Over the past 2 to 3 decades the concept of using sound generated by the interparticle collisions of mobile bed material has been investigated to assess if underwater sound can be utilised as a proxy for the estimation of bedload transport. In principle the acoustic approach is deemed to have the potential to provide non-intrusive, continuous, high-temporal-resolution measurements of bedload transport. It has been considered that the intensity of the sound radiated should be related to the amount of mobile material and the frequency spectrum to the size of the material. To be able to fully realise this use of acoustics requires an understanding of the parameters which control the generation of sound as particles impact. In the present work the aim is to provide scientists developing acoustics to measure bedload transport with a description of how sound is generated when particles undergo collision underwater. To investigate the properties of the sound generated, examples are provided under different conditions of impact. It is considered that providing an overview of the origins of the sound generation will provide a basis for the interpretation of acoustic data, collected in the marine environment for the study of bedload sediment transport processes.

Quantifying bedload transport in rivers, estuarine and coastal environments is generally challenging due to the difficulties of obtaining accurate measurements. For measuring the bedload transport of coarse sediments, such as gravels and cobbles, a number of methodologies have been developed. Many measurements have utilised box or tray samplers, and this approach is still common today. Hubbell (1964), Engel and Lam Lau (1981), Ergenzinger and de Jong (2003), Bunte et al. (2008) and Holmes (2010), along with many others, have considered this technique. Some of the major shortcomings of this direct sampling method are the need for operators in the field, the limited range of conditions when measurements are possible, dangerous conditions during large floods, the impact on the flow introduced by the presence of the sampler, the lack of spatial/temporal resolution, the variable efficiency of samplers, the problems in obtaining continuous records and other difficulties specific to the particular samplers.

To circumvent some of these difficulties, alternative measurement technologies have been investigated. Dorey et al. (1975) investigated, with limited success, the feasibility of using sidescan sonar to track acoustically transponding pebbles. The tagging of gravel particles radioactively was developed by Crickmore et al. (1972) and applied with success to monitoring the movement of gravel. Reid et al. (1984) utilised artificial pebbles constructed with a ferrite rod at its centre and deployed them in a brook. Particle mobility was detected using an electromagnetic sensing system installed in the bed and transport compared with the bed shear. Geophones and particle impacts on pipes, columns and plates are now commonly used to estimate coarse gravel transport (Turowski and Rickenmann, 2009; Gray et al., 2010; Rickenmann et al., 2012). In recent years acoustic Doppler velocity profiles, ADCPs, have been used to measure apparent bedload velocity using a combination of ADCP bottom tracking velocity and boat velocity derived from differential global positioning systems, DGPSs (Rennie and Church, 2010). Recently the measurement of seismic noise near rivers has been investigated to assess bedload transport (Burtin et al., 2011; Tsai et al., 2012). A workshop on contemporary methodologies for the monitoring of bedload transport has recently been published online by Rickenmann et al. (2013).

Another approach adopted, and the one focussed upon here, has been to monitor the movement of gravel by recording the acoustic sediment-generated noise, SGN, arising from particle–particle collisions as bedload transport occurs. Observations of this type have continued to be reported over the past 5 decades (Bedeus and Ivicsics, 1963; Johnson and Muir, 1969; Tywoniuk and Warnock, 1973; Jonys, 1976; Richards and Milne, 1979; Thorne et al., 1984; William et al., 1989; Mason et al., 2007; Barton et al., 2010; Camenen et al., 2012; Basset et al., 2013). The appeal of the acoustic approach is that it offers the potential to obtain, with very little interference with the state of the bed and the flow, the initiation of particle movement, continuous temporal records, sub-second assessment of mass transport rates and estimates of mobile particle size.

To be able to utilise and interpret SGN with any degree of confidence requires an understanding of the sound source generation. The source arises from the impact of two or more particles as interparticle collisions occur as the bed becomes mobile and bedload transport occurs. The generation of sound by impacting bodies has primarily been examined in air, usually by parties interested in machine noise emissions (Banerji, 1916, 1918; Koss and Alfredson, 1973; Koss, 1974a, b; Akay and Hodgson, 1978a, b; Akay, 1978). It is this work which was adapted for the study of acoustic radiation by colliding bodies underwater (Thorne and Foden, 1988; Thorne, 1990). The source of radiation has been labelled rigid body radiation due to the origin of the pressure disturbance being generated by the acceleration of the body, rather than due to the natural modes of vibration of the body (Koss and Alfredson, 1973). To solve the problem, each sphere is treated as an independent source which generates a transient that can be described by an impulse solution convolved with the acceleration time history during the collision. The impact process is assumed to be elastic so that a Hertzian acceleration description can be employed (Goldsmith, 1960). The sound field is then obtained by summing the transients radiated from each sphere with due allowance for the time difference for the sound to propagate from each sphere to the field measurement point.

