ASSESSMENT OF THE IMPACT OF UNCERTAINTY IN SEABED GEOACOUSTIC PARAMETERS ON PREDICTED SONAR PERFORMANCE

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1 ASSESSMENT OF THE IMPACT OF UNCERTAINTY IN SEABED GEOACOUSTIC PARAMETERS ON PREDICTED SONAR PERFORMANCE M.K. PRIOR AND C.H. HARRISON SACLANT Undersea Research Centre, Viale San Bartolomeo 400, La Spezia, Italy S.G. HEALY QinetiQ Unit, Southampton Oceanography Centre, Southampton, SO14 3ZH, UK 'Uncertainty' can be distinguished from 'variability' as the lack of knowledge of the input variables that a certain calculation must tolerate. In the case studied here, the calculation concerns sonar performance, and uncertainty may stem from many sources including the finite measurement precision of methods used to describe the physical environment. Lack of knowledge of the environmental inputs causes uncertainty in the predicted sonar performance. It is common for this uncertainty to be high but its impact is rarely taken into account. In this paper we take, as an example of an environmental descriptor, plane wave reflection loss already derived from measurements of ambient noise directionality. An inverse method is developed that allows the reflection loss as a function of angle and frequency to be converted to a geophysical description of the seabed in terms of density, sound speed and attenuation. The uncertainty in these geophysical 'inputs', i.e. the "error bar" associated with the inversion, is estimated and the impact of this uncertainty on the prediction of sonar performance is calculated. This is achieved by calculating reverberation and target echo in a series of environments lying within the uncertainty bounds. These calculations are repeated using seabed data derived from a geophysical description of a core. The relative impacts of the uncertainties associated with the two methods of describing the seabed are compared. The calculations performed also take into account uncertainty in sonar-related parameters such as target reflectivity. 1 Introduction When predicting sonar performance using sonar equation calculations, it is common practise to consider environmental input data as being fixed with no uncertainty. This approach is potentially misleading when one considers the sensitivity of acoustic propagation loss, ambient noise and reverberation to environmental changes and the poor quality of the environmental data that is often available. Sensitivity analyses can be carried out to see how changes in the environmental description affect predicted performance. This is usually not done because of lack of time or insufficient knowledge concerning the spread of environmental parameters. In this paper, we consider the impact, on one aspect of predicted sonar performance, of uncertainty in the description of the seabed. Two types of seabed 531 N.G. Pace and F.B. Jensen (eds.), Impact of Littoral Environmental Variability on Acoustic Predictions and Sonar Performance, Kluwer Academic Publishers. Printed in the Netherlands.

2 532 M.K. PRIOR ET AL. description are used and the impacts of their uncertainties are assessed. These are compared with the impact of uncertainty in a non-environmental parameter, namely the target scattering strength. Calculations are carried out for monostatic and bistatic sonars in a shallow water environment. Sonar performance is quantified via the calculation of regions in which a target, if it were to be present, would result in a positive signal-tonoise ratio (SNR) at the receiver. In the context studied here, noise is actually the sum of reverberation and the direct blast from the sonar transmission. 2 Seabed description Two methods were used to describe the seabed in this study. The first used estimates of plane-wave reflection loss derived from measurements of ambient noise. These reflection losses were input to a genetic algorithm (GA) inversion to produce estimates of the sound speed, density and attenuation of the seabed. The second method used a core sample (core 255 from [1]) taken in the same geographic location as the ambient noise data. This was used to produce a description of the seabed that allowed a range of possible values for the seabed density, sound speed and attenuation to be determined from a database of laboratory measurements on seabed sediment samples. Both descriptions include only compressional wave properties. The methods are now described in more detail. 2.1 Inversion of Reflection Loss Data Measurements of the ambient noise in the ocean, made on a vertical line array (VLA), can be processed to yield estimates of plane wave reflection loss [2]. While these estimates could be input directly into ray tracing propagation and reverberation models, there is a risk that glitches in the data might corrupt such model calculations. Furthermore, it may be that the propagation/reverberation models do not use plane-wave reflection loss directly in their calculations and require instead that the seabed should be described in terms of sound speed, density and attenuation. To translate from reflection coefficient as a function of angle and frequency to a geoacoustic description, an inverse method was developed. The method used standard techniques [3] based on genetic algorithms but employed a novel method for determining the fitness of each solution. The fitness was determined to be the product of two factors representing the closeness of fit and the geophysical realness respectively. The closeness of fit was assessed by a simple root-mean-square (rms) difference between the linear intensity reflection coefficients from the VLA data and Rayleigh reflection coefficients [4] produced using the trial values of density, sound speed and attenuation. The realness of each density and sound speed combination was assessed by determining how close the pair lay to a regression curve fitted to a scatter plot of density/sound-speed pairs taken from a database of laboratory measurements made on seabed sediments [5]. The form of the realness function was [ ( c c )/150) ] ; c = ρ ρ R = exp x (1) ρ ρ where R is the realness, c is the sound speed in m/s, ρ is the density in g/cm 3 and c ρ is the sound speed determined from the density, using the polynomial fit to the laboratory measurements.

