Fluctuations of Seafloor Backscatter Data From Multibeam Sonar Systems

IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 35, NO. 2, APRIL 2010 209

Fluctuations of Seafloor Backscatter DataFrom Multibeam Sonar Systems

Alexander N. Gavrilov and Iain M. Parnum

Abstract—Several theoretical models of seafloor backscatterstatistics developed over recent years show a reasonable agreementwith experimental measurements made with sonar systems. How-ever, methods of data collection and processing used in modernmultibeam systems are often not taken into consideration whenanalyzing statistical characteristics of observed backscatter data.Fluctuations of various backscatter parameters, which can bederived from raw multibeam data, and their statistical properties,are analyzed in this paper using data collected with a Reson SeaBat8125 system from two different seafloor types on the southerncontinental shelf of Western Australia. It is shown that fluctuationsof the backscatter envelope not affected by the sonar beam patterncan be reasonably well approximated by a Rayleigh distribution,when the seafloor insonification area is large compared to thehorizontal scale of the seafloor roughness. Based on data analysisand theory of extreme value statistics, it is demonstrated that thepeak backscatter intensity, collected by some sonar systems as asingle backscatter characteristic for each sonar beam, leads toconsiderable overestimation of the seafloor backscatter strengthat oblique angles of incidence when the beam footprint is muchlarger than the insonification area. Sidescan data synthesized insome modern multibeam systems are also affected by effects ofsignal processing on statistical properties of backscatter fluctua-tions. In contrast to the peak backscatter intensity, the backscatterenergy provides an almost unbiased estimate of the seafloorbackscatter strength. The gamma distribution is demonstrated tobe an adequate approximation for fluctuations of the backscatterenergy at oblique angles of incidence. It was also found that sonarparameters and settings, signal processing in sonar hardware, andthe incidence angle of seafloor observation have a much greatereffect on statistical characteristics of backscatter fluctuations thanthe difference in acoustical properties of the seafloor, except forthe first moment of backscatter variations which is governed bythe seafloor backscatter coefficient.

Index Terms—Acoustical backscatter, distribution model, multi-beam sonar system, seafloor backscatter coefficient.

I. INTRODUCTION

I T has been demonstrated both theoretically (e.g., in [1]) andexperimentally (e.g., in [2]) that, under certain conditions,

the statistics of acoustical backscatter from the seafloor can beessentially non-Gaussian, when the backscatter envelope is notRayleigh distributed. Such conditions are found, in particular,

Manuscript received March 17, 2009; revised October 16, 2009; acceptedDecember 03, 2009. Date of publication March 29, 2010; date of current versionMay 26, 2010.

Guest Editor: A. P. Lyons.The authors are with the Centre for Marine Science and Technology,

Curtin University of Technology, Perth, W.A. 6845, Australia (e-mail:[email protected]).

Digital Object Identifier 10.1109/JOE.2010.2041262

for high-frequency sonar systems, when the seafloor insonifi-cation area is smaller than the horizontal scale of the seafloorroughness. In that case, the number of statistically independentscattering elements contributing simultaneously to the backscat-tered sound field is not large enough to satisfy the central limittheorem [3]. Consequently, the backscatter statistics dependsnot only on acoustical frequency and morphological characteris-tics of the seafloor surface, but also on parameters and settingsof sonar systems, such as the beam width and the transmittedpulse length.

Non-Gaussian models for describing fluctuations of wavesscattered from a limited area of rough surfaces were suggestedby Jakeman [4]. It has been demonstrated that a -distribu-tion can be used as a physically reasonable model for describingfluctuations of scattering intensity when the horizontal scale ofthe surface roughness is not much smaller than the width of thescattering area [5]. A physical interpretation for -distributedfluctuations of seafloor backscatter measured by a narrow-beamsonar system was suggested by Lyons and Abraham [6]. It wasshown by Hellequin et al. [2] that a -distribution with dif-ferent parameters provided the best model for fluctuations ofthe seafloor backscatter intensity measured via a high-frequency(95 kHz) multibeam sonar system from rough beds, such asgravel and rock outcrops. The study was developed later byLe Chenadec et al. [7], where the angular dependence of the

-distribution parameters, scale and shape, was analyzed usinghigh-frequency multibeam sonar data collected from differentseafloor types ranging from soft and smooth (fine sand and mud)to very rough (rock outcrops). The authors found that the andthree-component Rayleigh models provided the best fit to thedistribution of experimental data fluctuations. Moreover, theyfound that the -distribution shape parameter varied signif-icantly with incidence angle. It generally tended to increaseas the incidence angle decreased from 75 to about 55 , butdropped rapidly to very small numbers ( 1) at smaller inci-dence angles. The authors suggested a physical model whichcould explain such a behavior of the shape parameter angulardependence.

Most of the modern sonar systems apply different pre-processing algorithms to the received signals to obtain moreaccurate bathymetry data and/or backscatter mosaics of betterquality. Such preprocessing affects statistical features ofbackscatter data collected with a sonar system, which maylead to serious misinterpretation of the processing results ifthe effects of system parameters and data processing are nottaken into account. This is especially critical for acousticalclassification of the seafloor, when the measured backscattercharacteristics and their statistical moments are compared with

0364-9059/$26.00 © 2010 IEEE

210 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 35, NO. 2, APRIL 2010

those predicted from theoretical models for different types ofthe seafloor.

The angular dependence of the seafloor backscatter strengthis one of the major backscatter characteristics commonlyused for seafloor characterization. This characteristic can bemeasured with sidescan and multibeam sonar systems by aver-aging the backscatter intensity observed at different incidenceangles, if those systems are adequately calibrated with respectto the transmission power, overall receive gain, and beampatterns. However, the seafloor insonification area changeswith incidence angle, which may lead to significant change inthe statistical distribution of backscatter intensity and, conse-quently, changes in the statistical moments including the meanvalue. As a result, the angular dependence of the measuredbackscatter strength depends on sonar parameters and settingsand can be noticeably different from the model prediction.

