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Seabed Variability and its Influence on 
Acoustic Prediction Uncertainty 

Charles W. Holland 
The Pennsylvania State University 
Applied Research Laboratory 
P.O. Box 30, State College, PA 16804-0030 
Phone:(814) 865-1724 Fax (814) 863-8783 email: holland-cw@psu.edu 

Award Number: N00014-01-1-0873 


LONG TERM GOALS 

The long term goal is to assess and characterize uncertainty in the tactical naval environment. The 
focus is on the contribution of seabed variability to uncertainty in sonar performance predictions. In 
littoral warfare, the seabed is often a controlling factor in sonar system performance. 

OBJECTIVES 

The specific objectives of this effort are to characterize the spatial variability of the seabed geoacoustic 
properties using remote acoustic methods and determine the uncertainties and errors associated with 
the estimation of the geoacoustic properties. In FY03 the objective was to develop the tools to 
describe how uncertainties propagate from remote acoustic measurements to meso-scale geoacoustic 
uncertainty and thence to system performance uncertainty. 

APPROACH 

The approach was broken into three main task areas: 1) characterize the uncertainties in the remote 
acoustic methods (in particular the seabed reflection measurements), 2) propagate those uncertainties 
to geoacoustic properties and 3) demonstrate how the geoacoustic uncertainties propagate to 
uncertainty in system performance measures. The main efforts were placed in tasks 1 and 2. In 
addition, modeling and analysis of seabed variability data were continued on the New Jersey shelf 
(STRATFORM) and the Malta Plateau. 

WORK COMPLETED 

A thorough uncertainty analysis was conducted for the seabed reflection technique. The agreement of 
the uncertainty estimates from a theoretical/modeling approach and an experimental approach 
indicated that the method and tools developed for uncertainty analysis are robust. 

The transfer of measurement uncertainty to geoacoustic uncertainty was studied in considerable detail. 
The geoacoustic uncertainties from the above-mentioned thcorctical/modeling approach agreed well 
with other methods of estimating uncertainty, again lending credence to the methods/tools. Finally the 
role of geoacoustic uncertainty on uncertainty in system performance was explored using an idealized 
model. 


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30 SEP 2003 2 - REPORT TYPE 

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Seabed Variability and its Influence on Acoustic Prediction Uncertainty 

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Applied Research Laboratory„The Pennsylvania State University„P.O. 

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RESULTS 


The dominant contribution to the uncertainty in the measured reflection coefficient is the variability of 
the source amplitude due to non-constant drag forces on the source plate and catamaran; ping-to-ping 
variability under ta nk conditions is quite small. A new normalizing processing approach was 
developed to help minimize effects of source variability. Specific uncertainty estimates depend upon 
frequency, experiment geometry, sea state and well as several other minor factors, but a typical 
standard deviation of the reflection loss (-20 logio\R \) is ±0.5-1 dB. The uncertainty can be reduced 
by trading-off variance with angular resolution. It was demonstrated that averaging over 1° window 
can reduce the standard deviation by about one half. 

Equations for the uncertainty associated with the angle estimates were derived that provide angle 
uncertainties as a function of experimental and environmental uncertainties [1]. The part of the angular 
range that is the most crucial for minimizing errors is dictated by the critical angle, since this angle 
controls long-range propagation. Ref [2] indicates that for unconsolidated sediments on the continental 
shelf, critical angles vary from 0-34°. In that range the seabed reflection angle uncertainty is predicted 
to be quite small, from about ±0.01-0.3° (see Fig 1). At normal incidence, the errors are considerably 
larger, however, the increase in errors are mitigated by the fact that the reflection coefficient itself is 
often nearly constant between 70-90°. 

Uncertainty was also estimated experimentally. Multiple measurements of the seabed reflection 
coefficient were taken at the same location (within several hundred meters) but at different times and 
under different experimental conditions. The variation in position of the peak (at 25°) and nulls (at 
32°) of the reflection loss from the various measurements were used to estimate the uncertainty. The 
experimentally derived estimates (‘±’ in Fig 1) agree quite well with those estimated theoretically. 



Figure 1. Estimates of uncertainty in reflection angle at the seabed from theory (solid and dashed 
black lines), from simulation (gray dashed line) and from multiple measurements at nearly the same 

location (+). 


A crucial part of the uncertainty DRI is concerned with the transfer of uncertainties. A Bayesian 
approach was used (with Stan Dosso [3]) to determine how the uncertainties in the seabed reflection 
transfer or propagate to uncertainty in the geoacoustic properties. This fully non-linear approach 
describes the uncertainties in the geoacoustic properties as well as the inter-parameter coupling via the 
posterior probability density (PPD) function. Fig 2 shows the marginal PPD from an inversion on 


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reflection data in the Straits of Sicily. There are several salient points. First of all, the uncertainties 
using the theoretical experimental errors (discussed in the preceding paragraphs) give consistent results 
with other commonly used methods for uncertainty estimation, giving further credence to the data 
uncertainty estimation. Second, note that the compressional speed and density are estimated to fairly 
high accuracy (± 2 m/s and ± 0.02 g/cc respectively) while the shear speed and attenuation are poorly 
constrained by the data. That is to say, that the shear properties play a minimal role in seabed 
reflection for this kind of soft sediment (silty-clay). 



