ESTIMATING INDEPENDENT-SCATTERER DENSITY FROM ACTIVE SONAR REVERBERATION

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1 Proceedings of the Eigth European Conference on Underwater Acoustics, 8th ECUA Edited by S. M. Jesus and O. C. Rodríguez Carvoeiro, Portugal June, 2006 ESTIMATING INDEPENDENT-SCATTERER DENSITY FROM ACTIVE SONAR REVERBERATION Douglas A. Abraham 1 and Mark K. Prior 2 1 The Pennsylvania State University, State College, PA, USA ( abrahad@ieee.org) 2 NATO Undersea Research Centre, La Spezia, Italy ( prior@nurc.nato.int) Abstract: Statistical models describing non-rayleigh active sonar reverberation that assume a finite number of scattering elements within a range-bearing resolution cell require knowledge of the spatial density of scatterers. A technique is presented in this paper wherein the K-distribution shape parameter is used to estimate the effective independent-scatterer density from measured sonar reverberation data. The technique is applied to data taken in the Capraia Basin during the NATO SACLANT Undersea Research Centre s SCARAB 1997 sea-trial. Regions of the Capraia Basin that typically produce Rayleigh-like reverberation were observed to have independent-scatterer densities of per square kilometer while regions typically producing heavier-tailed, non-rayleigh reverberation yielded estimates in the range INTRODUCTION Active sonar reverberation data are traditionally assumed to have an envelope following a Rayleigh probability density function (PDF) owing to a central limit theorem argument based on an infinite number of individual scatterers in each range-bearing resolution cell. Recent models, however, have shown that a finite number of randomly sized scatterering elements (e.g., sea-floor patches or discrete scatterers) can produce non-rayleigh reverberation following the K distribution with a shape parameter (α) that is proportional to the effective number of independent scattering elements in the sonar s resolution cell [1]. The shape parameter depends on several variables, but is proportional to the spatial density (i.e., the number per square kilometer) of scatterers. The focus of this paper is on estimating the effective independent-scatterer density (ISD) from measured active sonar reverberation. Through the K distribution, ISD is directly related to the probability of false alarm of an active sonar system and is therefore useful for predicting sonar performance, realistic simulation of active sonar clutter, setting optimal sonar operating points (e.g., bandwidth, center frequency, or beamwidth), and may even be useful in improving the performance of sonar detection, classification, and localization (DCL) algorithms.

2 Hindering the direct estimation of ISD from the statistics of measured reverberation are the effects of multipath propagation [2]. A technique proposed to account for these effects is described and demonstrated in the following sections on data from the NATO SACLANT Undersea Research Centre s SCARAB 1997 sea-trial in the Capraia Basin where a variety of sea-floor scattering mechanisms are known to exist [3, 4]. 2. ESTIMATING INDEPENDENT-SCATTERER DENSITY The model described in [1] derived the K-distribution shape parameter as a function of the ISD, bandwidth (W ), cosine of grazing angle (θ g ), the speed of sound (c w ), slant range (r s ), and sonar beamwidth 1 (θ b ). Inverting this relationship provides a means for estimating ISD from the K-distribution shape parameter measured from sonar reverberation data (ˆα), ISD = 4W cos (θ g) c w r s θ b ˆα 4W c w r s θ b ˆα (1) However, the development in [1] assumed that the backscattered signal arose solely from directpath propagation. Clearly multipath propagation will alter the backscatter statistics with an expectation of an increase in the K-distribution shape parameter over that expected for direct-path propagation [2, 6]. The size of the scattering elements may additionally increase the shape parameter at bandwidths where the scatterers are over-resolved [7]. Fortunately, based on observations in [7] and the analysis of [2], it is expected that the proportionality described in eq. (1) will hold at bandwidths low enough so that the multipath are not resolved by the pulsecompressed transmit waveform. Thus, it is expected that using eq. (1) to approximate ISD will result in a decreasing function as bandwidth is decreased followed by a leveling-out once the bandwidth is small enough that the multipath are not resolved. This trend is illustrated (from right to left) in the ISD estimates shown in Fig. 1 where the technique described in [7] for estimating the K-distribution shape parameter as a function of bandwidth is applied to data from the NATO SACLANT Undersea Research Centre s SCARAB 1997 sea-trial (see Section 3 for details). The results shown in Fig. 1 were obtained by processing blocks of data three seconds long for six beams centered at broadside to the array on one ping of data for ranges spanning approximately km. The potential effect of grazing angle was determined by using geoacoustic information from [4] on the softer-sediment eastern areas of the Capraia Basin to obtain a Gaussian-shapebased description of acoustic intensity with θ g [8] for ranges greater than a few water depths. Using bounding values of 100 m and 200 m for the water depth and an average range of interest of 20 km resulted in estimates for the half-width of the Gaussian curve of 0.4 milliradians and 0.5 milliradians, respectively, indicating that the effect of grazing angle in eq. (1) would be a constant multiplicative factor. The multiplicative factor may differ between these areas and the western part of the basin, where scattering is dominated by magmatic rock outcrops [3]. As such, the upper bound on the right side of eq. (1) is used to estimate ISD. The increase in ISD seen in Fig. 1 at the lowest bandwidth most likely arises from the extremity of the K-distribution shape parameter values and the correspondingly large variance of its estimator (the median estimate of α over these data is 43 and the maximum is over 1000). To alleviate this, extensions to the algorithm described in [7] were developed to improve the estimation performance. Though beyond the scope of this paper, these extensions involved 1 Based on the results of [5], the 6-dB down beamwidth is used.

