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Acoustic measurement of suspensions of clay and silt particles using single frequency attenuation and backscatter
Applied Acoustics 85 (2014) 123–129
Contents lists available at ScienceDirect
Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Acoustic measurement of suspensions of clay and silt particles using single frequency attenuation and backscatter Wayne O. Carpenter, Jr. a,⇑, Bradley T. Goodwiller a, James P. Chambers a, Daniel G. Wren b, Roger A. Kuhnle b a b
National Center for Physical Acoustics, University of Mississippi, 1 Coliseum Drive, University, MS 38677-1848, United States USDA-ARS-NSL, P.O. Box 1157, Oxford, MS 38655, United States
a r t i c l e
i n f o
Article history: Received 16 July 2013 Received in revised form 21 January 2014 Accepted 15 April 2014
Keywords: Sediment Ultrasound Attenuation Backscatter Fines
a b s t r a c t The use of ultrasonic acoustic technology to measure the concentration of fine suspended sediments has the potential to greatly increase the temporal and spatial resolution of sediment measurements while reducing the need for personnel to be present at gauging stations during storm events. The conversion of high-frequency attenuation and backscatter amplitudes to suspended silt and clay concentration has received relatively little attention in the literature. In order to improve the state of knowledge, a laboratory investigation was undertaken by the National Center for Physical Acoustics in cooperation with the USDA-ARS National Sedimentation Laboratory. In these experiments, two immersion transducers were used to measure attenuation and backscatter from 20 MHz acoustic signals propagated through suspended clay (smectite and kaolinite) and silt particles. The resulting data includes attenuation values for a wide range of concentrations (0.3–14 g/L) and particle sizes (0.03–14 lm diameter). Attenuation curves for each particle were compared to the theoretical attenuation curves developed by Urick (1948) and Sheng and Hay (1988) for scattering as presented by Landers (2010) [5,11,12]. In addition, it was found that the backscatter signal could be used to discriminate between suspensions dominated by clay or silt. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction In many streams, suspended sediment transport is dominated by a few significant storms each year [1]. These flood events are hard to predict and frequently occur at night, making it difficult and expensive to collect physical sediment samples. Traditional sampling techniques, including manually deployed isokinetic samplers and automatic pumping samplers, yield samples that are widely spaced in time and small in number. Ultrasonic measurement systems have the potential to measure the concentration of particles with a high degree of both spatial and temporal resolution, making them ideal for addressing the needs of those who rely on sediment data [2–4]. There is a relatively small body of literature relevant to the measurement of fine sediments with an ultrasonic system. Urick [5] measured attenuation with 1, 5, and 15 MHz frequencies pulsed ⇑ Corresponding author. Tel.: +1 662 915 7839. E-mail addresses: [email protected] (W.O. Carpenter, Jr.), btgoodwi@ olemiss.edu (B.T. Goodwiller), [email protected] (J.P. Chambers), Daniel. [email protected] (D.G. Wren), [email protected] (R.A. Kuhnle). http://dx.doi.org/10.1016/j.apacoust.2014.04.013 0003-682X/Ó 2014 Elsevier Ltd. All rights reserved.
in 1 ls bursts in an aqueous suspension of kaolinite and finely ground quartz and concluded that viscous interactions were largely responsible for the observed acoustic absorption. Flammer [6] measured attenuation due to the scattering of 2.5–25 MHz signals propagated through a suspension of 44–1000 lm particles. Measuring kaolinite/water suspensions with near 40% solid-volume at 3.5 and 7 MHz, Green and Esquivel–Sirvent [7] found that increasing frequency produced only a moderate increase in attenuation and a slight increase in the concentration of maximum absorption. Richards et al. [8] demonstrated over-prediction of attenuation by the spherically based model of Urick [5] when applied to suspensions of oblate spheroidal shape. This paper describes experiments aimed at the development of a device that uses measurements of acoustic signal attenuation and backscatter from clay and silt particles to determine the particle concentration. Unlike the methods discussed, this study investigates the use of a single ultrasonic quality to measure both attenuation and backscatter; thereby, reducing deployment costs associated with multifrequency systems. Silt and two clays, smectite and kaolinite, were used to represent typical constituents of the fine sediment load for streams.
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backscattered acoustic signals were each amplified by an Olympus 5682 500 kHz–25 MHz preamplifier and then captured with a National Instruments 2-channel, 8-bit, 2GS/s oscilloscope card (NI PXI-PCI-5152). The following procedure was used for experiments where a single particle type was used. 1. Conduct clear-water measurements of backscatter and attenuation to establish baseline signal levels. 2. Add 1 g of the test particle to the tank and allow to mix thoroughly then re-take acoustic measurements. 3. Increase the mass of the particle in pre-determined increments and take acoustic data. The following procedure was used for experiments where mixed particle-types were used. See Table 1 for the amounts of each particle-type used in the mixture experiments.
Fig. 1. Experimental lab setup.
