High Frequency Roughness Scattering from Various Rough Surfaces: Theory and Laboratory Experiments

Transcription

1 Open Journal of Acoutc, 1,, Publhed Onlne March 1 ( Hgh Frequency Roughne Scatterng from Varou Rough Surface: Theory and Laboratory Experment Vrgne Jaud 1, Jean-Perre Searego, Cedrc Gervae 3, Yann Stephan 4 1 Pave Acoutc, Superor Natonal School of Advanced Technque of Brttany, Bret, France LMA, French Natonal Centre for Scentfc Reearch, Marelle, France 3 GIPSA-LAB, SIGMAPHY, Natonal Center for Scentfc Reearch, Grenoble, France 4 The Naval Hydrographc and Oceanographc Servce, Bret, France Emal: vrgne.jaud@gmal.com Receved December 19, 11; reved January 18, 1; accepted January 3, 1 ABSTRACT The catterng trength of otropc and anotropc rough urface wa expermentally and theoretcally nvetgated for hgh frequence about 5 khz. Empha wa placed on tudyng the repone from three two-dmenonal rough urface whch roughne wa ether otropc (characterzed by a Gauan dtrbuton) or anotropc (characterzed by a modfed-ne urface). Theoretcal predcton rely on the frt-order mall lope approxmaton ether ncludng a Gauan tructure functon or a qua-perodc tructure functon. The combnaton of true data and theoretcal reult ndcate the mportance of takng nto account the anotropy of a urface n a catterng predcton proce. It hown that the catterng trength vare a lot dependng on the propagaton plane. In the longtudnal drecton of rpple, catterng trength motly n the pecular drecton, wherea n the tranveral drecton of the rpple, the catterng trength pread n a very dfferent way related to the partcular feature of the rpple, wth everal maxma and mnma ndependent of the pecular drecton. Contrary to the otropc urface, the catterng trength from an anotropc rough urface modfed from one propagaton plane to another, whch explan why the entre rough urface hould be taken nto account wthout any mplfcaton a t often een when dealng wth catterng model. Compared to uch a urface, poton of the emtter and of the recever are naturally gnfcant when meaurng catterng trength. Keyword: Btatc Scatterng; Tank Experment; Anotropc and Iotropc Roughne 1. Introducton Acoutc catterng from the ocean bottom a ubject of nteret for many remote enng acoutc enng marne actvte, uch a eabed clafcaton, or ecoytem habtat mappng [1,]. To thee purpoe, hgh frequency tool, a ngle beam or multbeam echoounder or de can onar, are ued to ae the bottom roughne and mprove the knowledge of the envronment [3,4]. However f uch ytem can generally provde a detaled mage of the bottom, the relatonhp between the acoutc meaurement and the phycal parameter of the bottom trongly depend on the type of envronment, and n partcular on the type of bottom roughne. To gan more nght nto catterng phenomena, dfferent well known model can be ued. One of the mot common model baed on the Krchhoff approxmaton [5,6] and need large curvature of the rough nterface compared to the acoutc wavelength. Another wdely ued model baed on the mall perturbaton method [7,8] and vald only when the mall-cale roughne maller than the acoutc wavelength. Then a compote model ha been derved to avod lmtaton of the two prevou catterng model [9,1], but only vald for monotatc cae and otropc rough eafloor. Jackon and coworker [1-1] have modfed the monotatc method to obtan a btatc model whch only work for otropc urface. Th model wa ued by Cho et al. [13,14] for comparng theory wth real data obtaned from ther meaurement above rpple feld. Neverthele ther comparon howed that the orentaton of the meaurement plane compared to the drecton of the rpple ha a great effect on the catterng, the catterng trength dtrbuton beng very dfferent from one propagaton plane to another over the rpple. Thu they conclude on the need of conderng the anotropc tate of a urface nto the catterng proce. To take nto account both an otropc or an anotropc eabed, the mall lope approxmaton, orgnally developed by Voronovch [15], nteretng nce t allow conderng varou rough nterface va the tructure functon. Th method ha been elaborated a a unfyng method able to reconcle mall perturbaton method and Krchhoff approxmaton [16]. Copyrght 1 ScRe.

