Sediment Particle Characterization for Acoustic Applications: Coarse Content, Size and Shape Distributions in a Shelly Sand/Mud Environment

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1 A Iakin. Partile size and shape distributions 1 Sediment Partile Charaterization for Aousti Appliations: Coarse Content, Size and Shape Distributions in a Shelly Sand/Mud Enironment Anatoliy. Iakin Abstrat Coarse partiles in the sediment samples olleted during the sediment aoustis experiment (SAX04) in shallow water off Fort Walton Beah, Florida, were analyzed in the 0 to 5 phi siee size range, at uarter-phi interals. Conentional size freueny histograms were determined and ompared with results obtained by others at the SAX04 site. In addition, the oarse ontent was analyzed separately for the two populations, uartz (sand) and arbonate (shell) partiles, using independent measurements of total weight and number of partiles in eah size interal. With this approah, four size distributions were measured, instead of a single one as in traditional sieing tehniues. This analysis resulted in a modified tehniue, whih an be used to improe geoaousti haraterization of the sediment. A partile shape fator was introdued for a simple uantifiation of the differene between the siee size and true size (euialent spherial partile diameter). It is shown that shells and shell fragments hae a shape fator signifiantly different from that for sand partiles. The size distributions for the two populations are also shown to be different. Empirial relationships are established between the shape fator, siee size, and true size, for both arbonate and uartz partile populations. Using these relationships, the true size distributions, reuired in aousti appliations, were determined by orretion of traditional siee size distributions. These orretions are based on replaement of the spherial shape assumption used in traditional tehniues by the typial shape assumption, using the shape fators measured for the two populations. Finally, to test the orreted distributions, they were ompared with those obtained using a new approah allowing estimation of the true size distributions without partile sieing and/or separating into size interals (bins). The true size distributions obtained in this work will proide input parameters and ground truth for model/data omparisons using SAX04 aousti baksattering measurements. Index Terms Coarse sand, grael, shell fragments, siee size, true size (euialent diameter), partile size and shape distributions. I. ITRODUCTIO M arine sediment is omprised of partiles haing different size, shape, mineral omposition, density, elastiity, and other properties. The partile size distribution is one of the major harateristis whih determine geotehnial, physial, and geoaousti properties of the sediment. The mean grain size has a signifiant statistial orrelation with, and, therefore, a apability to predit, suh fundamental physial and aousti parameters of the sediment as the bulk density, porosity, sound speed and attenuation [1]. Howeer, attempts to find empirial relationships with other aousti properties of the sediment hae had muh less suess. For example the bottom baksattering strength, reported in a number of omprehensie experimental studies in a wide 10- to 500-kHz freueny range, has shown little orrelation with the mean size of sediment partiles: see, e.g., [1,2], and referenes therein. Another ommon approah is to lassify sediments in terms of their mud, sand, and grael ontent, expressed as weight % (umulatie weight perentage), resulting in so-alled Folk lasses, e.g., sandy mud, graelly sand, et. Howeer, these parameters, usually presented in existing data bases as well as the mean size, also may be insuffiient for aousti haraterization of the sediment. For example, sandy sediments with 1% or less grael ontent are usually onsidered and doumented as belonging to just the sand Folk lass [1]. Howeer, een suh a small grael ontent an signifiantly hange the sattering harateristis of the seafloor [3,4], and, therefore, should be taken into aount for sediment aousti haraterization. Manusript reeied Marh 31, This work was supported by the U.S. Offie of aal Researh. A.. Iakin is with the Applied Physis Laboratory, Uniersity of Washington, Seattle WA 98105, , iakin@apl.washington.edu.

2 A Iakin. Partile size and shape distributions 2 Goff et al. [3] ame to a onlusion that oarse partile ontributions, ommonly signifiant in shallow water sediments, should be analyzed separately from fine (mud or silt/lay) and medium (sand) frations, and in terms somewhat different from Folk lasses. It was notied that the oarse ontent may inrease attenuation through sattering. Earlier experimental work [2] also proides examples where ariations in geoaousti measurements and oarse material (suh as shell hash) are orrelated. A strong positie orrelation was established between the oarse ontent and the measured bottom baksattering strength at high freuenies: 65 khz [3], 100 khz [5,6], 100 khz and 410 khz [7]. Physis-based theoretial models of bottom sattering apable of explaining this effet also hae been deeloped [4,8-10]. The modeling has showed howeer that prediting the bottom sattering strength in suh a wide freueny range reuires a more detailed desription of the oarse size distribution, rather than a single number haraterizing the total oarse ontent. Therefore, a more detailed study of the oarse sediment fration is important for an adeuate geoaousti haraterization of the seafloor. The size itself an be defined differently when different measurement tehniues are used [11-14], emphasizing different aspets of sediment partiles, whih are ommonly non-spherial. It is therefore not always appropriate to use diretly results of suh measurement as inputs in models, if they define the size differently. First, relationships between these different measures of partile size should be established. For example, siee analysis operationally defines the partile size from the dimension of the smallest suare mesh whih an be passed through by this partile. Models of aousti sattering from sediment inlusions or oarse partiles reuire inputs in the form of the number-size distribution, or the partile number per unit sediment olume per unit size interal, with the size defined as the euialent spherial diameter [4,9], whih is also alled the partile true size or the true nominal diameter [12]. In traditional weighing-sieing