2. Methods and equipment The experiments were performed in a 110 gallon (416.9 L) elliptically shaped (126 cm long, 85 cm wide, and 51.5 cm deep) recirculation tank at the University of Mississippi National Center for Physical Acoustics (NCPA). The water was processed by an Aries HY-122B-DI Hydra deionizing system and treated with Sodium Hexametaphosphate (SH) to inhibit particle aggregation. The water and particles were re-circulated using a Weg ½ hp 220 V centrifugal pump. Aluminum rails were mounted on top of the test tank to allow three-dimensional alignment of the transducers, and a point gauge was used to establish the water depth. The transducer setup in recirculation tank is illustrated in Fig. 1. Two 20 MHz immersion transducers were aimed at each other; one transducer sent the acoustic signals and one transducer received the transmitted signals. The transducer sending the acoustic signal also received the backscattered signal. The transducers were placed 4.5 cm under the water surface and separated by 18 cm, which was determined by Carpenter et al. [9] to be the distance that maximized the attenuated signal while allowing sufficient sensitivity at low concentrations. Statistical variations in backscattered signal due to the random relative motion of the particles were minimized by averaging 100 bursts per data set. A Hewlett Packard 3314A function generator was used to generate a continuous 10 Vpeak acoustic waveform. A Stanford Research Systems DS345 synthesized function generator created a modulated burst wave with a frequency of 200 kHz and amplitude of 1 Vpeak. Both signals were sent to a Ritec GA 2500 gated RF amplifier to create a composite gated signal at 300 Vpeak–peak. The resulting signal was sent and received with NDT Systems IBHG202 20 MHz immersion transducers with a 1=4 ’’ (6 mm) diameter. The near-field length, N, for the transducers was 13.6 cm and the half angle beam width was 0.365°. With a separation of 18 cm, the transducers were in the far field and had no multipath effects from the water surface. The attenuated and
1. Conduct clear water measurements of backscatter and attenuation. 2. Add 500 g of a given particle (A) and take backscatter and attenuation measurements. 3. Increase the mass of a second particle type (B) in increments (i.e. 1g, 2g, 5g, 10g, etc.) and continue to take measurements until the additions of (B) were 2:1 with respect to particle type (A). 4. Add material and take measurements for each of the following additions of A (100 g, 200 g, 500 g, and 1 kg) while holding particle (B) constant. The equation proposed by Urick [5] requires particle size information in order to estimate attenuation; however, obtaining accurate particle sizes for clays and silts is difficult. Particle aggregates caused by flocculation are difficult to measure and impossible to completely prevent, even when a deflocculant is used. Clay mineralogy affects the shape of the particles, making it difficult to determine a representative diameter. In addition, the sources of the obtained clay and silt in this study do not rigorously control the size range of particles. To confirm the composition of the clay particles, an X-ray diffraction study was performed by The Mineral Lab, Inc. (Table 2). The study indicates that the smectite sample was primarily comprised of smectite (>80%), while the kaolinite sample was 65% kaolinite. The study also included scanning electron micrographs,
Table 1 Mass of particles used in the mixture experiments. Run number
Mass of particle A (g)
Mass of particle B (g)
Total concentration (g/L)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
0 500 500 500 500 500 500 500 500 500 500 500 1000 1000 1100 1200 1500 2000
0 0 1 2 5 10 20 50 100 200 500 1000 1000 2000 2000 2000 2000 2000
0.000 1.404 1.407 1.410 1.419 1.433 1.461 1.545 1.685 1.966 2.809 4.213 5.618 8.427 8.708 8.989 9.831 11.236
W.O. Carpenter, Jr. et al. / Applied Acoustics 85 (2014) 123–129
spacing allows for larger fractions of the sampling volume to have minimal flow disturbance in streams.
Table 2 X-ray diffraction analysis results. Mineral name
Smectite Kaolinite Mica/Illite Quartz Plagiolcase feldspar K-feldspar Calcite Gypsum Goethite Rutile ‘‘Unidentified’’
125
Approx. wt.% Smectite sample
Kaolinite Sample
>80 – <3 <5 <5 <3 <5 <2 – – <5
>5 65 17 7 – 5 – – – – <5
4. Results 4.1. Attenuation The results in Fig. 3 shows that silt typically caused the most attenuation for a given particle concentration, followed by kaolinite and then smectite. The experimental results were compared with the combined attenuation curve from Urick [5] and the curve for backscatter form factor presented by Sheng and Hay [11] as presented by Landers [12]:
which showed that the dry particles were complex assemblages of aggregates (Fig. 2). Based on the X-ray diffraction analysis results, the samples were assumed to be entirely comprised of their main constituent. This assumption may introduce uncertainty, if the constituents other than the primary clay mineral affected the size and shape of the aggregates that were present in the test tank at the time of measurement. In concentration measurements, the specific mineralogy of the sediment is not typically important unless it affects the size of the particles. A Sequoia Scientific LISST-100X (Laser In-Situ Scattering and Transmissometry), which is an in-situ laser diffraction particle size measurement device, was used to measure the size of particles during experiments. The approach met with limited success, since the lower particle diameter limit of the instrument is 2.5 lm, which is too coarse to detect primary particles or small aggregates of either smectite or kaolinite. Nominal sizes of clays have been published by Mehta and McAnally [10]; however, it was clear that the clay particles in the experiments formed aggregates or flocs. Mean particle sizes of 30 lm for the silt and 8 lm for the kaolinite were measured with the LISST-100X during the single particle-type experiments. The diameter of the smectite particles, as measured by the LISST-100X, was incorrect since nearly all of the data were contained in the 2.5 lm size bin, indicating only that the particles were smaller than 2.5 lm.
3. Theory Attenuation was computed by measuring the signal loss through the suspended particle mixture and subtracting the clear water signal level from it. The hardware had a minimum resolution of approximately 0.5 dB, which imposed a minimum detectable concentration of approximately 0.3 g/L for the attenuation measurements. The backscatter amplitude was represented by the difference in the root mean square (rms) signal, calculated over a 15–20 microsecond interrogation window, for the clear water and particle laden cases. Since this time window fell within the ring-down of the transducer, the rms value of the clear water ring-down was used as the noise floor for each data run. Each data value was the average backscatter from 100 pings. The 20 MHz frequency was chosen as a frequency for which commercial transducers are available while insuring that the wavelength would be small enough to result in measurable attenuation values for particles <1 lm. The work of Carpenter et al. [9] demonstrated that there was measurable attenuation for suspensions of silts and clays, and it was found that a range of 180 mm was close enough to allow for measurable signal propagation at high sediment concentrations while still maintaining sensitivity to low concentrations. As opposed to smaller ranges, the 180 mm
Fig. 2. Scanning electron micrographs for (a) silt, (b) kaolinite, and (c) smectite.
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as ¼ SSC v kðc 1Þ2
!
s s2
þ ð c þ sÞ 2
4
þ
k a3s 2
4
5 1 þ 1:3k a2s þ 0:24k a4s
8:686 2
ð1Þ
where as is a coefficient of attenuation, measured in (dB/cm); SSCv is the volumetric sediment concentration (SSC divided by the sediment density); k is the wave number, k ¼ 2kp, where k is the wavelength in cm, c is the specific gravity of the sediment, and as h i h i h i 9 9 1 þ ba1s s ¼ 0:5 þ 4ba is the sediment radius in cm, s ¼ 4ba s s 0:5 b ¼ 2xm , x = 2pf and m is the kinematic viscosity of the water. Fig. 4 shows 20 MHz attenuation from Eq. (1) for a range of particle sizes for five particle concentrations. Implicit in the use of the Urick–Sheng–Hay approach is the assumption of spherical particles. Fig. 2 shows that this is a reasonable approximation for silt and smectite, and less appropriate for kaolinite, which appears to be more sheet-like. Nevertheless, for the simplicity of using a single attenuation model, the Urick–Sheng–Hay equation was used for all particle types. To measure the effectiveness of these estimations, the error of the fit relative to the error of the data was calculated using:
E¼
Ri ðai ei Þ2 Ri ðai aÞ2
Fig. 3. Attenuated signal level (dBV) for clay and silt concentrations (0.01–14.1 g/L).
