In March 2019, Teledyne RESON and the Applied Physics Laboratory at the University of Washington conducted surveys with a calibrated multibeam echosounder at ten sites in Sequim Bay, a shallow sheltered bay in Washington State, USA. For each site, the mean grain size was obtained from a diver core sample, and estimates of the backscattering strength at frequencies ranging between 200 and 350 kHz were calculated. The correlation between the backscattering strength and the normalized grain size have been investigated for the grazing angles 45° and 75°. For 45°, a correlation consistent with previous results has been found. It demonstrates the potential for simple seabed classification.

Remote sensing techniques pose an important supplement to physical sample collection, as they can reduce costs and increase the efficiency of seabed characterization. The acoustic backscattering cross section per unit area per unit solid angle1σb is a key parameter for acoustic seabed characterization; it varies with the grazing angle θg of the incoming field as well as with frequency f, i.e., σbσb(θg,f). The backscattering strength is obtained as Sb=10log10(σb). Throughout this text, “backscattering” will for brevity be denoted as “scattering.” Methods for seabed characterization using sonar include geo-acoustic inversion using a physics-based model,2,3 a generic model that uses a parametric description of the shape of the angular response curve,4 a statistical analysis of the measured Sb-values,5 and, finally, the use of Sb-values in combination with depth data.6 

In this work, a simple empirical relation for the estimation of the sediment mean grain size from the scattering strength will be presented. Snellen et al.5 studied the correlation between the median grain size D50 and backscatter values (dB) obtained by an uncalibrated multibeam echosounder (MBES) operating at 300 kHz. D50 ranged between 5ϕ and 5ϕ, where ϕ refers to base-two logarithmic units.1 The authors notice a “significant positive correlation” up to 1ϕ, above which the backscatter values gradually reach a plateau and then begin to decrease as the grain size increases further (see Ref. 5, Fig. 15). They conclude that a one-to-one relationship between the grain size and the backscatter values does not exist for the entire grain size spectrum. In this work, the observations are pursued by investigating the correlation between the scattering strength and the normalized grain size, i.e., the grain diameter divided by the acoustic wavelength d/λ (see, e.g., Boyle and Chotiros7 and Ivakin and Sessarego8). For the data presented by Snellen et al., the d/λ-values range between 0.006 and 3, and the positive correlation ends for d/λ0.1. Here, we present Sb-estimates obtained from ten sites at Sequim Bay (Washington State, USA) by application of an MBES operating between 200 and 350 kHz. The mean grain size of the sediments ranges between 7.11ϕ and 1.28ϕ, and thus, the d/λ-values range between 0.001 and 0.1. The MBES, a Teledyne RESON SeaBat T50-P (Teledyne RESON A/S, Slangerup, Denmark), was subject to a limited post-calibration at the Center for Coastal and Ocean Mapping (CCOM)/Joint Hydrographic Center (Durham, NH). Thus, the results presented here are restricted to the grazing angles 45° and 75°. For θg=45°, data found in the literature, where d/λ ranges between 0.0007 and 10, are included for comparison.

Figure 1(a) shows the coordinate system of the MBES: The origin is located at the acoustic center of the transmit array, the x-axis points in the starboard direction, the y-axis points in the along-track direction, and the z-axis points upwards. The normalized beam pattern of the acoustic pressure squared in the across-track direction is given as bxz2(θ)=(bTxz2bRCxz2bRxz2)(θ), where θ is the across-track angle depicted in Fig. 1(b); bTxz2 and bRCxz2 represent the wide beams of the transmitter and a single receiver channel, respectively; finally, bRxz2 represents the narrow beam produced by the receiver beam former (see Figs. 11, 17, and 18 in Ref. 9). The corresponding combined beam pattern for the along-track direction is byz2(ϑ)=(bTyz2bRyz2)(ϑ), where ϑ is the along-track angle depicted in Fig. 1(c), and where bTyz2 represents the narrow transmit beam and bRyz2 the wide receive beam; byz2 is dominated by bTyz2, and therefore bRyz2 will be neglected, i.e., bRyz2(ϑ)1. As the MBES platform moves forward, a three-dimensional (3D) geometry represented by plane facets is produced. The equation of the plane of a facet is estimated by the unweighted linear least square method by the use of about 32 bottom detection points (BDP): Across the swath, the number of facets is set to 1/4 of the number of beams, which for each ping leaves about four BDPs per facet depending on the topography; along the track, BDPs from seven previous pings are included.

