Fine-scale sedimentary structure: implications for acoustic remote sensing

Marine Geology 182 (2002) 141^159 www.elsevier.com/locate/margeo

Fine-scale sedimentary structure: implications for acoustic remote sensing K.B. Briggs a; , K.L. Williams b , D.R. Jackson b , C.D. Jones b , A.N. Ivakin b;c , T.H. Orsi d a

Sea£oor Sciences Branch, Naval Research Laboratory, Stennis Space Center, MS 39529, USA b Applied Physics Laboratory, University of Washington, Seattle, WA 98105, USA c Andreev Acoustics Institute, Shvernika 4, Moscow 117036, Russia d Planning Systems Incorporated, 115 Christian Lane, Slidell, LA 70458, USA Received 23 December 1999; accepted 14 March 2001

Abstract Detailed measurements of sediment properties and acoustic scattering were made at a carbonate sand^silt^clay site off Dry Tortugas in the Florida Keys. The sediment is characterized by varying scales of biologically controlled random roughness and heterogeneity as well as surficial stratification on centimeter scales. The interface roughness was determined from stereo photogrammetric digitization and parameterized by a power spectrum, whereas sediment volume heterogeneity was determined from core measurements and parameterized by first-order autoregressive models for sound speed and density fluctuations. In contrast to previous investigations, fine-scale sediment bulk density fluctuations were examined in sediment cores with computerized tomography in addition to the standard gravimetric technique. Furthermore, the strongly delineated sediment density and sound velocity transition layer was parameterized by piecewise linear fits. These characterizations of the random and deterministic properties were used in acoustic scattering models in an effort to determine the feasibility of remotely measuring fine-scale features of the seafloor. The result was negative: older, low-resolution models gave moderately good fits to the acoustic data, but the fit did not improve for newer, higher-resolution models. It is suggested that scattering due to shell fragments must be included to account for all features observed in the scattering data at this site. Published by Elsevier Science B.V. Keywords: sedimentation; bioturbation; acoustical properties; density; X-ray radiography

1. Introduction Sound scattering by the sea £oor at high frequencies (10^100 kHz) is governed primarily by centimeter-scale structure, including laminar strati¢cation, random heterogeneity and random * Corresponding author. Tel.: +1-206-543-1328; Fax: +1-206-543-6785. E-mailaddress: [email protected](K.B.Briggs).

roughness. In discussing these scattering mechanisms, it is helpful to divide sediments into two classes: those that permit substantial penetration of sound and those that do not. The former class typically includes muds: low-bulk-density, ¢negrained, cohesive material with consequently little impedance contrast across the sediment^water interface. Because of this lack of impedance contrast these sediments are more likely to scatter sound from the sediment volume rather than

0025-3227 / 02 / $ ^ see front matter Published by Elsevier Science B.V. PII: S 0 0 2 5 - 3 2 2 7 ( 0 1 ) 0 0 2 3 2 - 8

MARGO 2993 23-4-02

142

K.B. Briggs et al. / Marine Geology 182 (2002) 141^159

from the interface. Coarser, sandy sediments, on the other hand, have substantial impedance contrast, and scattering originates primarily from the rough sediment^water interface. These two contrasting scattering mechanisms can be used as a basis for acoustic classi¢cation of sediments (Ivakin, 1983, 1989, 1998c; Sternlicht, 1999), provided reasonably accurate scattering models are available for interpreting the data. Models for the scattering of high-frequency sound by sediment volume heterogeneities have been developed by several investigators (Ivakin and Lysanov, 1981; Ivakin, 1981, 1983, 1986; Hines, 1990; Pace, 1994; Lyons et al., 1994; Yamamoto, 1996). Rough-interface scattering models have been presented by Kuo (1964), Ivakin (1983), Jackson et al. (1986), and others. Whereas progress has been made in understanding volume and interface scattering through comparison of models and data, such comparisons have employed simpli¢ed models, considered only a single scattering direction (backscattering), and su¡ered from insu⁄cient spatial resolution in the accompanying environmental data (Ivakin, 1981, 1983, 1989; Stanic et al., 1988, 1998; Jackson and Briggs, 1992; Briggs, 1994; D. Jackson et al., 1996). Our goal is to use sediment property data with measurement intervals equal to or less than the acoustic wavelength and bistatic scattering data (that is, data taken with different incident and scattering directions) to test how well recent models predict scattering. These newer models treat the e¡ects of strati¢cation on scattering as well as the more general bistatic angular dependence. Following the usual practice, acoustic scattering by the sea £oor will be quanti¢ed in terms of the ‘scattering strength’ (Urick, 1983) for both backscattering and bistatic scattering. Questions that arise in connection with highfrequency sound scattering by sediments are: (1) Which is the dominant cause of scattering, interface roughness or volume heterogeneity ? (2) Does ¢ne-scale sediment structure a¡ect scattering strength? and, conversely, (3) Can acoustic remote sensing of the sea £oor be used to determine ¢ne-scale sediment structure? We will address these and other questions in the context of a

data set acquired at a site where the sediment shared characteristics of the ¢ne-grained, low-density type associated with dominant volume scattering and the high-impedance type associated with dominant roughness scattering. Sediment heterogeneity can be characterized by systematic measurements of sound velocity and density from sediment cores. The mean properties can be expressed in terms of vertical pro¢les of geoacoustic parameters (sediment density, compressional wave velocity, and absorption) and the £uctuations about the mean can be parameterized in terms of a structure function or powerlaw spectrum (Ivakin, 1981, 1982, 1994a; Ye¢mov et al., 1988; Yamamoto, 1995) or correlation lengths and variances (Lyons et al., 1994; Briggs and Percival, 1997; Briggs et al., 1998; Jackson et al., 2002). The latter approach to parameterization of £uctuating sediment properties is used in this paper. Interface roughness was measured using stereo photogrammetry and characterized in terms of the exponent and strength of a powerlaw spectrum. Previous reports of acoustic experiments have assessed the respective in£uences of interface roughness and sediment volume scattering from the sea £oor. D. Jackson et al. (1986), Mourad and Jackson (1989), and Jackson and Briggs (1992) did this using physical models for interface scattering and an empirical model for volume scattering. Jackson et al. (1996a) have interpreted results of ¢eld experiments using physical models for both processes. Interface scattering was treated using either the composite roughness model or small-roughness perturbation theory, and scattering from sediment heterogeneities was predicted using volume perturbation theory. These acoustic scattering models were used with measured sediment parameters to make comparisons with measured acoustic data. Whereas this earlier work showed reasonable agreement between models and data, some di¡erences are apparent in model^data comparisons for muddy sediments (Hines, 1990; Jackson and Briggs, 1992; Lyons et al., 1994). This warrants an examination of ¢ne-scale £uctuations in sediment volume properties as a cause of these discrepancies.

