A Multivariate Correlation Analysis of High- Frequency Bottom Backscattering Strength Measurements With Geotechnical Parameters

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A Multivariate Correlation Analysis of

High-Frequency Bottom Backscattering Strength

Measurements With Geotechnical

Parameters

Dick G. Simons, Mirjam Snellen, and Michael A. Ainslie

Abstract—Sound backscattered from the seabed has been mea-sured in a 10 10-nmi2 region of the North Sea, characterized by a variety of bottom types, including mud, sand, and gravel. The backscattering strength measurements are made by a for-ward-looking sonar, operating at 100 kHz and tilted at an angle of 30 from the horizontal. Fifty bottom-grab samples, represen-tative of the uppermost 20 cm, were taken and analyzed for gravel content, shell content, and grain-size distribution. The backscatter measurements are correlated with the gravel percentage, shell per-centage, and median grain size. A strong positive correlation of the measured backscatter strength with shell and gravel percentage is observed. Additionally, a small positive correlation between the backscatter strength and the median grain size of the sand and mud part exists. The derived values for the backscatter strength compare well to those presented in the recent literature. From a least squares curve-fitting analysis, an empirical expression is obtained giving backscatter strength as a function of gravel percentage, shell percentage, and the median grain size of the sand and mud part.

Index Terms—Modeling, scattering, seafloor, underwater acoustic measurements.

I. INTRODUCTION

K

NOWLEDGE about the scattering of sound from the seafloor is important for two reasons. The first reason is concerned with the limitations imposed on the performance of a sonar system due to the bottom backscattering. The second reason concerns the fact that the scattering can provide a means for remotely measuring the properties of the seafloor, and thus can be used by a bottom classification tool.

This paper deals with scattering measurements at grazing an-gles of approximately 25 –35 and at a frequency of 100 kHz, taken for a wide variety of sediment types. The area for which

Manuscript received September 14, 2005; revised September 12, 2006; ac-cepted October 6, 2006.

Associate Editor: D. J. Tang.

D. G. Simons was with the Underwater Technology Department, TNO Defence, Security and Safety, The Hague 2509 JG, The Netherlands. He is now with the Delft Institute of Earth Observation and Space Systems, Delft University of Technology, Delft 2629 HS, The Netherlands (e-mail: d.g.simons@tudelft.nl).

M. Snellen is with the Delft Institute of Earth Observation and Space Sys-tems, Delft University of Technology, Delft 2629 HS, The Netherlands (e-mail: m.snellen@tudelft.nl).

M. A. Ainslie is with the Underwater Technology Department, TNO Defence, Security and Safety, The Hague 2509 JG, The Netherlands (e-mail: michael. ainslie@tno.nl).

Digital Object Identifier 10.1109/JOE.2007.891890

the data were collected is in the North Sea and is well docu-mented from a geological point of view. Additionally, a large number of bottom grabs was taken during the experiments.

Marine geologists classify sediments in terms of their mud, sand, and gravel content, resulting in bottom identifiers such as “sandy mud” (sM) and “slightly gravelly sand” (g)S, i.e., the so-called Folk class [1]. Geographical maps providing this type of information are widely available from geological institutes. It would be useful if the bottom backscattering strength (SB) could be related to this relatively simple bottom information, e.g., for sonar performance modeling. In contrast, models for bottom backscattering make use of an extensive set of geoacoustic and geotechnical input parameters (see [2]–[5]). These parameters, comprising among others sediment sound speed, density, and interface roughness parameters, are, however, hardly available under operational conditions.

In this paper, the measured backscattering strength is corre-lated with measured bottom properties, such as gravel and shell percentages, grain-size distribution, and Folk class, i.e., we pro-vide a quantitative analysis of the correlation of the backscat-tering strength with measured geotechnical parameters.

From recent work on correlating high-frequency bottom scat-tering with measured geotechnical properties of the seafloor, we mention the papers by Stanic et al. [6]–[8]. In these papers, backscattering measurements are reported for the frequency range of 20–180 kHz and for grazing angles of 5 –30 . A single sediment type is considered in each: coarse sand in [8], fine sand in [6], and a sediment characterized by a 2-cm layer of coarse shell overlying medium sand in [7]. In [3], bottom backscattering measurements are reported for three bottom types, viz., a fine sand, a silt, and a silt-clay bottom. The frequency range is 15–45 kHz. The strength of our work lies in the wide variety of bottom types considered, i.e., from really soft sediments (no gravel, mean grain size 63 m) to coarse sand sediments (mean grain size 1 mm) with a large gravel and/or shell content. In [9] and [10], seafloor scattering strength measurements are presented as obtained by a 95-kHz multibeam echo sounder (MBES). We compare our backscattering data to the data of Stanic et al. [6]–[8], Goff et al. [9], Hughes-Clarke et al. [10], and others.