The use of SGN to acoustically measure bedload transport and the underlying theory of rigid body radiation is distributed among acoustic, geological, hydraulic, geophysical and sedimentological journals. The aim of the present work is to bring together an overview of SGN and its underlying theoretical basis, in a form which scientists interested in using acoustics for bedload transport would find useful. Here the main solutions from rigid body radiation analysis are simplified to make the topic more accessible and the outputs focussed more closely than previously on bedload transport. Therefore, using the rigid body radiation theory, initial calculations have been carried out to elucidate the origins of the structure of the radiated signal in the time and frequency domain. To investigate how changes in impact parameters affected the time domain signal and the frequency spectrum, a series of calculations were conducted. The intention of this work was to provide broad illustrations of the radiated signal response due to variation in sphere collision impact parameters. Some general features are identified and considered in the light of using SGN for the measurement of bedload transport. Some modelling of multiple impacts is presented as an analogy to the type of data that may be collected in a coastal or riverine environment. It is hoped that the present overview will stimulate further interest in SGN by making the acoustic analysis more straightforward and by illustrating its potential capability.

Geometry for the theory. The impactor of radius

The background theory for impacting spheres in water was developed in Thorne
and Foden (1988), and only the results from the theoretical analysis are
presented here. The geometry for the theory is given in Fig. 1. When solid
elastic spheres collide, the main source of sound generation is due to the
rigid body radiation associated with the acceleration of the impactee of
radius

A similar expression can be obtained for the frequency spectrum when two
spheres collide by using the time convolution theorem. This provides the
spectrum for the collision from the product of the Fourier transform of the
radiated pressure due to a unit impulse acceleration, with the Fourier
transform of the acceleration time history; this results in the expression
given below (Thorne and Foden, 1988):

Calculations for two glass spheres of the same size impacting with
radius

The aim here is to provide insight into the structure of the rigid body
radiation field as impact parameters were varied. Therefore a number of
calculations for the time domain waveform and the frequency spectrum were
carried out. Initially spheres of equal size were considered with radii of
0.005, 0.015 and 0.05 m. These spheres were chosen to represent a broad
range of particle sizes from fine pebbles to cobbles. This was considered to
be representative of the common sizes of materials on which the acoustic
technique would be used for bedload measurements. The results are considered
as indicative of the signals that would arise from individual particle pair
impacts in coarse sediment bedload transport. For the calculations Eqs. (1)
and (2) were evaluated with all the others parameter having the same
values as used to obtain Fig. 2. Figure 3 shows the results of the
computations. Considering the time domain waveforms shown in plots 3a–c, it
can be observed that both the duration and amplitude,

Calculations for glass spheres of the same size impacting as the
sphere size was increased.

In the marine environment particles of different size will generally be
impacting, and it is therefore interesting to examine this case. To assess
the radiated sound field from spheres of different size impacting,
calculations were carried out using the same parameters as used for Fig. 3,
but with the individual impacting spheres having a different radius. The
results are presented in Fig. 4 and can be directly compared with the
plots in Fig. 3. In the frequency spectrum plots in Fig. 4 the vertical
solid and dashed lines respectively show the location of the spectral peak
for the same size spheres impacting with radii

Calculations for glass spheres of different sizes impacting.

To assess how changes in the impact velocity,

Calculations for the time domain waveform using Eq. (1) and
the frequency spectrum using Eq. (2) for

The implications from the recently computed results presented in Figs. 3–5 are that, to first order, the duration of the time domain waveform, the width of the spectrum and the frequency at which the spectrum peaks are principally controlled by the size of the spheres impacting, while the amplitude of the time domain waveform and frequency spectrum depend upon sphere size and impact velocity, with the additional factor of the dipole structure for the amplitude of the radiated field.

Laboratory measurements on multiple particles impacting have been carried out by Jonys (1976), Millard (1976) and Thorne (1985, 1986a). The works of Thorne incorporated the results of the earlier works and are still the most comprehensive study of the underwater sound radiated from multiple collisions of quasi-bedload transport, and therefore the measurements from these two papers are used here to illustrate the salient acoustic features.