Fig. 1.

(a) For the footprint area computation, the Tx and Rx arrays are represented as line arrays in a coordinate system where the origin is located at the acoustic center of the Tx array, (b) across-track angle θ, and (c) along-track angle ϑ.

Fig. 1.

(a) For the footprint area computation, the Tx and Rx arrays are represented as line arrays in a coordinate system where the origin is located at the acoustic center of the Tx array, (b) across-track angle θ, and (c) along-track angle ϑ.

Close modal

From each receive beam, σb-estimates can be derived from several samples within the portion of the seabed backscatter time series.10 Here, a method based on integration of the backscatter time series of the seabed is applied;10 it only produces a single σb-estimate per beam. Each beam is associated with a specific facet so that the grazing angle of the incoming field as well as relevant points of intersection with the facet can be found. Thus, for a given beam the scattering cross section is obtained as

σb=E/(E0TbTxz2bRCxz2A),
(1)

where E (Pa2· s) is the time series of the backscattered pressure squared integrated over the time interval spanned by the acoustic response of the seabed; E0 (Pa2· s) is the time integral of transmit pressure squared at 1 m from the source; T is the transmission factor which includes energy losses due to spreading and absorption;11 finally, A is the footprint area. For the calculation of E in Eq. (1) magnitude data from a receive beam is converted from analog to digital converter (ADC) output values into sound pressure values by the use of relations obtained from tank measurements;11 subsequently, the sound pressure values are squared. The transmit signal is a continuous wave (CW) pulse of duration τ shaded by a trapezoidal function with a tapering parameter of ϵ=0.2 [see, e.g., Ref. 11, Eq. (12)]. Thus, E0=p02τe, where p0 is the acoustic pressure @ 1 m from the source, and where τe is the equivalent pulse duration [see, e.g., Ref. 11, Eq. (16)]. Since bTxz2 and bRCxz2 vary slowly with the across-track angle they are merely weighting scalars in Eq. (1). Thus, for each beam the transmit and receive arrays are considered as rotational symmetric line arrays characterized by bTyz2 and bRxz2, respectively. Therefore, for the calculation of the footprint area, the two equivalent beam widths are applied,12 

Δϑeq=π/2π/2bTyz2(ϑ)dϑ,
(2)
Δθeq(θs)=π/2π/2bRxz2(θ;θs)dθ,
(3)

where θs is the across-track steering angle. For a given steering angle θs each of the two vectors,

[0±sin(Δϑeq/2)cos(Δϑeq/2)],

are rotated around the y-axis by the angles θsΔθeq/2 and θs+Δθeq/2. Thus, four vectors point towards the seabed which leads to intersection points on the facet that form a quadrilateral with area A.

The standard SeaBat T50 bracket was used, and therefore, the acoustic center of the receiver was shifted from the origin of the MBES by (Δx,Δy,Δz)=(0, 0.192, 0.047 m). The grazing angle will be defined as 90° minus the angle between the normal vector of the seabed facet and the vector pointing from the bottom detection point up to the acoustic center of the receiver. Thus, for a plane and horizontal seabed at a depth of, say, H =20 m, the maximum grazing angle will be θg(max)=tan1((HΔz)/Δy)=89.45°. For the computation of the footprint area, the extent of the bistatic offset is considered negligible, and therefore, for the A-computation, the system is assumed monostatic.

Sequim Bay is located on the northern coast of the Olympic Peninsula in Washington State, USA. The test area was located in the northern part of the Bay and it covered an area of about 2 × 2 km2, where the water depth ranges between 5 and 30 m. A CTD drop showed that the temperature and the salinity were almost constant down through the water column, that is, 8.7 ± 0.1 °C and 31.2 ± 0.1 parts per thousand (PPT), respectively. The resulting speed of sound in the water column was 1481 ± 0.4 m/s. 10 sites with different sediment characteristics were used for the experiment. Gas bubbles, sediment layers, and special species were not observed; hence, the sediments are considered relatively uncomplicated. Diver core samples were collected between March 25 and 29, 2019. Table 1 lists the mean grain size Mz (as defined by Folk and Ward13) sand, silt, and clay percentages, as well as the location of the diver core sample station (DCSS).