tehniues, widely used for sediment partile size analysis, the number-size distribution is ommonly estimated using the assumption that the partiles are nearly spherial [1], and onseuently the partile true size is nearly eual to their siee size. Commonly, howeer, the sediment partiles are non-spherial, and, therefore, a more aurate relationship between the partile siee size and true size (instead of their simple euality for spherial partiles) is reuired. Their differene, from an aousti iewpoint, is the only measure of the non-spherial partile shape releant to this speifi appliation (modeling of aousti sattering). Obtaining empirial relationships, desribing this differene and allowing a orresponding size-orretion for the sediment non-spherial partiles, is one of the goals of this work. In this paper, we fous on analysis of the sediment partiles orresponding to a oarse tail of the size distribution, i.e., oarse partiles with size signifiantly larger than the mean grain size of the sediment. Information about this part of the size distribution is uite sparse in omparison with that for the entral part. One reason is that oarse partiles usually hae an insignifiant effet on the mean grain size and other traditional grain size statistis. Another reason is that obtaining suh information reuires larger sediment samples. This was taken into aount in planning auisition and analysis of the sediment oarse partiles olleted during a major sediment aoustis experiment (SAX04). This experiment was aompanied by extensie enironmental measurements to ealuate the aousti parameters of the sediments, inluding the density, sound speed and attenuation, their spatial ariations in the sediment (olume heterogeneity), as well as the sediment interfae roughness [15-21]. The main goal of suh measurements was to proide enironmental inputs to arious models of sound-bottom interation, and partiularly to SAX04 bottom sattering models and model/data omparisons in a wide range of freuenies: 20 khz to 500 khz [22]. To ealuate the role of the sediment disrete satterers in this freueny range, the partile size distribution has to be determined for sizes larger than about 1 mm [4], inluding ery oarse sand-, grael-, and pebble-sized partiles. Obtaining this size distribution for the SAX04 sediment oarse frations, its analysis, and an adeuate parameterization, are the main goals of this work. The paper is organized as follows. Setion II outlines methods used for sediment partile haraterization, sample olletion and proessing. Assumptions used in traditional weighing-sieing tehniues are disussed to show what additional measurements are reuired if these assumptions fail. In Setion III, aailable size distributions measured at the SAX04 site using traditional tehniues are summarized and ompared. ew results obtained using other approahes and additional measurements are presented. In partiular, size distributions are obtained, based on separate analysis of the two segregated populations (or phases), shell (arbonate) and sand (uartz) partiles, omprising the SAX04 sediment. In Setion IV, the shape fator is introdued and relationships between the partile true size (euialent diameter) and siee size are established. The true size and shape fator as funtions of the siee size are approximated by empirial power law relationships. In Setion V, the effet of the non-spherial shape of the partiles on the size distributions is disussed and orresponding orretions, based on empirial relationships obtained here, are proposed to proide reuired true size distributions. Also, another noel method for diret estimating the true size distribution without partile sieing is proposed. Setion VI gies a summary and onlusions. In Appendix A, empirial relationships used in this paper for partile haraterization are presented. Appendix B proides useful phase relationships for the uartz/arbonate mixture onsidered in this paper. A. SAX04 enironment and sediment sample olletion II. METHODS The SAX04 aousti experiments and supporting enironmental measurements took plae in shallow water about 1 km off shore near Fort Walton Beah, Florida, in September oember For the researh desribed in this paper, thirteen sediment samples were olleted and proessed, with a total olume of 189 liters. They were olleted in seeral loations,

3 A Iakin. Partile size and shape distributions 3 hosen in proximity to the three major SAX04 aousti measurement systems, the Benthi Aousti Measurement System (BAMS), the Syntheti Aperture Sonar (SAS), and the Sediment Transmission Measurement System (STMS). The STMS was loated about 60 meters westward from the SAS, and the BAMS loation was about 200 meters eastward from the SAS. The spatial layout and loations of these systems are desribed in [22,23] in more detail. The three sites, and samples olleted at these sites, are referred to below as BAMS, SAS, and STMS sites and samples respetiely. It is important to mention that not only the total olume of the sediment samples, but also the ross setion of eah sample should be hosen large enough to allow unbiased olletion of the larger, less numerous partiles. The dimensions of the samples olleted for this work were hosen to allow unbiased ealuation of the grael- and pebble-sized partiles, whih an be important for aoustial sattering at freuenies as low as 20 khz used in SAX04 experiments [4]. Ten ylindrial samples of 20 m diameter, the BAMS and SAS samples, with total olume about 19 liters were olleted by diers on 5 Otober 2004 and ontained the sediment of the upper 6 m. The fie BAMS samples were olleted along a westward line starting about 10 meters from the BAMS tower base and then with spaing 1, 2, 3 and 4 meters between adjaent samples. Fie SAS samples were olleted along a northeastward line starting about 1 meter from the east end of the SAS rail with the same spaing (1, 2, 3 and 4 meters). The three STMS samples were obtained on 6 Otober 2004 from a larger sediment olume (about 160 liters). This sediment was exaated from the upper 0 to 18 m during deployment of the STMS apparatus and diided into three layers 6 m eah. It should be notied that the SAX04 sediment had rather ompliated spatial distribution and struture, resulted from strong weather eents (Hurriane Ian and Tropial Storm Mathew) [19,21]. In partiular, the sediment textural ontent at the three sites was somewhat different. Aording to dier s reports [24,25], the sediment at the STMS site was omprised predominantly