This paper is organized as follows. In Section II, we present an overview of the experiments carried out. Also, the acoustic equipment used is briefly described here. Further, this section provides a description of the bottom-grab equipment, the results

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SIMONS et al.: CORRELATION ANALYSIS OF HIGH-FREQUENCY BOTTOM BACKSCATTERING STRENGTH MEASUREMENTS 641

Fig. 1. Surface sediment type or Folk class [1]. The square in the main figure indicates the trial area, shown in more detail in the inset on the right. Indicated is the track sailed in October 2000. The track was sailed a second time for collecting bottom grabs, the positions of which are indicated. The numbering of the horizontal legs is also indicated. In May 2001, legs 1, 3, 5, 7, and 9 were repeated for collecting acoustic data again.

of the bottom-grab analysis, and the oceanographic conditions. For retrieving the backscattering strength from the data, a simple model for the received sonar signal was used. This model and the method of deriving the backscattering strength are described in Section III. The results are given in Section IV. In Section V, the derived backscattering strength values are compared to those reported in literature. In this section, also the correlation of the obtained backscattering data with the geotechnical bottom-grab data is investigated. From a least squares curve-fitting analysis, a practical empirical equation for the backscattering strength as a function of the geotechnical parameters is derived. Its

prac-tical predictive capability is tested using Goff’s data [9] as an independent data set.

II. NORTHSEAEXPERIMENTS

A. Trial Area and Logistics

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Fig. 2. Sonar footprint (0 3 dB) for 30 tilt and a nominal water depth of 50 m.

10 10 nmi ) is indicated by the black square. It includes a va-riety of sediment types from soft and smooth (sM) to hard and rough (sG), with the water depth ranging from 30 m in the gravel area to 60 m in the mud area.

The track sailed in October 2000 is depicted in the inset of Fig. 1 and consists of ten parallel horizontal legs. The num-bering of the legs is indicated in this figure. The track was sailed twice, once for collecting acoustic data and once for taking bottom grabs. The bottom-grab positions are also indicated in this figure. The acoustic data turned out to be corrupt and the collection of the acoustic data was repeated in May 2001, where, due to limited measurement time, only legs 1, 3, 5, 7, and 9 could be sailed.

B. Acoustic Equipment

The acoustic data were acquired with a forward-looking sonar operating at a frequency of 100 kHz. It was put at a tilt angle of 30 , measured from the horizontal. The beam pattern of the transmitter is such that it has a full width at half maximum (FWHM) of 11 in the vertical plane, whereas it is omnidirec-tional in the horizontal. The received signal is beamformed (20 beams) in the horizontal. The horizontal FWHM is 1.5 .

The analog outputs for a few beams of the (horizontal) beam-former are fed into a dedicated data acquisition system. The signals are amplified and subsequently digitized at a sampling rate of 300 kHz. The data acquisition is triggered with the sonar pulse transmission. The acoustic data are stored together with the corresponding time and position as measured with a differ-ential global positioning system (DGPS). Only results for the most forward-looking beam are presented in this paper.

The received acoustic signals are expressed in Pascal units. For this, the electronic gain up to beamforming and the beam-former gain were determined through careful laboratory mea-surements. The hydrophone sensitivity was taken from the sonar manual as stated by the manufacturer, viz., 195.3 1 dB re 1 V/ Pa. This also holds for the source level, its value being specified as 214.7 dB re 1 Pa @ 1 m. Uncertainties in the backscatter strength measurements as presented in this paper are primarily due to uncertainties in the source level and the sensi-tivities of the receiving elements, respectively.

Fig. 2 shows the ensonified area (footprint) of the sonar at 30 tilt, together with its dimensions for a water depth of 50 m.

The normal incidence reflected energy was also present in all received signals, although the sidelobe level at normal incidence of the vertical beam pattern of the sonar is low. An example of the received signal is given in Fig. 3. The early part of each re-ceived signal consists of a sharp peak due to specular reflection at normal incidence, followed by a broader signal due to the backscattering at angles around 30 . The specular reflection is not used.