3 SEABED UNCERTAINTY AND SONAR PERFORMANCE 533 Figure 1 shows a contour plot of the realness function, the data points used to produce the polynomial fit and the fit itself. The figure shows that the realness function is high in regions with many density/sound-speed points and low in regions where the combination of these two closely linked parameters was unphysical. The attenuation of the seabed was left out of the realness function, effectively leaving the search for it unconstrained. This was done because the correlation between attenuation and the other two seabed parameters is usually poor [6]. Figure 1. Realness function as contours with density/sound-speed data as points and polynomial fit as line. The GA inversion searched simultaneously for seven parameters describing a twolayer seabed; sound speed, density and attenuation for each layer and a thickness of the upper layer. Figure 2 shows VLA-measured and inverted values of reflection loss as a function of frequency and angle. The general agreement is shown to be good. The areas of apparently zero loss around the edges of the figures arise due to array limitations (e.g. grating lobes in the top right corner) and were removed from consideration in the inversion. Uncertainty in the seabed description was obtained by running the inversion method ten times to yield ten seabed descriptions. Figure 2. Reflection loss for VLA and inverted data. 2.2 Geophysical Description In the area of interest, a sediment core had been previously obtained (Core 255 from [1]) and laboratory analysis had indicated that the seabed at the location of the core was silty-sand and sand. A range of sediment properties which may be attributed to sediment of the same general type as Core 255 was obtained to determine the spread of likely values of density, sound speed and attenuation. This information was extracted from the GEOSEIS database [5], a repository of geotechnical, seismo-acoustic and geochemical information on marine sediment and bedrock. 42 sediment records were selected from