Effects of sonar parameters on statistics of backscatter inten-sity are especially complex for multibeam systems. The direc-tivity pattern of sonar receive beams distorts the backscatter en-velope. Variations of the signal travel time from the sonar headto every scattering patch within the beam footprint on a roughbottom are not exactly known, so that it is not evident which ofthe backscatter samples correspond to the beam center and are,presumably, not distorted by the beam directivity pattern. Con-sequently, the backscatter samples taken from different sonarpings will have additional fluctuations if the envelopes are notadequately corrected for the beam pattern effect. These fluctu-ations may considerably distort the distribution of backscatterintensity and its statistical moments.

Effects of sonar parameters and signal processing on statis-tical characteristics of backscatter data collected with a ResonSeaBat 8125 multibeam system are considered in this paper.The Reson 8125 echo sounder is a modern high-frequencymultibeam system transmitting rectangular impulses of alter-able length at the carrier frequency of 455 kHz and forming 240receive beams spaced at 0.5 , to provide accurate bathymetrymeasurements up to a depth of 100 m. In addition to accuratebathymetry, the Reson 8125 system is capable of providingthree types of backscatter data, which are: 1) a single valuefor each beam and each ping called “backscatter intensity”; 2)sidescan-like data synthesized from backscatter signals in everybeam; and 3) so-called “snippet data” which are fragments ofthe backscatter signals taken around the bottom detection time[8]. The actual physical character of these backscatter data andthe seafloor backscatter characteristics, which can be derivedfrom the sonar data, are considered in Section II.

A set of sonar data collected over a relatively flat bottom areaat sea depth of about 35 m near the Recherché Archipelagooff the southern coast of Western Australia was selected foranalyzing statistics of backscatter data and seafloor backscattercharacteristics. These data were obtained as part of the CoastalWater Habitat Mapping (CWHM) project of the CooperativeResearch Centre for Coastal Zone, Estuary and Waterway Man-agement [9]. Two very distinct types of the seafloor were foundin this area, which were sand- and rhodolith-covered beds.Both types of the seafloor cover were relatively homogeneouswithin their boundaries. The sandy bottom was nearly evenwith a slightly undulated surface. Rhodoliths are benthic red

algae that deposit hard calcium carbonate features densely andrather randomly distributed on sandy substrates. The rhodolithfeatures grow to several centimeters in diameter and height, sothat the rhodolith beds should be considered as a very roughsurface for acoustical scattering at frequencies of hundredsof kilohertz, even though the rhodolith-covered areas of theseafloor can frequently be generally flat.

Statistics of the backscatter envelope (sometimes referred toas instantaneous amplitude) is considered in Section III alongwith an approximate method for determining the backscattersamples least affected by the beam directivity pattern. Changesin backscatter statistics after synthesizing sidescan data arebriefly discussed in Section IV. It is demonstrated in Section Vthat the backscatter intensity data measured by the Reson 8125system tends to be extreme value distributed at large anglesof incidence, which leads to overestimation of the seafloorbackscatter strength and incorrect measurements of its angulardependence. Estimates of the seafloor backscatter strengthderived from the backscatter energy in each sonar beam areshown to be almost unbiased at any angle of incidence, whichis discussed in Section VI.

II. EXPERIMENTAL DATA

The total length of nonoverlapping multibeam swath tracksover a sand-covered area selected for statistical analysis ofbackscatter was about 450 m. The backscatter data from sandwere taken from nearly 800 sonar pings. The swath tracks overa rhodolith bottom were about 600 m long in total, which wassampled by nearly 1200 sonar pings. The sea depth varied from33.5 to 35.5 m over sand and from 34 to 42 m over the rhodolithbed, so that the total surveyed area was about 54 000 m forsand and 79 000 m for rhodolith. The sonar pulse length was101 s. Two kinds of backscatter data, backscatter intensity andsnippet data, collected by the Reson 8125 system were usedto measure the seafloor backscatter coefficient and its angulardependence. The snippet data are fragments of the backscatterenvelope clipped out in each sonar beam around the bottomdetection time to span the backscatter signal approximatelywithin the beam width. It was found from personal communi-cation with Reson’s engineers [10] and from a sonar calibrationexercise carried out in a swimming pool [11] that the datareferred to as backscatter intensity in the Reson 8125 user’smanual are actually the peak amplitudes of the backscatterenvelopes taken from the snippet data in each beam, rather thantrue intensity values. Therefore, the energy of backscatteredsignals was calculated by integrating the squared envelope, andthe peak amplitude was squared to obtain values which willbe referred to as peak intensity in this paper. The backscatterenergy and peak intensity were used to estimate the seafloorbackscatter strength using an algorithm described in detailin [11] and [12]. In this algorithm, the backscatter energy iscorrected for the beam footprint area and the peak intensityis corrected for the seafloor insonification area in addition tocorrection for the transmission loss. It was possible to estimateabsolute values of the backscatter strength, because the echosounder was calibrated with respect to overall gain of thereceive channels with an accuracy of about 1.5 dB.

GAVRILOV AND PARNUM: FLUCTUATIONS OF SEAFLOOR BACKSCATTER DATA FROM MULTIBEAM SONAR SYSTEMS 211

Fig. 1. Example of snippet data (fragments of backscatter envelope) collectedfrom one sonar ping in beams 208–212 (solid lines) over a rhodolith bottom andsynthesized sidescan data (dashed line). The dots show the peak values whichare picked by the sonar system as backscatter intensity in each beam. The spatialinterval between backscatter samples of the seafloor is about 4 cm for thesebeams.

