IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 38, NO. 5, SEPTEMBER 2000 2419

Communications______________________________________________________________________

Seabottom Characterization Using MultibeamEchosounder Angular Backscatter: An Application of the

Composite Roughness Theory

Bishwajit Chakraborty, Hans Werner Schenke, Vijay Kodagali, andRick Hagen

Abstract—Composite roughness theory is used to characterize SouthernOcean bottom backscatter (multibeam) data. Spectral parameters basedon Helmholtz-Kirchhoff’s theory [1] are determined from measured near-normal incidence values. A splicing technique using Rayleigh-Rice theory[2] is employed beyond 20 incidence angles. Estimated roughness param-eters for six deep ocean areas correlate with geology.

Index Terms—Angular backscatter, composite roughness theory, multi-beam echosounder, roughness, seabottom characterizations.

I. INTRODUCTION

Seabottom geomorphologic studies using angular backscatterinformation from multibeam echosounding systems reveal significantresults related to seabottom geological processes ([3] and referencestherein). Jacksonet al., [1] had proposed simultaneous applicationof the two backscatter theories related to the large and small-scaleroughness to be used in the composite roughness theory. The splicingtechnique between the two theories (Helmholtz-Kirchhoff’s andRayleigh-Rice) is employed at the incidence angle of 20�. Normally,the splicing technique works well when three conditions (discussedin Section III) in connection with the bottom roughness are satisfied.Otherwise, a filtering technique is required to be employed. Inorder to employ splicing technique between the two theories in thecomposite roughness theory, it is necessary to acquire multibeamdeep ocean seabottom backscatter data of higher angular range (>

20� incidence angle). However, with the commercial availability ofthe multibeam-Hydrosweep system [4], which operates at a 45� halffan width, it has become possible to employ splicing technique at 20�

incidence angles to the multibeam backscatter data collected fromdifferent seabed areas of the Southern Ocean [5], [6]. In this paper,deep seabottom interface (power spectral parameters) and volumeroughness parameters are presented for six geologically different areasfrom the Southern Ocean using the composite roughness theory. Adetailed study in connection with the employed splicing technique isalso carried out.

II. M ULTIBEAM -HYDROSWEEPANGULAR BACKSCATTER DATA

A cruise of RV Polarstern (ANT XI/IV) was planned on a transectacross the frontal system of the Antarctic circumpolar current, in theAtlantic and Indian Ocean sector of the Southern Ocean. During thiscruise (conducted by the Alfred Wegener Institute for Polar and Ma-rine Research, Bremerhaven, Germany), which was undertaken from

Manuscript received April 26, 1999; revised December 13, 1999. This workwas supported by the European Community Marie Curie Fellowship (BC/VK).

B. Chakraborty and V. Kodagali are with the National Institute of Oceanog-raphy, Goa, India.

H. W. Schenke is with the Alfred Wegener Institute for Polar and MarineResearch, Bremerhaven, Germany.

R. Hagen is with the Seafloor Surveys International, Seattle, WA 98121 USA(e-mail: bishwajt@csnio.ven.nic.iw).

Publisher Item Identifier S 0196-2892(00)06229-X.

Capetown to Capetown (March 30, 1994–May 20, 1994) [7], a bottombackscatter study was carried out in sediment-sampled areas while theship was stopped. Study locations and general bathymetry is given inFig. 1.

The multibeam-Hydrosweep system operates at 15.5 kHz and adetailed technical description of the system is given in [4]. Processingof the acquired backscatter data were carried out using an algorithmNRGCOR (developed at MPL, Scripps Institution of Oceanography,and STN Atlas Elektronik, GmbH) [3]. Measured backscatteringstrength (dB) for each beam has been binned (1� angular bins) andaveraged over the number of samples in each bin (Fig. 2). Datacollection area A lies close to the eastern end of the Agulhas basinnear the Southwest Indian Ridge, and B is situated near the extremesoutheast end of the Southwest Indian Ridge. Area C lies close to theeastern part of the Enderby Abyssal plain. Similarly, area D lies closeto the northern flank of the Kainan Maru seamount at the CosmonautSea. The Kainan Maru seamount (area E) backscatter data werecollected at its summit. Similarly, area F exists near the Meteor Rise,north of the polar front area. In order to compute angular backscatterstrength, varying acoustic ping numbers: 774, 469, 724, 885, 444, and617 were collected for the areas of A, B, C, D, E, and F, respectively.Similarly, the seafloor in the areas A, B, C, D, E, and F lie at thedepths around 3510 m, 4420 m, 5280 m, 5060 m, 1700 m, and 4100m, respectively. The surficial sediment (0–2 cm) grain size analysesfrom the areas A, B, C, D, E, and F reveal (14.7% sand, 26.8% silt,and 58.5% clay), (29.5% sand, 61.3% silt, and 7.4% clay), (5.8%sand, 77.8% silt, and 16.1% clay), (2.5% sand, 53.1% silt, and 44.3%clay), (92.3% fine sand), and (18.8% sand, 35.3% silt, and 45.7%clay), respectively. Necessary sediment to seawater sound speed anddensity ratios are used from the estimated sediment grain size [8], andreflection coefficients are computed for modeling.