of lean sand with ery little (if any) mud, while the sediment at the SAS and BAMS sites was muh less lean, with a notieable mud ontent, most pronouned for the BAMS loations. Howeer, in aailable douments, in spite of uite non-uniform spatial distribution of mud, it was haraterized, as usual, by a single alue, the aerage mud ontent, obtained by aeraging oer all numerous sediment samples olleted at the SAX04 site. The aerage mud ontent in the SAX04 sediment was about 8.5% by olume [19]. Grael (mostly shell) ontent was less than 1% by olume. Suh small ontributions, from a geotehnial iewpoint, an be onsidered insignifiant and may be ignored. In ternary Folk diagrams based on grael-sand-mud ratio, see [1, p. 88], the SAX04 sediment is haraterized as just sand. More information about SAX04 sediment properties an be proided by parameters of the grain size statistis (mean size, sorting, skewness, and kurtosis), whih traditionally are onsidered as the main desriptors of the sediment type as well as related word-based harateristis (e.g., fine, medium, or oarse sand, well or moderately sorted). Along with the sediment textural parameters (defined by Folk-lass), they are ommonly well doumented in numerous existing data bases. Analysis of the grain size statistis larifies that the SAX04 sediment is a moderately well sorted medium sand, with mean grain size 0.36 mm [19]. Howeer, suh larifiation adds ery little to haraterization of aousti sattering properties of the sediment. From an aousti iewpoint, the SAX04 enironment an be more adeuately haraterized as a sand/mud [22], a shelly sand, or a shelly sand/mud mixture [4], with spatially arying mud and shell omponents, beause een suh small shell and mud ontent and their spatial distribution an be important inputs in models of bottom sattering and model/data omparisons. B. Sieing tehniues and size freueny histograms All our sediment samples were pre-sieed before analysis. The remaining sediment oarse partiles omprised only a small olume proportion of the sediment (about 1%), simplifying the following analysis and related proedures (onseration, transportation, et). The BAMS and SAS samples were pre-sieed after being deliered onboard, and only partiles with siee size 1 mm and larger were left in the samples. The STMS sediment was plaed in bags with 1.6 mm mesh and pre-sieed by shaking underwater. Hene, all mud, medium sand, and most of the oarse sand fration, were washed out. The partile size distributions were determined using a set of 20 standard siees in the 1.0 mm to 32 mm siee size range, or in the 0 to 5 phi range, at uarter-phi interals (bins). There were no partiles found with larger size. Therefore, the partile data base used for analysis in this paper inludes only the ery oarse sand-, grael-, and pebble-sized partiles. The olleted partiles are signifiantly larger than the mean grain size, and onstitute the oarse tail of the size distribution. The onentional sieing-weighing tehniues [1] define the weight-size distribution histogram, most ommonly used in the literature, as follows = W /, (1) W W s where W is the dry weight of all partiles in the siee-size interal [ d, d + d], and Ws is the total dry weight of all solid partiles of the entire (not pre-sieed) sediment sample. For pre-sieed sediment samples, the total dry weight an be estimated from the relationship W = ρ ( 1 P V, (2) s s ) if the total olume of the wet (water saturated) sediment sample, V, the sediment porosity, P, and the aerage density of all solid partiles in the entire sample, ρ, are known. s

4 A Iakin. Partile size and shape distributions 4 Another traditionally measured uantity is the freueny size umulatie funtion, whih is defined as a funtion of size, from summation of the histogram oer partiles larger than this size. Therefore, it integrates information about the oarse tail of the size distribution, whih, in this paper, is the primary interest. The freueny size umulatie funtion represents a umulatie weight perentage of oarse partiles, or the oarse ontent of the sediment, as funtion of its nominal oarse size. This is important, beause the oarse ontent an be defined differently, depending on the sediment type, related tehniues, aousti effets, et. For example, it an inlude all medium sand-sized partiles of predominantly fine sand or mud [1], or only pebblesized partiles (larger than 4 mm), as in [3], whih were found to be responsible for ertain aousti effets. In this paper, all partiles with the siee size larger than 1 mm, inluding ery oarse sand-, grael- and pebble-sized partiles, are inluded in the sediment oarse ontent. In predominantly medium sand sediment at the SAX04 site, all these partiles are signifiantly larger than the mean grain size, and therefore orrespond to the oarse tail of the partile size distribution. Also, they all hae a ertain effet on sattering properties of the SAX04 sediment in the reuired freueny range, 20 khz to 500 khz [4]. C. Outline of reuired additional measurements It should be notied that aousti haraterization of the sediment partiles, for example, desription of their sattering harateristis, reuires inputs for the partile size in a form different from gien by traditional weight-size freueny distributions. The inputs should be presented as histograms or distributions, showing the number of partiles in gien true size interals per unit olume of the sediment. The reuired size distributions an be obtained using seeral assumptions. The traditional approah is to assume that all partiles are nearly spherial. In this ase, the siee size is nearly eual to the true size, as it proides a suffiiently aurate estimate for the partile olume. It is ommonly assumed also that all partiles hae the same density. Then the number of partiles in eah size interal an be estimated from their total weight and the reuired number-size distribution an be obtained from the partile weight-size distribution as follows: = ( 1 P ) /, (3) s where s W s 3 ( d) = πd / 6, (4) s is the olume of a spherial partile with diameter d. Howeer, neither of these two mentioned assumptions were satisfied in the ase of the SAX04 sediment samples, omprised of partiles with different density and shape. Generally, the oarse partiles omprised a mixture of two isually distint populations, uartz (sand/grael) and alium arbonate partiles (mostly broken shells). They hae different shapes, espeially non-spherial for oarse shell partiles, and different