ð2Þ
where ai is the measured value for concentration (i) and, ei is the estimated value for concentration (i). The iterative process was performed by choosing a particle size followed by applying Eq. (2) and repeating this process until the lowest value of E from Eq. (2) was achieved. For a given fitting method, Eq. (2) was used to compare the estimated concentration to the measured concentration in order to get measure of the goodness of fit. Smaller values of E indicate a better fit. Note that this ratio can be greater than one (see Table 3). Fig. 5 shows the result of an iterative process aimed at finding the particle size that produced the best agreement between the attenuation data and Eq. (1). The resulting particle sizes were: silt = 14 lm, smectite = 0.029 lm, and kaolinite = 6 lm. The iteratively-determined sizes of the silt and kaolinite were in roughly the same range as the in situ sizes measured by the LISST-100X of 30 lm for the silt and 8 lm for the kaolinite. The results of the fitting process were chosen to represent the particle sizes for the remaining analyses. Fig. 2a shows that there are a range of particle sizes for the silt and that both 14 and 30 lm represent a significant fraction of the size distribution. A representative size for kaolinite in Fig. 2b is not as clear, although 8 lm does not appear to be unreasonable. In the absence of a device like the LISST-100X, the process of matching the attenuation and particle size is an approach that could be used by a practitioner to calibrate an acoustic system. The LISST-100X is an expensive device that may not be available; therefore, an approach that led to particle size estimates that were not dependent on its measurements was chosen. Additionally, the LISST-100X was not able to measure the size of the smectite, necessitating the use of an alternative method for estimating particle size. 4.2. Particle size discrimination using backscatter Using the attenuation and backscatter data, an approximate range for particle size can be found. Only the silt particles produced measurable backscatter, as shown in Fig. 6. Note that the signal levels are all changes relative to the clear water signal. For future applications in field research, this should allow a similar acoustic system to be calibrated relative to clear water measurements,
Fig. 4. Attenuation at 20 MHz from Eq. (1) for a range of particle sizes and concentrations.
Fig. 5. Data plotted with particle sizes that provided the best agreement with the measured attenuation data.
rather than requiring data collected from a full set of particle sizes. The following conditional statements can be used to make a coarse estimate of the particle size (also see Table 4): 1. If the backscatter level is greater than 1 dB and attenuation is greater than 2 dB, the particle type is likely silt.
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W.O. Carpenter, Jr. et al. / Applied Acoustics 85 (2014) 123–129 Table 3 Particle sizes resulting from optimizing the fit of Eq. (1) to the measured attenuation data. Lower values of E (Eq. (2)) represent a better fit.
E Particle size (lm)
Table 5 Error (E) values for concentration, calculated using measured attenuation data in Eq. (1), for a range of assumed particle sizes.
Smectite
Kaolinite
Silt
Mixture
0.026 0.029
0.011 6.0
0.025 14
Silt w/smectite Smectite w/silt Silt w/kaolinite Kaolinite w/silt Smectite only Kaolinite only Silt only
0.01 lm
0.1 lm
1 lm
10 lm
100 lm
2450 1020 1030 357 72.4 344 439
0.518 1.01 0.971 1.44 1.02 0.717 0.653
0.710 1.17 1.14 1.56 1.07 0.803 0.746
3.63 0.592 0.511 0.081 0.287 0.023 0.091
0.834 1.28 1.25 1.64 1.09 0.854 0.801
shape of the attenuation curve shown in Fig. 4, where it can be observed that the attenuation coefficient for a given concentration at 0.029 lm (found earlier by iteration as the best fit to the attenuation data) is similar to a given concentration at 10 lm, because of a dip in the curve. This resulted in a better fit using 10 lm than the tested particle sizes that were nearer to 0.029 lm, which again highlights the need for accurate particle size data. There is not a clear pattern among the mixtures, although the lowest set of E values was produced by the 0.1 lm particle size. If the set of E values for each particle-size assumption for combined mixture and single particle-type data is considered, the 10 lm size produced the smallest error value. Fig. 6. Backscattered signal level (dBV) for silt concentrations from 0.1 to 5.7 g/L.
Table 4 Classification of particle types using combined attenuation and backscatter data. Backscatter
Attenuation
Particle-type
High (>1 dB) Low (0–1 dB) Low (0 dB)
High (>2 dB) High (>1 dB) Low (<1 dB)
Silt Clay Very low concentration
2. If low backscatter (0–1 dB) and high attenuation (1–2 dB) are measured, the suspended material is likely fine clay. 3. Low attenuation and backscatter magnitudes (<0.5 dB) indicate sediment transport below the detection threshold of the hardware, which is approximately 0.3 g/L for the equipment used here. 4.3. Estimating suspended sediment concentration
4.3.2. Smallest particle size Here, the smallest particle-type present was assumed to be representative of the entire mixture. For the smallest particle size method, the size values determined from the iterative process were used. Thus, for mixtures featuring kaolinite, a size value of 6 lm was used and for mixtures featuring smectite, 0.029 lm was used for the particle diameter. This approach yielded a good correspondence between acoustically measured and known concentration for the experiments in which clay was dominant in the mixture. This includes the first parts of the smectite with silt additions, and kaolinite with silt additions shown in Figs. 7 and 8. Estimated concentrations for silt and smectite were nearly always higher than the measured concentrations, and the error increased with concentration (Fig. 7). Fig. 8 shows much better agreement for silt and kaolinite mixtures. 4.3.3. Largest particle size The largest particle-type in the mixture was used as the representative particle size, which was silt for both mixtures. This approach yielded good estimates of particle concentration when
Before Eq. (1) can be used to estimate particle concentration from attenuation measurements, a particle size must be selected. Four approaches for choosing a representative particle size are demonstrated below. 4.3.1. No information about particles in suspension available Five different particle sizes were used to illustrate the range of errors that may be expected if no information about particle size is available: 0.01, 0.1, 1, 10 and 100 lm. Eq. (1) was used to convert the measured attenuation for each particle size into concentration estimates for each of the mixtures shown in Table 1, and a separate estimate was calculated for each of the assumed particle sizes. These estimated concentrations were then compared to the measured concentrations using Eq. (2). Table 5 shows that the highest errors resulted from using the 0.01 lm particle size. All of the sizes larger than 0.01 lm yielded much lower error values. For kaolinite and silt, the lowest values of E were found for the 10 lm particle size, which most nearly corresponded to the sizes found from the iterative fit and from the LISST-100X measurements. Smectite also fit the best for the 10 lm size; this can be accounted for by the
Fig. 7. Concentrations from Eq. (1), based on the smallest particle size in the smectite/silt mixtures. The solid line indicates perfect agreement.