III. B ACKSCATTER MODELING USING THE COMPOSITEROUGHNESS

THEORY

We assume that the backscattering strength in dB [=10 � log10

(backscattering cross section per unit area per unit solid angle)], isequivalent to the sum of the contributions from the surface rough-ness and volume inhomogeneities. For an interface backscatteringstrength within the composite roughness theory, Jacksonet al. [1]had applied power law properties of the seafloor roughness spectrumto a Helmholtz-Kirchhoff’s formulation at steeper incidence angles[1, (38)]. In roughness power spectrum (W ), the terms� and� arerelated through the relationsW (k) = �k� , wherek is the spatialwavenumber, and is the spectral exponent, which is again related tothe term� as: [=( 2) � 1]. Also, � is known as spectral strength.Minimum mean square error (MMSE) criterion between the measuredbackscatter strength values (3� to 10� angles) and seabottom interfacebackscatter strength (Helmholtz-Kirchhoff’s theory) is employed. Avisual examination to observe the match between the theoretical andmeasured backscattering strengths is performed. In order to determineaccurate, unbiased power law parameters, we have avoided using thebackscattering strength values from beam overlapping zones of themultibeam-Hydrosweep system [>10� incidence angle, due to Rota-tional Directional Transmission (RDT)] and fluctuating backscattervalues near the normal incidence angles for curve fitting [3]–[6]. Also,because of the RDT, the measured angular backscattering strength datafrom six areas indicate a steep fall beyond the 30� incidence angles

0196–2892/00$10.00 © 2000 IEEE

2420 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 38, NO. 5, SEPTEMBER 2000

Fig. 1. Southern Ocean backscatter study sites and general bathymetry (1000m contour interval).

[5]. In view of the unavailability of a calibration facility for transducerarray size (�3 m for the multibeam-Hydrosweep system), relativevalues of the measured backscatter strengths are used. The structurefunction,D(r) [=C2

hr2�], is a function of the power law parameters.

Using interface roughness parameters (� and�), a parameter of thestructure function,Ch [(6) of [1]] is computed (dimensioned in unitsof cm(1��)). Conversion of the termCh in meter scale is being madeby using a multiplying factor [10�2(1��)] [3]. The root mean square(RMS) height difference(Chr

�) of the seafloor as a function of thehorizontal distance (r in m) is being presented for six geological areas.

For a small-scale part of the seafloor, the composite roughnessmodel uses the Rayleigh-Rice theory (beyond incidence angleof 20�). It requires that the term (2Kahs Sin �) related to thesmall-scale RMS relief,hs: [h2s = (2��k2� c )=( � 2)] should bemuch smaller(<1:0). The splicing angle�, is assumed to be 70�,grazing angle i.e., 20�-incidence angle. The termKa is an operatingwavenumber. For a large-scale part of the composite roughnesstheory, the RMS large-scale slopes: [s2 = (2��k4�

c )=(4 � )],and radius of curvatureR: [R�2 = (2��k6�

c )=(6 � )] shouldfollow certain conditions: [s < 0:1; fh00 � (2Kahs Sin �)g < 1.0,andfR00 � (2=KaRSin3�)g < 1:0]. The term ‘kc’ is the cutoffwavenumber. At the very first step, the cutoff wavenumber ‘kc’ ischosen to be equivalent to the2KaCos�, i.e., Bragg wavenumber.Along with the RMS slope of the seafloor, it is also essential tocompute RMS relief of the small-scale surfacehs and the radius ofcurvatureR of the bottom topography. Also, the conditions givenabove are required to be satisfied for a successful application of thecomposite roughness theory. The computed large-scale RMS slopeangle (s) is used to average for splicing [ (21) of [1]]. For large-scaleRMS slope,s > 0.1, the employed splicing is generally improper

