much work has been done in the area of environmental sensitivity and uncertainty.
In general, acoustic modelers look at how the acoustic field varies with the changing of
database values, and tactical navy personnel look at the variability in sonar performance
as a function of position and time. We seek a systematic approach to the environmental
uncertainty problem of sonar performance prediction that incorporates acoustic modeling
and system performance on real data.
In Section 2 we outline the geo-acoustic inversion approach to define a baseline
environment. In this section the data analysis procedure is presented for a bottom
mounted horizontal line array as well as the parameter extraction and inversion technique
for rapidly estimating a geo-acoustic profile. Section 3 concludes with how this
information could be used in-situ to provide accurate representations of the effect of
environmental uncertainty on the sonar performance.
2
Rapid geoacoustic characterization algorithm
2.1
Experimental Data
In 1999, the Applied Research Laboratory – University of Texas (ARL-UT) conducted
an ocean acoustics experiment off the south coast of the Florida panhandle. A small
portion of this experiment was run with the intention of performing geo-acoustic
inversions from a surface ship of opportunity. This dataset provides an excellent
opportunity for the development and demonstration of inversion techniques based upon
surface ships of opportunity. A 534-m 52-element array was deployed on the bottom.
The data analysis procedure is as follows:
•
•
•
Beamform to improve SNR and estimate number of interferers.
Compute track-beam spectra for various sub-apertures of the array.
Use the ship GPS and convert spectra to range/frequency data for geo-acoustic
inversion.
After beamforming with an array length (17 phones) that maximizes SNR while limiting
signal rejection due to small beamwidths, we fuse the acoustic (scissorgram) and the
position (GPS) data into a single data file that will permit geo-acoustic characterization.
The range-frequency data set is shown in Fig. 1. The striations resulting in coherent
multipaths propagation are clearly visible. These patterns are ubiquitous to surface ship
passes in shallow water environments.
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RAPID ENVIRONMENTAL CHARACTERIZATION
Range/Frequency Tracked Spectrogram
15
4000
10
3500
5
dB
3000
Range (m)
0
2500
−5
2000
−10
1500
−15
1000
−20
0
100
200
300
400
500
600
700
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900
1000
−25
Frequency (Hz)
Figure 1. Range/frequency curve from beamformed acoustic data and position data.
2.2
Robust Observables for Inversion
Three observables are chosen to perform the environmental characterization. These
features are chosen because they are robust, easily measured and sensitive to the bottom
parameters. The time-spread (∆t) between the fastest and slowest propagating rays is the
reciprocal of the spacing in frequency of the striations (∆f). It is related to the critical
angle of the bottom and depends on the sound speed in the sediment. The second
observable can be either the striation spacing in range or the slope of the striation
patterns. The slope of the striations is related to the waveguide-invariant β. It is a
measure of how important refraction in the bottom is. The final observable, α, is the
slope of the TL vs. range curve (after correcting for cylindrical spreading). α is a
measure of the overall attenuation. For very hard bottoms, α is nearly zero.
2.2.1
Time Spread/Critical Angle
The striations visible in Fig. 1 are the result of constructive and destructive interference
of the acoustic multipaths. Looking at the interference pattern in the frequency domain
leads to determination of the time spread of an acoustic pulse and therefore the spread in
group velocities of the propagating energy. At a range of 3 km and a frequency of 300
Hz, the frequency spacing is computed. A frequency spacing of 31 Hz is associated with a
time spread in the acoustics of 32 m/s. This is quite a small time spread and can easily be
associated with a soft-bottom.