aousti parameters (onstituent density and elasti moduli) resulting in differenes in their indiidual sattering harateristis. In this ase, sattering models reuire separate inputs for these two types of partiles [4]. Therefore, some modifiations of tehniue were made and additional measurements were performed to proide an appropriate desription of the sediment oarse partiles for aousti sattering models. One modifiation to traditional tehniues was that the two populations were segregated from eah other and analyzed separately. The bins of the pebble size range (4 mm and larger) ontained only arbonate partiles. The uarter-phi bins of the 0 to 2 phi range (1 to 4 mm), orresponding to ery oarse sandand grael-sized partiles, ontained a mixture of the two populations. They were segregated from eah other, and the total weight of partiles in eah of the two populations was measured in eah of the siee-size bins. A seond modifiation was to take into aount that oarse partiles were signifiantly non-spherial, espeially the shells. To do this, the following additional measurements were made. First, the partile number in eah siee size bin was determined for eah of the two populations. As the partile density in eah population is defined, the aerage olume of partiles in eah size bin was estimated from their weight without assumptions on their shape. Then the ratio of the aerage partile olume to the olume of a sphere with the same siee size was determined in eah size bin as a simple measure for uantifiation of the typial shape of partiles in eah population, defined in this paper as the shape fator. The partile olume also defines its true size (euialent diameter). Therefore, measuring the shape fator also allowed determination of the relationship between the siee size and true size of the partile. Then the reuired true size distributions were found using the orresponding orretions of the measured siee size distributions. Generally, these orretions are based on replaement of the spherial shape assumption by the typial shape assumption, using the two different shape fators measured for the two populations, arbonate and uartz partiles. Therefore, to proide the true size distributions for the SAX04 sediment oarse partiles, four different size distributions were to be measured, that is two distributions, olume- and number- based, for eah of the two populations. This approah was used in this paper and the results are desribed in more detail in the next setions. D. Other (non-sieing) tehniues There are many other ways of determining the size and shape of the sediment partiles. It is understood that 3-D non-spherial partiles generally may reuire three or more parameters to haraterize their size and shape [14]. umerous methods for suh haraterization are based on proessing of partile images. Many of them are based on rather time onsuming grain-by-grain analysis of partile projeted area for partiles plaed on a gridded sreen [11,14]. Also based on the image analysis, but without extrating indiidual grains from the sediment samples, are the methods using X-radiography and omputed tomography (CT):

5 A Iakin. Partile size and shape distributions 5 see, for example, [1, Ch. 7], [10,18,26]. These methods ause lesser disturbane to the sediment struture than the usual sieing proess, but also hae some disadantages, outlined as follows. First, CT methods do not proide diret measurements of the partile size, but rather 2D-images of ontours or ross-setions shifted with respet to the partile enters. Correspondingly, this allows estimation of size distributions for these 2D-images, whih, howeer, are different from the desired atual size distributions. To make orresponding orretions, een in the simpler ase of spherial partiles, some additional and rather ompliated numerial proedures are needed [10,27]. Seond, X- radiography and CT methods are based on distinguishing partiles by density ontrast, and therefore an be less effiient in the ase where partiles with ery different shapes hae relatiely small differene in density, as for the arbonate (shells) and uartz (sand) partiles onsidered here. In the only known (to the author of this paper) example presenting final results on the sediment partile size distribution measured by this tehniue [10], these two types of partiles were not distinguished. And last, but most important in pratie, this method is muh more ompliated and expensie than sieing. It should be noted also that obtaining the tails of the partile size distribution from inersion of 2-D images reuires numerially muh more stable algorithms than for estimating parameters of the entral part of the size distribution. This stability is known to be the main problem of urrently used inersion tehniues [27]. Therefore, the pratial appliability of X- radiography and CT methods in determining the partile size distribution in granular sediments (espeially the size distribution tails) has yet to be tested. Suh tests ould be proided by omparison of size distributions resulting from these proedures with atual size distributions measured diretly, using, for example, traditional sieing tehniues, or modified as desribed in this paper, if needed. This has not been done yet and ould be an interesting task for future work. In this paper another simple and pratial approah, not based on partile sieing, is proposed for an independent measurement of the partile true size distribution. This method is based on a grain-by-grain analysis of a relatiely small number of the largest partiles and an be pratially useful for estimating the oarse tails of the true size distribution. This approah was used in this paper to proide a omparison of different tehniues, sieing- and non-sieing based. The results are presented and disussed in next setions. The proposed new tehniues also an be used to test other methods based on non-diret estimation of the partile size distributions. A. Size freueny histograms III. SIZE DISTRIBUTIOS In this paper, as an initial part of partile size analysis, the traditional weight-size distribution histograms were determined for all 13 pre-sieed sediment samples, using relationships (1) and (2). Typial alues of the sediment porosity and solid density at the SAX04 site, P = and ρ = g/m 3 [19], were used for alulations. The sediment olume for alulations was s taken to be 1885 m 3 for eah of the fie BAMS and fie SAS samples, and m 3 for eah of the three STMS samples. The histograms obtained in the