Fig. 3. Example of the envelope of the received pressure signal as a function of time. Both the normal incidence reflected signal (at 0.06 s) and the backscattered signal are shown. The black smooth line represents the modeled backscattered signal (see Section III).

C. Bottom Grabs

The geological map for the area of the experiment originated from 1987 and, therefore, 50 bottom grabs were taken in the trial area for obtaining up-to-date information of the surface sed-iment of the sea bottom. Five grabs per leg were taken at roughly 2-nmi separation. Use was made of the so-called “Hamon grab” and a “Van Veen grab.” For both devices, the sampling depth in the sea bottom amounts to approximately 20 cm, i.e., large com-pared to the acoustic wavelength of 1.5 cm in water at 100 kHz. Also, the sampling depth is sufficiently large compared to the acoustic penetration depth at 100 kHz. See [12] for further de-tails about the characteristics of the grab equipment.

The laboratory analysis of the bottom samples comprised the following steps. First, the samples were dried. Next, the sam-ples were sieved with a mesh of 2 mm, thereby separating the gravel and shells from the sand and mud. Both the gravel and shell weight percentage were subsequently determined and are presented in Figs. 4 and 5, respectively.

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Fig. 4. Gravel weight (expressed as a percentage of the total grab sample weight) in each of the bottom grabs. The numbering of the grabs is indicated in the figure.

Fig. 5. Shell weight percentage in each of the bottom grabs.

changes. The differences illustrate the importance of collecting up-to-date ground-truthing information.

The precise grain-size distribution of the sediment samples (after the gravel was removed) was determined by optical mi-croscopy. The median values of the grain-size distributions are given in Fig. 8. This parameter is defined such that 50% of the grains, by weight, are smaller than (and 50% are larger). Other useful descriptors of the grain-size distribution are the tenth and ninetieth percentiles and . The value of is thus a measure of the width of the grain-size dis-tribution. Values for , and , together with the Folk class, gravel, and shell percentage are given in Table I.

Fig. 6. Folk class as a function of percentage gravel, sand, and mud.

Fig. 7. Folk class for each bottom grab. The sM and sG boundaries, see Fig. 1, are also indicated.

D. Oceanographic Conditions

The oceanographic conditions during the May 2001 trial are described in the following. In particular, numerical values for the sound speed and the absorption coefficient of the water column, needed to derive the backscatter strength (see Section III), are determined.

1) Sound-Speed Profile: Sound-speed profiles were mea-sured immediately before and after sailing the horizontal legs using a sound velocimeter. The sound-speed value, denoted , decreases from a maximum of 1482 m/s at the surface to 1478.5 m/s at a depth of 40 m.

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Fig. 8. Thed value (median) in micrometer of the grain-size distribution measured for each of the bottom grabs.

TABLE I

DATA TOWHICH ALEASTSQUARESCURVE-FITTINGANALYSISISAPPLIED

measurements of the temperature and salinity profiles were not made at the time of the experiment, a reliable estimate of the ab-sorption profile can nevertheless be made from available data.

The salinity profile based on climatology (World Ocean Atlas 94 (WOA94) [15]) increases from 34.4 ppt (parts per thousand) at the sea surface to 34.8 ppt at a depth of 50 m. The climato-logical temperature profile decreases from 8.9 C at the surface to 7.6 C at 50 m.

In principle, these WOA94 profiles can be used to estimate an absorption profile, but such a calculation could be unreliable because of annual and daily fluctuations in the temperature pro-file. We derive an improved estimate of the temperature profile from the measured sound speed by inverting Leroy’s “simpli-fied” sound-speed formula [16, first line of Table IV]. In other words, the temperature (in Celsius degrees) as a function of depth from the sea surface (in meters) is estimated from the WOA94 salinity profile (in parts per thousand) and mea-sured sound-speed profile (in meters per seconds) using (1), shown at the bottom of the page.

The temperature profile thus calculated is then combined with to obtain an absorption profile, which we estimate using [14]. The resulting absorption profile varies from 31.9 dB/km (3.7 Np/km) at the sea surface to 30.6 dB/km (3.5 Np/km) at 40-m depth.

3) Wind Conditions: The wind speed varied during the course of the experiment between forces 3 and 4 on the Beau-fort scale.