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Fig. 8. Concentrations from Eq. (1), based on the smallest particle size in the kaolinite/silt mixtures. The solid line indicates perfect agreement.
Fig. 11. Concentrations from Eq. (1), based on the mass-weighted particle size for the smectite/silt mixtures. The solid line indicates perfect agreement.
smectite flocs as added. In turn, the larger initial smectite concentrations would potentially yield greater smectite flocs initially. Fig. 10 shows good correspondence between the estimated and measured values for the silt with kaolinite additions, but the concentrations for kaolinite with silt additions were consistently underestimated. 4.3.4. Mass-weighted particle size Figs. 11 and 12 show the results of using the weighted-mean particle size in the conversion to concentration. The weightedmean particle size was based on the mass of each particle-type:
ar ¼
Fig. 9. Concentrations from Eq. (1), based on the largest particle size in the smectite/silt mixtures. The solid line indicates perfect agreement.
M 1 a1 þ M2 a2 M1 þ M2
ð3Þ
where ar is the representative particle size, and a1, M1 are the particle size and mass of one particle-type. Fig. 11 shows that the estimated concentrations were typically higher than the measured concentrations, and the error increased with concentration. Fig. 12 demonstrates better agreement for the silt/kaolinite mixtures.
silt was dominant in the mixture (Figs. 9 and 10). Fig. 9 has a higher estimated than measured concentration for the silt with smectite additions; however, the smectite with silt additions plot shows the opposite. One explanation for this occurrence can be attributed to the larger silt concentration creating shearing of the
Error values of a given clay/silt mixture are shown in Table 6 for each method of choosing particle size. It is evident that incorrect
Fig. 10. Concentrations from Eq. (1), based on the largest particle size for the kaolinite/silt mixture. The solid line indicates perfect agreement.
Fig. 12. Concentrations from Eq. (1), based on the mass-weighted particle size for the kaolinite/silt mixtures. The solid line indicates perfect agreement.
4.4. Comparison of methods for choosing particle size
W.O. Carpenter, Jr. et al. / Applied Acoustics 85 (2014) 123–129 Table 6 Error (E) values for concentration, calculated using measured attenuation data in Eq. (1), for three particle size estimation strategies. Mixture
Smallest particle
Largest particle
Mass-weighted particle size
Silt w/smectite Smectite w/silt Silt w/kaolinite Kaolinite w/silt
27 8.0 0.58 0.090
0.86 0.090 0.020 0.37
2.7 0.80 0.53 0.11
choice of particle size can result in large errors and that the lowest error values were generated by using the largest particle-type to represent the mixture. This result is also supported by Fig. 3, where it was shown that silt caused the highest attenuation among the particle-types. Mixtures with smectite present were almost uniformly underestimated for each of the methods. This may be due to the strong aggregation effect of smectite which was shown in the LISST-100X size data collected during the mixture experiments. Further research will be needed before accurate attenuation-based concentration measurements in smectite mixtures will be possible. For a suspension of clays and silts, where the particle sizes or relative concentrations are not known, the best strategy may be to assume a size in the silt range. If the results here can be extended to natural streams, which is unknown at this point, a size in the lower end of the silt-size range may be preferable. Note that the combination of backscatter and attenuation described above could be used to determine the dominant size fraction. 5. Conclusions Acoustic measurement of fine particle concentration in water using a combination of backscatter and attenuation was investigated. A method for combining attenuation and backscatter measurements for discriminating between clay and silt particles was presented. Backscatter amplitudes were not responsive to suspended clays, but were weakly responsive to suspended silts. Based on the data presented here, it is likely that the combination of backscatter and attenuation will allow for a rough discrimination between suspensions dominated by clay or silt in the field. Specific summary conclusions are listed below: 1. Backscatter data made it possible to distinguish between clays and silts for concentrations greater than approximately 0.5 g/L.
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2. Using the combined Urick–Sheng–Hay equation (Eq. (1)) to convert attenuation to concentration worked well for single particle types with known particle sizes and concentrations greater than 0.3 g/L. 3. For mixtures, using the largest particle-type as a representative particle size generally provided the best estimate of particle concentration. 4. Attenuation-based concentration estimates for mixtures containing smectite were difficult and resulted in high error values for several methods of choosing a representative particle size.
Acknowledgements This work was funded by the Federal Interagency Sedimentation Project (FISP). Capable technical support was provided by Glenn Gray of the National Sedimentation Laboratory and Alex Kajdan at the University of Mississippi. References [1] Nelson ME, Benedict PC. Measurement and analysis of suspended loads in streams. Trans Am Soc Civ Eng Proc Separate 1950(31):891–918. Paper No. 2450. [2] Shen C, Lemmin U. Ultrasonic measurements of suspended sediments: a concentration profiling system with attenuation compensation. Measur Sci Technol 1996;7:1191–4. [3] Thorne PD, Holdaway GP, Hardcastle PJ. Constraining acoustic backscatter estimates of suspended sediment concentration profiles using the bed echo. J Acoust Soc Am 1995;98(4):2285–6. [4] Moore SA, Le Coz J, Hurther D, Paquier A. Using multi-frequency acoustic attenuation to monitor grain size and concentrations of suspended sediment in rivers. J Acoust Soc Am 2013;133(4):1959–70. [5] Urick RJ. The absorption of sound in suspensions of irregular particles. J Acoust Soc Am 1948;20(1):283–9. [6] Flammer GH. Ultrasonic measurement of suspended sediment. U.S.G.S. Bul 1962;1141-A:48. [7] Green DH, Esquivel-Sirvent R. Acoustic behavior at the fluid/solid transition of kaolinite suspensions. J Geophys 1999;64(1):89. [8] Richards SD, Leighton TG, Brown NR. Visco-inertial absorption in dilute suspensions of irregular particles. Proc R Soc London A 2003;459(2153):2167. [9] Carpenter Jr WO, Chambers JP, Wren DG, Kuhnle RA, Diers JA. Acoustic measurements of clay-size particles. J Acoust Soc Am Express Lett 2009; 126(6):EL190–5. [10] Mehta AJ, McAnally WH. Fine-grained sediment transport in sedimentation engineering. ASCE Manual 2008;110:253–306. Chapter 4. [11] Sheng J, Hay AE. An examination of the spherical scatterer approximation in aqueous suspensions of sand. J Acoust Soc Am 1988;83(2):598–610. [12] Landers MN. Review of methods to estimate fluvial suspended sediment characteristics from acoustic surrogate metrics. Joint Federal Interagency Conf. 2010;2:1–2.