4 534 M.K. PRIOR ET AL. GEOSEIS by choosing samples with properties that fitted the description of Core 255. This approach relied on the premise that there were good inter-relationships between sediment physical properties (e.g. porosity, grainsize) and the resulting geoacoustic properties such as velocity and attenuation [6]. Geological materials are generally complex, so samples with identical porosities or grainsizes may have significant differences in structure and composition and so are likely to exhibit a range of possible values of density, velocity and attenuation. 3 Sonar scenario The impact of seabed uncertainty was translated into a spread of sonar performance using the SUPREMO [7] multistatic model to predict target echo and reverberation in one monostatic and one bistatic scenario. SUPREMO used the Gamaray [8] eigenray model to calculate propagation paths for the prediction of target echo, reverberation and direct blast (in the bistatic case). Gamaray allows the seabed to be described in terms of its sound speed, density and attenuation. The seabed data from both sources was therefore directly inserted into the model. In both cases, an omnidirectional source was used, transmitting an 80 Hz bandwidth LFM signal centred on 500 Hz. The signal was received by a 64-element horizontal line array with 1.5 m spacing between elements. The target was represented as a cylinder with hemispherical end-caps and had length 100 m and radius 5 m. Receiver and target headings were arranged so that the source signal was specularly reflected and detected by the receiver in its broadside beam. The environment had a 1500 m/s isovelocity water column above a seabed described using data from the two methods. The area of study was a 20 km (x,y) square grid centred on (0,0) with the monostatic sonar placed at this central point. The bistatic scenario had the source at (-5km,0) and the receiver at (5km,0). Sonar performance was quantified by the SNR, calculated as the highest value of the ratio of the intensities of the target echo and reverberation plus direct blast. It was recognised that a positive SNR alone does not qualify as indicating a detection possibility but the inclusion of sonar-specific terms such as detection threshold [9] was rejected so as to avoid difficulties in widely disseminating the results of the study. In addition to uncertainty arising from the environmental description, it is important to remember that the non-environmental terms under consideration are also not known perfectly. To reflect this, an uncertainty of +/-3 db was arbitrarily placed on the target strength calculated by SUPREMO. Quantification of the impact of seabed uncertainty was achieved by calculation of the area in which SNR was positive. Further description of the impact of uncertainty was achieved by determining for each target location whether the SNR was always negative, always positive or changed sign due to the changes in seabed description and target strength. This approach resulted in five different descriptions of the SNR due to a target at each possible location; 1) always positive, 2) always negative, 3) uncertain due to environmental factors, 4) uncertain due to non-environmental factors 5) uncertain due to both environmental and non-environmental factors.

5 SEABED UNCERTAINTY AND SONAR PERFORMANCE Results 4.1 Seabed Data Figure 3 shows the density and attenuation of the seabed plotted as a function of the sound speed for the laboratory measurements and for the results of the inversion. The results of the inversion can be seen to lie within the range of the laboratory measurements but the attenuation coefficient returned from the inversion is large. The reason for this is not known but it is possible that some process not included in the stratified fluid model of the seabed was interpreted as extra attenuation when the inversion was carried out. Figure 3. Seabed data from lab measurements and inversion. 4.2 Sonar Performance Figure 4 shows the impact on sonar performance of uncertainty in the seabed description and target strength with the seabed description derived from the laboratory measurements. Figure 4a shows the SNR averaged over all target positions with mean values plotted as crosses and the error bars indicating the standard deviation from the mean. The x-axis of the plot is the value of the gradient of reflection loss versus angle calculated using Weston s equation [10] 10 ( 2 ) 3/ 2 ραλ αw = c (2) 10π log () ( ) 2 c / c 1 ( c / ) w w e where α λ is the attenuation in db per wavelength and α W is the gradient (Weston s Alpha). α W is a useful single value that expresses the impact of the seabed on reflection and Harrison showed [11] that for targets beyond a critical range, R c, R c ( 8H )/( α θ ) = (3) (where H is the water depth and θ c is the critical angle) the SNR is a constant value for shallow water conditions. Figure 4a shows that the mean SNR is linked to α W. SNR remains constant for small values of α W then increases with it for values beyond 5dB. This value corresponds to R c being 10 km and the transition occurred when the area of interest lay within the region where SNR was proportional to α W. The connection between α W and SNR is further shown in Fig. 4b where the Area Of Positive SNR (AOPS) is shown to increase with α W. W c

6 536 M.K. PRIOR ET AL. a d b e c f Figure 4. Sonar performance as quantified by SNR (top), area of positive SNR (middle) and SNR description (bottom). Results for laboratory measurements. Monostatic sonar left, bistatic right. The impact of the seabed uncertainty is high with changes in area of over 200 km 2. The error bars in Fig. 4b indicate the change in AOPS associated with the +/-3dB uncertainty in target strength, plotted on the median value of AOPS from the environmental uncertainty set. The impact of environmental uncertainty is greater than the nonenvironmental uncertainty. Figure 4c shows the area of interest with colour coding indicating the nature of the uncertainty in SNR. Black, white, green, red and blue refer to the numbers given in Sect. 3. The dominance of environmental uncertainty is illustrated. Figure 4d-f shows the results for the bistatic configuration and the same trends are shown to be present as for the monostatic case. The main differences are the reduction in AOPS and the bistatic pattern in Fig. 4f.