III. MODELING THEBACKSCATTEREDSONARSIGNALS

An example of the received signals is given in Section II (see Fig. 3). As mentioned in that section, the early part of each received signal consists of a sharp peak due to normal incidence reflection followed by a broader signal due to the backscattering at angles around 30 . This section describes the method of retrieving the backscattering strength from the received signal.

Use is made of a simple model for the received acoustic signal. The assumptions as given in [17] are assumed to be valid. These comprise, among other things, straight line prop-agation paths and a homogeneous distribution of scatterers throughout the area producing the scattering at any one instant in time.

Additionally, the effect of bottom slope and ship attitude is not accounted for. Here, the slope is taken as the angle of large scale features. Significant slopes ( 3 ) occur at the edges of the mud area (see Fig. 1). However, at the core positions, slopes are very small (fraction of a degree). The effect of ship attitude is assumed to be cancelled out by considering mean values of the backscattering values as determined by the analysis presented in the following (Section V).

We consider the sound path launched at the source with ver-tical angle (see Fig. 9). The corresponding intensity received

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Fig. 9. (Top) Straight-line propagation path for vertical angle' (corresponding grazing angle at bottom 90 0 '). The ' equals 90 minus transducer tilt (30 ). The dashed lines indicate the 3-dB beamwidth in the vertical. (Bottom) Elemental scattering area. (D and H in meters; in seconds; x and 1x in meters.)

at the sonar due to direct backscattering at incidence angle from the bottom is approximated by

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intensity at 1 m of the source, i.e., the source level of the sonar;

vertical beam pattern of the transducer; slant range of the sound path;

absorption coefficient in the water (neper per meter) (taken from [14]);

horizontal distance of the sound path; along-track length of the elemental scattering area (see Fig. 9);

opening angle of the horizontal beams of the receiver (being 0.026 rad or 1.5 )

area of elemental scattering area;

SB bottom backscattering strength in decibels.

The and are given by and

, respectively, whereas is given by . , and are the water depth, the sonar depth, and the duration of the transmitted sonar pulse, respectively. equals 3.5 m and equals 0.5 ms. is the average sound speed in the water. The mean values used for and (see Section II) are 1480 m/s and 3.6 Np/km, respectively.

Assuming the sound originating from a continuous vertical line , the vertical beam pattern of the transducer is

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with being the vertical dimension of the transducer elements ( 8 cm), being the acoustic wavelength, and 60 (see Fig. 9). In the following, the 3-dB vertical beamwidth is denoted

(being 11 ).

Scattering strengths exhibit a systematic variation with grazing angle that is uniquely determined by the geometry of the problem and encapsulated by Lambert’s rule, i.e.,

SB (4)

for the backscatter strength SB where , the Lambert parameter, is in decibels.

Theoretical models of the scattering strength using perturba-tion theory have been found to achieve good agreement with measurements, e.g., [3]. Such models show that rough surface scattering dominates up to the critical angle and volume scat-tering dominates at steeper angles. It may be possible to im-prove on a conversion based on Lambert’s rule by using a theo-retical model, especially if a transition across the critical angle is involved. However, to do so requires detailed knowledge of the sediment geoacoustic parameters that is not generally avail-able (such as the roughness spectrum of the water–sediment boundary, or the volume scattering strength of the sediment). Furthermore, Lambert’s rule permits a surprisingly good fit in many cases; see [6] and [3].

The root-mean-square (rms) pressure as a function of can now be written as

(5) with being the density of the water. The rms pressure as a function of time can be determined by using

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Fig. 10. The as a function of longitude derived for legs 1, 3, 5, 7, and 9.

Equations (5) and (6) determine the shape of the received signal as a function of time, whereas the amplitude of the signal

scales as .

Lambert’s parameter is retrieved from the backscattered data by minimization of the following function with respect to : (7) i.e., the usual quadratic measure for the deviation between the measured received rms pressure signal and the calculated signal. and are the envelope of the measured and modeled pressure samples in the time domain, respectively.

The simplest form of 1-D minimization without calculation of the derivative, i.e., the “golden section search,” is used [18]. Basically, this efficient and robust method was designed to handle the worst case situation of 1-D function minimization. The method is alternated with parabolic interpolation [18]. The practical implementation of the minimization algorithm used is taken from MATLAB, which is described in [19]. The algorithm is capable of finding the optimum value within 5–10 iterations for a tolerance of 0.5 dB set on . The search range for is [ 25 dB, 0 dB].