Contents lists available at ScienceDirect
Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Acoustic measurement of suspensions of clay and silt particles using single frequency attenuation and backscatter Wayne O. Carpenter, Jr. a,⇑, Bradley T. Goodwiller a, James P. Chambers a, Daniel G. Wren b, Roger A. Kuhnle b a b
National Center for Physical Acoustics, University of Mississippi, 1 Coliseum Drive, University, MS 38677-1848, United States USDA-ARS-NSL, P.O. Box 1157, Oxford, MS 38655, United States
a r t i c l e
i n f o
Article history: Received 16 July 2013 Received in revised form 21 January 2014 Accepted 15 April 2014
Keywords: Sediment Ultrasound Attenuation Backscatter Fines
a b s t r a c t The use of ultrasonic acoustic technology to measure the concentration of fine suspended sediments has the potential to greatly increase the temporal and spatial resolution of sediment measurements while reducing the need for personnel to be present at gauging stations during storm events. The conversion of high-frequency attenuation and backscatter amplitudes to suspended silt and clay concentration has received relatively little attention in the literature. In order to improve the state of knowledge, a laboratory investigation was undertaken by the National Center for Physical Acoustics in cooperation with the USDA-ARS National Sedimentation Laboratory. In these experiments, two immersion transducers were used to measure attenuation and backscatter from 20 MHz acoustic signals propagated through suspended clay (smectite and kaolinite) and silt particles. The resulting data includes attenuation values for a wide range of concentrations (0.3–14 g/L) and particle sizes (0.03–14 lm diameter). Attenuation curves for each particle were compared to the theoretical attenuation curves developed by Urick (1948) and Sheng and Hay (1988) for scattering as presented by Landers (2010) [5,11,12]. In addition, it was found that the backscatter signal could be used to discriminate between suspensions dominated by clay or silt. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction In many streams, suspended sediment transport is dominated by a few significant storms each year [1]. These flood events are hard to predict and frequently occur at night, making it difficult and expensive to collect physical sediment samples. Traditional sampling techniques, including manually deployed isokinetic samplers and automatic pumping samplers, yield samples that are widely spaced in time and small in number. Ultrasonic measurement systems have the potential to measure the concentration of particles with a high degree of both spatial and temporal resolution, making them ideal for addressing the needs of those who rely on sediment data [2–4]. There is a relatively small body of literature relevant to the measurement of fine sediments with an ultrasonic system. Urick [5] measured attenuation with 1, 5, and 15 MHz frequencies pulsed ⇑ Corresponding author. Tel.: +1 662 915 7839. E-mail addresses: [email protected] (W.O. Carpenter, Jr.), btgoodwi@ olemiss.edu (B.T. Goodwiller), [email protected] (J.P. Chambers), Daniel. [email protected] (D.G. Wren), [email protected] (R.A. Kuhnle). http://dx.doi.org/10.1016/j.apacoust.2014.04.013 0003-682X/Ó 2014 Elsevier Ltd. All rights reserved.
in 1 ls bursts in an aqueous suspension of kaolinite and finely ground quartz and concluded that viscous interactions were largely responsible for the observed acoustic absorption. Flammer [6] measured attenuation due to the scattering of 2.5–25 MHz signals propagated through a suspension of 44–1000 lm particles. Measuring kaolinite/water suspensions with near 40% solid-volume at 3.5 and 7 MHz, Green and Esquivel–Sirvent [7] found that increasing frequency produced only a moderate increase in attenuation and a slight increase in the concentration of maximum absorption. Richards et al. [8] demonstrated over-prediction of attenuation by the spherically based model of Urick [5] when applied to suspensions of oblate spheroidal shape. This paper describes experiments aimed at the development of a device that uses measurements of acoustic signal attenuation and backscatter from clay and silt particles to determine the particle concentration. Unlike the methods discussed, this study investigates the use of a single ultrasonic quality to measure both attenuation and backscatter; thereby, reducing deployment costs associated with multifrequency systems. Silt and two clays, smectite and kaolinite, were used to represent typical constituents of the fine sediment load for streams.
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backscattered acoustic signals were each amplified by an Olympus 5682 500 kHz–25 MHz preamplifier and then captured with a National Instruments 2-channel, 8-bit, 2GS/s oscilloscope card (NI PXI-PCI-5152). The following procedure was used for experiments where a single particle type was used. 1. Conduct clear-water measurements of backscatter and attenuation to establish baseline signal levels. 2. Add 1 g of the test particle to the tank and allow to mix thoroughly then re-take acoustic measurements. 3. Increase the mass of the particle in pre-determined increments and take acoustic data. The following procedure was used for experiments where mixed particle-types were used. See Table 1 for the amounts of each particle-type used in the mixture experiments.
Fig. 1. Experimental lab setup.