3 Figure 1: Example of estimated ISD as a function of bandwidth. overlapping blocks of data within the sub-band filtering, zero-padding of the FFT to produce a larger number of (now overlapping) sub-bands, and bootstrapping the method of moments estimator of the K-distribution shape parameter. In particular, bootstrapping can significantly improve estimation performance when α is large, although at the expense of an increased computational effort. This was verified by extended bootstrapping of the data shown in Fig. 1 and resulted in half-hertz-bandwidth estimates closer to the minimum value observed at the one- Hertz bandwidth. Of more fundamental interest, and the subject of the following section, is the analysis of ISD estimated as a function of geographic area. In order to accomplish this, one statistic from each range-beam window of data (one of the dotted lines in Fig. 1) must be associated with the geographic region representing the source of its dominant scattering. Based on the results of [2, 7], a bandwidth chosen for ISD estimation should be low enough that neither the multipath nor scatterers are resolved. Based on the reflection loss gradient associated with the seabed in the softer-sediment eastern areas (3.0 nepers per radian, as estimated from the geoacoustic parameters reported in [4]), the multipath time spread described by eq. (5) of [8] is only expected to be ms at ranges greater than a few water depths. This might indicate that a bandwidth of 10 Hz would be sufficiently low. However, the data in Fig. 1, which come from the western portion of the basin and are expected to have a greater time-spread, indicate the need for a smaller bandwidth. As such, the one-hertz bandwidth data were chosen to produce the geographically-indexed ISD estimate. 3. DATA ANALYSIS The data analysed in this section were taken during the NATO SACLANT Undersea Research Centre s SCARAB 1997 sea-trial which was led by Dr. Charles Holland. The data under consideration are those obtained from the (nominally) east-west (EW) and north-south (NS) tracks and resulted from transmission of a 2-s linear frequency modulated waveform spanning