In principle, this search is not needed as can directly be ob-tained from the total acoustic energy conob-tained in the backscat-tered signal. One advantage of our method, however, is that for

each received sonar signal a comparison is made with the simple model given by (5); see Fig. 3. Note that this model is, among other things, based on the assumption that the bottom type (or ) does not change within the sonar footprint. A comparison of the measured and modeled received signal for each sonar ping can be regarded as a continuous test of this assumption. Another advantage of our method is that the derived is less sensitive to contaminating noise in the backscattered signal. When is de-rived directly from the total energy in the backscattered signal, a correction for noise is mandatory.

IV. RESULTS

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Fig. 11. Measured SB at 30 grazing angle plotted against corresponding Folk class of the bottom grabs.

V. DISCUSSION

A. Comparison of Measured With Literature

In Fig. 11, we compare the Folk class of the bottom grabs with the corresponding measured SB at 30 grazing angle. Here, SB at 30 is obtained using (4), i.e., SB . Here, is the mean of -values at positions around the core position, thereby eliminating fluctuations due to, e.g., ship roll and pitch. This result seems consistent with the expectation of an increasing SB when going from muddy to the more sandy and gravelly sediments [20]. However, from a closer look at this figure, we can perhaps only conclude that sediments without gravel (or shell) (sM, mS, and S) have a lower ( 11 dB) backscattering strength than sediments with gravel (gS, msG, and sG), i.e., SB 26 2 dB for sM, mS, and S and SB 15 2 dB for gS, msG, and sG.

Although useful, this analysis is too simple, as Folk class is a classification based on mud, sand, and gravel content only (see Section II). It does not account for other grab parameters, such as grain size and shell content. This will be taken up in Section V-B.

In Fig. 12, we compare the measured SB at 30 with the grain size as derived from the corresponding North Sea grabs for sediments without gravel (practically, this means 1%). Also given in the figure are measurements that have been published in [6], [8], [21], and [22]. Our data and the data from literature are in good agreement and they show that there is virtually no re-lation between scattering strength and grain size [6]. Boyle and Chotiros [23] suggest that the absence of a correlation between scattering strength and grain size is due to gas bubbles trapped in the sediment.

Also indicated in the figure are the model results given in [20]. The slightly increasing SB with increasing is driven by the roughness parameter “spectral strength” used as input to the model (spectral strength increases with increasing grain size). On the other hand, the numerical values of the Applied Physics Laboratory (APL, University of Washington, Seattle, WA) model [20] are in good agreement with our data. Again, the

Fig. 12. Measured SB at 30 plotted against grain sized as derived from the corresponding grabs for sediments without gravel (squares). Also indicated are data from the literature, converted where necessary to 30 using Lambert’s law. The solid line corresponds to the APL model results.

conclusion is that at 100 kHz, SB 26 2 dB for gravel-free sediments from mud (30 m) to coarse sand (700 m).

In addition, we have included in Fig. 12 the SB measurements of [9] and [10] measured by a 95-kHz MBES. For the data of [9], we have included only those data points that contain less than 5% coarse material, where coarse material is defined by Goff as shell and gravel fragments with grain sizes larger than 4 mm. Use was made of Lambert’s law to convert Goff’s data from 45 to 30 . We estimate the error in applying Lambert’s rule to convert from scattering strengths measured at 45 to 30 to be between 1 and 2 dB in magnitude and unbiased in sign. This estimate is based on measurements between 8 and 100 kHz [21], [24], [25]. Both MBES data sets confirm that there is hardly any correlation between scattering strength and grain size. In [9], it is concluded, however, that there is a strong relationship between the occurrence of coarse material (gravel and shell) and SB, in accordance with our data. Both MBES data sets show somewhat lower SB values for the same range. In both [10] and [9], the values found for SB are about 4–5 dB lower, i.e., SB 30 3 dB and 31 2 dB, respectively.

B. Correlating Measured With Geotechnical Bottom-Grab Parameters

For the data considered in this paper, the variables divide nat-urally in a group containing the geotechnical parameters and a group containing acoustic parameters , where this latter group consists of a single parameter, viz., . For the -variables,

we select the median grain size , gravel

percentage , and shell percentage . Note that is not simply made equal to , but is weighted by the mud and sand percentage to account for the fact that grain size was determined after the gravel and shell was removed from the bottom grab. Both the and data are presented in Table I.