Comparison of the measured and calculated spectra using Eq. (2)
with smoothing, for quasi-bedload conditions in a rotating drum for;

The instrumentation used has been previously described (Thorne, 1985);
therefore only a brief description is given here. Sediments were agitated in
a vertical wooden drum 1 m in diameter and 0.5 m deep; this rotated about a
horizontal axis and was totally submerged underwater in a concrete tank (3

Presented in Fig. 6 are the spectrum for particles centred on nominal
radii of 0.00075, 0.0015 and 0.005 m. In Fig. 6a data for spheres and gravel of
radius of 0.005 m are shown; both data sets are broadband in nature, with
spectral peaks frequencies being around 15 kHz. The fact that spectral
levels are lower for the gravel is not necessarily significant because
measurements were made under different conditions of mass and rotation
speed. Owing to the impact velocities,

To represent the variation of the spectra with particle size, the frequency
at which the spectrum nominally peaks, or the centroid of the spectrum, has
been used to define a characteristic central frequency. This is illustrated
in Fig. 7a, where results from the studies of Jonys (1976), Millard (1976)
and Thorne (1985, 1986a) are presented. What can be clearly seen is that the
characteristic central frequency has to first order an inverse dependency on
particle size. From rigid body radiation theory the frequency at which the
spectrum peaks,

In the marine environment the amount of material transported as bedload will
vary over time depending on the size of the sediments on the bed and the
hydrodynamic conditions. To simulate this variability, a series of
measurement were carried out on gravels of different radii, with

In general therefore, it can be seen that the relatively simple rigid body
radiation model captures in broad terms the form of the spectrum for large
numbers of particles impacting in a quasi-bedload manner, although for
reasons not resolved in the present analysis the lower frequency components
are somewhat underpredicted. The spectrum can be broadly specified as
having a characteristic central frequency which is inversely related to
particle size and with a bandwidth nominally between

Comparison of the proxy for sediment transport, acoustic
intensity, with the magnitude of the kinematic stress,

There have been a number of field trials of the SGN technique, and the
results have been variable (Bedeus and Ivicsics, 1963; Tywoniuk and Warnock,
1973; Jonys 1976; Richards and Milne, 1979; Thorne et al., 1989; Williams et
al., 1989; Voulgaris et al., 1995; Mason et al., 2007; Barton et al., 2010;
Belleudy, 2010; Bassett et al., 2013). One of the more successful and
interesting studies was to utilise the non-intrusive high-temporal-resolution
measuring capability of SGN to examine the relationship between
turbulent bursting in tidal flows and the bedload transport of coarse
gravels (Heathershaw and Thorne, 1985; Thorne et al., 1989). Using an
instrumented frame, concurrent measurements of the three orthogonal
components of the turbulent flow and instantaneous bedload transport were
collected above a gravel bed in a tidally dynamic environment with currents
peaking at around 1.0 ms

The measurements demonstrated quite clearly in Fig. 8a and b that the
acoustic intensity, and hence gravel transport, associated with sweep events
were substantially higher than the intensity levels during ejection events
at high stress values. This difference increased as the magnitude of the
kinematic stress increased. From this it was concluded that of the two types
of motion that contributed to the bulk of the kinematic Reynolds stress,
ejections and sweeps, only sweeps were capable of supporting appreciable
coarse sediment movement. It was also noted that unexpectedly outward
interaction events, although weaker and less frequent than sweeps, as shown
in Fig. 8c and e, were capable of supporting greater sediment movement
than sweeps for the same stress levels. This is despite the fact that they
make a negative contribution to the Reynolds stress. Correspondingly, there
was little sediment movement associated with inward interactions. The
results showed that horizontal turbulent velocity fluctuations, u, may have
greater dynamical significance in terms of coarse sediment movement than
the instantaneous contributions,

This study illustrated that SGN can provide detailed high-temporal-resolution measurements of sediment response to turbulent flow conditions and showed for the first time that the bedload movement of seabed gravels is caused principally by sweep-type motions in the bottom boundary layer and to a lesser extent by outward interactions. This observation could be explained if form drag rather than shear stress were assumed to be the principle cause of gravel movement. It was speculated that such relationships between sediment transport and turbulent motions could lead to a new generation of sediment transport equations which accounted for the turbulent bursting process (Clifford et al., 1995; Williams, 1996; Sumer et al., 2003).