Fig. 1 demonstrates snippet data from five adjacent beams208–212 (incidence angles from 44 to 46 ) and a fragment ofsidescan data synthesized from these beams. The sidescan datawere generated using a root mean square (RMS) method [8].It is clearly seen in Fig. 1 that the coincident backscatter sam-ples in the overlapping adjacent beams, which return from thesame features on the seafloor, have different amplitudes due tothe beam pattern distortion. It is also evident that the peak am-plitude values (dots in Fig. 1), collected by the sonar systemas backscatter intensity values in each beam, do not necessarilycorrespond to the footprint center. The angular dependence ofthe seafloor backscatter strength derived from the peak inten-sity and energy of backscatter from sand and rhodolith is shownin Fig. 2. For oblique angles of incidence, backscattering fromrhodolith is much stronger than that from sand. Moreover, theangular dependences of the backscatter strength estimated fromthe peak intensity and energy are considerably different, whichseems unexpected at first glance. The difference is small fornear vertical incidence. As the angle increases, the estimatesof the seafloor backscatter strength from these two differentbackscatter characteristics slightly diverge to about a 1-dB dif-ference at an angle of approximately 12 , where the transversewidth of the receive beam footprint becomes comparable to thewidth of the insonification area. At such angles, an approxima-tion of the insonification area by a simple rectangular shape lim-ited by the transmitted pulse length in the transverse directionoverestimates the effective insonification area [13]. As the inci-dence angle further increases, the estimates become divergingin an opposite way—the backscatter strength derived from thepeak intensity rapidly increases relative to the estimate from thebackscatter energy. An explanation of this effect will be consid-ered in Section V based on the theory of extreme value statistics.

Fig. 2. Angular dependence of the seafloor backscatter strength from sand andrhodolith derived from backscatter energy (solid) and peak intensity (dashed)which were measured in all 240 beams and averaged over all sonar pings withinthe two trial areas of different beds. � and � are insonification and foot-print areas, respectively.

III. INSTANTANEOUS BACKSCATTER AMPLITUDE

To statistically analyze fluctuations of backscatter intensitynot affected by the variations due to directivity characteristicsof the sonar receive beams, it is necessary either to make appro-priate corrections of the backscatter envelopes for the beam pat-tern or to determine the samples of backscatter envelopes whichare least affected by the beam pattern. To find such samples, weassumed that the maximum of the receive beam pattern is lo-cated near the center of mass of the backscatter envelope. Thesample index of this center can be found from

where is th sample of the backscatter envelope anddenotes the nearest integer operator. All backscatter envelopesrecorded from different sonar pings were aligned in each beamwith respect to their center of mass and then averaged to obtainthe beam directivity pattern not affected by random backscatterfluctuations within the footprint. The backscatter samples lo-cated at the center of the beam pattern in each beam and pingwere assumed to be the samples least distorted by beam direc-tivity. The longitudinal (along-track) distance between the beamfootprints of contiguous sonar pings was large enough for thebackscatter fluctuations to be uncorrelated, even for the outer-most beams with the widest footprints on the seafloor. Fluctua-tions of the backscatter amplitude in adjacent beams were alsouncorrelated, because the samples were taken from the centralsections of footprints which did not overlap with each other.Consequently, all the backscatter samples taken from the foot-print centers could be used for statistical analysis.

To take into account possible dependence of backscatter sta-tistics on incidence angle, the backscatter samples were groupedby the angle of incidence of the corresponding beam in differentangular domains of 10 wide from 0 to 60 . As a result, eachangular domain was represented by more than 20 000 samplesfor both sand and rhodolith. To remove the effect of the angulardependence of the seafloor backscatter coefficient on the distri-bution of backscatter fluctuations, the backscatter amplitudes in


Fig. 3. Probability of false alarm calculated for the instantaneous backscatter amplitude measured from sand (left panels) and rhodolith (right panels) at small(top), moderate (middle), and large (bottom) angles of incidence. The best fits by different distribution models are shown by dashed and dotted lines. The numbersshown in the legends are �-values of the Kolmogorov–Smirnov test.

each angular group were mean-normalized to unity, i.e., dividedby the mean value. A maximum-likelihood method was used tofind the best-fit parameters of various model distributions, ex-cept for the -distribution model where a method of momentswas used for estimating the best-fit parameters.

Fig. 3 shows the probability of false alarm for the backscatterfluctuations observed from sand and rhodolith at vertical, mod-erate, and most oblique angles of incidence and the distributionmodels, which reveal the best fit. The probability of false alarmhas been used in many studies as the most indicative charac-teristic to test tails of experimental distributions and find thebest-fit models (for example, see [6]). The selection of modeldistributions to test for best fit to the experimental data wasmade primarily based on findings of previous studies of seafloorbackscatter statistics [14]. At nearly vertical angles of incidence,gamma and Weibull distribution models provide the bestfit to the experimental data collected from sand, which is alsoindicated by the -values of the Kolmogorov–Smirnov good-ness-of-fit test shown in the legend. The -distribution modelwas tested for the squared envelope, so the corresponding dis-tribution model for the envelope amplitude is denoted by .

A Rayleigh-distribution model also demonstrates a reasonablefit, although the tail is slightly overestimated. For rhodolith, the

and Weibull best-fit models tend to the Rayleigh distribu-tion and they all overpredict the experimental distribution tail.