MARGO 2993 23-4-02

K.B. Briggs et al. / Marine Geology 182 (2002) 141^159

In this paper, the issues outlined above will be considered using combined sediment property and acoustic data sets acquired at a site o¡ the Dry Tortugas in the Florida Keys (see Brandes et al., 2002; Jackson et al., 2002). The water depth is 25 m, and the site is characterized by intense biological mixing that creates roughness features as well as steep gradients in physical and acoustic properties in the upper 6 cm of carbonate sand^silt^clay sediment (Briggs and Richardson, 1997). Random sediment heterogeneity at this site is due to burrows and mollusk shell debris, and roughness appears to be biogenic. Although the sediment is su⁄ciently low in bulk density (1.76 g/cm3 ) that one might expect volume scattering to dominate roughness scattering, our ¢rst model^data comparisons (D. Jackson et al., 1996; Williams and Jackson, 1997) indicated that the opposite was most likely the case. Considering the uncertainty that stems from the possible in£uence of gradients and the di⁄culty of resolving cm-scale heterogeneity, however, it may be that volume scattering is dominant at this site. Although the model^data agreement in this previous work was deemed satisfactory, certain discrepancies were evident. The angular dependence of backscattering data in D. Jackson et al. (1996) was stronger than that of the model, and the bistatic data of Williams and Jackson (1997) showed slight oscillations as a function of angle not seen in the model. Thus, we revisit the Dry Tortugas acoustic data set equipped with more extensive and higher-resolution sediment property data and more detailed acoustic models. Our primary aim is to test the feasibility of remotely measuring ¢ne-scale features of the sea £oor.

2. Materials and methods 2.1. Sediment collection and analysis Sediments were collected for laboratory analysis of compressional wave velocity and attenuation, porosity, grain size, and X-radiographic density structure via computed tomography (CT) with cylindrical (6.1- and 8.3-cm diameter) cores. Also, rectangular (36U44U3 cm thick) cores were

143

collected for two-dimensional X-radiography. The cores were collected by divers, exercising care in insertion, extraction, capping, and handling during recovery. Upon allowing the 6.1-cm cylindrical cores to equilibrate with laboratory temperature for 24 h, sediment compressional wave velocity and attenuation were measured at 1-cm intervals by transmitting/receiving a 400-kHz, pulsed signal directly through the sediment core with oil-¢lled, rubber transducers (Briggs, 1994). After the cores were measured aboard ship for acoustic properties and carefully transported to a pierside laboratory, they were sectioned at 2-cm intervals and assayed for sediment water content and grain size distribution. Sediment porosity and density were calculated from water content and average grain density measurements as described in Jackson and Briggs (1992). Sediment grain size was measured from disaggregated samples by dry sieving to quarter-phi intervals with a sieve shaker for gravel- and sand-sized particles and by use of a Micromeritics Model 5000 sedigraph (Micromeritics Instrument, Norcross, GA, USA) for silt- and claysized particles (Briggs, 1994). X-radiographs were made from specially designed rectangular cores that collected a 36-cm wideU3-cm thick sediment slab (P. Jackson et al., 1996). Sediment slabs were X-rayed within a few hours of collection with a model PX-20N portable X-ray unit (Kramex, Saddle Brook, NJ, USA). Fig. 1 is an example of a positive image made from an X-radiograph. The light area indicating the overlying water clearly contrasts with the lower, darker area signifying the sediment. Within the sediment appear relatively darker and lighter features and zones, with dark areas representing denser or less porous features (e.g., shells, compact sediment) and light areas representing less dense or more porous features (e.g., burrows, reworked sediment). For CT analysis, ¢ve 8.3-cm-diameter sediment cores were collected throughout the study site. Scans were made of the whole, intact cores using the Technicare 2060 CT scanner at Texaco EpP, Houston, TX. The cores were scanned every 2 mm, using a 2-mm-thick X-ray beam, to ensure complete length coverage with no overlap of im-

MARGO 2993 23-4-02

144

K.B. Briggs et al. / Marine Geology 182 (2002) 141^159

Fig. 1. An X-radiograph typical of the sediment collected from the Dry Tortugas experiment site. The less dense, bioturbated zone is evident as a lighter layer about 5^6 cm thick.

ages. (Note the X-ray scan [CT image] plane is parallel to horizontal bedding in the sediment core.) Each scan produces a 512U512-voxel image, with each voxel assigned a value (a CT number) that is directed related to bulk density. The (x, y, z) dimensions of a voxel are 0.25U0.25U2 mm, representing a sediment volume of 0.125 mm3 . Of course, averaging of density variability does occur over this volume. However, smoothing at this scale is miniscule, particularly when one considers the volume averaging that occurs using traditional gravimetric analysis. An average of 138 CT images was taken for each core. To estimate acoustic properties at the frequency (40 kHz) used in the ¢eld experiments, in situ measurements of sediment compressional wave velocity and attenuation were made with an In Situ Sediment geoAcoustic Measurement System (ISSAMS) described by Richardson (1997). Use of the 38-kHz data from ISSAMS avoided possible frequency dispersion that might a¡ect the laboratory-measured 400-kHz compressional wave velocities. The £uctuations in laboratory-measured compressional wave velocity, however, were used to estimate variance and correlation length parameters for modeling.

2.2. Sea£oor roughness measurements Sea£oor roughness was determined using stereo photographs made by divers with a module containing a 35-mm underwater stereo camera and 100-J underwater strobe (Photosea model 2000M, SubSea Systems, Houston, TX, USA). Eight representative stereo photographs were digitized at a 0.42-cm sampling interval to better than 1-mm horizontal and vertical accuracy (Wheatcroft, 1994) with a Benima stereo comparator (W.B. Geomap, Gotheburg, Sweden). Sea£oor roughness was then calculated as the roughness power spectrum for three cross-sectional pro¢les in each of the eight stereo pairs (Briggs, 1989). Roughness measurements were collected from one azimuthal orientation and determined to be isotropic based on the roughness features being entirely biogenic in origin. Ultimately, the roughness spectra from the experiment site were smoothed by averaging all spectra together. 2.3. Acoustic scattering data collection Two types of acoustic scattering measurements were conducted; backscattering measurements

MARGO 2993 23-4-02

K.B. Briggs et al. / Marine Geology 182 (2002) 141^159

Fig. 2. Bistatic scattering angular de¢nitions. The incident and scattered grazing angles are denoted ai and as , respectively, and the angle, Ps , speci¢es the change in azimuth due to scattering.

employing the same array for transmission and reception and bistatic measurements employing a separate transmitter and receiver. In either geometry, the transmitter was a bottom-mounted sonar