7 SEABED UNCERTAINTY AND SONAR PERFORMANCE 537 a d b e c f Figure 5. Sonar performance as quantified by SNR (top), area of positive SNR (middle) and SNR description (bottom). Results for inversion. Monostatic sonar left, bistatic right. Figure 5 shows the sonar performance results for seabed uncertainty arising from the ambient noise inversion method. The smaller uncertainty arising from this method of determining the seabed type is reflected in the very small spread of values of α W present on the x-axes of Fig. 5a. Non-environmental effects dominate the uncertainty in area. Trends are the same for both monostatic and bistatic sonars with the main difference between the two being the lower AOPS in the latter case.

8 538 M.K. PRIOR ET AL. 5 Summary and discussion The impact on sonar performance of uncertainty in seabed data was shown to differ for the two types of seabed data. The inversion of acoustic measurements was shown to yield a smaller spread in geoacoustic parameters and this spread was shown to predict a negligible spread in sonar performance. This stemmed from the repeatability of the inversion method and from the self-compensating nature of the process. That is, the ambient noise measurements gave reflection loss estimates and the SNR was linked to α W, a measure of reflection loss. The uncertainty arising from laboratory measurements of sediments resulted in larger uncertainty in SNR. It is important that this uncertainty should be compared with uncertainty arising from target strength and any assessment of the impact of environmental uncertainty should also include estimates of uncertainty in non-environmental factors. The work reported here illustrated the usefulness of accompanying numerical calculations of sonar performance with mathematical analysis. The importance of α W indicates a possible way in which the impact of uncertainty could be estimated directly without the need for numerical models. References 1. Tonarelli, B., Turgutcan, F., Max, M.D. and Akal, T., Shallow sediment composition at four localities on the Sicilian-Tunisian platform. In UNESCO Reports in Marine Science: Geological Development of the Sicilia-Tunisian Platform 58, (1992). 2. Harrison, C.H. and Simons, D.G., Geoacoustic inversion of ambient noise: A simple method. In Proc. Institute of Acoustics: Acoustical Oceanography 23(2), (2001). 3. Houck, C., Joines, J. and Kay, M., A genetic algorithm for function optimization: A Matlab implementation. NCSU-IE TR (1995). 4. Brekhovskikh, L. and Lysanov, Yu., Fundamentals of Ocean Acoustics (Berlin, Springer- Verlag, 1982). 5. McCann, C., McDermott, I., Grimbleby, L., Marks, S.G., McCann, D.M. and Hughes, B.C., The GEOSEIS database. A study of the acoustic properties of sediments and sedimentary rocks. In Proc. Oceanology 1994 (1994). 6. Hamilton, E.L., Acoustic properties of sediments. In Acoustics and Ocean Bottom, edited by A. Lara, C. Ranz and R. Carbo, pp (1987). 7. Harrison, C.H., Prior, M.K. and Baldacci, A., Multistatic reverberation and system modelling using SUPREMO. In Proc. 6th European Conference on Underwater Acoustics, Gdansk, Poland (2002). 8. Westwood, E.K., Tindle, C.T. and Chapman, N.R., A normal mode model for acoustoelastic ocean environments, J. Acoust. Soc. Am. 100, (1996). 9. Urick, R.J., Principles of Underwater Sound for Engineers (McGraw-Hill, 1975). 10. Weston, D.E., Intensity-range relations in oceanographic acoustics, J. Sound and Vib. 18, (1971). 11. Harrison, C.H., Reverberation and signal excess with mode stripping and Lambert s law. SACLANTCEN Report (2002).