At moderate angles of 25 –35 , all three distributions demon-strate nearly the same fitting performance with reasonably high

-values for both sand and rhodolith. The shape parameters ofthe best-fit and Weilbull models at these angles are nearly 1and 2, respectively, which means that the amplitude fluctuationscan be modeled by the Rayleigh model with an acceptable ac-curacy. Best-fit estimates for the -distribution model cannotbe found by the method of moments for the data at small andmoderate incidence angles, because the tail of the experimentaldistributions is generally lighter than that of the Rayleigh model.

As the angle of incidence further increases, the experimentaldistribution tails become heavier and the -distribution modelcan be fitted to the experimental distributions. At large angles ofincidence (50 –60 ), the -distribution provides the best fit tothe tail of the experimental distributions, although the Weibullmodel is comparable in accuracy of predicting of backscatteramplitudes of high probability. The shape parameter of the


-distribution estimated from the experimental data at large in-cidence angles is about 20 and 9 for sand and rhodolith, respec-tively. These values are similar to the estimates of the shape pa-rameter made by Le Chenadec et al. [7] for multibeam sonardata collected from soft (fine sand) and rough (rock outcrops)sediments at oblique angles of 50 –60 .

There is a likely explanation for the backscatter fluctuationsto be differently distributed at moderate and large angles of in-cidence in the particular conditions of these experimental mea-surements. At small and moderate incidence angles, the widthof the seafloor insonification varied between 3 and 4 m, whichmight be large enough, comparing to the seafloor roughness cor-relation length, for the backscatter process to be nearly Gaussianand the backscatter envelope to be Rayleigh distributed. How-ever, the transverse width of the insonification area decreasedto about 10 cm at the most oblique angles, which was prob-ably comparable to or shorter than the correlation length ofthe large-scale roughness of the seafloor surface. In this case,Rayleigh-distributed rapid fluctuations are randomly modulatedby slower variations due to the large-scale roughness. However,such speculation is not valid for the backscatter fluctuations atsteep angles of incidence, where the experimental distributiontails are even lighter than those of the Rayleigh model. Otherreasons should be considered to explain this effect, includingthose due to possibly unknown peculiarities of signal processingin the sonar hardware.

IV. SYNTHETIC SIDESCAN DATA

Sidescan data can be generated in the Reson 8125 systemby two different methods, using either RMS or average valueprocessing [8]. In the RMS method applied to the data setfrom the Recherché Archipelago, an RMS value is calculatedat every sampling time for all coincident samples of overlap-ping backscatter envelopes from neighboring receive beams.As a result, the amplitude variations due to the beam patterneffect are corrected to some extent in the synthesized swathdata. To examine a potential effect of RMS processing on thedistribution of backscatter fluctuations, we selected statisti-cally independent samples from each swath data set and thengrouped them into seven angular domains according to thecorresponding incidence angle, as described in Section III.Based on the autocorrelation function of fluctuations in thesynthesized swath data, taking every fifth sample providedstatistical independence of the selected sets of samples.

Fig. 4 shows the probability of false alarm calculated forfluctuations of the sidescan data collected from rhodolith atsmall, moderate, and large incidence angles. It is obviousafter comparing Fig. 4 with the right panels of Fig. 3 thatthe RMS processing changes significantly the distribution ofbackscatter fluctuations at nearly vertical angles of incidence,so that the Rayleigh distribution model is no longer suitable forapproximation even for the high probability values. At smallincidence angles, the sidescan samples are synthesized frommultiple backscatter envelopes which have a large overlap intime due to a small difference in the slant range to the bottom,but arrive from almost nonoverlapping beam footprints on theseafloor. If the backscatter envelope in each individual beam isRayleigh distributed and fluctuations of backscatter from the

Fig. 4. Probability of false alarm calculated for sidescan data generated fromthe multibeam data from rhodolith at small (top), moderate (middle), and large(bottom) angles of incidence. The best fits by different distribution modelsare shown by dashed and dotted lines. The numbers shown in the legends are�-values of the Kolmogorov–Smirnov test.

footprints of different beams are statistically independent, thena sum of the squared envelopes will be gamma distributedas discussed in more detail in Section VI. This seems to be themost likely explanation for the distribution model as thebest approximation for the experimental distribution.

For moderate (35 –45 ) and larger angles of incidence,change in the distribution of backscatter fluctuations after RMSprocessing is also noticeable. The RMS operation makes thedistribution tail considerably heavier, so that the -distributionmodel becomes a much better approximation for the experi-mental distribution than the other models. There is no obviousexplanation for such change in the distribution of fluctuations,because there are different factors which might affect the re-sulting distribution in a complex way. Such factors are a partialfootprint overlap of adjacent beams and a relatively smalldistance between the centers of adjacent footprints comparedto the width of the insonification area.

Changes in the distribution of backscatter variations causedby RMS processing are less significant at large angles ofincidence. The -distribution model provides the best fitto the experimental distributions compared to the andWeibull models, which was also the case for the instantaneous


backscatter amplitude (Fig. 3, right bottom panel). The trans-verse width of the insonification area becomes small at largeangles of incidence, so that the backscatter samples coincidingin the overlapping envelopes of different beams represent thesame elementary scattering patches on the seafloor. Conse-quently, the amplitude fluctuations of the coinciding backscattersamples from different beams are correlated. Hence, the RMSoperation should not significantly change the distribution ofresulting fluctuations.