145

system referred to as the Benthic Acoustic Measurement System (BAMS). Operating at 40 kHz, the BAMS sonar employs a planar transmitter array mounted on a rotator mechanism at the top of the 5-m tripod. The maximum response axis of the array was pointed downward at a depression angle of approximately 12.5‡ below the horizontal. The transmitted signal was an FM waveform having constant amplitude over its 2ms duration. During this 2-ms interval, the frequency was swept from 39 kHz to 41 kHz with the transmitter providing a source level of 217 dB re 1 WPa (see Williams and Jackson, 1998 for further details). Backscatter data received on the BAMS array were recorded digitally and processed by a standard method using the sonar equation (Urick, 1983). Bistatic measurements employed BAMS as the transmitter and a mobile, ship-deployed receiving

25 m

5m

Box cores

Diver cores

In-situ probes

Fig. 3. A diagram of the experimental geometry for the acoustic scattering measurements. The Benthic Acoustic Measurement System (BAMS) is housed in a bottom mounted tripod. BAMS was used to obtain backscattering data and also served as the source for bistatic measurements, with the receiver deployed from a ship in a four-point mooring.

MARGO 2993 23-4-02

146

K.B. Briggs et al. / Marine Geology 182 (2002) 141^159

array. Fig. 2 de¢nes the geometry of bistatic scattering by the sea £oor. Under the assumption that the sea£oor is transversely isotropic, as indicated by analysis of the roughness data, a particular geometry is speci¢ed by three angles, the incident and scattered grazing angles, ai and as , and the ‘bistatic’ angle, Ps , specifying the change in azimuth due to scattering. The objective of the acoustic measurements was to cover as much of this three-dimensional angular space as practicable. As scattering by the sea£oor is a random process, multiple measurements for each triplet of angles are required to obtain statistical averages.

Fig. 3 shows a simpli¢ed diagram of the bistatic experimental geometry. The ship-deployed linear, horizontal, receiving array was divided in four equal sections (‘quads’) each about 32 cm long. The bistatic scattering results reported here were acquired using a single quad at two di¡erent gains to increase dynamic range. The array was deployed over the side of the ship after it was placed in a four-point moor near the BAMS tripod, and a pneumatic heave compensation system was used to decouple the ship’s aft deck motion from the array. The receiving array was steered so that the center of the transmit and receive beams intersected each other on the bottom such as to realize

Fig. 4. Vertical pro¢les of sediment (a) compressional wave velocity ratio, (b) compressional wave attenuation in dB m31 kHz31 , (c) bulk density, and (d) mean grain size in phi units measured on diver cores from the experiment site. A solid line connects measurements at each interval for individual cores.

MARGO 2993 23-4-02

K.B. Briggs et al. / Marine Geology 182 (2002) 141^159

147

Fig. 5. Biological structures as seen in CT images. Top row, (burrows/tubes): left (low-density structures, Core 223-2-KW-PL, 87 mm depth); right, (high-density features, Core 214-KW-PL, 235 mm depth); middle row, (shells/fragments): left (shell, Core 2282-KW-PL, 147 mm depth), right, (shell and fragment, Core 2384-KW-PL, 191 mm depth); bottom row, (miscellaneous): left (urchin? Core 223-2, 165 mm depth), right, (feeding structure, Core 238-1, 149 mm depth). The outer diameter of the core image is 8.3 cm.

MARGO 2993 23-4-02

148

K.B. Briggs et al. / Marine Geology 182 (2002) 141^159

di¡erent bistatic scattering angles, de¢ned in Fig. 2 (see Williams and Jackson, 1998 for further details). Measuring the geometrical parameters needed to determine these bistatic angles required several supplemental sensors including compasses, ranging transducers, and inclinometers. The range from BAMS to the mobile array was measured by means of a transponder mounted on the tripod. In the data to be presented the horizontal distance between BAMS and the receiving array was always less than 70 m. While backscattering strength is easily estimated using the sonar equation owing to the simple correspondence between acoustic time-of£ight and backscattering angle, it is much more di⁄cult to estimate bistatic scattering strength. To aid in this process, a simulation was developed that predicts the mean-square output of the receiver array as a function of time (Williams and Jackson, 1998) using the ‘baseline’ model for scattering, to be discussed in Section 4. Using experimentally determined geometric parameters, the simulation was used to produce a synthetic mean-square receiver output time series for each transmission. This synthetic time series was then compared with the data time series to determine the experiment bistatic scattering strength (Williams and Jackson, 1998).

3. Results 3.1. Geoacoustic data Fig. 4 displays the vertical distribution of sediment compressional wave velocity ratio, attenuation, density, and mean grain size for ten cores (only seven cores were assessed for grain size) collected from within the acoustic experiment site in the Dry Tortugas. The variability and number of measurements of each parameter are graphically indicated by the plotted symbols. Individual lines connecting the symbols indicate variation within individual cores. Although more cores were collected in the experiment (D. Jackson et al., 1996), only the longest ones were chosen for this study. Variability of sediment compres-

sional wave velocity, attenuation, grain size, and to a lesser extent, sediment density is controlled by the presence of burrows and coarse shell fragments within the sediment matrix (Briggs and Richardson, 1997; Richardson et al., 1997). The Xradiograph in Fig. 1 shows that burrows and mollusk shell fragments are prominent in sediments from the Dry Tortugas site. In accordance with radiographic and gravimetric analyses (Figs. 1 and 4), CT imagery of the Dry Tortugas cores revealed considerable inhomogeneity, with the dominant source of this variability being biological in origin (Fig. 5). Particularly prevalent are tubes and burrows, with walls composed of both low- and high-density material, which generate localized structures easily detected and quanti¢ed by CT. Present but less common are shells and shell debris. Large intact gastropod shells occur (Fig. 5), whereas the shell fragments that we observe are probably derived from broken pelecypods. Most of the gastropod shells are sediment-¢lled, but several contain pockets of water (or sediment^water slurry) that could result in considerable intratest porosity. Acoustically, shell fragments of 2-cm diameter and larger are expected to be most signi¢cant as ‘Bragg’ scatterers at the 40-kHz frequency utilized here. The distribution of 2-cm particles in the upper 30 cm of sediment, however, is extremely sparse (Fig. 6). Grain-size analysis of eight cores showed no fragments larger than 33.25 P diameter (9.5 mm). In a total sediment volume of 6.605 l, however, we found average weight fractions of 1.8% (71 ml of calcium carbonate) for fragments larger than 33.0 P diameter (8 mm) at 17 cm depth (Fig. 6, bottom) but less than 0.1% (3.6 ml of calcium carbonate) for all gravel-size fragments larger than 31.0 P diameter (2 mm) in the top 6 cm (Fig. 6, top). The CT imagery reveals several large feeding structures, possibly created by foraging heart urchins or some other type of large macrofauna. The compressional wave velocity (Vp ) ratio is an important acoustic model parameter obtained by dividing the sound velocity in the sediment by the sound velocity in the overlying water. The density ratio is the analogous ratio of sediment density to overlying water density. Table 1 sum-