for a Bragg wavenumber [1]. In such cases, a filtering techniqueis to be employed for proper splicing. For filtering technique, thecutoff wavenumberkc is shifted toward the lower value whichgives low s. And, higher values of thehs andR are obtained withthe low cutoff wavenumber. At low cutoff wavenumber, the givenconditions (s; h00, andR00) based on the estimated terms (s; hs, andR) are required to be satisfied. Using low value of the large-scaleRMS slope (s) for the averaging of the Rayleigh-Rice backscatterexpression [(16) of [1]], accurate splicing can be achieved. Theshadowing term is also included. The surface scattering strengthcomponent due to the sediment volume roughness (�v : scatteringcross section per unit solid angle per unit sediment volume) is givenas�vs(�) = f5�v[1 � g2(�)]2 Sin2�g=f�b ln 10Sin(�b)g [1]. Thesubscriptsv ands stand for “volume” and “small-scale,” respectively.Necessary expressions forSin(�b) andg(�) are given in (42) and (43)of [1]. Here,�v=�b (ratio between the volume scattering strength tothe attenuation coefficient) is considered as a free parameter, whichis mentioned as a volume scattering parameter. The validity lies inthe single scattering regime i.e.,(�v=�b) < 0.004. This scatteringterm using volume roughness parameter is used for incidence anglesbetween the 0� and 45�, and the overall scattering term is obtainedby summing up both the interface and volume roughness (the dashedlines in the Fig. 2). The solid lines in this figure represent computedbackscattering strength values based on the model estimated interfaceroughness parameters.

IV. SOUTHERN OCEAN MULTIBEAM BACKSCATTER MODEL STUDY

RESULTS

The roughness parameters of� = 0.54 and� = 0.009, and�v=�b =0.0012, are obtained from area A.The measured data are found to bematching well with the computed values of the backscatter strengthusing estimated roughness parameters (Fig. 2). Like Agulhas plateauarea [5], the computed large-scale RMS slope is found to be equivalentto the 9.8� at Bragg wavenumber (0.44 cm�1). Initial slope values werepresented in radian, and from now on they will be presented in degrees.As already mentioned, the area slope value does not fulfill the essentialconditions of slope (s � 5.72�), whereas the values of theh00 andR00 are equivalent to 0.43 and 0.15, respectively. Changing the cutoffwavenumber toward a lower value (0.14 cm�1), a lower RMS slopevalue (s � 5:72�), small-scale RMS relief (h00 �0.81), and large-scale radius of curvature (R00 �0.03) conditions are computed at 20�,which allows proper splicing between the theories (extended model).The upper sediment consists of foraminiferal nannofossil ooze at thewater depth of 3510 m. The sediment grain size analysis of area Ashows that it is comprised of “silty clay,” i.e., relatively finer sedimentcompared to the Agulhas plateau. The RMS height difference (Chr

�)at 1 m, 100 m, and 1000 m between two points are found to be 0.039m, 0.473 m, and 1.64 m, respectively.

For Area B, the roughness parameters [�; � and (�v=�b)] are foundto be 0.52, 0.02, and 0.0013, respectively. The extended model is alsoused here to combine the curves at 20� incidence angle. The condi-tions related to RMS relief height (h00 �0.65), and large-scale ra-dius of curvatures (R00 �0.23) are found to be satisfied at the Braggwavenumber. Because of higher RMS large-scale slope (s �13.7�), afiltering technique is employed. The RMS slope value (s �1.2�) fora very small cutoff wavenumber (< 0.01 cm�1) is found to be appro-priate for splicing between the theories at 20� incidence angles (Fig. 2).At this cutoff wavenumber, the small-scale RMS relief height conditionis computed to be higher (h00 > 4.05), though the conditions related toradius of curvature (R00 < 0.0008) are much less than required. Byshifting the cutoff wavenumber toward the lower wavenumber end, thelarge-scale conditions are allowed to be satisfied, which occasionally

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 38, NO. 5, SEPTEMBER 2000 2421