2 V. JAUD ET AL. 51 Theoretcal expreon have been developed at dfferent order by Thoro and Brochat n [17,18] wthout takng nto account qua-perodc eafloor and further tuded by Gragg et al. and Jackon et al. [19,] n the cae of otropc nterface. In th paper, the man concern to better undertand how an anotropc rough urface can mpact the acoutc propagaton and catterng. The mall lope approxmaton allow u to modfy drectly the heght tattc, ether by ung true meaurement of a rough urface [1] or by ung theoretcal model va the heght covarance functon of the eabed to decrbe t roughne. Th modellng approach dffer from many computaton where anotropy drectly mplemented n the cattered feld. The advantage of ncludng the roughne traghtforwardly n the model ha to be tempered by the unque lmtaton of SSA of frt order whch that the elevaton lope have to be mall enough to avod hadng, partcularly at very grazng angle. However, th an aet compared to other catterng model where lmtaton are more numerou. Th paper whoe man goal to tudy the effect of a twodmenonal anotropc rough urface on the catterng trength repone ung the mall lope approxmaton organzed a follow. Secton decrbe the catterng problem and how n theory the dfference between predcton of catterng from an otropc rough urface and from an anotropc rough urface ung the frt order mall lope approxmaton. In Secton 3, tank experment, whch confguraton are mlar to the theoretcal one tuded n Secton, are reported. Scatterng data from an otropc urface and from an anotropc urface are obtaned for dfferent angular confguraton and from three dfferent rough plate. We fnally dcu, n Secton 3, the effect of the relef combnng true data and mulated catterng trength reult.. Modellng of Scatterng Strength wth SSA-1.1. SSA-1 Modellng The catterng problem depcted n Fgure 1 and analyzed trough the catterng trength, SS, whch defned n decbel (db) a: I, SS,,, 1log1 I, (1) 1log m,,, 1 where I the ncdent ntenty, I the cattered ntenty and m the dmenonle catterng coeffcent. The latter parameter repreent how the acoutc wave cattered from the rough urface (ref. at 1 m-dtance over a 1 m urface). In th tudy, m evaluated by ung the frt-order mall lope approxmaton [1,15,17,19] and wrtten a: ource ncdent wave z y cattered wave recever Fgure 1. Geometry of the catterng problem wth the grazng ncdent angle θ, the grazng cattered angle θ and the azmuth cattered angle equal to the azmuth ncdent angle (ncdent and cattered wave n a ame plane). 4 m,,, k A,,, pm kz kz 4π e e e 1 1 k z k z D r k z k z D Kr where K kx k x, ky ky x dxdy the wavevector dfference, r x, y the poton on the (x, y)-plane and D(r) the tructure functon. The ncdent wave defned by t grazng ncdent angle,9 wherea the cattered wave depend on the grazng cattered angle,18. For th tudy we aume that the emtter and the recever are alway n the ame plane, thu the azmuth angle are equal for both ncdent and cattered wave and,,18. Fgure how example of varou angular confguraton of nteret n th paper. Scatterng from edment volume and multple catterng are not condered n th paper. The loe of energy due to tranmon nto the edment (from homogeneou or tratfed eafloor) are condered through Apm,,, whch depend on the plane wave reflecton coeffcent and on the ncdent and cattered wave [1,]. The edment defned a a flud or a an elatc medum, thu Apm,,, repectvely related to the expreon found n [1] or n [3]. The SSA model parametrzed wth ether a tructure functon baed on a Gauan dtrbuton (ee Equaton (3)) or on a tructure functon baed on a ne functon (ee Equaton (4)). () Copyrght 1 ScRe.

3 5 V. JAUD ET AL. (y,z)-plane φ = 9 φ = 9 z (x,z)-plane φ = φ = (y,z)-plane φ = 9 φ = 9 z (x,z)-plane φ = φ = Fgure. Angular confguraton for dfferent cae of nteret: (left) confguraton for an otropc urface a a functon of the cattered angle ; (rght) confguraton for an anotropc urface a a functon of the cattered angle. θ.5 x 1 D g x y L 1 e x L r h y rm (3) The tructure functon D g ued ether to model an otropc urface or an anotropc urface, dependng on the value appled to the correlaton length, L x and L y, repectvely n the x and y drecton. To deal wth a part of perodcty and drectonalty of an nterface, uch a andy rpple, we ugget another tructure functon, D p whch baed on a ne functon. D p r x y π L 1 co co n e x L h y rm p x p y p (4) The tructure functon D p ued to model a rough urface wth perodc feature, thu the urface anotropc and repect few but mandatory tattcal properte uch a the econd-order tatonary of the urface and t ergodcty. Surface baed on th tructure functon are called rpple hereafter. The term φ p and λ p are repectvely the angle for the drecton of the perodc ne hape and the wavelength of the ne functon. The correlaton length L x and L y allow to get a rough urface wth perodc feature more or le dordered... Scatterng Strength Predcton from an Iotropc Surface wth SSA-1 We addre frt the cae of an otropc Gauan eabed. Th cae may be condered a a reference cae for further comparon wth anotropc cae. Fgure 3 how Fgure 3. Predcton of catterng trength, SS, a a functon of grazng cattered angle θ, for θ 5 ; (dahed lne and quare) medum and parameter; (full lne and crcle) concrete parameter; (dahed lne and full lne) propagaton plane n the (x, z)-plane wth φ φ ; (crcle and quare) propagaton plane n the (y, z)-plane wth φ φ. the catterng trength, SS, a a functon of the cattered angle for a grazng ncdent angle 5 nto two dfferent propagaton plane, the (x, z)-plane wth, beng perpendcular to the (y, z)-plane wth 9, a t hown n Fgure. The rough urface otropc and baed on a Gauan dtrbuton. The dmenon are mlar to the rough plate, Plate 1, ued n experment and decrbed n the expermental ecton (ee Secton 3). It heght devaton between 1.5 mm and +1.5 mm wth a zero-mean reference plane. The correlaton length n both x-drecton and y-drecton are mlar wth Lx Lx.5 cm. The frequency of the ncdent wave 5 khz, correpondng to a wavelength of 3 Copyrght 1 ScRe.