MARGO 2993 23-4-02

K.B. Briggs et al. / Marine Geology 182 (2002) 141^159

Fig. 6. Weight percentage frequency histograms for sandand gravel-sized particles from nine cores collected from the ensoni¢ed area, sectioned at 2-cm intervals, sieved, and averaged over (top) the top 6 cm and (bottom) the 16^18 cm depth interval. Particles exceeding the Bragg wavelength of 2 cm are the primary scatterers of 40-kHz sound. Dry weight percentage is converted to wet volume percentage by a factor of 0.6.

marizes mean geoacoustic parameters obtained by averaging over cores and over depth within each core. In addition to the compressional wave velocity and density ratios, other parameters are at-

149

tenuation (k), shear wave velocity (Vs ), porosity, and mean grain size. In situ measurements of Vp , k, and Vs were collected from ISSAMS ; laboratory measurements of Vp , attenuation, porosity, mean grain size and density ratio were performed on sediment from cores. Because the averages of Table 1 were computed from values measured from 1- to 30-cm sediment depth, any depth dependence of geoacoustic parameters is obscured. Fig. 7 shows pro¢les of mean sediment density ratio and compressional wave velocity ratio. The compressional wave velocity and gravimetric density averages were obtained from 10 cores by averaging at each depth, while the CT density data were obtained by similar averaging of four separate cores. Both the sediment compressional wave velocity pro¢le and the density pro¢le obtained from gravimetric measurements show a de¢nite transition layer of 6-cm thickness. The sediment compressional wave velocity and density ratios increase rapidly with depth in this transition layer and then remain essentially constant at greater sediment depths. The CT density data show a somewhat less-pronounced transition layer, possibly due to settling during transport from the ¢eld to the CT facility. Also shown in Fig. 7 are two model representations of the data, the ‘strati¢ed’ model assigns the transition layer a linear depth dependence and approximates the pro¢les at greater depths as constant. The ‘baseline’ model, used by D. Jackson et al. (1996) and by Williams and Jackson (1997), assigns values extrapolated from the sediment^water interface to all depths. Statistics describing the heterogeneity of compressional wave velocity ratio and density ratio are essential model inputs. Fig. 8 shows correlation functions for these parameters obtained by subtracting the mean pro¢les of Fig. 7 and estimating lagged covariance as a sum over cores and overlapping samples. The data are adequately ¢t by a ¢rst-order autoregressive model (Briggs and Percival, 1997). This model gives spatial covariances of the form: 6xðz0 þ zÞxðzÞs ¼ c 2x e3z=1c where x is the random variable of interest (£uc-

MARGO 2993 23-4-02

150

K.B. Briggs et al. / Marine Geology 182 (2002) 141^159

Fig. 7. Vertical pro¢les of density ratio and sound velocity ratio. Data obtained by averaging over 10 cores are shown with the symbol ‘+’. Density ratio data obtained by averaging CT data over ¢ve cores are shown with the symbol ‘U’. The solid, piecewise-linear curves are the approximate representation of the pro¢les used in the ‘strati¢ed’ model. The dashed lines are the representation used in the ‘baseline’ model.

tuations in sediment compressional wave velocity ratio or density ratio with mean removed), z is the lag in the depth coordinate, cx is the standard deviation, and lc is the correlation length. The sample standard deviations of the gravimetric and CT density ratio data were in close agreement, being 0.025 and 0.015, respectively. The more representative value of 0.025 is employed in the acoustic modeling of Section 4, favoring the gravimetric density data due to their larger sample size in terms of number of samples

(2.5U) and sediment volume (105 U). This density ratio standard deviation is smaller by nearly a factor of two than that given in D. Jackson et al. (1996). Previously, a linear trend was estimated for each core and subtracted, and the standard deviation was determined from the residuals (D. Jackson et al., 1996). The procedure employed in the present paper subtracts a nonlinear trend, which follows the strong near-surface gradient, and yields smaller residuals. This procedure is consistent with the assumptions of the strati¢ed

Table 1 Average values for sediment compressional wave velocity (Vp ) ratio, sound attenuation (k), shear wave velocity (Vs ), porosity, density, and mean grain size Vp ratio In situ 1.020

k Laboratory 1.018

Vs

Porosity

Density

Mean grain size

In situ (dB/m/kHz)

Laboratory (dB/m/kHz)

(m/s)

(%)

(g/cm3 )

(P)

0.32

0.83

50.8

58.4

1.76

6.50

MARGO 2993 23-4-02

K.B. Briggs et al. / Marine Geology 182 (2002) 141^159

model and is adopted for the baseline model as well to ensure consistency between the two models. Either procedure, however, leads to the same result, to be discussed later: continuous £uctuations in density and sound speed are too weak to account for observed scattering levels. The correlation length was given a value of 4 cm in accordance with the model ¢t to the data. Although the ¢t appears to be poor for lags greater than 5 cm, the data have little statistical signi¢cance in that region as shown by the 90% con¢dence intervals. These con¢dence intervals were generated by subjecting synthetic pro¢le data (generated via a stochastic ¢rst-order autoregressive algorithm) to the same covariance estimation as applied to the actual data. The 90% con¢dence intervals are based upon 100 such Monte Carlo simulations. Also

151

shown in Fig. 8 are the Monte Carlo realizations that most closely matched each of the data types. While the data fall slightly beyond the 90% con¢dence interval in some cases, it can be seen that model results very similar to the data can be found within 100 realizations. We have ¢tted both the sediment compressional wave velocity ratio and density ratio data with the same correlation length (4 cm) though better ¢ts could have been obtained if this constraint were not used. This constraint is assumed in most prior acoustic modeling work, and is supported by the high correlation observed between sediment compressional wave velocity and density (Hamilton and Bachman, 1982; Richardson and Briggs, 1993). The lack of a better model ¢t is likely due to a combination of systematic measurement errors and fail-

Fig. 8. Correlation vs. lag for sound velocity (top), density ratio determined from gravimetric measurements (middle), and density ratio determined from CT measurements (bottom). Also shown are curves representing the ¢rst-order autoregressive model, 90% con¢dence intervals obtained by Monte Carlo runs of the model, and points from particular Monte Carlo runs that are similar to the data.