Fig. 2. Backscattering strength for measured values (cross lines) and the composite roughness model fitted values from six areas of the Southern Ocean. Thesolid and dashed lines represent backscattering strength values based on the model estimated interface roughness parameters, and overall backscattering strengthvalues (interface and volume roughness parameters), respectively.

cost accuracy criteria necessary for the Rayleigh-Rice approximationsi.e., the value of theh00 becomes higher. The presence of north-southtrending fracture zones in this areas along with the low sediment thick-ness, support the observation that the area possesses relatively higherinterface roughness and low volume roughness parameters for a siltybottom (Fig. 1). The RMS height difference (Chr

�) between the pointsseparated at 1 m, 100 m, and 1000 m are found to be 0.054 m, 0.59 m,and 1.97 m, respectively.

Backscatter modeling results from the Enderby Abyssal plain (AreaC) provide interface roughness:� = 0.84,� = 0.002, and volumeparameter of�v=�b = 0.000 33. The computed interface roughnessvalues are observed to be higher, when compared with data from otherabyssal plain areas. The employed splicing technique shows goodmatching between the theories at 20� incidence angle (Fig. 2). Thesplicing between theories is successful even for the higher RMS slopevalue of (9.91�) at the Bragg wavenumber. Also, the conditions ofRMS relief height (h00 �0.21) and radius of curvature (R00

�0.11)are satisfied. In this area, the application of filtering technique isnot required even for the reported higher RMS slope value. Thesurface layer of the seabottom consists of silt material, which isdiatomaceous ooze. The presence of silt sediment and model resultssuggest either of the two environments. The area may be covered byterrigenous sediment from the nearby Antarctic continental marginsor the roughness may be due to the existence of bottom currents inthis area (Fig. 1). The dominance of silt and sand in any abyssal plainprovince indicate bottom currents which help in forming scour [9].The low value of the volume roughness parameter indicates a lackof sediment inhomogeneity in this area. The RMS height differences(Chr

�) between the points separated at 1.0 m, 100 m, and 1000 m areestimated to be 0.0812 m, 3.88 m, and 26.88 m, respectively.

Area D backscatter data, close to the base of Kainan Maru seamountin the Cosmonaut Sea, give interface roughness parameters:� = 0.86

and� = 0.004. The volume roughness parameter, (�v=�b), is esti-mated to be zero. The sediment grain size analyzes of the surface sed-iment reveal “clayey silt” and, the sediment consists of diatoms inter-mixed with mud. The interface roughness values are higher, as may beinferred from the location of this area, which is close to small canyonsoriginating near the Kainan Maru seamount/Gunnerus Ridge (Fig. 1).The large-scale RMS slope (s) is estimated to be 15.3�, though theh00 andR00 values are satisfying necessary conditions (h00 �0.29 andR00

�0.15). Employing filtering technique, higher value of the RMSslope (s �8.6� is obtained at a very-2 low cutoff wavenumber (�0.01cm�1). Under this condition, no proper matching at the incidence angleof 20� is obtained. The large-scale radius of curvature (R00

� 0:002) issatisfying the necessary conditions. However, the small-scale RMS re-lief is much higher than the required value for this cutoff wavenumber(h00 �7.7). The filtering technique is found to be unsuccessful andsplicing between the theories is impossible for the backscatter dataof this area. The computed backscatter strength values are presented(Fig. 2) using the Helmholtz-Kirchhoff’s interface theory up to the in-cidence angle of 45�. The plotted curve for the interface theory is foundto be matching well up to the incidence angle of 30�. No volume rough-ness plot is presented, since the curve fitted well only with the estimatedinterface roughness parameters. Reported geophysical studies [10], re-veal the existence of north east-south west trending fracture zones inthis area. The RMS height differences (Chr

�) of 0.131 m, 6.8 m, and49 m are obtained between the two separated points of 1.0 m, 100 m,and 1000 m respectively.

The interface roughness parameters obtained from the summit of theKainan Maru seamount (Area E) are:� = 0.2 and� = 0.036. Thevolume roughness parameter (�v=�b) is estimated to be 0.002. Thelarge-scale RMS slope (s) is estimated to be 11.1�, andh00 andR00

values are satisfying necessary conditions (h00 �0.11 andR00�0.21).