1465 1470 1475 1480 1485 0.0 0.5 1.0 1.5 

Vp (m/s) £ 






a 


._ 

. . 





C 



1.32 1.34 1.36 1.38 1.40 0.20 0.25 0.30 0.35 0.40 

p (g/ cm5 ) «p ( dB A) 


a — -a 

b ——- --b 



0 50 100 150 200 0 1 2 3 4 5 

V s (m/s) a s (dB/A) 


Figure 2. Marginal probability distributions for uncertainty estimation using a) maximum 
likelihood scaling, b) fast Gibbs sampling standard deviation scaling and c) using theoretically 
estimated experimental errors. The geoacoustic parameters are sediment compressional and shear 
speed (Vp and Vs), density (p), compressional and shear wave attenuation (a p and a s ). 


The geoacoustic properties from such inversions are important inputs for propagation, reverberation 
and system performance models. In order to determine how the uncertainty further propagates to 
system performance models, an analytic model [4] for signal-to-reverberation ratio (SRR) in a Pekeris 
waveguide was employed in conjunction with the PPD from an inversion for boulder clay [5], Fig 3 
shows the SRR cast as a probability distribution considering uncertainty in the geoacoustic properties. 
Typically, the SRR is given as a single number (SRR is independent of range if the scattering strength 
follows a Lambert’s Law [4]) probability distribution). However, a probability distribution may be a 
more meaningful metric than a single number. 

In order to detennine which geoacoustic uncertainty was the most significant factor controlling the 
SRR distribution, the SRR distribution was calculated with all of the uncertainties present (see Fig 3 a) 
and then with each parameter fixed at its mean and the other parameters allowed to vary across the 
PPD. The analysis indicates that (for this PPD) the total uncertainty in the signal-to-reverberation ratio 
(due to seabed geoacoustic properties) is dominated by uncertainties in the attenuation. While this will 


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certainly not hold for every environment, an approach has been demonstrated for how to describe and 
transfer measurement-to-geoacoustic-to system performance uncertainties. 




3000 
2500 
2000 
1500 
1000 
500 
0 

-10 0 10 20 
SRR (dB) 


p=<p> 

c) 




SRR (dB) 


Figure 3. Signal-to-reverberation ratio (SRR) distribution for geoacoustic uncertainties - the 
geoacoustic uncertainties are expressed as a PPD, a) all geoacoustic uncertainties, b) all 
geoacoustic uncertainties except sound speed, c) all geoacoustic uncertainties except density, d) all 

geoacoustic uncertainties except attenuation. 


IMPACT/APPLICATIONS 

The results of this work demonstrates a viable approach for capturing, characterizing and transferring 
uncertainty from remote measurements of the seabed through the geoacoustic properties and on to a 
measure of active system performance. We have proposed using a probability density function 
approach for transferring uncertainty. This approach needs to be examined by other researchers in the 
DRI, particularly in the end-to-end teams. While the focus here has been on the seabed, clearly there 
are other sources of uncertainty (e.g., the oceanography and target) that need to be incorporated into 
the analysis. 

RELATED PROJECTS 

ONR GeoClutter: Providing high resolution acoustic and geoacoustic data required for estimating 
seabed spatial variability and uncertainty on the New Jersey shelf. 


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Boundary Characterization Joint Research Project ONR-NATO SACLANT Centre: Providing high 
resolution acoustic and geoacoustic data required for estimating seabed spatial variability and 
uncertainty estimates in the Straits of Sicily and the Tuscany Shelf. 

ONR SWAT Program: Collaborating on geoacoustic findings on the New Jersey Shelf. 

REFERENCES 

[1] Holland, C.W., Seabed Reflection Measurement Uncertainty, J. Acoust. Soc. of Am, (in press). 

[2] Hamilton, E.L., “Geoacoustic modeling of the seafloor,” J. Acoust. Soc. Am., 68, 1313-1339, 1980. 

[3] Dosso, S. E. and Holland, C.W., “Geoacoustic uncertainties from inversion of seabed reflection 
data,” J. Acoust. Soc. of Am., in review. 

[4] Harrison, C.H., “Signal and reverberation with mode-stripping and Lambert’s Law,” SACLANT 
Undersea Research Centre, La Spezia, Italy, SR-356, 2002. 

[5] Riedel, M., Dosso, S. and B. Laurens, “Uncertainty Estimation for AVO Inversion, Geophysics, in 
review. 

PUBLICATIONS 

Holland, C.W., Seabed Reflection Measurement Uncertainty, J. Acoust. Soc. of Am, [refereed, in 
press]. 

Dosso, S. E. and Holland, C.W., “Geoacoustic uncertainties from inversion of seabed reflection data,” 
J. Acoust. Soc. of Am. [submitted]. 

Holland, C.W., and C. Harrison, Measurement of the Seabed Reflection Coefficient in Shallow Water: 
A comparison of two techniques, in International Conference on Theoretical and Computational 
Acoustics, August 2003 proceedings. 


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