MARGO 2993 23-4-02

152

K.B. Briggs et al. / Marine Geology 182 (2002) 141^159

ure of the data to conform to the ¢rst-order autoregressive model. Two possible sources of systematic error are alteration of sediment properties in the course of core sampling and smearing of data due to ¢nite spatial resolution. The CT and sediment compressional wave velocity data have approximate resolutions of 2 mm and 1 cm, respectively, while the gravimetric data have 2-cm resolution. The CT and sediment compressional wave velocity data were in close agreement with regard to correlation length and were therefore given priority in the ¢t to determine correlation length. This ¢tting process simply consisted in adjustment of the correlation length of the Monte Carlo model to the point where the CT and velocity data remained within the 90% con¢dence interval in the 0^5-cm lag region while the gravimetric data were at the lower edge of this interval. The Monte Carlo simulations show that the autoregressive model is satisfactory for scales of 2 mm to 5 cm but also shows that the data are insu⁄cient to support this model at longer scales. This is not a problem in the present context as the acoustic wavelength is about 3.8 cm and scales signi¢cantly larger do not play a prominent role in scattering, at least in the perturbation models employed here. To conclude, the availability of high resolution CT density data has con¢rmed previous estimates of sediment £uctuation statistics with a minor modi¢cation : the correlation length appears to be closer to 4 cm than to 3 cm, the previously reported estimate (D. Jackson et al., 1996), although the older value is within the error bounds set by Monte Carlo simulations. 3.2. Stereo photogrammetric data The averaged roughness power spectrum for the sea £oor at the experiment site appeared to ¢t a linear regression of log spectral density (dB cm3 ) on log spatial frequency (1/cm) of slope 32.29 and intercept 2.092U1033 cm3 (Jackson et al., 1996a). The averaged power spectrum, which spanned a spatial wavelength range from less than a cm to just beyond 53 cm, fell within the 95% statistical con¢dence limits of the regression line except at spatial wavelengths above 25

cm and near 4 cm. Because the largest deviation from the power-law ¢t exists at the longest wavelengths and is consistent with spectrum ‘roll o¡’ at low spatial frequency (Briggs, 1989), the powerlaw ¢t is judged to be quite reasonable. Most importantly, the measured spectra include information at the high spatial frequencies of acoustic interest corresponding to the Bragg wavelength near 2 cm and beyond. The roughness spectrum is sensitive to subtle di¡erences in microtopography. This sensitivity was demonstrated at the experiment site by remeasuring roughness from the same sea £oor after being physically smoothed by divers. The spectrum calculated from the physically altered sea £oor had a statistically steeper slope (32.60) and a depressed intercept (0.725U1033 cm3 ) as a result of the lack of high spatial-frequency roughness. The two average spectra were shown to be signi¢cantly di¡erent by an analysis of covariance that tests the di¡erence between the slopes of the regression lines (Sokal and Rohlf, 1969). Each regression ¢t was made from 24 measurements and tested at the K 6 0.05 level of signi¢cance. 3.3. Acoustic data The acoustic measurements include both monostatic and bistatic geometry. The monostatic geometry, with transmitter and receiver at the same location, produced the scattering strength data shown in Fig. 9. These data are averages over a single scan of the BAMS system, taken before objects were placed on the sea£oor as part of a target scattering study. Averaging included the entire 360‡ scan interval, as no anisotropy was evident in the data. Together with the baseline model curve shown, Fig. 9 replicates the model^ data comparison reported in Jackson et al. (1996a) except for a slight shift in the data resulting from improved directivity corrections in processing. The vertical bars indicate systematic errors due to possible 1‡ uncertainty in array pointing angle and 2-dB uncertainty in transducer sensitivity and receiver gain. Statistical errors and other known systematic errors are smaller and are not shown. The baseline model and other models will be discussed in Section 4.

MARGO 2993 23-4-02

K.B. Briggs et al. / Marine Geology 182 (2002) 141^159

153

Fig. 9. Backscattering strength data at 40 kHz compared with the baseline and strati¢ed models. The volume and roughness contributions are shown separately for the baseline model, illustrating the dominance of roughness scattering.

The measured bistatic scattering strength is a function of the triplet of angles de¢ned in Fig. 2. Bistatic data from other sites have been previously (Williams and Jackson, 1998) displayed via three-dimensional plots. However, a simpler view of the data will be used here. All data for incident and scattering angles falling within speci¢ed angular bins were grouped and are plotted in Fig. 10. The points shown are averages over 5‡ azimuthal bins including data points from separate data subsets (as de¢ned in Section 2.3). A mean value was determined for the data in each bin and a 90% con¢dence interval (indicated by the vertical line through each point) was established assuming that the intensity and thus the scattering strength were independent samples from a chi-squared distribution (Ulaby et al., 1982). The data in the vicinity of the ‘specular’ direction (ai = as , Ps = 0) were not obtainable in previous experiments (Williams and Jackson, 1998). The predictions of the ‘baseline’ model, to be discussed, are also plotted for the lower and upper ends of the angular bins. In the top/left panel of Fig. 10, for example, the upper curve is for ai = as = 15‡ and the lower curve

is for ai = as = 5‡. This technique eliminates data where the incident and scattering angles are not similar but facilitates comparisons of data and models. Certain features are evident in the data. Scattering strength shows a prominent peak in the specular direction, the direction of re£ection that would result if the sea£oor were perfectly £at. Except for this peak, the data show only a slight angular dependence in the form of a slow oscillation as a function of the bistatic angle, Ps .

4. Model^data comparisons In three acoustic models to be examined, the scattering cross section is decomposed into an interface roughness component and a volume heterogeneity component. The ‘baseline’ model is representative of much of the work seen in prior literature and is de¢ned by Williams and Jackson (1998). This model assumes the average sediment properties have no vertical gradients, i.e., vertical strati¢cation is ignored, and sur¢cial values are

MARGO 2993 23-4-02

154

K.B. Briggs et al. / Marine Geology 182 (2002) 141^159

Fig. 10. Bistatic scattering strength data at 40 kHz compared with baseline model predictions. The upper and lower model curves correspond to the upper and lower extremes of the grazing angle ranges given in each panel.

used at all depths (see Fig. 7). The interface scattering cross section is formed by smooth interpolation between the Kirchho¡ cross section near the specular direction and the small-roughness perturbation-theory cross section elsewhere. The volume scattering cross section is based entirely on perturbation theory, but neglects half-space e¡ects caused by the truncation of heterogeneity at the sediment^water interface. The ‘half-space’

model (Ivakin, 1984; Jones and Jackson, 1997; Jones, 1999) includes this e¡ect in volume perturbation theory, but does not allow layering. The ‘strati¢ed’ model of Ivakin (1994a,b, 1998a,b) uses small-roughness perturbation theory to treat scattering by rough interfaces separating homogeneous strata. It is related to, but more general than, the models of Lyons et al. (1994) and Moe and Jackson (1994). In the present work, the

Table 2 Values of parameters used in the perturbation models Model type Vp ratio

b ratio

cb lc W (g/cm3 ) (cm)

N

Roughness spectral slope (U1033 )

Roughness spectral intercept

1.475 Fig. 7

0.025 0.025

9.15 9.15

32.29 32.29

0.002092 0.002092

(cm3 ) Baseline Strati¢ed

1.0 Fig. 7

4.00 4.00

31.31 31.31

Sediment compressional wave speed (Vp ) ratio, and density (b) ratio parameters are changed in the strati¢ed model. Fig. 7 depicts the Vp and b ratios as a function of sediment depth in the strati¢ed model. c b is the normalized (gravimetric) density standard deviation, lc is the density correlation length from Fig. 8, W is the ratio of compressibility to density £uctuations and N is the compressional wave loss.