Table 1.

Mean grain size and percentages of sand, silt, and clay for the 10 sites at Sequim Bay, March 2019. A diver core sample was not collected at site 7, where the seafloor consists of gravel. The location of a DCSS for each site is given as Latitude=48°+0.01°×δLAT and Longitude=123°+0.01°×δLON, where δLAT and δLON are listed.

Site/DCSS number12345678910
Mz (ϕ3.14 6.14 3.54 7.11 2.11 1.91  1.28 2.08 5.92 
Sand/Silt/Clay (%/%/%) 76/14/8 23/50/28 71/16/11 7/63/31 94/3/2 91/4/3  98/1/1 90/5/4 29/45/25 
δLAT 7.7233 7.5683 7.6467 6.7267 7.0533 7.5533 7.6850 7.4450 7.3983 7.7800 
δLON −3.2600 −3.0567 −3.1483 −2.0300 −3.7883 −1.9383 −4.3967 −3.3550 −3.1683 −2.7800 
Site/DCSS number12345678910
Mz (ϕ3.14 6.14 3.54 7.11 2.11 1.91  1.28 2.08 5.92 
Sand/Silt/Clay (%/%/%) 76/14/8 23/50/28 71/16/11 7/63/31 94/3/2 91/4/3  98/1/1 90/5/4 29/45/25 
δLAT 7.7233 7.5683 7.6467 6.7267 7.0533 7.5533 7.6850 7.4450 7.3983 7.7800 
δLON −3.2600 −3.0567 −3.1483 −2.0300 −3.7883 −1.9383 −4.3967 −3.3550 −3.1683 −2.7800 
Table 2.

Reference Sb-data obtained at θg= 45° applied for Fig. 3. The references cover an d/λ-interval between 0.0007 and 10.

ReferenceFrequency (kHz)Mz (ϕ)Origin of Mz/ Origin of Sb/ Comments
Weber and Ward (Ref. 15200, 250 1.15 to −3.96 Table 1a/Fig. 7/ 
Eleftherakis et al. (Ref. 6300 0 to −6 Fig. 9/Fig. 9 at incidence angles ±44°/ 
Simons and Snellen (Ref. 16300 5 to −1 Fig. 4(b)/ Fig. 4(a) at ±45 °/ 
Williams et al. (Ref. 17200 250,…,500 1.46 Briggs et al. (Ref. 18) (Fig. 4, Rail 2)/Fig. 8 at θg=42° (Ref. 17) / 
Goff et al. (Ref. 1995 4.27 to 0.49 Table 1/ Table 1/μa instead of Mzb 
Ivakin and Sessarego (Ref. 8150–8000 2.03 and −0.63 In text/Fig. 3 at 50° incidence angle / 
Greenlaw et al. (Ref. 20266–1860 1.27 In text/Fig. 5/Sb= Lambrt Prm. + 10 ×log10[sin2(45°)] 
McKinney and Anderson (Ref. 21100 8.97 to −2.07 Table 1/ Fig. 1 / 
Pouliquen and Lyons (Ref. 22140 4.30 to 7.20 Table 1/ Fig. 25, 26, 28/ Locations TE, VA, PdM 
Haris et al. (Ref. 2395 6.66 to 1.16 Table 1/ Fig. 3, MB 95 kHz/Locations 1, 10, and 8 
ReferenceFrequency (kHz)Mz (ϕ)Origin of Mz/ Origin of Sb/ Comments
Weber and Ward (Ref. 15200, 250 1.15 to −3.96 Table 1a/Fig. 7/ 
Eleftherakis et al. (Ref. 6300 0 to −6 Fig. 9/Fig. 9 at incidence angles ±44°/ 
Simons and Snellen (Ref. 16300 5 to −1 Fig. 4(b)/ Fig. 4(a) at ±45 °/ 
Williams et al. (Ref. 17200 250,…,500 1.46 Briggs et al. (Ref. 18) (Fig. 4, Rail 2)/Fig. 8 at θg=42° (Ref. 17) / 
Goff et al. (Ref. 1995 4.27 to 0.49 Table 1/ Table 1/μa instead of Mzb 
Ivakin and Sessarego (Ref. 8150–8000 2.03 and −0.63 In text/Fig. 3 at 50° incidence angle / 
Greenlaw et al. (Ref. 20266–1860 1.27 In text/Fig. 5/Sb= Lambrt Prm. + 10 ×log10[sin2(45°)] 
McKinney and Anderson (Ref. 21100 8.97 to −2.07 Table 1/ Fig. 1 / 
Pouliquen and Lyons (Ref. 22140 4.30 to 7.20 Table 1/ Fig. 25, 26, 28/ Locations TE, VA, PdM 
Haris et al. (Ref. 2395 6.66 to 1.16 Table 1/ Fig. 3, MB 95 kHz/Locations 1, 10, and 8 
a