4 V. JAUD ET AL. 53 mm. Two dfferent eabed edment (wth the ame roughne parameter gven prevouly) are alo ued for the predcton, one beng defned by the parameter of a uual marne edment [11,1] (medum and wth a ound velocty 177 m/ of and a ma denty of 1845 kg/m 3 ) and the other one beng baed on the parameter of the concrete ued n the experment n Secton 3 (ma denty 16 kg/m 3 and compreonal ound peed 37 m/). For medum and and concrete, the catterng trength predcted n the (x, z)-plane obvouly mlar to the one predcted n the (y, z)-plane. The hghet value for both medum and and concrete found for 5, thu n the pecular drecton and decreae for cattered angle lower and hgher than the angle 5. The man dfference between the two type of edment the global level whch hgher for concrete nce loe due to aborpton are le mportant. In any cae, the catterng trength dtrbuton a a functon of the propagaton plane nce catterng trength pread mlarly n the (x, z)-plane and n the (y, z)-plane..3. Scatterng Strength Predcton from an Anotropc Surface wth SSA-1 The predcton from an anotropc plate are now condered to analyze the effect of anotropc roughne on the catterng trength dtrbuton a a functon of grazng cattered angle. Fgure 4 and 5 how the catterng trength a a functon of the grazng cattered angle for a grazng ncdent angle 5. The rough urface a qua-perodc anotropc eabed and baed on a ne tructure functon a decrbed by D p (r) whch expreon gven by Equaton (4). The dmenon are cloe to the one of Plate and of Plate 3, ued n the experment n Secton 3. The peak-to-peak heght 3 mm, the wavelength of the urface p.5 cm, the orentaton angle, φ p, et to zero and the correlaton length L x and L y, needed for D p (r) are et to 1 m whch much longer than the urface wavelength ( Lx Ly p ). The frequency of the ncdent wave 5 khz, thu a wavelength of 3 mm. Three dfferent anotropc plate are ued to mulate the catterng trength, one beng defned by the parameter of a uual edment [11,1] (medum and wth a ound velocty 177 m/ of and a ma denty of 1845 kg/m 3 ), the econd one baed on the parameter of concrete ued n the experment (ma denty 16 kg/m 3 and compreonal ound peed 37 m/). The lat cae baed on wax parameter (ma denty 7 kg/m 3 and compreonal ound peed 17 m/), ued a well n the experment n Secton 3. One hould notce that the wax how a ound peed mlar to a andy edment but a ma denty much lower than the water, that may have an effect on Fgure 4. Predcton of catterng trength, SS, a a functon of grazng cattered angle, for θ 5, n the (y, z)- plane wth φ φ ; (full lne) medum and parameter; (dahed lne) concrete parameter, (red lne wth dot) wax parameter. Fgure 5. Predcton of catterng trength, SS, a a functon of grazng cattered angle, for θ 5 n the (x, z)-plane wth φ φ ; (full lne) medum and parameter; (dahed lne) concrete parameter, (red lne wth dot) wax parameter. the catterng trength nce t predcton alo related to edment loe nto the eafloor. Fgure 4 how the predcton of the catterng trength, SS, for the three type of urface (full lne for medum and, dahed lne for concrete and red lne wth dot for wax) for a propagaton plane n the (y, z)-plane, 9, thu n the longtudnal drecton of the ne dtrbuted relef (ee Fgure for the propagaton plane and t angular confguraton). For each tet cae, the maxmum value found n the pecular drecton for 5. The hghet value, about 15 db, obtaned for the concrete edment, then medum and how a lower level cloe to 1 db. The lowet one, about 15 db, Copyrght 1 ScRe.