MARGO 2993 23-4-02

K.B. Briggs et al. / Marine Geology 182 (2002) 141^159

piecewise linear ¢ts to compressional wave velocity ratio and density ratio shown in Fig. 7 are used as inputs (Table 2). All other parameters are assumed to be depth independent. In the case of compressional wave loss (N) this assumption is reasonable, as the model is rather insensitive to this parameter. In the case of £uctuation statistics, this assumption is dictated by the lack of su⁄cient data to estimate depth dependence. The models require an additional parameter, W, the ratio of compressibility £uctuations to density £uctuations, which are assumed to be perfectly correlated. We adopt the depth-independent value W = -1.31 calculated by D. Jackson et al. (1996). 4.1. Baseline model For the baseline model, which cannot deal with strati¢cation, the compressional wave velocity and density ratios were assigned the sur¢cial values of 1.0 and 1.475, respectively (Fig. 7). A comparison

155

of this model with backscattering data shows that the model matches the level of scattering within a few dB but shows less dependence on grazing angle than the data (Fig. 9). Two curves are shown for the baseline model, one representing the contribution of volume scattering and the other giving the contribution of roughness scattering. It can be seen that the model predicts that roughness scattering is dominant. Fig. 10 compares the baseline model with bistatic scattering data. An initial examination of Fig. 10 indicates good overall agreement between the data and the baseline model. Close inspection of Fig. 10, however, reveals small but systematic di¡erences. First, the data points in the top/right panel seem to have an oscillation not seen in the model in the region 70‡ 6 P 6 180‡. Second, in the same panel, the model seems to overpredict the scattering cross section in the region 30‡ 6 P 6 70‡. Finally, there is some indication in the bottom two panels that the model underpredicts the scattering in the re-

Fig. 11. Comparison of bistatic volume scattering predictions of the baseline and half-space models for a frequency of 40 kHz and incident grazing angle of 20‡ showing that half-space e¡ects do not enhance volume scattering su⁄ciently to compete with roughness scattering.

MARGO 2993 23-4-02

156

K.B. Briggs et al. / Marine Geology 182 (2002) 141^159

gion 130‡ 6 P 6 180‡ for the higher grazing angles of those panels. It is worthwhile to remember that the model has no free parameters, but these di¡erences may indicate that some details of scattering are not properly modeled.

comparison with that in other sites covered by analogous types of sediments (see, e.g., Ye¢mov et al., 1988) and having signi¢cant volume scattering. 4.3. Strati¢ed model

4.2. Half-space model Because the baseline model neglects half-space e¡ects in its treatment of volume scattering, we compare the baseline and half-space space models for bistatic scattering (Fig. 11). Although halfspace e¡ects elevate the volume scattering contribution near the specular direction, the e¡ect is too small to compensate for the dominance of interface scattering. This supports the earlier conclusion of D. Jackson et al. (1996). Dominance of interface scattering at this site is rather surprising, given the low bulk density of the sediment, typical of silty mud. However, it should be mentioned that the spectral strength of volume £uctuations in this site was found to be relatively weak in

If volume scattering is negligible, the modest discrepancies between the baseline model and the data may lie in the treatment of roughness scattering. It is possible that interference e¡ects caused by refraction in the upper layer of the sediment cause oscillations in the angular dependence of scattering strength (Ivakin, 1986, 1989, 1994a,b, 1998b; Moe and Jackson, 1994). Fig. 9 includes a curve for the strati¢ed model in the backscattering case. The slight angular ‘bump’ is indeed a result of interference, but it worsens, rather than improves, the model^data ¢t. We have also considered scattering from the interface at 6-cm depth, but plausible guesses at the roughness of this interface fall far short of changing the

Fig. 12. Comparison of bistatic scattering predictions of the baseline and strati¢ed models for a frequency of 40 kHz and an incident grazing angle of 20‡. In the right-hand plot, the two model curves are indistinguishable.

MARGO 2993 23-4-02

K.B. Briggs et al. / Marine Geology 182 (2002) 141^159

model prediction. This is because there is little acoustic contrast across this interface. The backscattering bump is a robust feature of the strati¢ed model that persists when model predictions are averaged over likely lateral variations in parameters or when details of the vertical pro¢les for density and sound velocity ratios are altered within experimental uncertainty. Fig. 12 compares the baseline model with the strati¢ed model for the bistatic case. According to the model, the observed strati¢cation has little e¡ect on bistatic scattering and does not cause oscillations with respect to the bistatic angle.

5. Discussion The CT data have led to a re¢nement in the geoacoustic model originally developed for the Dry Tortugas site, but the resulting acoustic predictions are changed very little, even when the e¡ects of strati¢cation are included. This outcome is signi¢cant because it implies that the inverse is true: acoustic sensing of the sea £oor at this frequency would not provide de¢nition of the ¢nescale £uctuations of the geoacoustic properties in the sediment volume. The primary modeling result is that scattering due to roughness of the sediment^water interface dominates scattering due to volume heterogeneity, as de¢ned here. Although the acoustic models match the data reasonably well in terms of scattering level and approximate angular dependence, certain details in the data are marginally di¡erent than the model predictions. It should be noted that the volume scattering component of the model considered here only treats continuous spatial variations in sediment compressional wave speed and density. Such variations in these parameters are due to the presence of burrow structures, open (water-¢lled) or in¢lled with sediment. Coarse skeletal material (i.e., mollusk shells, urchin tests, coral rubble), however, is another likely source of scattering that may not be adequately characterized by ¢ne-scale measurements of sediment compressional wave speed and density. Scattering due to discrete carbonate fragments has not been considered, but a crude calculation shows that a shallow layer of 10^20 gas-