From the grain size distribution (Table 1 15) Mz is found here from estimates of ϕ16,ϕ50, and ϕ84 using the Folk and Ward (Ref. 13) graphical measures for stations A–F (December 2013), and the estimated grain sizes are 1.30, 1.15, −3.96, −2.74, 2.94, and 2.84, respectively.

b

μa is the geometric rms over the full grain size distribution. Ninety-eight data points are reduced to 26 by grouping them into grain size bins of 0.022 mm width. For each bin Sb is found from the mean value the of scattering cross-sections within the group.

The sea trial was carried out on the APL-UW research vessel “R/V Robertson” between March 21 and 22, 2019. The MBES was mounted on a pole attached to the starboard side of the vessel. At each site, surveys of 200 m length were carried out for the frequencies 200 250, 300, and 350 kHz by the use of a CW pulse of 100 μs duration. The MBES was set to form 256 equiangular beams covering a 150° swath. At each site, pre-surveys were conducted in order to find the source level and receive gain settings that would not lead to ADC clipping of the nadir returns, but still ensure outer beam signal levels well above the quantization noise floor.

Six weeks after the Sequim Bay experiment, the MBES was subject to a control calibration in CCOM's Engineering Tank, an indoor freshwater test tank, 18 m long, 12 m wide, and 6 m deep. The water temperature was around 20 °C. The MBES was mounted on a rotatable pole. A tungsten carbide sphere was positioned along the centerline of the MBES at a distance of 14.2 m. Due to limited available time at the facility, measurements were limited to rotor angle intervals of 1° to 1° in 0.1° steps around the rotor angles θr=±45° and θr=±15°. Thus, only beams around these angles were calibrated, but for all four frequencies. For the MBES, the target strength is estimated as TS(MBES)=10log10(pb2/(p02TbTxz2bRCxz2)), where pb is the backscattered sound pressure from the sphere, and p0 is the sound pressure of the transmitted signal at 1 m from the source. The theoretical Target Strength TS(Theory) is found from a partial-wave series solution14 by the use of the material parameters of the sphere. Consequently, for the four frequencies in ascending order, the corrections, TS(MBES)TS(Theory), are (0.6,1.7,1.9,2.1) dB for |θr|=15°, and (0.6,0.9,0.9,1.4) dB for |θr|=45°.

For a flat seabed, the calibrated beams will correspond to the grazing angles 45° and 75°. Therefore, the Sb-analysis will be limited to these two angles. Consequently, Sb-values will not be included when the seafloor has a significant across-track slope; for example, when θg=45° and the Sb-value has been obtained from an uncalibrated beam such as, e.g., 57°. Since the vessel was manually controlled, the paths varied between the different lines of a site, and the maximum distance between the vessel and the DCSS reached up to 25 m. Only the 40 pings closest to a DCSS were included for the analysis. A DCSS located in the proximity of a transition between two sediment types, and where MBES data include both types, is inspected manually to ensure that only data from sediments that correspond to the DCSS are used.