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2.2.2
KEVIN D. HEANEY AND HENRY COX
Striation Slope (β)
The slope of the striations is easily obtained from the display in Fig. 2. The slope of the
striations is an indication of the angle spread between the lowest and highest angle
acoustic energy and is therefore another robust feature that depends upon the geoacoustic parameters as well as the water column sound speed. Along a ridge of constant
intensity, the relative phases or phase differences between components are nearly
constant. Consider two interfering components with travel times T1 and T2 and phases φ1
and φ2, respectively. Let φ12 be the phase difference, φ2-φ1. Then
φ
12
= 2πf (T − T ) + ε − ε
2 1
2 1
(1)
where ε1 and ε 2 are the phase changes associated with boundary interactions and are
constant (unless on a caustic)
1 1
dφ = 2πf  −  dr + 2π (T − T ) df
12
2 1
 v2 v1 
(2)
Applying the stationary phase condition dφ12 = 0 yields the following relationship that is
satisfied along a ridge on constant intensity
1 1
1 1
 − 
 − 
v  dr
 v2 v1 
v
df
dr = −  2 1 
=−
f
T −T
 T2 − T1  r
2 1


 r 
(3)
or
df
dr
=β
12 r
f
(4)
where β12 is the non-dimensional parameter:
1 1
 − 
v 
v
β = −  2 1
12
T −T
2 1
r
(5)
Equation (5) is very general. No assumptions about range independence of the
environment, or details of the sound speed profile, have been made. β12 depends on both
local properties: the difference in phase slowness of the two components at the field point
(r, z) and the travel time difference that involves the accumulated effects of propagation
from the source to the field point. The quantityµi = r/Ti is the average horizontal
propagation speed or average group velocity of the i-th component. Thus, Eq. (5) can be
written as
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RAPID ENVIRONMENTAL CHARACTERIZATION
1 1
 − 
v 
v
β = −  2 1
12
1
1
 − 
 u2 u1 
(6)
A number of important simplifications occur. In range-independent environments, the
group velocities can replace the range-averaged group velocities. In general βij depends
on which components are interacting. There are two situations in which βij is nearly
invariant with regard to the components that are involved. These are the iso-speed sound
profile that is often a useful approximation in shallow water and steep angles, and the
duct with a linear sound speed profile.
2.2.3
Transmission Loss Attenuation (α)
We are interested in matching the general characteristics of propagation and are not
concerned (at this point) about matching the locations of the peaks and valleys. With
received level measurements made over various ranges, the band-averaged transmission
loss is computed. This reduces the high spatial frequency variability. Using a bandwidth
of 60 Hz, the received levels for 200 and 500 Hz are shown in Fig. 3. It should be noted
at this point that the hydrophones have not been calibrated. The more rapid attenuation
with range of the higher frequency is consistent with a soft bottom.
Band Averaged Received Level
40
200Hz (−.0028)
500Hz (−.0046)
Received Level (dB + 10logR)
35
30
25
20
15
10
0
500
1000
1500
2000
Range (km
2500
3000
3500
Figure 2.Band-averaged received level (RL) with cylindrical spreading taken out. Received levels
matched with linear fits with alpha coefficients (200 Hz = -2.8 dB/km, 500Hz = -4.6 dB/km).
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KEVIN D. HEANEY AND HENRY COX
2.3
Forward Computation for RGC
To perform the Rapid Geo-acoustic Characterization, a simple geo-acoustic model that
can represent a large variety of sediments and is consistent with our knowledge of geoacoustics is needed. To this end, a simple two-layer sediment model is used. The
sediment layer is considered to be of thickness H, overlaying a basement (or acoustic
half-space). The sediment layer is inferred as having a unimodal particle size distribution
with mean grain diameter φ, with associated geo-acoustic parameters ascribed by
regression formulas presented in Hamilton and Bachman [2,3].
•
•
•
•
•
•
•
Density:ρ = (22.85 - φ)/10.275
Velocity ratio:(Cw/Cp) = 1.180 - 0.034 φ + 0.0013 φ2
Sediment Phase Speed:Cp(z):
Sand:φ < 3.25: Cp(z) = Cp(0) * (20z)0.015
Silt:φ > 5.75: Cp(z) = Cp(0) + 0.712 z
Mixtures:3.25 < φ < 5.75: use silt factor: α = (φ - 3.25)/(5.75 - 3.25)
Cp(z) = α Cp(silt) + (1- α) Cp(sand)
where z is the depth of the sediment in meters, measured from the water sediment
interface. The attenuation was chosen as a linear fit from 1.0 dB/Wavelength for sand to
.05 for fine silt. It has a linear dependence on frequency, which may be suspect. The
parameters for the basement are Cp = 2000 m/s, ρ = 2.0, α = 0.1. For sediment thickness
greater than 5 m, there is little dependence of the acoustics on these parameters. It must
be stated here that we are not after the exact parameters of the bottom.