157

tropod shells per m2 of the size seen in the CT images could compete with interface roughness as a source of backscattered energy. This type of scattering would tend to ‘¢ll in’ angular regions where interface scattering is relatively weak. In such a scenario, scattering from shells might obscure the bump predicted by the strati¢ed model. Discrete scatterers should be considered in future modeling e¡orts (see Bunchuk and Ivakin, 1989). It is the generation and maintenance of biogenic structures such as burrows that control the physical and acoustic properties of the sediment at Dry Tortugas. Localized, time-dependent variations in acoustic backscattering intensity have been linked with measurements of changing porosity (and thus density) and sound velocity (Briggs and Richardson, 1997). Moreover, X-radiographs of these areas of dilated sediment display burrow networking and presence of burrowing crustaceans. Because these burrowers are operationally restricted to the uppermost 5^10 cm of sediment, their reworking activities create and maintain a pronounced gradient in sediment density and, consequently, sediment sound velocity as depicted in Fig. 4. The time scale over which decorrelation of acoustic backscattering response due to bioturbation occurs at any particular spot at Dry Tortugas is on the order of 2 days and the decorrelation within the ensoni¢ed area is about 23^24% complete after 2.25 days (see ¢g. 8 in Briggs and Richardson, 1997). Thus, the top few cm of sediment throughout the area of study are reworked to an acoustically detectable extent in the course of weeks. The dynamic nature of the sea £oor as a result of intensive bioturbation may provide the strong gradient capable of refracting acoustic energy and creating interference e¡ects in the model (though not seen in the data). Furthermore, the intensive reworking of the sediment by burrowing organisms is generating the interface roughness that is the dominant cause of acoustic scattering from the sea £oor. From diver observations as well as stereo photogrammetry, the distinguishing roughness features are identi¢ed as the sediment mounds created by crustaceans, polychaete worms, and heart urchins (D’Andrea and Lopez, 1997). Although the mean

MARGO 2993 23-4-02

158

K.B. Briggs et al. / Marine Geology 182 (2002) 141^159

height of the biogenic roughness features is modest (0.66 cm) and the sediment comprising the volcano-shaped mounds that predominate among the roughness features necessarily has a low bulk density, the grain density of carbonate skeletal material is relatively high (mean: 2.76 g/cm3 ) (Wright et al., 1997; Stephens et al., 1997). Apparently, this reworked sediment provides enough impedance contrast with the overlying water to account for the dominance of interface scattering over volume scattering. With regard to inversions to determine sediment properties, our results show that scattering is sensitive to sur¢cial properties (density and sound velocity). Although the modeling results indicate that strati¢cation should be evident in a small but persistent backscattering feature, this feature is not seen and may be obscured by scattering due to shells. The contribution that shells and shell fragments make to acoustic scattering, however, is not quanti¢ed adequately by sediment sound speed and bulk density measurements, even at relatively high resolution (2 mm).

Acknowledgements We wish to thank Michael Richardson, Richard Ray, David Young, Nancy Carnaggio, and Kevin Shea for help in the shipboard and/or laboratory operations. Russell Light, Le Olsen, and Vern Miller were responsible for the design and deployment of the acoustic apparatus. This work was funded by the Coastal Benthic Boundary Layer program sponsored by the Office of Naval Research, Program Element No. 601153N, managed by the Naval Research Laboratory, M.D. Richardson, chief scientist. The work of A.N. Ivakin was funded by the Office of Naval Research. The NRL contribution number is NRL/JA/7431-00-0008.

References Brandes, H.G., Silva, A.J., Walter, D.J., 2002. Geo-acoustic characterization of calcareous seabed in the Florida Keys. Mar. Geol., this issue.

Briggs, K.B., 1989. Microtopographical roughness of shallowwater continental shelves. IEEE J. Oceanic Eng. 14, 360^ 367. Briggs, K.B., 1994. High frequency acoustic scattering from sediment interface roughness and volume inhomogeneities. Ph.D. dissertation, University of Miami, Coral Gables, FL, 143 pp. Briggs, K.B., Percival, D.B., 1997. Vertical porosity and velocity £uctuations in shallow-water sur¢cial sediments and their use in modeling volume scattering. In: Pace, N.G., Pouliquen, E., Bergem, O., Lyons, A.P. (Eds.), High Frequency Acoustics in Shallow Water. NATO SACLANT Undersea Res. Ctr., La Spezia, pp. 65^73. Briggs, K.B., Richardson, M.D., 1997. Small-scale £uctuations in acoustic and physical properties in sur¢cial carbonate sediments and their relationship to bioturbation. GeoMar. Lett. 17, 306^315. Briggs, K.B., Jackson, P.D., Holyer, R.J., Flint, R.C., Sandidge, J.C., Young, D.K., 1998. Two-dimensional variability in porosity, density, and electrical resistivity in Eckernfo«rde Bay sediment. Cont. Shelf Res. 18, 1939^1964. Bunchuk, A.V., Ivakin, A.N., 1989. Energy characteristics of an echo signal from discrete scatterers on the ocean bottom. Sov. Phys. Acoust. 35, 5^11. D’Andrea, A.F., Lopez, G.R., 1997. Benthic macrofauna in a shallow water carbonate sediment: major bioturbators at the Dry Tortugas. GeoMar. Lett. 17, 276^282. Hamilton, E.L., Bachman, R.T., 1982. Sound velocity and related properties of marine sediments. J. Acoust. Soc. Am. 72, 1891^1904. Hines, P.C., 1990. Theoretical model of acoustic backscattering from a smooth seabed. J. Acoust. Soc. Am. 88, 325^334. Ivakin, A.N., Lysanov, Yu.P., 1981. Theory of underwater sound scattering by random inhomogeneities of the bottom. Sov. Phys. Acoust. 27, 61^64. Ivakin, A.N., 1981. Sound scattering by multi-scale bottom inhomogeneities. Oceanology 21, 26^27. Ivakin, A.N., 1982. Sound Scattering and Re£ection by Inhomogeneities of a Seabed. Ph.D. Thesis, Andreev Acoustics Institute, Moscow (in Russian). Ivakin, A.N., 1983. Sound scattering by random volume inhomogeneities and small surface roughness and of underwater ground, Voprosy sudostroeniya (in Russian). Akustika 17, 20^25. Ivakin, A.N., 1984. Sound scattering by volume inhomogeneities of strongly absorbing media. Andreev Acoust. Inst. Sci. Report (in Russian). Ivakin, A.N., 1986. Sound scattering by random inhomogeneities of strati¢ed ocean sediments. Sov. Phys. Acoust. 32, 492^496. Ivakin, A.N., 1989. Backscattering of sound by the ocean bottom. Theory and experiment. In: Brekhovskikh, L.M., Andreeva, I.B. (Eds.), Acoustics of the Ocean Medium. Nauka, Moscow, pp. 160^169 (in Russian). Ivakin, A.N., 1994a. Modelling of sound scattering by the sea £oor. J. Phys. IV Coll. C5 4, 1095^1098. Ivakin, A.N., 1994b. Sound scattering by rough interfaces of