The sediment is coarser in this area (92.3% “fine sand”). In view of

2422 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 38, NO. 5, SEPTEMBER 2000

nonavailability of information on similar seabottom in deep ocean, thesediment to seawater sound speed and density ratio data for clayeysand sediment bottom in the deep sea region of the calcareous sediment(Ontong-Java plateau) is being used for modeling [8]. The backscattercurves plotted based on the estimated parameters, fit well within therange of 3� to 25� incidence angle. For this type of hard bottom, themismatch beyond 25� angle may be due to the overlapping beam modetransmissions (RDT) [4]–[6]. Previous estimation of interface rough-ness power spectral parameters using backscatter dataset from this areaindicated possible artifact generations in this hard bottom due to theinherent design difficulty of the multibeam system [5]. The splicingtechnique was found to be unsuccessful for this area data. We have pre-sented the backscatter curve up to 45� for interface roughness param-eters using Helmholtz-Kirchhoff’s theory (Fig. 2). The overall curveincluding volume roughness parameter is also plotted. Extremely lowRMS height difference (Chr

�) between two points separated at 1.0 m,100 m and 1000 m are estimated, which are equivalent to the 0.0262m, 0.0658 m, and 0.104 m, respectively.

The roughness parameters determined for area F (off Meteor Rise),reveal that the area is significantly rough. The interface roughness pa-rameters,� = 0.48 and� = 0.03, and very small sediment volumeroughness parameter (�v=�b = 0.0002) are obtained. From this areaof silty clay, the considered model parameters for diatom are similarto those of Bering and Okhotsk sea [8]. Higher large-scale RMS slopevalue (16.0�), and lower values of the small-scale RMS relief heightand radius of curvature conditions (h00 �0.80 andR00

�0.26) areseen. Though the RMS slope value (s � 5:72�), and radius of cur-vature conditions are found to be satisfied at the lower wavenumbervalue (0.05 cm�1), but splicing technique does not work well for thisRMS slope value. Interestingly, the curves are found to be matching fora very small RMS slope value of (0.103�) at a significantly low valueof the cutoff wavenumber (�0:01 cm�1). At this cutoff wavenumber,higherh00 (�4.93), and lower radius of curvature(R00

�0.008) areobtained. A very-2 low value of the volume roughness from this areasignifies that the area does not contain sediment inhomogeneity. TheRMS height differences(Chr

�) are found to be 0.057 m, 0.518 m, and1.566 m between the points at 1 m, 100 m, and 1000 m, respectively.

V. CONCLUSION

In this communications, the composite roughness model applicationfor extensive deep oceans multibeam-backscatter data sets is being re-ported first time. The model data results reveal some important infor-mation related to the seabottom interface and volume roughness param-eters. The filtering technique employed with splicing at 20� incidenceangle combining two theories (Helmholtz-Kirchhoff’s and Rayleigh-Rice) is successful for three different seabottom provinces (A, B, andF). The splicing technique did not work for the backscatter strength datafrom the Cosmonaut Sea (area D) and Kainan Maru seamount summit(area E). Even for higher estimated slope values (9.91�), no filteringtechnique was required to be applied for the Enderby Abyssal Plain(area C) backscatter data. The sediment volume parameters reportedfrom the areas show significantly low values. The success or failure ofthe splicing technique is difficult to relate with large-scale RMS slope,radius of curvature, and small-scale relief height. The applicability ofthe estimated power law parameters within the spectral regions dependon physiographic provinces. In order to determine seafloor RMS re-lief height and correlation functions, Kirchhoff’s approximations mayprovide accurate results when used within the well-defined parameterregime. We are continuing our study on the same lines to apply Kirch-hoff’s approximations for comparisons with the presently estimated pa-rameters.

ACKNOWLEDGMENT

The authors would like to thank Drs. G. Kuhn, Alfred Wegner In-stitute (AWI), Bremerhaven, Germany, V. Spies, D. Volker (Universityof Bremen, Bremen, Germany), E. Desa, Director, National Instituteof Oceanography, NIO, Goa, India, and D. Fuetterer, Deputy Director,AWI. They also wish to thank the anonymous reviewer for suggestions.

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[10] Y. Nogi, N. Seama, and N. Isezaki, “The direction of magnetic anomalylineations in enderby basin off antarctica,” inRecent Progress inAntarctic Earth Science. Tokyo, Japan: Terra Scientific, 1992, pp.649–654.