three sites (BAMS, SAS, and STMS) were aeraged oer the orresponding number of samples, 5 for eah of BAMS and SAS sites, and 3 for STMS site. Results are shown in Fig. 1 (by blak symbols) in the form of the weight perentage, or freueny size distribution for the three sites. Fig. 1 shows the orresponding umulatie funtions. Fig. 1 also shows (in green) three data sets obtained at the SAX04 site by other authors. Two of these data sets [28] were obtained at the same time a few months before the SAX04 experiment, using the methods mentioned aboe for pre-sieed and entire samples. A relatiely large olume of the sediment from the bottom surfiial 5 m layer was olleted by diers and plaed underwater in two 5-gallon bukets. The sediment in one of the bukets was pre-sieed using a 1.6 mm mesh, and only the remaining partiles were used later to determine the oarse partile size distribution. This method is similar to that used for olletion of our STMS samples. The sediment from the seond buket was saed and later proessed in laboratory onditions as an entire sample, to determine another size distribution. The oarse ontent, howeer, was onsidered too small, and oarse partiles larger than 2 mm were aumulated in one size lass (with siee-size 2 mm). At smaller sizes, this seond size distribution and orresponding umulatie funtion hae a onsistent ontinuation (toward smaller sizes) of the first distribution, obtained for oarse partiles from the pre-sieed sample. The third size distribution shown in Fig. 1 (in green) [19,29] represents results aeraged oer 23 ylindrial ores with 5.9 m diameter olleted during SAX04 and proessed as entire samples. Comparison of all the data presented in Fig. 1, ours and those obtained by other authors, shows two notieable effets. First effet is seen from omparison of the two distributions measured using small and large sampling apertures (5.9 m s 20 m), and onfirms that the large but less numerous partiles (with the size larger than 5 mm) an be missed if the ross setion of eah sample is not big enough for unbiased olletion of these partiles. The seond effet is seen from omparison of our data obtained in the three loations at the SAX04 site. It shows positie orrelation between the spatial ariations in ontent of oarse partiles in our pre-sieed sediment samples and the spatial ariations in the mud ontent of the sediment reported by diers, that is greater oarse ontent was found in loations with greater mud ontent. Unfortunately, there is no other, more uantitatie, assessment of suh a orrelation, whih might be important for more adeuate haraterization of the SAX04 sediment for aousti appliations. This ould be an interesting topi for future researh in ompliated enironments (suh as at the SAX04

6 A Iakin. Partile size and shape distributions 6 site). B. Volume-size distributions for arbonate and uartz partiles Unlike traditional tehniues, the two populations, shells and sand partiles, were segregated and the weight of partiles belonging to eah bin was measured separately for eah population. Gien the same density for partiles in eah population, relatie measurements of weight and olume of grains are euialent. The olume-size distribution histograms an be obtained as follows: = V / V, (5) where V = W / ρ is the total olume of partiles in eah bin, and ρ is the partile density. It should be notied that unlike traditional size freueny histograms gien by (1) and (2), determining this histogram does not reuire knowledge of the sediment porosity and solid density, whih annot be measured if only pre-sieed samples are aailable. This olume-size distribution histogram, or, for breity, V-histogram, an be also alled partial olume onentration, representing the olume fration oupied by partiles of a gien population (with a gien density) in a gien siee-size interal. In the following alulations, the typial alues used for densities of uartz (sand) partiles and alium arbonate (shell) partiles were taken to be 2.65 g/m 3 and 2.75 g/m 3, respetiely (see, e.g., [1, p.112]). The orresponding umulatie funtion represents a umulatie olume onentration of a gien population inluding oarse partiles larger than a gien size. It gies, for example, grael ontent, if this gien size is hosen to be 2 mm. An important property of the umulatie onentration is that, unlike the partial onentration, it is independent of the size of interals or siee bins, whih an be different in different measurement tehniues. This property will be used later in omparison with results obtained with different (sieing and non-sieing) tehniues. Fig. 2 shows the V-histograms and orresponding umulatie funtions for eah of the three sites, BAMS, SAS, and STMS, alulated separately for shells and sand partiles. It is seen that shells hae ery different properties than oarse sand (mainly uartz partiles). For example, the slopes of the size distributions of shells are ery different than those for sand partiles (being muh steeper for sand). From Fig. 2, one an easily see that this differene in slopes results in dominane of the shell partiles (by oupied olume) oer uartz sand partiles at all siee sizes larger than a ertain transition size, whih appears to be the same, about 2 mm, for all three loations. Fig. 2 also demonstrates muh spatial ariability of the size distribution and oarse ontent for both uartz and arbonate partiles. One an notie also their substantial inrease in loations with greater mud ontent. It is interesting to note, howeer, that the ratio of the olume-size distributions of the two populations, shell and sand partiles, or the olume ratio R, is muh less dependent on mud ontent and is about the same for all three loations, and, therefore, is not affeted by the mud ontent. Fig. 3 demonstrates this effet and shows the olume ratio as a funtion of the siee size. One an see that it an be well approximated by a power-law dependene; see (A.1) in Appendix A. For a mixture of partiles with different densities, the definition (5) for the V-histogram is still alid assuming, howeer, that the density ρ represents the aerage alue for the mixture of partiles with gien siee size. The aerage density in the uartz/arbonate mixture is related with the olume ratio of the two omponents, R (see Fig. 3 and (B.1) in Appendix B), and also is size dependent. It is shown as a funtion of the siee size in Fig. 3 for the three loations. The solid line shows the relation (B.1) for the aerage density with the power-law approximation