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Fig. 13. Measured Lambert parameter plotted against median grain size (of the sand and mud part), gravel percentage, and shell percentage for each bottom-grab position. The lowest right plot shows the estimated Lambert parameter, as obtained from the least squares curve-fitting analysis, plotted against the corresponding measured Lambert parameter for each of the bottom-grab positions.

At this stage, we note that the calculated correlation coeffi-cients are based on quite a limited number of data pairs (being 25). In such a situation, it is important to also report the statis-tical significance or confidence of each correlation coefficient [26]. For low correlation coefficient values, such as the 0.20 be-tween and , the confidence is only 65%, i.e., there is a prob-ability of 35% that the observed correlation can occur between two random (uncorrelated) data sequences of length 25. The confidence of the other two entries 0.87 and 0.65 is very high, being 100% and 99%, respectively. Usually, a minimum confi-dence of 95% is used to “define” the correlation to be genuine.

For quantifying the relation between , the estimated Lam-bert parameter, and the three geotechnical variables, we employ the least squares curve-fitting method. For this, we write

(8) with being the coefficients describing the linear relationship between and . Defining matrix as the matrix containing in the first column all 25 measurements of , in the second column the measurements, in the third column the mea-surements, and 1’s in the fourth column, we have

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where column vectors and contain all 25

-mea-surements and the four coefficients , respectively, e.g., ( denoting the transpose). We assume the measurements to be uncorrelated with equal measurement

errors, i.e., . Solving the system of (9) in the least squares sense, we then obtain the well-known solution

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For , we find , resulting in the

following empirical relation between and the three geotech-nical variables:

(11) where is in millimeters and and are in percent. Consid-ering the correlations between the three geotechnical variables, we find for

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Fig. 14. Predicted backscatter strength at 30 plotted against measured backscatter strength at 30 for Goff’s data. The error bars originate from the errors on the coefficientsc of the predictive equation. A distinction is made between data with little gravel (g < 5%) and a larger amount of gravel.

impact (by a factor of ten on the average) on backscattering strength than gravel percentage.

A plot of against measured (Table I) is given in Fig. 13. Empirical equation (11) can, in principle, be used as a simple predictive model for the high-frequency scattering properties of the seabed of the North Sea. The least squares method also pro-vides the error on as the covariance matrix

(12) where the measurement error is calculated as

with . We obtain 2.1 dB for . The

er-rors on the coefficients are given as the square root of the diagonal elements of and are equal to (0.035, 0.021, 0.45, 0.9). Equation (11), together with these errors, allows for an estimate of and its precision given a measurement of median grain size, gravel, and shell content at a certain position in the North Sea.

We will now apply (11) in a predictive sense. Fig. 14 shows the results of applying our empirical relation, as given by (11), to the data of [9]. Due to lack of knowledge regarding the gravel content and the shell content , we have assumed all coarse material to consist of gravel, i.e., . As already mentioned, the SB values as measured by Goff et al. [9] are some 5 dB lower than the values measured in the North Sea experiment. We assume this deviation to stem from calibration errors (in one or both of the data sets) and have added a 5-dB offset to Goff’s data to eliminate this deviation. For assessing the relative influence of the different terms of (11) separately, i.e., the and terms, a distinction is made between data points with a low percentage of coarse material ( 5%) and data points with a larger coarse percentage. In general, our empirical expression is found to predict values for SB that are in good agreement with the measured values for gravelly samples. For the nongravelly

samples, there is a tendency to overestimate Goff’s scattering strength measurements, especially for measured SB values less than 26 dB in Fig. 14.

VI. SUMMARY ANDCONCLUSION

High-frequency (100 kHz) acoustic backscattering experi-ments were carried out in the North Sea using a forward-looking sonar. The marine geology of the trial area is well known. In addition, a large number of bottom grabs were taken providing a large amount of geotechnical information of the surface sediments of the sea bottom. This information consists of mud, sand, gravel, and shell content as well as the grain-size distribu-tion. Backscattering strength data is obtained from the received sonar signals at 25 –35 grazing angles at the bottom and for a wide variety of sediment types, ranging from sM to sG.

The backscattering strength is derived from a comparison of the calibrated received sonar signals with a simple geometrical model for the signal directly backscattered from the bottom. In this model, the backscattering strength as a function of grazing angle is assumed to follow a Lambert’s rule. In fact, the Lambert parameter is derived for each received signal.