2. Methods and equipment The experiments were performed in a 110 gallon (416.9 L) elliptically shaped (126 cm long, 85 cm wide, and 51.5 cm deep) recirculation tank at the University of Mississippi National Center for Physical Acoustics (NCPA). The water was processed by an Aries HY-122B-DI Hydra deionizing system and treated with Sodium Hexametaphosphate (SH) to inhibit particle aggregation. The water and particles were re-circulated using a Weg ½ hp 220 V centrifugal pump. Aluminum rails were mounted on top of the test tank to allow three-dimensional alignment of the transducers, and a point gauge was used to establish the water depth. The transducer setup in recirculation tank is illustrated in Fig. 1. Two 20 MHz immersion transducers were aimed at each other; one transducer sent the acoustic signals and one transducer received the transmitted signals. The transducer sending the acoustic signal also received the backscattered signal. The transducers were placed 4.5 cm under the water surface and separated by 18 cm, which was determined by Carpenter et al. [9] to be the distance that maximized the attenuated signal while allowing sufficient sensitivity at low concentrations. Statistical variations in backscattered signal due to the random relative motion of the particles were minimized by averaging 100 bursts per data set. A Hewlett Packard 3314A function generator was used to generate a continuous 10 Vpeak acoustic waveform. A Stanford Research Systems DS345 synthesized function generator created a modulated burst wave with a frequency of 200 kHz and amplitude of 1 Vpeak. Both signals were sent to a Ritec GA 2500 gated RF amplifier to create a composite gated signal at 300 Vpeak–peak. The resulting signal was sent and received with NDT Systems IBHG202 20 MHz immersion transducers with a 1=4 ’’ (6 mm) diameter. The near-field length, N, for the transducers was 13.6 cm and the half angle beam width was 0.365°. With a separation of 18 cm, the transducers were in the far field and had no multipath effects from the water surface. The attenuated and
1. Conduct clear water measurements of backscatter and attenuation. 2. Add 500 g of a given particle (A) and take backscatter and attenuation measurements. 3. Increase the mass of a second particle type (B) in increments (i.e. 1g, 2g, 5g, 10g, etc.) and continue to take measurements until the additions of (B) were 2:1 with respect to particle type (A). 4. Add material and take measurements for each of the following additions of A (100 g, 200 g, 500 g, and 1 kg) while holding particle (B) constant. The equation proposed by Urick [5] requires particle size information in order to estimate attenuation; however, obtaining accurate particle sizes for clays and silts is difficult. Particle aggregates caused by flocculation are difficult to measure and impossible to completely prevent, even when a deflocculant is used. Clay mineralogy affects the shape of the particles, making it difficult to determine a representative diameter. In addition, the sources of the obtained clay and silt in this study do not rigorously control the size range of particles. To confirm the composition of the clay particles, an X-ray diffraction study was performed by The Mineral Lab, Inc. (Table 2). The study indicates that the smectite sample was primarily comprised of smectite (>80%), while the kaolinite sample was 65% kaolinite. The study also included scanning electron micrographs,
Table 1 Mass of particles used in the mixture experiments. Run number
Mass of particle A (g)
Mass of particle B (g)
Total concentration (g/L)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
0 500 500 500 500 500 500 500 500 500 500 500 1000 1000 1100 1200 1500 2000
0 0 1 2 5 10 20 50 100 200 500 1000 1000 2000 2000 2000 2000 2000
0.000 1.404 1.407 1.410 1.419 1.433 1.461 1.545 1.685 1.966 2.809 4.213 5.618 8.427 8.708 8.989 9.831 11.236
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spacing allows for larger fractions of the sampling volume to have minimal flow disturbance in streams.
Table 2 X-ray diffraction analysis results. Mineral name
Smectite Kaolinite Mica/Illite Quartz Plagiolcase feldspar K-feldspar Calcite Gypsum Goethite Rutile ‘‘Unidentified’’
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Approx. wt.% Smectite sample
Kaolinite Sample
>80 – <3 <5 <5 <3 <5 <2 – – <5
>5 65 17 7 – 5 – – – – <5
4. Results 4.1. Attenuation The results in Fig. 3 shows that silt typically caused the most attenuation for a given particle concentration, followed by kaolinite and then smectite. The experimental results were compared with the combined attenuation curve from Urick [5] and the curve for backscatter form factor presented by Sheng and Hay [11] as presented by Landers [12]:
which showed that the dry particles were complex assemblages of aggregates (Fig. 2). Based on the X-ray diffraction analysis results, the samples were assumed to be entirely comprised of their main constituent. This assumption may introduce uncertainty, if the constituents other than the primary clay mineral affected the size and shape of the aggregates that were present in the test tank at the time of measurement. In concentration measurements, the specific mineralogy of the sediment is not typically important unless it affects the size of the particles. A Sequoia Scientific LISST-100X (Laser In-Situ Scattering and Transmissometry), which is an in-situ laser diffraction particle size measurement device, was used to measure the size of particles during experiments. The approach met with limited success, since the lower particle diameter limit of the instrument is 2.5 lm, which is too coarse to detect primary particles or small aggregates of either smectite or kaolinite. Nominal sizes of clays have been published by Mehta and McAnally [10]; however, it was clear that the clay particles in the experiments formed aggregates or flocs. Mean particle sizes of 30 lm for the silt and 8 lm for the kaolinite were measured with the LISST-100X during the single particle-type experiments. The diameter of the smectite particles, as measured by the LISST-100X, was incorrect since nearly all of the data were contained in the 2.5 lm size bin, indicating only that the particles were smaller than 2.5 lm.
3. Theory Attenuation was computed by measuring the signal loss through the suspended particle mixture and subtracting the clear water signal level from it. The hardware had a minimum resolution of approximately 0.5 dB, which imposed a minimum detectable concentration of approximately 0.3 g/L for the attenuation measurements. The backscatter amplitude was represented by the difference in the root mean square (rms) signal, calculated over a 15–20 microsecond interrogation window, for the clear water and particle laden cases. Since this time window fell within the ring-down of the transducer, the rms value of the clear water ring-down was used as the noise floor for each data run. Each data value was the average backscatter from 100 pings. The 20 MHz frequency was chosen as a frequency for which commercial transducers are available while insuring that the wavelength would be small enough to result in measurable attenuation values for particles <1 lm. The work of Carpenter et al. [9] demonstrated that there was measurable attenuation for suspensions of silts and clays, and it was found that a range of 180 mm was close enough to allow for measurable signal propagation at high sediment concentrations while still maintaining sensitivity to low concentrations. As opposed to smaller ranges, the 180 mm
Fig. 2. Scanning electron micrographs for (a) silt, (b) kaolinite, and (c) smectite.
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as ¼ SSC v kðc 1Þ2
!
s s2
þ ð c þ sÞ 2
4
þ
k a3s 2
4
5 1 þ 1:3k a2s þ 0:24k a4s
8:686 2
ð1Þ
where as is a coefficient of attenuation, measured in (dB/cm); SSCv is the volumetric sediment concentration (SSC divided by the sediment density); k is the wave number, k ¼ 2kp, where k is the wavelength in cm, c is the specific gravity of the sediment, and as h i h i h i 9 9 1 þ ba1s s ¼ 0:5 þ 4ba is the sediment radius in cm, s ¼ 4ba s s 0:5 b ¼ 2xm , x = 2pf and m is the kinematic viscosity of the water. Fig. 4 shows 20 MHz attenuation from Eq. (1) for a range of particle sizes for five particle concentrations. Implicit in the use of the Urick–Sheng–Hay approach is the assumption of spherical particles. Fig. 2 shows that this is a reasonable approximation for silt and smectite, and less appropriate for kaolinite, which appears to be more sheet-like. Nevertheless, for the simplicity of using a single attenuation model, the Urick–Sheng–Hay equation was used for all particle types. To measure the effectiveness of these estimations, the error of the fit relative to the error of the data was calculated using:
E¼
Ri ðai ei Þ2 Ri ðai aÞ2
Fig. 3. Attenuated signal level (dBV) for clay and silt concentrations (0.01–14.1 g/L).