5 54 V. JAUD ET AL. obtaned for the wax. The angular band around the maxmum value for each edment cae about few degree 1 db below the maxmum value, thu the catterng trength fall down traghtaway. Fgure 5 how the catterng trength, SS, a a functon of cattered angle for a propagaton plane n the (x, z)-plane,, thu n the tranvere drecton of the ne dtrbuted relef (ee Fgure for the propagaton plane and t angular confguraton). The catterng dynamc completely dfferent from the prevou mulaton n the (y, z)-plane and trong varaton are obtaned for the dfferent rough urface under tet. The hghet value are obtaned n cae of a concrete eafloor, then from a medum edment and fnally from the wax eafloor. For each type of edment, eventeen peak are found. Thee peak vary between 9 db and 15 db, between 5 db and 1 db and between 3 db and db, repectvely for a edment made of concrete, medum and and wax. In the cattered angular band,15, the maxmum level are very mlar from one peak to the other, partcularly for a eafloor made of concrete or medum and and not for the wax edment. The latter tet cae how a much lower value for the cattered angle around 4 (around 3 db). Th due to the partcular charactertc of th urface whch properte are far from a real eafloor and are not accurately proceed by the catterng model. Th explan why expected catterng behavor, takng nto account loe nto the edment, are ealy defned for concrete and medum and. The cattered angular band at 1 db below each maxmum value only about decbel (equal or le than 5 ) and probably related to the dmenon of the qua-perodc urface and partcularly to the relatonhp between the acoutc wavelength and the heght and urface wavelength. The mot mportant reult from Fgure 4 and 5 are that the catterng trength predcted n a plane dfferent from tranveral to longtudnal drecton. In the longtudnal drecton, the roughne eem moother n the tranveral drecton where the ne hape of mportance. Furthermore the catterng trength dtrbuton clearly related to the hape and dmenon of the urface compared to the acoutc wavelength and the angular poton of the ource and recever. To valdate the man reult obtaned wth the mall lope approxmaton, tank experment are performed and are preented n the followng ecton. 3. Scatterng Data n a Tank 3.1. Expermental Set-Up The acoutc experment were performed at a water tank faclty of Laboratore de Mécanque et d Acoutque (LMA, Marelle, France) n May 11. The tank dmenon were about 9 cm 14 cm and the meaured ound peed n the water wa about 1478 m/ at a temperature equal to 18.6 C. Three dfferent plate were teted. Two plate, o-called Plate 1 and Plate, were made of concrete and were about 3 cm 3 cm n ze, wth a mean thckne of 6 cm. Plate 1 wa otropc, t heght devaton wa between 1.5 mm and +1.5 mm wth a zero-mean reference plane. The correlaton length n x-drecton and y-drecton were mlar wth Lx Lx.5 cm. Plate wa anotropc, the wavelength of the ne relef wa.5 cm and the peak-peak heght wa 3 mm. Both plate have been bult to repreent dered tructure functon. The otropc one wa baed on a Gauan dtrbuton and the anotropc one wa baed on a modfed ne functon whch bottom larger than the top of the ne. The ma denty ha been calculated for both plate, baed on a ample of concrete whoe weght and dmenon were known, and about 16 kg/m 3. The compreonal ound peed n the edment ha been meaured ung a ample of concrete and on tme meaurement for a gnal gong through th ample. The ound peed wa approxmately 37 m/. Fgure 6 (top) how a cloe-up photo of Plate 1 and of Plate. The thrd plate, Plate 3, very mlar n dmenon to Plate, but made of wax whch properte are 17 m/ and 7 kg/m 3 repectvely for compreonal ound peed and ma denty. Thee parameter have acoutcally been meaured on a ample of wax whch dmenon and weght were known. Th plate perfectly homogeneou and hown on the cloe-up photo n Fgure 6 (bottom). Fgure 6. (Top left) Plate 1, cloe-up photo on the otropc plate (3 cm 3 cm) made of concrete; (top rght) Plate, cloe-up photo on the anotropc plate (3 cm 3 cm) made of concrete. The ruler graduated n centmeter; (bottom) Plate 3, cloe-up photo on the anotropc plate (34.5 cm 34.5 cm) made of wax. The ruler graduated n centmeter. Copyrght 1 ScRe.