V. PEAK INTENSITY

The footprint of oblique sonar beams contains a number ofnonoverlapping insonification areas, if the transmitted sonarpulse is short [13]. This number increases with beam incidenceangle. Fluctuations of backscatter from nonoverlapping insoni-fication areas are expected to be statistically independent, if thecorrelation length of the seafloor roughness is smaller than thespatial separation between adjacent insonification areas. Vari-ations of backscatter from each insonification area measuredwith different sonar pings can be considered as a stochasticprocess with a certain statistical distribution. Such a processwill be referred to as an elementary process. Let the footprintof a particular beam contain nonoverlapping insonificationareas, which can also be called scattering cells. The variationof the full backscatter signal in this beam comprises a series of

elementary stochastic processes. If the complex amplitudeof these backscatter processes is Gaussian distributed, thenthe backscatter intensity has an exponential distribution.Let be a process constituted from the maximum valuesof statistically independent and identically exponentiallydistributed elementary processes with a unit variance. Theprobability of obeys the following equation [15]:

(1)

The right-hand side of (1) rapidly tends to with, which is the Gumbel distribution widely used in the

theory of extreme value statistics. A generalized Gumbel dis-tribution, sometimes referred to as the Fisher–Tippett ( – )distribution, can be derived from (1) for the exponentially dis-tributed elementary processes which have the mean value dif-ferent from unity

(2)

where is the location parameter and is the scaleparameter. The probability density function (pdf) of this distri-bution is

(3)

the mean value , and the variance ,where is the Euler–Mascheroni constant. Extremevalues of elementary processes, which have other than ex-ponential distributions but an exponential falloff rate of the pdftail, such as the Rayleigh, gamma, and -distributions, also

Fig. 5. First moment (mean) of the maximum value distribution expected forseries of exponentially (dashed) and �-distributed (dotted) processes versusthe number of processes� . The solid line shows the prediction for exponentialprocesses from the � –� distribution model.

Fig. 6. Ratio of the mean values of peak and instantaneous intensity versus theratio� �� measured for sand (dashed line) and rhodolith (dotted line). Thesolid line shows prediction from the model based on extreme value statistics.

tend to be – distributed with increasing [16]. However,there is no closed-form expression for the relationship betweenthe – location parameter and the number for thesedistributions.

The variation of the mean value of (expressed in decibels)with the number shown in Fig. 5 was numerically modeledfor two different series of the elementary processes with the ex-ponential distribution and the -distribution (and ). The solid line shows the mean of the – distribu-tion with the location parameter . The – meanrapidly tends to the mean of the peak values picked from the se-ries of exponentially distributed processes at .

To compare the experimental results with the prediction fromthe extreme value theory, we examined the ratio ofthe mean values of peak intensities and the backscatter inten-sity samples not affected by the beam directivity pattern in eachbeam (as discussed in Section III). Averaging was performed fortwo sets of sonar pings received from sand and rhodolith. Theratio of the footprint and insonification areaswas also calculated for each beam, based on the beam width,incidence angle, water depth, and sonar pulse length. If fluc-tuations of backscatter intensity from nonoverlapping insonifi-cation areas are statistically independent and almost exponen-tially distributed, then the ratio should depend pri-marily on the number of distinct scattering cells within thebeam footprint. Fig. 6 shows the ratio as a functionof a noninteger number . The variation of this


Fig. 7. Probability of false alarm calculated for the peak intensity measured from sand (left panels) and rhodolith (right panels) at small (top), moderate (middle),and large (bottom) angles of incidence. The best fits by different distribution models are shown by dashed and dotted lines. The numbers shown in the legends are�-values of the Kolmogorov–Smirnov test.

ratio with the number is remarkably similar for backscatterfrom sand and rhodolith. The solid line shows the prediction of

for exponentially distributed processes based onextreme value statistics. The agreement between the measuredand predicted values is good in general. At small , theexperimental values are slightly higher than the prediction. Forlarger , the difference between measured and modeled valuesstays within approximately 5% of the prediction. Fig. 6 alsoclearly demonstrates that estimates of the seafloor backscatterstrength derived from the mean value of peak intensities will beincreasing with the number of scattering cells contained in thebeam footprint, which will lead to overestimation of the seafloorbackscatter strength at oblique angles of incidence. The meanof peak intensity equals approximately the mean intensity onlywhen the footprint contains one scattering cell.

Fig. 7 shows the probability of false alarm of the peak in-tensity measured from sand and rhodolith in three different an-gular domains: near-vertical, moderate, and large incidence an-gles, and different model fits to the experimental distribution.The -values of the Kolmogorov–Smirnov test are given in the

legends. At vertical angles of incidence, none of the chosen dis-tribution models fits well with the experimental distributions.The exponential and models provide a reasonable approxi-mation of the distribution tail for sand and rhodolith, respec-tively. The insonification area is limited by the beam footprintat these incidence angles and, hence, the distribution of peakintensity fluctuations is expected to be similar to that of the in-stantaneous intensity. However, in contrast to the distributionsof instantaneous intensity at vertical incidence, the tails of thepeak intensity distributions are noticeably heavier than those ofthe exponential distribution. This is probably an effect of a rel-atively large sampling interval of backscatter envelopes, whichis about 35 s in the Reson 8125 sonar system. The sonar beamwidth projected onto the travel time axis at near-vertical inci-dence is comparable to the sampling interval, so that randomfluctuations of the sampling moments relative to the pulse ar-rival time introduce additional fluctuations of the peak intensity.

The exponential distribution model fails totally in approxima-tion of the peak intensity distribution at moderate incidence an-gles of about 30 . At these angles, the number is larger than


unity, but still too small (less than 3) for extreme value statisticsto be applicable. A log-normal distribution model provides themost accurate approximation of the experimental distribution,although it is far from adequate.