for the olume ratio, gien by (A.1) in Appendix A. This figure more learly demonstrates the transition effet, notied first in Fig. 2. Fig. 3 also shows that in the uartz/arbonate mixture there is a transition size, about 2 mm, and that uartz partiles dominate at smaller sizes, while at sizes greater than this transition size the arbonate partile population is the dominant one. ote also that the aerage partile density, as well as the olume ratio, appears to be spatially independent. This an be important in a pratial sense beause it an proide alternatie ways for estimating the olume-size distributions of the arbonate and uartz partiles, based on simple phase relationships for the mixture of the two omponents (or phases), see (B.2) and (B.3) in Appendix B. C. umber-based size distributions In addition to measuring the weight of partiles, their number in eah bin for eah of the two populations, arbonate and uartz partiles, was ounted as well. Corresponding number-size histograms were defined as follows: = /V, (6) where is the total number of the partiles in the siee size interal [ d, d + d]. Therefore, unlike traditional estimates based on the assumption that the partiles are nearly spherial, see (3), the partile number-size distributions were measured independently of the weight-size histograms. It should be noted that segregation and ounting of smaller and more numerous partiles is a rather time onsuming proess. In bins with the two smallest siee sizes, 1.0 mm and 1.18 mm, the number of partiles was estimated, in eah of the two bins for eah sample, from analysis of a ertain proportion of the partile population hosen to be large enough to keep statistial errors within 1% limits. Usually it was suffiient to ount about a uarter or one

7 A Iakin. Partile size and shape distributions 7 eighth (by weight) of the partiles. The number-size distribution histogram, or, for breity, -histogram, an be also alled the partial number onentration, representing the number of partiles of a gien population per unit sediment olume in a gien siee-size interal. The orresponding umulatie funtion represents a umulatie number onentration of a gien population inluding oarse partiles larger than a gien size. Fig. 4 shows the -histograms and orresponding umulatie funtions for eah of the three sites, alulated separately for shells and sand partiles. Fig. 4, as well as Fig. 2, demonstrates the ery different properties of oarse sand and shell partiles, and show a substantial inrease in leel of their size distributions in loations with greater mud ontent. Howeer, the ratio of the size distributions of the two populations is again pratially independent from the mud ontent. The arbonate-to-uartz number ratio, R, is shown in Fig. 5 to demonstrate this interesting independene. It is seen also that this ratio parameter an be well approximated by power law dependene, gien by (A.2) in Appendix A, with the slope defined by the power exponent, not muh different from that for the olume ratio parameter shown in Fig. 3. The ratio of ratios, or the R -parameter, =, is shown in Fig. 5. One an see that its typial leel is about 0.4, and slightly dereases with R R / R inreasing size. This behaior is approximated by a power-law dependene (shown by a solid line) gien by (A.3) in Appendix A. As it will be seen later, the R -parameter also plays a role in haraterization of the partile shape. A. Shape fator IV. PARTICLE SHAPE AD TRUE SIZE Independent measurements of the partile number, unlike traditional tehniues using the spherial partile assumption to estimate this number, see (3), an be used also for uantifiation of the deiation of the partile shape from spherial. Indeed, the aerage olume of partiles with gien siee size an be estimated as follows: ( d) = V /, (7) and then ompared with the orresponding olume of the spherial partile s, see (4)-(6). The ratio F( d) = ( d) / ( d) (8) s an be onsidered as a parameter haraterizing the differene of the partile shape from spherial, or as a shape fator. For spherial partiles, F = 1. Partiles with a lesser shape fator hae olume smaller than the estimate based on their siee size. These partiles tend to hae platy, disk-like shapes [12,14,26]. Partiles with a greater shape fator, F > 1, hae olume exeeding the spherial, and tend to hae an elongated shape. The results of measurements for the partile shape fator are shown in Fig. 6 for all three loations, presented as funtions of the siee size. This figure also illustrates the differene between the typial shape of sand and shell partiles. One an notie that the ratios of their shape fators, and olume-to-number histograms, are the same, i.e., = / = / =. (9) R R R F / F This was taken into aount to proide onsisteny of power-law empirial approximations for the shape fators of arbonate and uartz partiles, whih are gien by (A.4) and (A.5) in Appendix A. It is seen that shells are espeially non-spherial, with the shape fator for most of them being in the range 0.5 to 0.1, whih orresponds to platy shapes. Most sand partiles hae shape fator in the range 1.0 to 1.3, whih orresponds to muh more round and slightly elongated shapes. For a mixture of partiles with different shape fators, the definition (8) gies the aerage shape fator, whih is related to the number ratio of the two omponents, R, see (B.4) in Appendix B. The aerage shape fator is shown as funtion of the siee size in Fig. 6 for the three loations. The solid line shows the approximation using (B.4) for the shape fator with empirial relations (A.2), (A.4.), and (A.5), see Appendix A. ote also that the aerage shape fator, as well as the number ratio, appears to be spatially independent. This an be important pratially beause it an proide alternatie ways for estimating the number-size distributions of the two omponents, based on simple phase relationships in their mixture, and without the time onsuming proess of their segregation and ounting, see (B.5) and (B.6) in Appendix B. B. True size The true size (euialent diameter) of a non-spherial partile, D, or the diameter of the sphere haing the same olume, as a funtion of the partile siee size, an be determined from the euality s ( D) = ( d). (10) It also an be expressed through the partile shape fator using definition (8), whih an be written as a relationship 3 F = ( D / d). (11) F (d Therefore, gien the shape fator as a funtion of the siee size, ), the partile true size also an be determined at any siee