ð2Þ
where ai is the measured value for concentration (i) and, ei is the estimated value for concentration (i). The iterative process was performed by choosing a particle size followed by applying Eq. (2) and repeating this process until the lowest value of E from Eq. (2) was achieved. For a given fitting method, Eq. (2) was used to compare the estimated concentration to the measured concentration in order to get measure of the goodness of fit. Smaller values of E indicate a better fit. Note that this ratio can be greater than one (see Table 3). Fig. 5 shows the result of an iterative process aimed at finding the particle size that produced the best agreement between the attenuation data and Eq. (1). The resulting particle sizes were: silt = 14 lm, smectite = 0.029 lm, and kaolinite = 6 lm. The iteratively-determined sizes of the silt and kaolinite were in roughly the same range as the in situ sizes measured by the LISST-100X of 30 lm for the silt and 8 lm for the kaolinite. The results of the fitting process were chosen to represent the particle sizes for the remaining analyses. Fig. 2a shows that there are a range of particle sizes for the silt and that both 14 and 30 lm represent a significant fraction of the size distribution. A representative size for kaolinite in Fig. 2b is not as clear, although 8 lm does not appear to be unreasonable. In the absence of a device like the LISST-100X, the process of matching the attenuation and particle size is an approach that could be used by a practitioner to calibrate an acoustic system. The LISST-100X is an expensive device that may not be available; therefore, an approach that led to particle size estimates that were not dependent on its measurements was chosen. Additionally, the LISST-100X was not able to measure the size of the smectite, necessitating the use of an alternative method for estimating particle size. 4.2. Particle size discrimination using backscatter Using the attenuation and backscatter data, an approximate range for particle size can be found. Only the silt particles produced measurable backscatter, as shown in Fig. 6. Note that the signal levels are all changes relative to the clear water signal. For future applications in field research, this should allow a similar acoustic system to be calibrated relative to clear water measurements,
Fig. 4. Attenuation at 20 MHz from Eq. (1) for a range of particle sizes and concentrations.
Fig. 5. Data plotted with particle sizes that provided the best agreement with the measured attenuation data.
rather than requiring data collected from a full set of particle sizes. The following conditional statements can be used to make a coarse estimate of the particle size (also see Table 4): 1. If the backscatter level is greater than 1 dB and attenuation is greater than 2 dB, the particle type is likely silt.
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W.O. Carpenter, Jr. et al. / Applied Acoustics 85 (2014) 123–129 Table 3 Particle sizes resulting from optimizing the fit of Eq. (1) to the measured attenuation data. Lower values of E (Eq. (2)) represent a better fit.
E Particle size (lm)
Table 5 Error (E) values for concentration, calculated using measured attenuation data in Eq. (1), for a range of assumed particle sizes.
Smectite
Kaolinite
Silt
Mixture
0.026 0.029
0.011 6.0
0.025 14
Silt w/smectite Smectite w/silt Silt w/kaolinite Kaolinite w/silt Smectite only Kaolinite only Silt only
0.01 lm
0.1 lm
1 lm
10 lm
100 lm
2450 1020 1030 357 72.4 344 439
0.518 1.01 0.971 1.44 1.02 0.717 0.653
0.710 1.17 1.14 1.56 1.07 0.803 0.746
3.63 0.592 0.511 0.081 0.287 0.023 0.091
0.834 1.28 1.25 1.64 1.09 0.854 0.801
shape of the attenuation curve shown in Fig. 4, where it can be observed that the attenuation coefficient for a given concentration at 0.029 lm (found earlier by iteration as the best fit to the attenuation data) is similar to a given concentration at 10 lm, because of a dip in the curve. This resulted in a better fit using 10 lm than the tested particle sizes that were nearer to 0.029 lm, which again highlights the need for accurate particle size data. There is not a clear pattern among the mixtures, although the lowest set of E values was produced by the 0.1 lm particle size. If the set of E values for each particle-size assumption for combined mixture and single particle-type data is considered, the 10 lm size produced the smallest error value. Fig. 6. Backscattered signal level (dBV) for silt concentrations from 0.1 to 5.7 g/L.
Table 4 Classification of particle types using combined attenuation and backscatter data. Backscatter
Attenuation
Particle-type
High (>1 dB) Low (0–1 dB) Low (0 dB)
High (>2 dB) High (>1 dB) Low (<1 dB)
Silt Clay Very low concentration
2. If low backscatter (0–1 dB) and high attenuation (1–2 dB) are measured, the suspended material is likely fine clay. 3. Low attenuation and backscatter magnitudes (<0.5 dB) indicate sediment transport below the detection threshold of the hardware, which is approximately 0.3 g/L for the equipment used here. 4.3. Estimating suspended sediment concentration
4.3.2. Smallest particle size Here, the smallest particle-type present was assumed to be representative of the entire mixture. For the smallest particle size method, the size values determined from the iterative process were used. Thus, for mixtures featuring kaolinite, a size value of 6 lm was used and for mixtures featuring smectite, 0.029 lm was used for the particle diameter. This approach yielded a good correspondence between acoustically measured and known concentration for the experiments in which clay was dominant in the mixture. This includes the first parts of the smectite with silt additions, and kaolinite with silt additions shown in Figs. 7 and 8. Estimated concentrations for silt and smectite were nearly always higher than the measured concentrations, and the error increased with concentration (Fig. 7). Fig. 8 shows much better agreement for silt and kaolinite mixtures. 4.3.3. Largest particle size The largest particle-type in the mixture was used as the representative particle size, which was silt for both mixtures. This approach yielded good estimates of particle concentration when
Before Eq. (1) can be used to estimate particle concentration from attenuation measurements, a particle size must be selected. Four approaches for choosing a representative particle size are demonstrated below. 4.3.1. No information about particles in suspension available Five different particle sizes were used to illustrate the range of errors that may be expected if no information about particle size is available: 0.01, 0.1, 1, 10 and 100 lm. Eq. (1) was used to convert the measured attenuation for each particle size into concentration estimates for each of the mixtures shown in Table 1, and a separate estimate was calculated for each of the assumed particle sizes. These estimated concentrations were then compared to the measured concentrations using Eq. (2). Table 5 shows that the highest errors resulted from using the 0.01 lm particle size. All of the sizes larger than 0.01 lm yielded much lower error values. For kaolinite and silt, the lowest values of E were found for the 10 lm particle size, which most nearly corresponded to the sizes found from the iterative fit and from the LISST-100X measurements. Smectite also fit the best for the 10 lm size; this can be accounted for by the
Fig. 7. Concentrations from Eq. (1), based on the smallest particle size in the smectite/silt mixtures. The solid line indicates perfect agreement.