For a given environmental estimate, a CW normal mode solution is generated and the
striation spacing (slope and time-spread) are computed as well as the incoherent
Transmission Loss (equivalent to the band-averaged). We now have a way of rapidly
mapping parameters of a simple model to the observables. An exhaustive search of the
predicted observables is performed for the two parameters that define the geo-acoustic
model (φ, H). This is done for each range and frequency. We can add to the list of
observables that we search over; however, this leads to the problem of finding a best fit in
a large multidimensional search space.
2.4
Inversion Results
To determine the goodness of fit of a particular sediment estimate, we take the frequency
mean of the square of the difference between the predicted and data observations. Each
observable is normalized by it’s mean and the and then the global cost function is
determined by summing across the normalized observables. This yields a single cost
function value for each sediment estimate. The results for each observable and for the
final cost function are shown in Fig. 3. The total cost function is plotted in the lower
right, revealing a global minimum at H = 14 m and Cp = 1535 m/s (φ = 2.6
corresponding to a thin soft sand sediment).
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RAPID ENVIRONMENTAL CHARACTERIZATION
Beta
Time Spread
1500
2
Cp (m/s)
1550
1500
2
1550
1.5
1600
1.5
1600
1
1
1650
1650
0.5
1700
1750
10
20
30
40
50
0.5
1700
0
1750
2
1500
10
ALPHA
30
40
50
1550
2
1550
1.5
1600
1.5
1600
1
1
1650
1650
0.5
1700
1750
0
Cost Function
1500
Cp (m/s)
20
10
20
30
H (m)
40
50
0.5
1700
0
1750
10
20
30
H (m)
40
50
0
Figure 3. Cost functions for three observables and sum.
Once the RGC geo-acoustic model is chosen, a synthetic broadband TL curve is
computed and used to generate a striation pattern that subsequently is compared to the
data. Before comparing with the data however, the received level (RL) must be
converted to TL, requiring an estimate of both the source level (SL) and the source
spectrum. From historical work on ambient surface noise, a simple (1/f2) fall-off for the
spectrum of the surface ship is used. The results are shown in Fig. 4.
Range (m)
GOM Tracked Spectrogram Data
500
100
1000
90
1500
80
2000
70
2500
60
3000
50
3500
100
200
300
400
500
600
700
800
40
Range (m)
Rapid Geoacoustic Characterization
500
100
1000
90
1500
80
2000
70
2500
60
3000
50
3500
100
200
300
400
500
Frequency (Hz)
600
700
800
40
Figure 4. GOM beamformed data and RGC solution TL striations.
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KEVIN D. HEANEY AND HENRY COX
This result shows that the gross features of the data (slope, frequency dependence,
spacing, TL) have been well matched. This is particularly encouraging because only data
at 1 range (3 km) and 4 frequencies (200–500 Hz) were used and there is good agreement
at higher frequencies and other ranges. There are places where the simulated field has
much higher spatial frequencies than the data. This may be due to poor range resolution
in the data (owing to the time it takes to do an FFT) or to a mismatch in the environment.
This is conceded as a limitation of the RGC solution, but it is not a requirement for
accurate use of TDAs in tactical sonar situations. A full global optimization will lead to
higher precision results.
3
System approach
We have shown that by using data from a passing surface ship on a horizontal line array
(similar to many navy systems) we can generate an estimate of the acoustic propagation
for a particular region. This data has been taken through the sensor and therefore
contains much information about what is important to the sonar system. To understand
the system performance variability as a function of environmental uncertainty we take this
estimate (and the information about sensitivity) as a starting point. Acoustic modeling
with various perturbations to the environment can now be done to examine sensitivity and
determine the robustness of the acoustic performance prediction. Communicating this
uncertainty to the end user is a primary goal of this research.
References
1. Collins, M.D. and Kuperman, W.A., Simulated annealing applied to the geo-acoustic
inversion problem, J. Acoust. Soc. Am. 98 (2002).
2. Hamilton, E.L., Geoacoustic modeling of the seafloor, J. Acoust. Soc. Am. 68 (1980).
3. Bachman, R.T., Parameterization of geoacoustic properties, J. Acoust. Soc. Am. 85 (1989).