8 A Iakin. Partile size and shape distributions 8 size as follows: 1/ 3 D ( d) = d F ( d). (12) The results of measurements for the partile true size are shown in Fig. 7 for the three loations. Fig. 7a shows the true size separately for uartz (sand) and arbonate (shell) partiles. It is seen that they are different and an be well approximated by two different power-law funtions (solid ures), gien by (A.6) and (A.7) in Appendix A. The euation (12) defines also the aerage true size of partiles in the sand/shell mixture, whih is shown in Fig. 7. The solid line orresponds to (12), where the shape fator is approximated by dependene (B.4) shown preiously by solid ure in Fig. 6, and proides a good fit to measured data. A. Spherial shape assumption-based distributions V. CORRECTIO FOR SIZE DISTRIBUTIOS The number of partiles an be estimated from their total olume using arious assumptions on their shapes. For spherial partiles it an be obtained as follows: = /, (13) s s whih is similar to estimating the number of spherial partiles from their total weight, see (3). Results for these estimates are shown in Fig. 8 for uartz and arbonate partiles by irles. They were obtained from the olume-size histograms shown in Fig. 2 for BAMS and SAS sites and aeraged oer all ten samples. For omparison, the diretly measured number-size histograms are shown by -symbols, also aeraged for these ten samples. It is seen that using the sphere assumption results in a signifiant underestimate of the number onentration of arbonate shells, while giing a slightly oerestimated number for uartz sand partiles. Analogously, if the number of partiles is known, their total olume an be estimated using the assumption of a spherial shape as follows: =. (14) s s Results for these estimates are shown in Fig. 8 by irles. They were obtained by using number-size onentrations aeraged oer ten BAMS and SAS samples shown in Fig. 4a. Diretly measured olume-size histograms are also shown (by ) for omparison. It is seen that using the sphere assumption results in a signifiant oerestimate of the relatie olume of arbonate shells, while giing a somewhat underestimated relatie olume for uartz sand partiles. B. Typial shape orretion for size distributions Corretions for the number- and olume- siee size distributions an be made by allowing a non-spherial shape of the partiles. For example, empirial relationships for shape fators of arbonate and uartz partiles obtained in this work an be used assuming that they desribe typial shapes for partiles of these two types, whih is an improement ompared to the spherial shape assumption. This typial shape assumption results in estimating the number-size distributions of non-spherial partiles as follows: =. (15) s / F Results for suh estimates are shown in Fig. 8 (by triangles, ) and were obtained from preiously shown (by irles) estimates orreted by using (15) with the shape fator of arbonate and uartz partiles gien by empirial relationships (A.4) and (A.5) in Appendix A. It is seen that suh orretion results in a good fit to the atually measured number-size histograms disussed aboe. Analogously, if the number-size distribution of partiles is known, their olume-size distribution an be estimated using the typial shape assumption as follows: =. (16) s F Results for these estimates are presented in Fig. 8 (by ) and show a good fit to diretly measured olume-size histograms aeraged for all BAMS and SAS samples (shown by ). The omparisons in Fig. 8 demonstrate the potential pratial use of the empirially introdued orretions for traditional tehniues based on replaing the spherial shape assumption by the typial shape assumption. Using empirial relationships between siee size and true size of the partiles, the measured siee size distributions an be also presented as funtions of true size. It should be noted that the orresponding siee size and true size interals an be different for non-spherial partiles. This, howeer, does not affet the size distribution umulatie funtions, whih are independent of the size interal. Results for the umulatie funtions for both arbonate and uartz partiles, based on measured siee size distributions gien in Figs 8 and 8, are shown in Figs. 9 and 9, respetiely (also by ). They are plotted as funtions of the partile true size, using relationships (A.6) and (A.7) proiding orretions for the siee size, and illustrate results of the

9 A Iakin. Partile size and shape distributions 9 modified sieing tehniue desribed in this paper. In following omparisons, these funtions are alled the orreted siee size distributions. C. A method for diret measurements of the true size distributions Another approah, not based on partile sieing, an be used for an independent measurement of the partile true size distribution. This approah is based on a grain-by-grain weighing of the largest partiles in both arbonate (shell) and uartz (sand) partile populations. A threshold of 0.1 g was set as a minimal weight for shells, and 43 suh partiles were found in all ten ylindrial (BAMS and SAS) samples. The true size (euialent diameter) of eah partile was estimated from its weight using the known arbonate density. Then the partiles were rearranged in the order of desending weight. Some partiles had the same weight, within resolution of weight measurements (0.01 g), and to eah weight in this desending series the number of partiles haing this weight was assigned. This number an be also understood as a number of partiles in a weight resolution ell (or a bin for the orresponding weight). For the two series, weights and numbers, the two umulatie funtions were alulated ersus partile true size (defined by its weight). This method was applied also to analysis of sand (uartz) partiles, whih were smaller and lighter. Only six partiles were found to hae weight not less than 0.05 g, the threshold set for sand grains. A lower threshold was not set beause the limited resolution of the weighing sales did not allow a reasonably aurate segregation by weight for smaller partiles. This method, therefore, has limitations related only with resolution of the aailable weight measurement method. The resulting series of weights (with orresponding true size) and numbers an be presented as a table, whih proides a simple example for a data base (here for six uartz partiles) used in this tehniue: Weight, g True size, mm umber Results for both arbonate and uartz partiles are gien in Figs. 9 and 9 (by irles) for olume- and