6 V. JAUD ET AL. 55 The tranmtted gnal wa a hort pule of man frequency 5 khz (bandwdth 3 khz at 3 db), thu a 3 mm-wavelength emtted wth a Panametrc-v31 tranducer whoe drectvty functon mlar to the drectvty of a crcular pton of 6 mm-dameter wth a beam wdth of 3dB 7. Acoutc gnal recordng were ampled at 3 mhz wth a 64 bt reoluton. The recever wa Panametrc-v31 tranducer whch drectvty wa mlar to the one ued for emttng the gnal. Fgure 7 how the temporal and pectral character- tc of the tranmtted gnal, obtaned from a reference meaurement (calbraton) between the emtter and the recever wthout any plate n between. The dtance between the emtter and recever beng the ame durng the experment, the correcton of the loe due to the dtance automatcally taken nto account for each meaurement. In the reult preented n the followng, the meaured catterng trength ha been calculated for dfferent et of angle (ncdent and cattered wave) from the meaured tme ere by computng t Fourer tranform. The catterng coeffcent obtaned from Equaton (5) P,,f m m,,f (5) P cal f where cal (calbraton) at a frequency f, P,,f P f the ampltude of the reference gnal cal the ampltude obtaned for a partcular poton of the tranmtter, for a partcular poton of the recever and at a freq uency f. The reult are preented for f = 5 khz. The catterng trength obtaned n db from the cat- m,,5 khz v. terng coeffcent m The man angular confguraton decrbed n Fgure 1. The meaurement have been done for an emtter wth dfferent poton wth 3, 5 and 7. For each ncdent grazng angle, the rece ver wa moved automatcally from 1 to 17 every 1. The emtter and the recever were alway n the ame plane and meaurement have been performed nto two dfferent plane, n the (x, z)-plane and n the (y, z)-plane a decrbed n Fgure, for each rough plate. Dependng on the angle, the nonfcaton area vared from about a 1 cm-dameter (tranducer perpendcular to the plate) to a 5 cm-dameter (tranducer oblque to the plate), aumng a dtance of 1 m between the tranducer and the plate. For each angular confguraton and each rough plate, the experment ha been proceed everal tme (a mnmum of 5 tme up to a maxmum of 1 tme dependng on the rough plate and on propagaton plane of nteret) and data are hown through ther medan. One hould notce that from one meaurement to the other, n the ame confguraton, data were extremely mlar, wth a maxmum tandard error of.1 db. 3.. Meaured Reult: From an Iotropc Surface (Plate 1) The catterng trength meaured a a functon of cattered trength for the otropc plate hown n Fgure 8 and n Fgure 9 for an ncdent wave 5 and 7 repectvely. For both angular confguraton the data are meaured uch a the emtter and the recever are n a plane, ether the (x, z)-plane or the (y, z)-plane a t decrbed n Fgure. In Fgure 8, the maxmum value appear around 5, whch the pecular drecton and the mnmum value are found for value of the cattered angle Fgure 7. (Top) Tme repone of the 5 khz tranducer from the reference meaurement; (bottom) pectrum of the 5 khz tranducer from the reference meaurement. Fgure 8. Plate 1, catterng trength a a functon of the grazng cattered angle θ for θ 5, medan of 6 meaurement per angle; (blue full lne) propagaton plane n the (x, z)-plane; (black full lne wth tar) propagaton plane n the (y, z)-plane. Copyrght 1 ScRe.

7 56 V. JAUD ET AL. further than an angular band around the pecular drecvalue found around ton. The catterng trength predcted n the (x, z)-plane manly of the ame order than the one n the (y, z)- plane, the ame dynamc obtaned for meaurement from one plane to the other one. In Fgure 9, the maxmum 7, whch the pecular drecton n th tet cae. The catterng trength predcted n the (x, z)-plane are manly of the ame order than the one n the (y, z)- plane Meaured Reult: From an Anotropc Surface (Plate and Plate 3) Fgure 1 and 11 how the catterng trength a a functon of cattered angle n cae of the anotropc urface, Plate. The catterng trength data are obtaned for 5 n Fgure 1 and for 7 n Fgure 11. For both an gular confguraton the data are meaured uch a the emtter and the recever are n a plane, ether the (x, z)-plane or the (y, z)-plane a t decrbed n Fgure. In Fgure 1, there an evdent dfference between the dynamc n the (y, z)-plane and the one n the (x, z)- plane. In the (y, z)-plane, the maxmum value clearly obtaned n the pecular drecton for 5. An angular lobe of about 5 urroundng the pecular drecton oberved wth a mnmum value of about 15 db. Then, for cattered angle n the band [1, 35 ] and [6, 17 ], the catterng trength manly equal or lower than 15 db wth a mnmum value below db. In the (x, z)- plane, the catterng trength n the pecular drecton not preponderant. The catterng trength vare a lot, and goe down to a value around 15 db for cattered angle n the band [1, 17 ]. The maxmum value around 5 db obtaned for dfferent cattered angle n the band Fgure 9. Plate 1, catterng trength a a functon of grazng cattered angle for θ 7, medan of 6 meaurement per angle; (blue full lne) propagaton plane n the (x, z)-plane; (black full lne wth tar) propagaton plane n the (y, z)-plane. Fgure 1. Plate, catterng trength a a functon of grazng cattered angle θ for θ 5, medan of ten meaurement per catter ed angl e; (blue full lne) propagaton plane n the (x, z)-plane; (black full lne wth tar) propagaton plane n the (y, z)-plane. Fgure 11. Plate, catterng trength a a functon of graz- ng cattered angle θ for θ 7, medan of ten meaurement per catter ed angl e; (blue full lne) propagaton plane n the (x, z)-plane; (black full lne wth tar) propagaton plane n the (y, z)-plane. [1, 5 ] and then a econd maxmum value around 7 db obtaned many tme n the band [5, 11 ]. There are many maxma and mnma of mportance n th propagaton plane. Fgure 11 how an apparent dfference between the dynamc n the (y, z)-plane and the one n the (x, z)-plane too. In the (y, z)-plane, the maxmum value of 5 db clearly obtaned n the pecular drecton for 7. Then the catterng trength goe down to 15 db, frt at cattered angle equal to 5 and 85. Below 5 and above 85, the catterng trength var e wth value equal or lower than 15 db. In the (x, z)-plane, the catterng trength n the pecular drecton not preponderant a n the other propagaton plane. The catterng trength vare between 15 db and 5 db for the cattered angle band [1, 13 ]. For a cattered angle h- Copyrght 1 ScRe.