MARGO 2993 23-4-02

K.B. Briggs et al. / Marine Geology 182 (2002) 141^159 layered media. In: Crocker, M.J. (Ed.), Third International Congress on Air- and Structure-Borne Sound and Vibration, International Publications, Auburn University, vol. 3, pp. 1563^1570. Ivakin, A.N., 1998a. A uni¢ed approach to volume and roughness scattering. J. Acoust. Soc. Am. 103, 827^837. Ivakin, A.N., 1998b. Models of sea£oor roughness and volume scattering. In: Proc. Oceans ’98, IEEE Publ. No. 98CH36259, vol. 1, pp. 518^521. Ivakin, A.N., 1998c. Models for acoustic scattering from the ocean bottom: State of the art. In: Brekhovskikh, L.M. (Ed.), School-Seminar, Ocean Acoustics. GEOS, Moscow, pp. 84^91 (in Russian). Jackson, D.R., Winebrenner, D.P., Ishimaru, A., 1986. Application of the composite roughness model to high-frequency bottom backscattering. J. Acoust. Soc. Am. 79, 1410^1422. Jackson, D.R., Briggs, K.B., 1992. High-frequency bottom backscattering: roughness vs. sediment volume scattering. J. Acoust. Soc. Am. 92, 962^977. Jackson, D.R., Briggs, K.B., Williams, K.L., Richardson, M.D., 1996. Tests of models for high-frequency sea-£oor backscatter. IEEE J. Oceanic Eng. 21, 458^470. Jackson, P.D., Briggs, K.B., Flint, R.C., 1996. Evaluation of sediment heterogeneity using micro-resistivity imaging and X-radiography. GeoMar. Lett. 16, 219^226. Jackson, P.D., Flint, R.C., Briggs, K.B., Holyer, R.J. and Sandidge, J.C., 2002. Two- and three-dimensional heterogeneity in carbonate sediments using resistivity imaging. Mar. Geol., this issue. Jones, C.D., Jackson, D.R., 1997. Temporal £uctuations of backscattered ¢eld due to bioturbation in marine sediments. In: Pace, N.G., Pouliquen, E., Bergem, O., Lyons, A.P. (Eds.), High Frequency Acoustics in Shallow Water. NATO SACLANT Undersea Res. Ctr., La Spezia, pp. 275^282. Jones, C.D., 1999. High-Frequency Acoustic Volume Scattering from Biologically Active Marine Sediments. Ph.D. Thesis, University of Washington, Seattle. Kuo, E.Y., 1964. Wave scattering and transmission at irregular surfaces. J. Acoust. Soc. Am. 36, 2135^2142. Lyons, A.P., Anderson, A.L., Dwan, F.S., 1994. Acoustic scattering from the sea£oor: modeling and data comparisons. J. Acoust. Soc. Am. 95, 2441^2451. Moe, J.E., Jackson, D.R., 1994. First-order perturbation solution for rough surface scattering cross section including the e¡ect of gradients. J. Acoust. Soc. Am. 96, 1748^1754. Mourad, P.D., Jackson, D.R., 1989. High frequency sonar equation models for bottom backscatter and forward loss. In: Proc. Oceans ’89. IEEE Pub. No. 89CH2780^5, pp. 1168^1175. Pace, N.G., 1994. Low frequency backscatter from the seabed. Proc. Inst. Acoust. 16, 181^188. Richardson, M.D., 1997. In-situ, shallow-water sediment geoacoustic properties. In: Zhang, R., Zhou J. (Eds.), Shal-

159

low-Water Acoustics. China Ocean Press, Beijing, pp. 163^ 170. Richardson, M.D., Briggs, K.B., 1993. On the use of acoustic impedance values to determine sediment properties. In: Pace, N.G., Langhorne, D.N. (Eds.), Acoustic Classi¢cation and Mapping of the Seabed. Institute of Acoustics, Bath, pp. 15^25. Richardson, M.D., Lavoie, D.L., Briggs, K.B., 1997. Geoacoustic and physical properties of carbonate sediments of the Lower Florida Keys. GeoMar. Lett. 17, 316^324. Sokal, R.R., Rohlf, F.J., 1969. Biometry. Freeman, San Francisco, 776 pp. Stanic, S., Briggs, K.B., Fleischer, P., Ray, R.I., Sawyer, W.B., 1988. Shallow-water high-frequency bottom scattering o¡ Panama City, Florida. J. Acoust. Soc. Am. 83, 2134^2144. Stanic, S., Goodman, R.R., Briggs, K.B., Chotiros, N.P., Kennedy, E.T., 1998. Shallow-water bottom reverberation measurements. IEEE J. Oceanic Eng. 23, 203^210. Stephens, K.P., Fleischer, P., Lavoie, D., Brunner, C., 1997. Scale-dependent physical and geoacoustic property variability of shallow-water carbonate sediments from the Dry Tortugas, Florida. GeoMar. Lett. 17, 299^305. Sternlicht, D.D., 1999. High Frequency Acoustic Remote Sensing of Sea£oor Characteristics. Ph.D. Thesis, University of California, San Diego. Ulaby, F.T., Moore, R.K., Fung, A.K., 1982. Microwave Remote Sensing: Active and Passive. Addison-Wesley, Reading, MA, pp. 486^488. Urick, R.J., 1983. Principles of Underwater Sound. McGrawHill, New York, Ch. 8. Wheatcroft, R.A., 1994. Temporal variation in bed con¢guration and one-dimensional bottom roughness at the mid-shelf STRESS site. Cont. Shelf Res. 14, 1167^1190. Williams, K.L., Jackson, D.R., 1997. Bistatic bottom scattering: experimental results and model comparison for a carbonate sediment. In: Pace, N.G., Pouliquen, E., Bergem, O., Lyons, A.P. (Eds.), High Frequency Acoustics in Shallow Water. NATO SACLANT Undersea Res. Ctr., La Spezia, pp. 601^605. Williams, K.L., Jackson, D.R., 1998. Bistatic bottom scattering: model, experiments, and model/data comparison. J. Acoust. Soc. Am. 103, 169^181. Wright, L.D., Friedrichs, C.T., Hepworth, D.A., 1997. E¡ects of benthic biology on bottom boundary layer processes, Dry Tortugas Bank, Florida Keys. GeoMar. Lett. 17, 291^298. Yamamoto, T., 1995. Velocity variabilities and other physical properties of marine sediments measured by crosswell acoustic tomography. J. Acoust. Soc. Am. 98, 2235^2248. Yamamoto, T., 1996. Acoustic scattering in the ocean from velocity and density £uctuations in the sediments. J. Acoust. Soc. Am. 99, 866^869. Ye¢mov, A.V., Ivakin, A.N., Lysanov, Yu.P., 1988. A geoacoustic model of scattering by the ocean bottom based on deep sea drilling data. Oceanology 28, 290^293.

MARGO 2993 23-4-02