As the angle of incidence increases further, the numberalso rapidly increases up to approximately 30 at 60 . For

such a moderately large number of scattering cells in thebeam footprint, the – distribution based on the extremevalue theory demonstrates a reasonable approximation forthe tail of experimental distributions, especially for the datacollected from rhodolith. On the other hand, the log-normaldistribution provides a noticeably better fit to the whole shapeof the experimental distribution function. There are no evidentunderlying physical or statistical principles that could be sug-gested for justifying the log-normal distribution as a rationalmodel for approximating distributions of the peak intensityfluctuations. A relatively good performance of the log-normaldistribution model in approximating fluctuations of some otheracoustical backscatter characteristics has been noticed before(for example, see [17]). Some sensible explanations for usingthe log-normal distribution for approximating fluctuations ofnear-surface and volume backscatter data were given in [14].However, such explanations are not applicable to the seafloorbackscatter characteristics considered in this paper. The –distribution appears to be a more rational model for the distri-bution of peak intensity fluctuations at large numbers .

VI. BACKSCATTER ENERGY

Middleton demonstrated that fluctuations of the averagebackscatter intensity tend to be -distributed, if the scatteringprocess is Gaussian [18]. This follows from the fact that a sumof statistically independent and identically exponentiallydistributed stochastic processes has a -distribution. Inother words, if the pdf of is , where

, then

(4)

where is the shape parameter and is thescale parameter. The mean value of the -distribution is

, i.e., it is equal to the mean value of . Sig-nals received by a multibeam sonar system from the seafloorconsist of a series of backscatter returns from different insoni-fication areas. As in the previous section, nonoverlapping in-sonification areas can be considered as statistically independentscattering cells, if the correlation length of the seafloor rough-ness is significantly smaller than the width of the insonifica-tion area. If the beam footprint contains a number of suchscattering cells, then the energy of backscatter signals is ap-proximately a sum of statistically independent backscatter pro-cesses . If all are identically distributed and have the samemean value, fluctuations of this sum normalized by the foot-print size are expected to be -distributed withthe mean value . This means that the backscat-tering coefficient estimated from the mean backscatter energyis approximately equal to the backscattering coefficient deter-mined from the mean intensity. At the same time, the variance

Fig. 8. Probability of false alarm calculated for the mean value of a seriesof � numerically simulated random processes, which are statistically in-dependent and have the same exponential distribution and the amplitudes� � � (dashed line) and � � �� ,� � � �� (dotted line). The numbers shown in the legends are�-values of the Kolmogorov–Smirnov test. The solid lines show the probabilityof false alarm for the theoretical �-distribution.

of the -distribution decreases with ,which means that the variations of the backscattering coefficientderived from the backscatter energy decrease with incidenceangle when . This is an expected result of averaging.

Equation (4) is a good approximation for a sum of exponen-tially distributed processes with the same mean value. However,the receive beam pattern distorts the backscatter envelope, sothat the left-hand side of (4) should be written as

(5)

where the coefficients allow for the variation of thebackscatter envelope in the time domain due to the beampattern effect. The mean values of the elementary exponentialprocesses summed in (5) are no longer the same for different .There is no evident closed-form expression for approximationof the distribution in (5). However, it can be expected thatthe -distribution should also be a reasonable approximationfor (5), because the resulting processes consist of a linearcombination of exponentially distributed processes. This canbe examined by numerical modeling.

Fig. 8 shows the probability of a false alarm for a seriesof numerically generated random processes with an expo-nential distribution and two different functions for the ampli-tude coefficients: (ideal rectangular beam pattern) and

,(beam pattern of a linear array). It is clearly seen from Fig. 8that the -distribution remains a good approximation for (5) atsmall and large , even when the coefficients vary from 0at the envelope edges to 1 at the center.

It was shown in the authors’ previous study [13] that approx-imation of the beam pattern by a rectangular window causes


Fig. 9. Probability of false alarm calculated for the backscatter energy measured from sand (left panels) and rhodolith (right panels) at small (top), moderate(middle), and large (bottom) angles of incidence. The best fits by different distribution models are shown by dashed and dotted lines. The numbers shown in thelegends are �-values of the Kolmogorov–Smirnov test.

an error, when estimating the seafloor backscatter strength bybackscatter energy received in individual beams. However, thiserror is as small as about 0.6 dB and, moreover, it is nearly con-stant for different angles of incidence from 0 to 60 . This errorarises partly from the difference between the mean values ofand due to decrease of the coefficients far from the beamcenter.

For statistical analysis of backscatter energy fluctuations,the energy estimates were made only for every second beam,which excluded possible effects of footprint overlap for ad-jacent beams and provided statistical independence of theenergy fluctuations in different sonar beams. Fig. 9 shows theprobability of false alarm of backscatter energy fluctuationsmeasured in different angular domains and the best fits of thelog-normal and -distribution models. Other models, such asthe Weibull distribution and -distribution (for square rootof energy), do not demonstrate reasonable fit and thereforeare not shown. At small incidence angles, neither of thesetwo models provides good approximation results, although the

-distribution approximates reasonably well the tail of the ex-

perimental distribution measured for rhodolith. The log-normaldistribution demonstrates a remarkable fit to the data obtainedfrom sand at moderate incidence angles. The log-normal fit tothe backscatter data from rhodolith is reasonable for the valuesof high probability in this angular domain. Surprisingly, the

-distribution does not demonstrate an acceptable performance,especially in approximating the distribution tail, even if thebackscatter envelope is nearly Rayleigh distributed at theseangles (Fig. 3).

At oblique angles of incidence, when the number is large,the -distribution model provides the best approximation for thedistribution of backscatter energy fluctuations measured fromsand and rhodolith.