8 V. JAUD ET AL. 57 gher than 1, the catterng trength vare wth trong varaton gong manly down. Fgure 1 and 13 how the meaured catterng trength a a functon of cattered angle n cae of the anotropc urface, Plate 3. Smlarly to the meaured data obtaned wth Plate, there a gnfcant dfference between catterng trength from the (x, z)-plane and the one from the (y, z)-plane. In Fgure 1, the catterng trength obtaned n the (y, z)-plane how a maxmum value about 7 db n the pecular drecton, thu for 5. For a cattered angle lower and hgher than the ncdent angle, the level decreae, gong down to mnmum value around 3 db, partcularly n the backward drecton ( >9). In the (x, z)-plane, the pecular drecton doe not how the max- Fgure 1. Plate 3, catterng trength a a functon of grazng cattered angle for θ 5, medan of 5 meaurement per cattered angle; (b lue full lne) propagaton plane n the (x, z)-plane; (black full lne wth tar) propagaton plane n the (y, z)-plane. Fgure 13. Plate 3, catterng trength a a functon of grazng cattered angle θ for θ 7, medan of 5 meaurement per cattered angl e; (blue full lne) propagaton plane n the (x, z)-plane; (black full lne wth tar) propagaton plane n the (y, z)-plane. mum value of the catterng trength. The catterng trength fluctuate a lot from one maxmum to a mnmum, ometme wth db dfference (around 9). The maxmum value are about 7 db for cattered an- gle n the forward drecton ( <5) and goe down n changng a lot to end around 3 db n the backward drecton >11. From 11 to 17, catterng trength ha got the ame dynamc nto the two dfferent propagaton plane. Fgure 13 how, a well a the prevou tet cae, a dfference between the dynamc n the (y, z)-plane and the one n the (x, z)-plane. In the (y, z)-plane, the maxmum value of 1 db clearly obtaned n the pecular drecton for 7. The catterng trength goe down to 3 db and vare around th value for cattered angle <5 and >9. The catterng trength hgher manly n the forward drecton around the pecular drecton and much lower n the backward drecton a well a at hallow grazng angle. In the (x, z)-plane, the catterng trength n hgher and fluctuate a lot around 15 db for cattered angle between 1 and 1. For >1, the catterng trength tll vare a lot but t mean value decreae to about 3 db. For >14, catterng trength globally mlar to the one mea- ured n the other propagaton plane, the (y, z)-plane. 4. Summary and Dcuon The objectve of th tudy wa to evaluate the effect of partcular rough urface through the btatc catterng trength obtaned n a water tank and to tudy the valdty of the mall lope approxmaton of frt order ued wth partcular tructure functon. Tank experment have been et up to valdate theoretcal reult obtaned by tetng the frt mall lope approxmaton wth the tructure functon of dfferent rough urface. The expermental valdaton ha focued on three dfferent plate. Plate 1 had been made baed on a Gauan dtrbuton and partcularly wth the otropc feature. Plate and Plate 3 were baed on a modfed ne functon, thu anotropc and perodc. Notce that Plate 1 and Plate have been bult followng a partcular proce. Frt the rough urface have been computed baed on an analytcal heght covarance dependng on the gven parameter of each one. Once the heght varaton known, a ample urface ha been made for each plate, then each one ha been mould to fnally get the plate n concrete. Due to th homemade proce, Plate 1 and Plate were heterogeneou (ar bubble nto concrete) and alo how a mall roughne (ze of order of a fne gran ze), n addton to the roughne of nteret, due to the and ued to make concrete. Plate 3 ha been manufactured, wa made of wax and wa perfectly homogeneou. For the mulaton, the tattc of a Gauan dtrbuted urface were obtaned traghtforwardly ung a Copyrght 1 ScRe.