The aim of the present paper has been to provide scientist and engineers who
are interested in the measurement of coarse sediment bedload transport with an
overview of the background to sediment-generated noise. The new
calculations presented here on sphere impacts and comparisons with
quasi-bedload transport have illustrated that the rigid body radiation
approach should provide a first-order framework for understanding and
interpreting SGN collected in riverine and coastal environments. When the
bed becomes mobile, interparticle collisions occur which radiate sound into
the water, and this SGN can been used as a proxy for bedload transport rates.
To understand and predict the sound field generated by the collision of
particles, a theoretical framework based on rigid body radiation has been
presented. Initially predictions were made with colliding pairs of glass
spheres, and the impact of sphere size, impact velocity and field point angle
was examined to assess the effect these had on the measured time domain signal
and the frequency spectrum. Limited comparison with available data was
carried out to assess the veracity of the theory. To move beyond simple
two-particle impacts, larger numbers of particles were impacted using a rotating
drum arrangement; this experimental configuration was employed to simulate
quasi-bedload conditions. In these studies data were collected on glass
spheres and natural gravels. Spectral analysis of the measurements showed
comparable spectra to the two sphere impact results, and rigid body radiation
gave reasonable first-order agreement with the rotating drum data.
Assessment of a characteristic central frequency for the spectra showed a
clear inverse relationship with the size of the impacting particles, and an
expression derived from the impact duration of the collision time,

The outcome from the two sphere impact studies and the measurements in the rotating drum indicated that the relatively simple Eqs. (1)–(4), derived from rigid body radiation, and the linear summation of mean square pressures, provide a framework for a first-order understanding of SGN. The results showed that, for pairs of spheres impacting, the amplitude of the signal is a function of the sphere size, impact velocity and the location of the position of observation. For measurements of bedload in the field, the location of the receiver will normally remain fixed relative to the bed and the size of the bedload material will be nominally constant; therefore the signal amplitude will essentially depend on the impact velocity and the number of particles impacting. If it is assumed that impact velocity is proportional to the velocity on the mobile material, then the mean square signal amplitude should be acting ostensibly as a nominal proxy for the bedload transport, and this has been reported in a number of studies (Johnson and Muir, 1969; Thorne, 1986b; Barton et al., 2010). The form of the spectrum has been shown to be primarily dependent on the size of the impacting particles, with the impact velocity and measurement location having only second-order effects. The form of the spectrum is therefore a reasonably robust indicator of the size of the mobile material and as such has been used to estimate the size of the bedload material (Thorne, 1986a; Mason et al., 2007; Belleudy et al., 2010; Basset et al., 2013).

One of the more common difficulties in the application of SGN to the measurement of coarse sediment bedload transport is the level of the background aquatic soundscape (Wenz, 1972; Thorne, 1986b; Vracar and Mijic, 2011). Contributions from biophony (sounds from aquatic animals), geophony (sounds from natural abiotic phenomenon) and anthrophony (sounds from manmade activities) can make interpretation and assessment of the SGN problematic. To-date most SGN measurements have been collected using nominally omnidirectional hydrophones. Looking to the future, the mounting of such hydrophones in acoustically reflective housings to increase directionality (as with an omnidirectional bulb in a car headlight), and thereby rejecting erroneous background noise, could be an interesting step forward. Also given that predictions can be made for the spectrum of the sound from a knowledge of particle size, this may be used with bandpass filtering to enhance the SGN signal relative to the general soundscape. One area which is still deficient is rigorous assessments of the SGN technique using independent measurements of coarse sediment bedload transport. Further studies in flumes and in the field would establish, with greater veracity than available at present, the capabilities and uncertainties in the application of SGN to the robust measurement of bedload transport and particle size.

This overview on sediment-generated noise and coarse bedload transport originated from an invitation to the author to provide a keynote presentation at the International Workshop of Acoustic and Seismic Monitoring of Bedload and Mass Movements held in Zurich, Switzerland, 4–7 September 2013. The author thanks the organisers of the workshop and in particular Jonathan Laronne for the invitation. The preparation of this manuscript was carried out following an invite to make a submission to a special issue section on “Acoustic and seismic monitoring of bedload and mass movements” as part of the journal Earth Surface Dynamics. The study was supported by funding from the Natural Environmental Research Council, UK, National Capability. Edited by: J. Turowski