Here, the mean grain diameter will be given in units of meters, that is, d=103×2Mz. For θg=75°, Fig. 2(a) shows the scattering strength as a function of frequency (left) and normalized grain size (right). For each sediment group (DCSS 1–10, Table 1), Sb decreases with frequency. Earlier observations in the 200–350 kHz interval for grazing angles above 70° show almost no frequency dependence (Wendelboe,11 Fig. 29, θg=85°), or they show slightly weak negative, as well as weak positive, trends (Fezzani et al.,4 Fig. 10, θinc=20°). Conversely, Sb increases with the normalized grain size. Furthermore, the negative frequency dependency within a sediment group gets stronger as the grain diameter increases. Finally, it is unclear whether the upward bends of about 0.5–1 dB at 350 kHz are caused by the sediment or by changes in the MBES characteristics. For site 10, the 200 kHz data point seems to be an outlier. For θg=45°, Sb increases with frequency [Fig. 2(b), left]. Moreover, the Sb-values almost collapse into a straight line when plotted as a function of d/λ [Fig. 2(b), right]. This result seems to represent a clear-cut case for simple geo-acoustic inversion, but the question is to what extent it can be expanded to other sites and to d/λ-values outside the 0.001–0.1 interval. Thus, in the following our results will be compared with data found in the literature for θg=45° (see Table 2). Figure 2 outlines the chosen references and the associated frequencies and grain sizes required for the estimation of the (d/λ,Sb) pairs. For the references where the water sound speed has not been stated, a value of 1500 m/s will be used; since the sound speed typically varies between 1480 and 1530 m/s, the resulting error on d/λ will be less than 2%. Figure 3 shows the scattering strengths from Sequim Bay and the references. The overall picture shows a scattering strength that increases linearly with log10(d/λ) up to d/λ0.1, above which it seems to fluctuate around a constant level. The point of change is consistent with the findings by Snellen et al.5 as mentioned in Fig. 1. For the 0.02–0.1 interval (very fine to medium sand for frequencies between 100 and 350 kHz), the data from Goff et al.,19 Simons and Snellen,16 and Williams et al.17 altogether show a trend that is different from the Sequim Bay data, including Sb-levels 2–4 dB lower than those of the Sequim Bay. For Goff et al.,19 the fraction of large particles, i.e., particles for which d/λ>0.25, is 2.6%; the value corresponds to the median of all the data sets from Goff et al. used here. For the Sequim Bay data, the corresponding value is only 0.7%. Thus, a higher fraction of large particles (for example shell fragments) will lead to a larger mean grain diameter, but Sb may not necessarily increase with d/λ with the same rate as the same sediment with a low fraction of large particles. For the other reference data in the 0.0005–0.1 interval, a rough assessment concludes that six out of eight data points from Weber and Ward,15 three out of five from McKinney and Anderson,21 one out of three from Pouliquen and Lyons,22 and finally, two out of three data points from Haris et al.23 are in the region of being well-aligned with the Sequim Bay data. The remaining six points are located around 0.02, where the two ()-points exceed the Sequim data by 6 dB, and in the interval 0.0005–0.002, where five points exceed the Sequim data by 10 dB. It is unclear what the reasons are, but air bubbles produced by bioturbation might be an explanation.

Fig. 2.

Frequency versus Sb and normalized grain size versus Sb for grazing angles 75° (a) and 45° (b). The legends refer to the Sequim Bay sites listed in Table 1. For the gravel site the grain size has not been measured, and therefore, site 7 is not a part of the d/λ-plots.

Fig. 2.

Frequency versus Sb and normalized grain size versus Sb for grazing angles 75° (a) and 45° (b). The legends refer to the Sequim Bay sites listed in Table 1. For the gravel site the grain size has not been measured, and therefore, site 7 is not a part of the d/λ-plots.

Close modal
Fig. 3.

Scattering strength versus d/λ for θg=45°. The Sequim Bay data from Fig. 2(b) are plotted together with data obtained from other experiments (see, e.g., Table 2). Since the mean particle diameter is unknown for site 7, each Sb-value [see, e.g., Fig. 2(a)] is represented across the entire interval 0.08–10 in order to indicate that grain size is unknown. The solid line corresponds to the regression line given in Eq. (4).

Fig. 3.

Scattering strength versus d/λ for θg=45°. The Sequim Bay data from Fig. 2(b) are plotted together with data obtained from other experiments (see, e.g., Table 2). Since the mean particle diameter is unknown for site 7, each Sb-value [see, e.g., Fig. 2(a)] is represented across the entire interval 0.08–10 in order to indicate that grain size is unknown. The solid line corresponds to the regression line given in Eq. (4).