9 58 V. JAUD ET AL. tructure functon. For conderng the tattc of Plate and Plate 3, t wa a bt more complcated n a ene that the tructure functon wa obtaned conderng at the begnnng a urface whch tattcally baed on a random tatonary proce. Aumng th rule, the tructure functon depended on a functon takng nto account the ne hape feature but alo a random dtrbuton of the heght. Due to the dfference between the theoretcal rough urface and the rough urface ued n practce, dfference have been found between both predcted catterng trength and meaured catterng trength (ampltude, angular lag between peak, and o on). Furthermore, one hould notce that n theory the rough urface wa aumed to be nfnte. Contrary to the expermental data, the effect of the tranducer, t drectvty and the nonfed area were not mulated when predctng the catterng trength. Thu, n cae of Plate and Plate 3, only few perodcte (and not an nfnte number) are taken nto account n the expermental catterng proce, th may be one of the reaon why dfference between predcted catterng trength and meaured catterng trength have been found. Due to the dfference between the theoretcal et-up and the expermental one, the comparon were baed on the dynamc, the hape, and o on, of the catterng trength, but not on t abolute ampltude. Neverthele, mlar concluon have been obtaned between predcton and meaured data and how the effect of partcular rough urface (otropc and anotropc) on the catterng trength dtrbuton. For both mulaton and experment, catterng trength were analyzed a a functon of grazng cattered an- gle for a partcular grazng ncdent angle and an ncdent wave whch frequency wa 5 khz, thu a 3 mmwavelength. The ource and the recever were n a ame propagaton plane, ether n the (x, z)-plane or n the (y, z)- plane. For a perodc urface, the (x, z)-plane ft wth the tranveral drecton of the ne relef (very rough), wherea the (y, z)-plane ft wth t longtudnal drecton (very mooth). All expermental data were obtaned many tme (mnmum of 6 tme and maxmum of 1 tme) wth the ame confguraton and howed very mlar reult for each repeated tet cae wth a maxmum tandard error of.1 db. Analyng theoretcal and expermental reult lead to the followng concluon. Frt, for an otropc urface, the catterng trength mlar n one propagaton plane compared to the other propagaton plane, the (x, z)-plane veru the (y, z)-plane. The cattered energy motly dtrbuted n the pecular drecton. Due to the fact that the catterng trength dtrbuton mlar from one plane to another, t would poble n theory to mplfy the catterng model. Intead of beng baed on a two dmenonal urface, the tructure functon could be baed on one-dmenonal urface, that a gan for mplfyng the model and t calculaton tme. Then, for an anotropc rough urface, the behavor completely dfferent from the analy n the (x, z)-plane and the one n the (y, z)-plane. In the longtudnal drecton of the ne urface, the cattered energy manly dtrbuted n the pecular drecton. Compared to the acoutc wavelength, the effect of the relef on the catterng phenomena mlar to the effect of a very mooth urface. On the contrary, n the (x, z)-plane, thu n the tranveral drecton of the ne relef, the catterng dynamc totally dfferent and tend to fluctuate a lot. The pecular drecton not the prncpal drecton for the cattered trength dtrbuton anymore. Maxmum value of catterng trength appear at dfferent cattered angle, a well a many mnmum value. The catterng trength vare a lot a a functon of the cattered angle. Th probably due to the effect of the ne hape whch perfectly perodc for the experment and partally perodc n theory. Neverthele the catterng trength dtrbuton may be related to the rato between the acoutc wavelength and the dmenon of the relef, whch are of the ame order for the heght and a bt larger for the urface wavelength. On the one hand, the dtrbuton of the cattered energy from an anotropc urface howed that predcton va a model mut take nto account the entre two-dmenonal urface n order to be ure of etmatng all parameter whch have an effect on the catterng trength dtrbuton. On the other hand, the dfference between propagaton plane a relevant pece of nformaton, partcularly for etmatng the roughne from catterng trength data obtaned from btatc meaurement and dependng on the poton on the ource and recever. It would be worth alo to analye the catterng trength from an anotropc urface a a functon of everal recever whoe poton not n the ame propagaton plane a the emtter. It would be of nteret n order to fnd the mot approprate confguraton where catterng data are the mot ueful, e.g. for etmatng the roughne from catterng trength. 5. Acknowledgement The author would lke to acknowledge the contrbuton of R. Gullermn for her atance for the experment at the Laboratore de Mécanque et d Acoutque (Marelle, France), M. Jaffrè and P.Martnat of ENSTA Bretagne (Bret, France) for provdng the orgnal anotropc plate, B. Jaouen of IUP Géne Mécanque et Productque (Bret, France) for provdng the orgnal otropc plate. REFERENCES [1] J. T. Anderon, D. Van Hollday, R. Kloer, D. G. Red Copyrght 1 ScRe.