The obtained -values are positively correlated with the gravel and shell content of the corresponding bottom grabs. Also, a small but positive correlation is observed between and the median grain size of the remaining sand and mud. These observations fully agree with those presented in the literature. The obtained numerical values for the backscatter strength agree well with most of those found in the recent literature.

A useful practical relation between and the geotechnical data of the bottom grabs is obtained by the application of a mul-tivariate correlation analysis between and gravel content, shell content, and median grain size. Shell appears to be, by weight, a stronger scatterer than gravel. The applicability of this practical relation was tested using an independent data set.

ACKNOWLEDGMENT

The authors would like to thank the crews of the vessels for their assistance during the sea trials, The Netherlands Institute for Applied Geoscience, TNO, for the grab analysis, and the reviewers for their useful comments.

REFERENCES

[1] R. L. Folk, “The distinction between grain size and mineral compo-sition in sedimentary-rock nomenclature,” J. Geol., vol. 62, no. 4, pp. 344–359, 1954.

[2] D. R. Jackson, D. P. Winebrenner, and A. Ishimaru, “Application of the composite roughness model to high-frequency bottom backscattering,”

J. Acoust. Soc. Amer., vol. 79, no. 5, pp. 1410–1422, May 1986.

[3] D. R. Jackson and K. B. Briggs, “High-frequency bottom backscat-tering: Roughness versus sediment volume scattering,” J. Acoust. Soc.

Amer., vol. 92, no. 2, pp. 962–977, Aug. 1992.

[4] J. C. Novarini and J. W. Caruthers, “The partition wavenumber in acoustic backscattering from a two-scale rough surface described by a power-law spectrum,” IEEE J. Ocean. Eng., vol. 19, no. 2, pp. 200–207, Apr. 1994.

[5] J. C. Novarini and J. W. Caruthers, “A simplified approach to backscat-tering from a rough seafloor with sediment inhomogeneities,” IEEE J.

Ocean. Eng., vol. 23, no. 3, pp. 157–166, Jul. 1998.

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[7] S. Stanic, K. B. Briggs, P. Fleischer, W. B. Sayer, and R. I. Ray, “High-frequency acoustic backscattering from coarse shell ocean bottom,” J.

Acoust. Soc. Amer., vol. 85, no. 1, pp. 125–136, Jan. 1989.

[8] S. Stanic, R. R. Goodman, K. B. Briggs, and N. P. Chotiros, “Shallow-water bottom reverberation measurements,” IEEE J. Ocean. Eng., vol. 23, no. 3, pp. 203–210, Jul. 1998.

[9] J. A. Goff, B. J. Kraft, L. A. Mayer, S. G. Schock, C. K. Sommerfield, H. C. Olsen, S. P. S. Gulick, and S. Nordfjord, “Seabed characterization on the New Jersey middle and outer shelf: Correlatability and spatial variability of seafloor sediment properties,” Mar. Geol., vol. 209, pp. 147–172, Aug. 2004.

[10] J. E. Hughes Clarke, B. W. Danforth, and P. Valentine, “Areal seabed classification using backscatter angular response at 95 kHz,” in Proc.

High Frequency Acoust. Shallow Water, 1997, pp. 243–250.

[11] Rijks Geologische Dienst and British Geological Survey, Holocene en oppervlaktesedimentkaart “Indefatigable,” 1987, Sheet 53 N-02 E. 1 : 250 000 Ser..

[12] D. G. Simons and M. Snellen, “High frequency measurements of bottom backscattering strength in the north sea: Correlation with grain size, shell content and gravel content,” in Proc. Boundary Influences

High Frequency, 2005, pp. 177–184.

[13] E. L. Hamilton and R. T. Bachman, “Sound velocity and related prop-erties of marine sediments,” J. Acoust. Soc. Amer., vol. 72, no. 6, pp. 1891–1903, Dec. 1982.

[14] R. E. Francois and G. R. Garrison, “Sound absorption based on ocean measurement. Part II: Boric acid contribution and equation for total absorption,” J. Acoust. Soc. Amer., vol. 72, no. 6, pp. 1879–1890, Dec. 1982.

[15] National Oceanographic Data Center, World Ocean Atlas 1994 [On-line]. Available: http://www.nodc.noaa.gov/OC5/pr_woa4.html [16] C. C. Leroy, “Development of simple equations for accurate and more

realistic calculation of the speed of sound in seawater,” J. Acoust. Soc.