Close modal

Transition points,5 i.e., unique maxima, for which Sb begins to decay for increasing d/λ-values, are observed for the data from Greenlaw et al.20 for d/λ0.2; and a weaker maximum is observed for the Eleftherakis et al.6 data for d/λ1.3. The data from Ivakin and Sessarego8 fluctuate from −19 dB up to about −6 dB. It is unclear whether the large fluctuations are caused by flattening and degassing the sand, but the remote data point at (0.1,35 dB ) may be a consequence of this: A similar drop in scattering strength with decreasing normalized grain size for flattened and degassed sand is presented by Boyle and Chotiros7 (Fig. 2, Group 1, laboratory sand). The data from Simons and Snellen,16 Weber and Ward,15 McKinney and Anderson,21 Williams et al.,17 and, finally, from Sequim Bay at the gravelly site indicate the existence of a plateau of about –15 dB. The Sb-levels obtained by Elefterakis et al.6 appear too low compared to the other Sb-values; since their MBES was calibrated by the use of the seabed and the corresponding grain size information, and not a well-defined calibration setup, the estimated Sb-levels are uncertain. For θg=45° and d/λ0.1, we therefore obtain the following regression equation which is based on the Sequim Bay data only:

Sb=c1log10(d/λ)+c2,
(4)

where c1=9.63 dB, and c2=8.42 dB, and where the fit has been obtained with a coefficient of determination of r2=0.98. When expressed as a function of Mz we obtain

Mz={[1c1]Sb+[c2c13]log10(λ)}log2(10).
(5)

Hence, simple geo-acoustic inversion of the mean grain diameter can be conducted for θg=45°, when the scattering strength is less than the threshold of –18 dB. If Sb is greater than the threshold, it can only be stated that d>λ/10. For example, if the frequency is 350 kHz and Sb>18 dB, the minimum mean grain size will be 1.2 ϕ, i.e., medium sand; thus, the sediment can be anything between medium sand and, for example, pebble or cobble. However, if the frequency is 200 kHz, and Sb>18 dB, the minimum mean grain size will be 0.42 ϕ, i.e., coarse sand; thus, the sediment can be anything between coarse sand and stones. Hence, by lowering the frequency from 350 to 200 kHz the ambiguity interval can be reduced by one Udden-Wenworth class. Expressions similar to Eq. (4) have also been found for the beams not subject to the control calibrations. For grazing angles between 35° and 70°, fits have been obtained with r2-values that range between 0.98 and 0.99, and the potential for classification exists on a wider range of grazing angles.

It should be noted that mechanisms controlling seafloor scattering strength are usually angular dependent. The two grazing angles considered here are both well above the critical angle for the sediment, which may make the volume scattering mechanism more pronounced, while below the critical angle, the roughness scattering can become comparable and in many cases (such as for sand sediments at high frequencies) larger than the volume scattering (see Ref. 1 for more details). We believe the correlation between Sb and the d/λ-ratio may indicate the importance of scaling effects of the sediment granular structure, mentioned for instance in Ref. 8. However, modeling of these effects is beyond the scope of this express letter and will be subject to future research and more detailed papers.

For θg=75°, the scattering strength increases with rising grain diameter but decreases with frequency (Fig. 2). Thus, a simple linear relation between log10(d/λ) and Sb for the frequency interval 200–350 kHz has not been found. For θg=45°, the scattering strength increases with rising grain diameter as well as with increasing frequency. The mean grain size can be derived from Sb and λ by the use of Eq. (5) provided that Sb is less than −18 dB or d/λ<0.1. For larger Sb-values, it can only be stated that the mean grain diameter is d>λ/10. Expressions similar to Eq. (5) can be found for grazing angles between 35° and 70°. Although it requires extended calibrations, it opens up for producing maps of the grain size in real time.

This work was supported by the U.S. Department of Defense's Strategic Environmental Research and Development Program (SERDP), Project No. MR-2229. Many thanks to CCOM for the use of the Engineering Tank and for the expert help needed to conduct the control calibrations.

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