The shape parameter of the -distribution best-fitted to theexperimental data was compared with the ratio .If backscatter from adjacent nonoverlapping insonification areasis statistically independent, then the shape parameter is ex-pected to be a linear function of . Fig. 10 demonstratesthat the shape parameter rapidly grows with , but the depen-dence is not linear. For , the -shape parameter estimated


Fig. 10. Variation of the shape parameter � of the �-distribution fit to thebackscatter energy fluctuations as a function of the ratio � �� of beamfootprint and insonification areas measured for backscatter from sand (solid line)and rhodolith (dashed line).

for backscatter energy fluctuations is larger than by approxi-mately 1. As the ratio increases, the growth rate of tends tobe lower, so that the estimates of become somewhat smallerthan the ratio . There are several possible factors that couldexplain such behavior of this relationship. First, the backscatterintensity, as a function of time, is not a series of statisticallyindependent samples. As discussed in [18], the correlation be-tween samples depends on the bandwidth of sonar signals andthe -distribution may not fit well the average intensity whenthe number of samples is small. The other possible reason ofpartial disagreement between the experimental and modeling re-sults is that the width of the insonification area at oblique anglesmay become smaller than the correlation length of the seafloorroughness. Consequently, the number of statistically indepen-dent scattering cells within the beam footprint will be smallerthan that predicted from the ratio .

VII. CONCLUSION

Only two different seafloor types were considered in this casestudy of statistical characteristics of backscatter data collectedwith a high-frequency multibeam sonar system. However, theresults obtained and conclusions made from this analysis canbe easily generalized to some other types of seafloor covering.

It is shown that the Rayleigh-distribution model can be an ac-ceptable approximation for the distribution of backscatter fluc-tuations even for the data collected with a narrow-beam sonarsystem at very high frequencies of hundreds of kilohertz, whenthe Rayleigh number is much larger than unity. If the seafloorroughness is more or less homogeneous and the width of theseafloor insonification area is larger than the roughness correla-tion length, then the Rayleigh model demonstrates a reasonablyaccurate fit to experimental distributions of the backscatter en-velope. Because the transverse width of the insonification areadecreases with increasing incidence angle, it can become com-parable to or smaller than the roughness correlation length atoblique incidence angles, if the sonar pulse is short. In suchcases, the -distribution is more appropriate than the Rayleighmodel for predicting the distribution of backscatter fluctuations.

Such observations are valid only if backscatter data are notsignificantly affected by sonar parameters and settings andsignal processing methods implemented in the sonar system.

One of the major problems in analyzing statistics of multibeambackscatter data arises from the sonar beam directivity pattern,which is significantly different from an ideal rectangular shape.A method of correction for the beam pattern effect suggestedin Section III demonstrated reasonable results. The other kindof such problems appears when a sonar system processes theraw backscatter signals in one way or another (often unknown)and then offers the resulting values as a measure of backscatter.As an example, the Reson 8125 system measures the peak am-plitude of backscatter signals received in each beam with eachping and presents this characteristic as “backscatter intensity.”As a result, estimates of the seafloor backscatter strength de-rived from this characteristic are radically biased especially atoblique angles of incidence. This effect was explained in detailin Section IV based on the theory of extreme value statistics.Another example is the method implemented in some multi-beam systems for synthesizing sidescan data from backscattersignals in individual beams. It was demonstrated and explainedin Section III that the RMS process, used in particular in theReson 8125 system for generating sidescan data, distorts con-siderably the distribution of backscatter fluctuations, especiallyat small angles of incidence.

An analysis given in Section VI shows that the estimates ofthe seafloor backscatter strength and its angular dependence de-rived from the backscatter energy in individual beams are ro-bust with respect to the effects of insonification area and beampattern. The backscatter strength estimated from the backscatterenergy is comparable to the values from the instantaneous inten-sity, apart from a minor bias of about 0.6 dB independent on in-cidence angle. However, in contrast to the intensity, the varianceof backscatter energy decreases with incidence angle. Fluctua-tions of backscatter energy can be satisfactorily modeled by the

-distribution at oblique incidence angles, where the ratio ofthe footprint and insonification areas is much larger than unity.Change in the variance of backscatter energy with incidenceangle is primarily due to the variation of the -shape parameterwith the ratio . This makes the seafloor backscatter images,derived from backscatter energy and corrected for the angulardependence, considerably less noisy at the edges of swath tracksthan at their middle.

It is obvious from comparing distributions of backscatterfluctuation measured from two very different seafloor typesthat the difference between acoustical properties of the seafloorhas a much lesser effect on the distribution of backscatterfluctuations than the signal processing methods implementedin the sonar hardware and postprocessing software. The effectof incidence angle on fluctuations of multibeam backscatterdata is also much more significant than that of the differencebetween morphological and physical properties of differentseafloor covers. Once the effect of the seafloor backscatterstrength is removed from backscatter variations by normalizingbackscatter data with respect to their mean value, the experi-mental distributions of backscatter characteristics observed atthe same incidence angles look similar for different seafloortypes. This means that the first moment of backscatter distri-butions directly related to the seafloor backscatter strength is amuch more informative characteristic for seafloor classificationthan the higher moments of backscatter distributions.


ACKNOWLEDGMENT

The authors would like to thank Dr. J. Siwabessy of Geo-science Australia for playing a key role in collecting the seafloorbackscatter data from the Recherché Archipelago region. Theywould also like to thank Prof. J. Penrose who was a leading sci-entist of the CWHM project providing the authors with valu-able comments on this study. They would also like to thankDr. A. Lyons of the Pennsylvania State University who madeseveral useful comments and suggestions regarding the analysispresented in this paper.

REFERENCES

[1] D. A. Abraham and A. P. Lyons, “Novel physical interpretations of�-distributed reverberation,” IEEE J. Ocean. Eng., vol. 27, no. 4, pp.800–813, Oct. 2004.