Amer., vol. 46, no. 1B, pp. 216–226, Jul. 1969.

[17] R. J. Urick, Principles of Underwater Sound. New York: McGraw-Hill, 1983, ch. 8.

[18] W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. A. Vetterling,

Numerical Recipes in C, The Art of Scientific Computing. Cambridge, U.K.: Cambridge Univ. Press, 1988, ch. 10.

[19] G. E. Forsythe, M. A. Malcolm, and C. B. Moler, Computer Methods

for Mathematical Computations. Englewood Cliffs, NJ: Pren-tice-Hall, 1977, pp. 182–187.

[20] “APL-UW High-Frequency Ocean Environmental Acoustic Models Handbook,” Tech. Rep. APL-UW TR 9407 AEAS 9501, Oct. 1994. [21] C. M. McKinney and C. D. Anderson, “Measurements of

backscat-tering of sound from the ocean bottom,” J. Acoust. Soc. Amer., vol. 36, no. 1, pp. 158–163, Jan. 1964.

[22] K. L. Williams, D. R. Jackson, E. I. Thorsos, D. Tang, and S. G. Schock, “Comparison of sound speed and attenuation measured in a sandy sed-iment to predictions based on the Biot theory of porous media,” IEEE

J. Ocean. Eng., vol. 27, no. 3, pp. 413–428, Jul. 2002.

[23] F. A. Boyle and N. P. Chotiros, “A model for high-frequency acoustic backscatter from gas bubbles in sandy sediments at shallow grazing angles,” J. Acoust. Soc. Amer., vol. 98, no. 1, pp. 531–541, July 1995. [24] M. Gensane, “A statistical study of acoustic signals backscattered from the sea bottom,” IEEE J. Ocean. Eng., vol. 14, no. 1, pp. 84–93, Jan. 1989.

[25] K. L. Williams, D. R. Jackson, E. I. Thorsos, D. Tang, and K. B. Briggs, “Acoustic backscattering experiments in a well characterized sand sed-iment: Data/model comparisons using sediment fluid and Biot models,”

IEEE J. Ocean. Eng., vol. 27, no. 3, pp. 376–387, Jul. 2002.

[26] J. S. Bendat and G. A. Pierson, Random Data: Analysis and

Measure-ment Procedures. New York: Wiley, 1971, pp. 125–129. [27] P. Legendre and L. Legendre, Numerical Ecology, 2nd English ed.

New York: Elsevier, 1998, pp. 519–520.

Dick G. Simons received the M.Sc. degree in physics

and the Ph.D. degree from the University of Leiden, Leiden, The Netherlands, in 1983 and 1988, respec-tively. His Ph.D. research topic involved the develop-ment of an imaging gas scintillation spectrometer for X-ray astronomy.

In 1990, he joined the Underwater Technology Department of TNO Defence, Security and Safety, The Hague, The Netherlands. From March 2004, he has been holding the part-time Seafloor Mapping Chair at the Delft Institute of Earth Observation and Space Systems (DEOS), Faculty of Aerospace Engineering, Delft University of Technology, Delft, The Netherlands, where on 1 October 2006, he was ap-pointed a full-time Professor on the chair Acoustic Remote Sensing. His main research interests are inversion problems in acoustics and seafloor classification and mapping.

Prof. Simons is a member of the Scientific Committee of the European Con-ferences on Underwater Acoustics (ECUA).

Mirjam Snellen received the M.Sc. degree in

aerospace engineering from the Delft University of Technology, Delft, The Netherlands, in 1995 and the Ph.D. degree in geoacoustic inversion from the University of Amsterdam, Amsterdam, The Netherlands, in 2002.

She was a Research Scientist at The Netherlands Organization for Applied Research (TNO), where she was working in the group of underwater acoustics and in the group of aeroacoustics until 2003. Currently, she is the Assistant Professor in the group of Acoustic Remote Sensing at the Delft Institute of Earth Observation and Space Systems, Delft University of Technology.

Michael A. Ainslie received the degree in physics

from Imperial College, London, U.K., in 1981, the degree in mathematics from the University of Cambridge, Cambridge, U.K., in 1982, and the Ph.D. degree from the Institute of Sound and Vibration Research, University of Southampton, Southampton, U.K., in 1992.

His research interests include the interaction of sound with ocean boundaries and geoacoustic inversion. Currently, he is with the Underwater Technology Department of TNO Defence, Security and Safety, The Hague, The Netherlands.