number-size distribution umulatie funtions. The omparison between these distributions, the diretly measured true size distributions based on the non-sieing tehniue, and the orreted siee size distributions based on a modified sieing tehniue (shown by -symbols and disussed earlier), demonstrates a good fit and proides a test for the modified tehniue and empirially introdued orretions. Generally, the method proposed here for diret measurements of the true size distributions seems to be pratially useful for analysis of oarse partiles, whih are larger but less numerous, and for whih there is no rationale for separating into size lasses or bins. It an be used, for example, for rapid estimation of the size distribution of large partiles in sediment grab samples, normally olleted in oeanographi expeditions, bottom mapping sureys, et. Large olumes of the sediment, usually deliered on-board in suh grabs, an be pre-sieed to separate oarse partiles, whih an be uikly analyzed using this express-method reuiring only simple weighing, from finer partiles, whih an be saed, if needed, and analyzed later in laboratory onditions using traditional tehniues. Therefore, this approah an proide omplementary aoustis-related inputs to traditional sediment data bases, whih are being ommonly updated by data obtained during numerous sea trials and sureys. In partiular, the results and tehniues presented in this paper an be used for upgrades of sediment parameter data bases and empirial algorithms, suh as desribed in [3,30]. Also, beause this method proides diret measurement of true size distributions, it an be used as a testing tool for results obtained using traditional sieing and other non-diret measurement tehniues. VI. SUMMARY AD COCLUSIOS To proide inputs to aousti sattering models, a more detailed desription of the oarse tail of the sediment partile size distribution than it is ommonly aailable is neessary. This also reuires sediment samples haing larger ross setional areas and larger olumes, than ommonly used for traditional analysis foused mainly on the entral part of the size distributions. Also, a more aurate lassifiation of the sediment type than is ommonly aailable is reuired. In partiular, from an aousti iewpoint, the SAX04 enironment an be more adeuately haraterized as a shelly sand/mud mixture, with spatially arying mud and shell omponents, beause the small shell and mud ontents in SAX04 sediment (ommonly to be ignored) and their spatial distributions an be important inputs in models of bottom sattering and model/data omparisons. In this paper, traditional weighing-sieing tehniues were used with some modifiations to proide orretions for the nonspherial shape of oarse partiles. The SAX04 oarse partiles an be desribed as a mixture of two populations, represented by arbonate (shells) and uartz (sand) partiles, with different densities, as well as different shape and size distributions. The sieesize distribution histograms and umulatie funtions were determined for siee sizes 1 mm and larger, at uarter-phi interals. The size and shape distributions for both populations an be desribed by power laws, but with different power exponents. The

10 A Iakin. Partile size and shape distributions 10 size distribution of uartz partiles is muh steeper than the size distribution of shells. This results in dominane of uartz partiles oer arbonate (shells) in the oarse sand size range, while shells are dominant in grael and larger size ranges. Shells and shell fragments are shown to hae ery different shapes than sand partiles. To uantify the differene, a shape fator was introdued and determined. The measured shape fator was used also to determine the partile true size (euialent diameter). For both populations, sand partiles and shell fragments, the shape fator and true size, as funtions of the partile siee size, are shown to be well approximated by empirial power law dependenes. These empirial relationships were used to proide orretions to measured siee-size distributions and to determine the true-size distributions reuired in aousti sattering models. These orretions are based on replaing the spherial shape assumption, used in traditional tehniues, by the typial shape assumption using empirial relationships for the shape fator. The true size umulatie distribution for a relatiely small fration of the largest partiles was determined independently by means of a grain-by-grain analysis, not using traditional sieing tehniues. The omparison with the true size distributions obtained by orretion of the siee-size distributions was used as a test for the proposed orretion tehniues. The true size distributions of oarse partiles obtained in this paper will proide neessary input parameters for modeling of seafloor sattering. These inputs will be used in model/data omparisons and analysis of the SAX04 aousti baksattering measurements. The results of this paper also an be used for upgrades of existing sediment parameter data bases and empirial algorithms. APPEDIX A EMPIRICAL RELATIOSHIPS FOR PARTICLE CHARACTERIZATIO: POWER LAW APPROXIMATIO Seeral empirial relationships between parameters haraterizing the partile shape and size distributions were presented in this paper. They all are approximated by power law expressions and summarized below. The olume ratio for the two populations, shell (arbonate) and sand (uartz) partiles, R, and orresponding number-ratio, R, are of the form and 4.5 R ( d) = 0.06 d (A.1) 4.62 R ( d) = 0.13d, (A.2) where the siee size d is expressed in millimeters. Correspondingly, the R - parameter, the ratio of the shape fators of arbonate and uartz partiles,, is of the form F / F, also referred to as the ratio of the ratios, R / R 0.12 R ( d) = 0.45d. (A.3) The shape fators themseles an be approximated by power laws as follows: 0.45 F ( d) = 0.7 d (A.4) for arbonate partiles, and 0.33 F ( d) = 1.56d (A.5) for uartz partiles. They an be used to uantify a typial shape of partiles in eah population. The euialent diameters are found to be and 0.85 D ( d) = 0.89 d (A.6) 0.89 D ( d) = 1.16d (A.7) for arbonate and uartz partiles, respetiely. APPEDIX B PHASE RELATIOSHIPS I QUARTZ/CARBOATE MIXTURE The aerage density in the uartz/arbonate mixture, ρ, and the olume ratio of the two omponents, follows: ρ = R ρ + ρ, R + 1 R ρ ρ = ρ ρ, (B.1) R, are related as where ρ and ρ are the uartz and arbonate densities, respetiely. The olume-size distributions of the arbonate and uartz