10 V. JAUD ET AL. 59 and Y. Smard, Acoutc Seabed Clafcaton: Current Practce and Future Drecton, ICES Journal of Marne Scence, Vol. 65, No. 6, 8, pp do:1.193/cejm/fn61 [] A. J. Kenny, I. Cato, M. Deprez, G. Fader, R. T. E. Schüttenhelm and J. Sde, An Overvew of Seabed-Mappng Technologe n the Context of Marne Habtat Clafcaton, ICES Journal of Marne Scence, Vol. 6, No., 3, pp do:1.116/s (3)6-7 [3] K. Seme, M. Snellen, D. G. Smon, J.-P. Hermand, M. Meyer and J.-C. Le Gac, Hgh Frequency Multbeam Echoounder Clafcaton for Rapd Aement, Acoutc 8, Par, 9 June-4 July 8, pp [4] L. Hellequn, J.-M. Boucher and X. Lurton, Proceng of Hgh-Frequency Multbeam Echo Sounder Data for Seafloor Characterzaton, IEEE Journal of Oceanc Engneerng, Vol. 8, No. 1, 3, pp do:1.119/joe..885 [5] C. Eckart, The Scatterng of Sound from the Sea Surface, Journal of the Acoutcal Socety of Amerca, Vol. 5, No. 3, 1953, pp do:1.111/ [6] E. I. Thoro, The Valdty of Krchhoff Approxmaton for Rough Surface Scatterng Ung a Gauan Roughne Spectrum, Journal of the Acoutcal Socety of Amerca, Vol. 83, No. 1, 1988,pp do:1.111/ [7] F. G. Ba and I. M. Fuk, Wave Scatterng from Stattcally Rough Surface, Pergamon Pre, New York, [8] E. I. Thoro and D. R. Jackon, The Valdty of Perturbaton Approxmaton for Rough Surface Scatterng Ung a Gauan Roughne Spectrum, Journal of the Acoutcal Socety of Amerca, Vol. 86, No. 1, 1989, pp do:1.111/ [9] D. R. Jackon, D. P. Wnebrenner and A. Ihmaru, Applcaton of the Compote Roughne Model to Hgh-Frequency Bottom Backcatterng, Journal of the Acoutcal Socety of Amerca, Vol. 79, No. 5, 1986, pp do:1.111/ [1] D. R. Jackon, APL-UW Hgh-Frequency Ocean Envron- and D. R. Jackon, Btatc Bottom Scatmental Acoutc Model Handbook, Techncal Report, Seattle, [11] K. W. Wllam terng: Model, Experment, and Model/Data Comparon, Journal of the Acoutcal Socety of Amerca, Vol. 13, No. 1, 1998, pp do:1.111/ [1] D. R. Jackon and M. D. Rchardon, Hgh Frequency Seafloor Acoutc, the Underwater Acoutc Sere, Sprnger, New York, 7. [13] J. W. Cho, J. Na and W. Seong, 4-kHz Btatc Bottom Scatterng Meaurement n Shallow Water, IEEE Journal of Oceanc Engneerng, Vol. 6, No. 1, 1, pp do:1.119/ [14] J. W. Cho, J. Na and K.-S. Yoon, Hgh-Frequency Btatc Seafloor Scatterng from Sandy Rpple Bottom, IEEE Journal of Oceanc Engneerng, Vol. 8, No. 4, 8, pp do:1.119/joe [15] A. G. Voronovch, Wave Scatterng from Rough Surface, Sprnger, New York, [16] T. M. Elfouhaly and C.-A. Guern, A Crtcal Survey of Approxmate Scatterng Theore from Random Rough Surface, Wave Random Complex Meda, Vol. 14, No. 4, 4, pp do:1.188/ /14/4/r1 [17] E. I. Thoro and S. L. Brochat, An Invetgaton of the Small Slope Approxmaton for Scatterng from Rough Surface. Part I. Theore, Journal of the Acoutcal Socety of Amerca, Vol. 97, No. 4, 1995, pp do:1.111/1.411 [18] S. L. Brochat and E. I. Thoro, An Invetgaton of the Small Slope Approxmaton for Scatterng from Rough Surface. Part II. Numercal Stude, Journal of the Acoutcal Socety of Amerca, Vol. 11, No. 5, 1996, pp do:1.111/ [19] R. F. Gragg, D. Wurmer and R. C. Gau, Small Slope Scatterng from Rough Elatc Ocean Floor: General Theore and Computatonal Algorthm, Journal of the Acoutcal Socety of Amerca, Vol. 11, No. 6, 1, pp do:1.111/ [] S. L. Brochat and E. I. Thoro, An Invetgaton of the Small Slope Approxmaton for Scatterng from Rough Surface. Part II. Numercal Stude, Journal of the Acoutcal Socety of Amerca, Vol. 11, No. 5, 1996, pp do:1.111/ [1] A. P. Lyon, W. L. J. Fox, T. Haot and E. Poulquen, Characterzaton of the Two-Demenonal Roughne of Wave-Rppled Sea Floor Ung Dgtal Photogrammetry, IEEE Journal of Oceanc Engneerng, Vol. 7, No. 3,, pp do:1.119/joe [] J. E. Moe and D. R. Jackon, Frt-Order Perturbaton Soluton for Rough Surface Scatterng Cro Secton Includng the Effect of Gradent, Journal of the Acoutcal Socety of Amerca, Vol. 96, No. 3, 1994, pp do:1.111/ [3] D. R. Jackon, Hgh-Frequency Btatc Scatterng Model for Elatc Seafloor, Techncal Memorandum, Techncal Report, Seattle,. Copyrght 1 ScRe.