4 the band Hz. The source and receiver were both towed from the R/V Alliance with the receiver array comprising 128 hydrophones spaced every half meter. The data were basebanded, matched filtered, and normalized as described in [7]. Estimates of the K-distribution shape parameter were obtained for blocks of data 3 s long (750 samples at a 250 Hz sampling rate) for the reverberation-limited regions of all beams not dominated by shipping noise. The method of moments estimator [1] was used along with the subband filtering of [7] and the extensions described in the previous section. The estimates from each range-beam window were associated with each cell of a one-square-kilometer grid from which the data might have been generated assuming delay time (τ) and slant range are related according to r s = c w τ/2. In general, this biases the locations of the data away from the sonar system (i.e., any features observed in the data probably arise from scattering conditions occurring closer to the sonar). The median ISD values for cells containing at least 15 ISD estimates are displayed for the two tracks in Figs. 2 (EW) and 3 (NS). The ping locations are the dots between the colored regions. Note that the EW tracks occurred over a two-day period. Downward refracting sound velocity profiles and low sea-states indicated that reverberation was dominated by backscattering from the bottom. Backscattering in the Capraia Basin is known to arise from sub-bottom sediment volume inhomogeneities in the central and eastern regions and from magmatic rock outcrops in the western region [3, 4]. The former tend to produce Rayleigh-like reverberation and are expected to yield large values of ISD while the latter tend to produce heavier-tailed non-rayleigh reverberation and are expected to produce small values of ISD. The results shown in Fig. 2 strongly corroborate this expectation with ISDs in the range of per square kilometer in the eastern areas and ISDs in the range of 5 25 in the western region. The southwestern area ( degrees longitude) with ISD ranging from 20 to 30 is somewhat unexpected, although it is substantiated by some Rayleigh-like reverberation observed in this area as reported in [3] and most likely arises from a change in bottom type compared to the rocky canyon just to the east. The results shown in Fig. 3 support the expectation of higher ISD values in the eastern region; however, the western areas have values that are unexpectedly high and not in accordance with the results of the EW track, most likely a result of the left/right ambiguity of the line array. In fact, both figures illustrate the difficulty in interpreting data when there exists a left/right ambiguity in the receiving array. The results shown in Fig. 2, however, are more likely to be reliable as the scattering mechanisms in this area generally have greater NS symmetry than EW. In comparing the data from the two tracks, they appear to be in agreement in the northern and eastern regions. Particularly compelling is the agreement of the densest scattering as measured in the eastern region between 10.3 and 10.4 degrees longitude where aspects approximately 90 degrees apart yielded similar values of ISD, as might be expected from potentially aspectindependent scattering from sub-bottom sediment volume inhomogeneities. The small values on the southeastern (Fig. 2) and easternmost edges (Fig. 3) of the displayed data correspond to regions where the data spread, as measured by the inter-quartile range divided by the median, is large (e.g., 4 6) and therefore are unreliable. The majority of the other areas have data-spread values near 2 indicating some measure of consistency over multiple looks. 4. CONCLUSIONS A technique was presented in this paper for estimating the independent-scatterer density, a quantity representative of the statistical character of active sonar reverberation and clutter,

5 Figure 2: ISD estimates for EW tracks. Figure 3: ISD estimates for NS track.

6 from measured active sonar reverberation data. The technique appears to adequately account for the effects of multipath and, on the one data set analyzed, produced consistent estimates of ISD within the intersection of the sonar system s ambiguity and the environment s symmetry. Regions of the Capraia Basin that typically produce Rayleigh-like reverberation were observed to have scatterer densities of per square kilometer while regions typically producing heavier-tailed, non-rayleigh reverberation yielded estimates in the range In addition to improving our understanding of the statistical nature of scattering as a function of bottom characterization, there is a clear application of ISD estimation in the rapid environmental assessment of an operational area for a priori characterization of sonar performance as well as the potential for in situ measurement and use in DCL algorithms or for adaptation of sonar parameters such as bandwidth and center frequency. There are, however, still several issues that need to be addressed in future research including frequency, grazing angle, and scatterer aspect or orientation dependencies. 5. ACKNOWLEDGEMENTS This work was sponsored in part by the Office of Naval Research. The authors acknowledge the efforts of Charles Holland and the staff of the NATO SACLANT Undersea Research Centre for their efforts in carrying out the SCARAB 1997 sea-trial. REFERENCES [1] D. A. Abraham and A. P. Lyons, Novel physical interpretations of K-distributed reverberation, IEEE Jnl. of Oceanic Eng., 27:4, pp , Oct [2] D. A. Abraham, A. P. Lyons, and K. M. Becker, The effect of multipath on reverberation envelope statistics, in Proc. of 7 th European Conf. on Underwater Acoustics, Delft, The Netherlands, July [3] D. A. Abraham and C. W. Holland, Statistical analysis of low-frequency active sonar reverberation in shallow water, in Proc. of 4 th European Conf. on Underwater Acoustics, Rome, Italy, Sep. 1998, pp [4] C. W. Holland and J. Osler, High-resolution geoacoustic inversion in shallow water: A joint time- and frequency-domain technique, Jnl. of the Acoust. Soc. of Amer., 107:3, pp , Mar [5] D. A. Abraham and A. P. Lyons, Array modeling of non-rayleigh reverberation, in Proc. of Institute of Acoustics Conf. on Sonar Signal Proc., Loughborough, England, Sep [6] K. D. LePage, Statistics of broad-band bottom reverberation predictions in shallow-water waveguides, IEEE Jnl. of Oceanic Eng., 29:2, pp , Apr [7] D. A. Abraham and A. P. Lyons, Reverb. envelope statistics and their dependence on sonar bandwidth and scatterer size, IEEE Jnl. of Oceanic Eng., 29:1, pp , Jan [8] M. K. Prior and C. H. Harrison, Estimation of seabed reflection loss properties from direct blast pulse shape (L), Jnl. of the Acoust. Soc. of Amer., 116:3, pp , Sep