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Fig. 8. Concentrations from Eq. (1), based on the smallest particle size in the kaolinite/silt mixtures. The solid line indicates perfect agreement.
Fig. 11. Concentrations from Eq. (1), based on the mass-weighted particle size for the smectite/silt mixtures. The solid line indicates perfect agreement.
smectite flocs as added. In turn, the larger initial smectite concentrations would potentially yield greater smectite flocs initially. Fig. 10 shows good correspondence between the estimated and measured values for the silt with kaolinite additions, but the concentrations for kaolinite with silt additions were consistently underestimated. 4.3.4. Mass-weighted particle size Figs. 11 and 12 show the results of using the weighted-mean particle size in the conversion to concentration. The weightedmean particle size was based on the mass of each particle-type:
ar ¼
Fig. 9. Concentrations from Eq. (1), based on the largest particle size in the smectite/silt mixtures. The solid line indicates perfect agreement.
M 1 a1 þ M2 a2 M1 þ M2
ð3Þ
where ar is the representative particle size, and a1, M1 are the particle size and mass of one particle-type. Fig. 11 shows that the estimated concentrations were typically higher than the measured concentrations, and the error increased with concentration. Fig. 12 demonstrates better agreement for the silt/kaolinite mixtures.
silt was dominant in the mixture (Figs. 9 and 10). Fig. 9 has a higher estimated than measured concentration for the silt with smectite additions; however, the smectite with silt additions plot shows the opposite. One explanation for this occurrence can be attributed to the larger silt concentration creating shearing of the
Error values of a given clay/silt mixture are shown in Table 6 for each method of choosing particle size. It is evident that incorrect
Fig. 10. Concentrations from Eq. (1), based on the largest particle size for the kaolinite/silt mixture. The solid line indicates perfect agreement.
Fig. 12. Concentrations from Eq. (1), based on the mass-weighted particle size for the kaolinite/silt mixtures. The solid line indicates perfect agreement.
4.4. Comparison of methods for choosing particle size
W.O. Carpenter, Jr. et al. / Applied Acoustics 85 (2014) 123–129 Table 6 Error (E) values for concentration, calculated using measured attenuation data in Eq. (1), for three particle size estimation strategies. Mixture
Smallest particle
Largest particle
Mass-weighted particle size
Silt w/smectite Smectite w/silt Silt w/kaolinite Kaolinite w/silt
27 8.0 0.58 0.090
0.86 0.090 0.020 0.37
2.7 0.80 0.53 0.11
choice of particle size can result in large errors and that the lowest error values were generated by using the largest particle-type to represent the mixture. This result is also supported by Fig. 3, where it was shown that silt caused the highest attenuation among the particle-types. Mixtures with smectite present were almost uniformly underestimated for each of the methods. This may be due to the strong aggregation effect of smectite which was shown in the LISST-100X size data collected during the mixture experiments. Further research will be needed before accurate attenuation-based concentration measurements in smectite mixtures will be possible. For a suspension of clays and silts, where the particle sizes or relative concentrations are not known, the best strategy may be to assume a size in the silt range. If the results here can be extended to natural streams, which is unknown at this point, a size in the lower end of the silt-size range may be preferable. Note that the combination of backscatter and attenuation described above could be used to determine the dominant size fraction. 5. Conclusions Acoustic measurement of fine particle concentration in water using a combination of backscatter and attenuation was investigated. A method for combining attenuation and backscatter measurements for discriminating between clay and silt particles was presented. Backscatter amplitudes were not responsive to suspended clays, but were weakly responsive to suspended silts. Based on the data presented here, it is likely that the combination of backscatter and attenuation will allow for a rough discrimination between suspensions dominated by clay or silt in the field. Specific summary conclusions are listed below: 1. Backscatter data made it possible to distinguish between clays and silts for concentrations greater than approximately 0.5 g/L.
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2. Using the combined Urick–Sheng–Hay equation (Eq. (1)) to convert attenuation to concentration worked well for single particle types with known particle sizes and concentrations greater than 0.3 g/L. 3. For mixtures, using the largest particle-type as a representative particle size generally provided the best estimate of particle concentration. 4. Attenuation-based concentration estimates for mixtures containing smectite were difficult and resulted in high error values for several methods of choosing a representative particle size.
Acknowledgements This work was funded by the Federal Interagency Sedimentation Project (FISP). Capable technical support was provided by Glenn Gray of the National Sedimentation Laboratory and Alex Kajdan at the University of Mississippi. References [1] Nelson ME, Benedict PC. Measurement and analysis of suspended loads in streams. Trans Am Soc Civ Eng Proc Separate 1950(31):891–918. Paper No. 2450. [2] Shen C, Lemmin U. Ultrasonic measurements of suspended sediments: a concentration profiling system with attenuation compensation. Measur Sci Technol 1996;7:1191–4. [3] Thorne PD, Holdaway GP, Hardcastle PJ. Constraining acoustic backscatter estimates of suspended sediment concentration profiles using the bed echo. J Acoust Soc Am 1995;98(4):2285–6. [4] Moore SA, Le Coz J, Hurther D, Paquier A. Using multi-frequency acoustic attenuation to monitor grain size and concentrations of suspended sediment in rivers. J Acoust Soc Am 2013;133(4):1959–70. [5] Urick RJ. The absorption of sound in suspensions of irregular particles. J Acoust Soc Am 1948;20(1):283–9. [6] Flammer GH. Ultrasonic measurement of suspended sediment. U.S.G.S. Bul 1962;1141-A:48. [7] Green DH, Esquivel-Sirvent R. Acoustic behavior at the fluid/solid transition of kaolinite suspensions. J Geophys 1999;64(1):89. [8] Richards SD, Leighton TG, Brown NR. Visco-inertial absorption in dilute suspensions of irregular particles. Proc R Soc London A 2003;459(2153):2167. [9] Carpenter Jr WO, Chambers JP, Wren DG, Kuhnle RA, Diers JA. Acoustic measurements of clay-size particles. J Acoust Soc Am Express Lett 2009; 126(6):EL190–5. [10] Mehta AJ, McAnally WH. Fine-grained sediment transport in sedimentation engineering. ASCE Manual 2008;110:253–306. Chapter 4. [11] Sheng J, Hay AE. An examination of the spherical scatterer approximation in aqueous suspensions of sand. J Acoust Soc Am 1988;83(2):598–610. [12] Landers MN. Review of methods to estimate fluvial suspended sediment characteristics from acoustic surrogate metrics. Joint Federal Interagency Conf. 2010;2:1–2.