[2] L. Hellequin, J.-M. Boucher, and X. Lurton, “Processing of high-fre-quency multibeam echo sounder data for seafloor characterization,”IEEE J. Ocean. Eng., vol. 28, no. 1, pp. 78–89, Jan. 2003.

[3] V. V. Olchevskii, Characteristics of Seafloor Reverberation. NewYork: Plenum, 1976, ch. 2.

[4] E. Jakeman, “Non Gaussian models for the statistics of scatteredwaves,” Adv. Phys., vol. 37, no. 5, pp. 471–525, 1988.

[5] E. Jakeman and P. N. Pusey, “Significance of � distributions in scat-tering elements,” Phys. Rev. Lett., vol. 40, no. 9, pp. 546–550, 1978.

[6] A. Lyons and D. Abraham, “Statistical characterization of high-fre-quency shallow-water sea-floor backscatter,” J. Acoust. Soc. Amer., vol.106, no. 3, pp. 1307–1315, 1999.

[7] G. Le Chenadec, J.-M. Boucher, and X. Lurton, “Angular dependenceof �-distributed sonar data,” IEEE Trans. Geosci. Remote Sens., vol.45, no. 5, pp. 1224–1235, May 2007.

[8] “SeaBat 8125 Operator’s Manual,” ver. 0.3.02, RESON Inc., Goleta,CA, 2003.

[9] J. Penrose, “Coastal water habitat mapping,” in Building theBridges—Seven Years of Australian Coastal Cooperative Research,R. Souter, Ed. Indooroopilly, Qld., Australia: Cooperative ResearchCentre for Coastal Zone, Estuary and Waterway Management (CoastalCRC), 2007, ch. 6, p. 75.

[10] B. Bridge, Private Communication. Oct. 2003, RESON Inc., Goleta,CA.

[11] I. M. Parnum, “Benthic habitat mapping using multibeam sonarsystems” Ph.D. dissertation, Dept. Appl. Phys., Curtin Univ.Technol., Perth, W.A., Australia, 2008 [Online]. Available:http://espace.library.curtin.edu.au/R?func=dbin-jump-full&ob-ject_id=18584&local_base=gen01-era02)

[12] A. N. Gavrilov, A. J. Duncan, R. D. McCauley, I. M. Parnum, J. D.Penrose, P. J. W. Siwabessy, A. J. Woods, and Y.-T. Tseng, “Charac-terization of the seafloor in Australia’s Coastal Zone using acousticaltechniques,” in Proc. 1st Int. Conf. Underwater Acoust. Meas.: Technol.Results, Crete, Greece, 2005.

[13] J. Penrose, A. Gavrilov, and I. M. Parnum, “Statistics of seafloorbackscatter measured with multibeam sonar systems,” in Proc. Acoust.Conf., Paris, France, 2008, pp. 617–622.

[14] T. C. Gallaudet and C. P. de Moustier, “High-frequency volume andboundary acoustic backscatter fluctuations in shallow water,” J. Acoust.Soc. Amer., vol. 114, no. 2, pp. 707–725, 2003.

[15] P. Embrechts, C. Kluppelberg, and T. Mikosch, Modelling ExtremalEvents in Insurance and Finance. Berlin, Germany: Springer-Verlag,1997, ch. 3, p. 113.

[16] J. Beirlant, Y. Goebegeur, J. Segers, and J. Teugels, Statistics of Ex-tremes: Theory and Applications, ser. Probability and Statistics. WestSussex, U.K.: Wiley, 2004, ch. 2.5.

[17] M. V. Trevorrow, “Statistics of fluctuations in high-frequency low-grazing angle backscatter from a rocky seabed,” IEEE J. Ocean. Eng.,vol. 29, no. 2, pp. 236–245, Apr. 2004.

[18] D. Middleton, “New physical-statistical methods and models for clutterand reverberation: The ��-distribution and related probability struc-tures,” IEEE J. Ocean. Eng., vol. 24, no. 3, pp. 261–284, Jul. 1999.

Alexander N. Gavrilov was born in 1955. He re-ceived the M.S. degree in physics from the MoscowState University, Moscow, Russia, in 1999 and thePh.D. degree in acoustics from Andreyev Institute ofAcoustics, Moscow, Russia, in 1995.

From 1979 to 1995, he was with the Arctic Acous-tics Department, Andreyev Institute of Acoustics,and from 1995 to 2003, he was with the ShirshovInstitute of Oceanology, Russian Academy of Sci-ence, Moscow, Russia. His main research interestsin Russia were in the area of Arctic Ocean acoustics

and, in particular, acoustic thermometry of the Arctic Ocean. He joined theCentre for Marine Science and Technology (CMST), Curtin University ofTechnology, Perth, W.A., Australia, as an Associate Professor in 2003. Hisresearch interests at CMST include remote acoustic observations of climatedriven environmental changes in the Arctic and Antarctica, acoustic scatteringfrom the seafloor and using echosounders for seafloor classification, passiveacoustic monitoring of marine mammals, and acoustic array processing.

Iain M. Parnum was born in 1977. He received a firstclass honors degree in chemistry from the Universityof Bristol, Bristol, U.K., in 1999, the M.Sc. degreein marine environmental protection from the Univer-sity of Wales, Bangor, Wales, U.K., in 2004, and thePh.D. degree from Curtin University of Technology,Perth, W.A., Australia, in 2008. His doctoral workwas carried out at the Centre for Marine Science andTechnology (CMST) and focused in seafloor map-ping using multibeam sonar systems.

Since completing his doctoral studies, he hascontinued with the CMST as a Research Associate. His research interests arein seafloor mapping using acoustic techniques with emphasis on physics ofbackscatter, and water column biomass estimation.

Documents

Fluctuations of Seafloor Backscatter Data From Multibeam Sonar Systems