Marine Geophysical Research (2018) 39:105–120 https://doi.org/10.1007/s11001-018-9350-y

ORIGINAL RESEARCH PAPER

Backscattering from a sandy measured by a calibrated multibeam echosounder in the 190–400 kHz frequency range

Gorm Wendelboe1

Received: 2 July 2017 / Accepted: 16 March 2018 / Published online: 2 April 2018 © The Author(s) 2018

Abstract A SeaBat T50 calibration that combines measurements in a test tank with data from numerical models is presented. The calibration is assessed with data obtained from a series of tests conducted over a sandy seabed outside the harbor of Santa Barbara, California (April 2016). The tests include different tone-burst durations, sound pressure levels, and receive gains S S in order to verify that the estimated seabed backscattering strength ( b) is invariant to settings. Finally, b-estimates ◦ ◦ obtained in the frequency range from 190 kHz in steps of 10 kHz up to 400 kHz, and for grazing angles from 20 up to 90 ◦ in bins of width 5 , are presented. The results are compared with results found in the literature.

Keywords Multibeam echosounder calibration · Backscattering strength · Multifrequency

Introduction Between 2011 and 2016 efforts have been made to use the MBES for the estimation of the seafloor scattering strength In this paper, scattering strength (Sb) refers to the backscat- (Wendelboe et al. 2012). This paper presents how the cali- tering strength from the seabed. During the last 2–3 decades, bration has been made, and results from tests and verifica- the number of multibeam echosounders (MBES) for bathy- tions from subsequent field trials are presented. metric purposes has increased significantly. MBES systems The compensation of the MBES influence on the recorded are used in all ocean depths and operate at frequencies from data may be carried out in different ways. Hellequin et al. about 10 kHz in the deepest oceans up to 400–500 kHz for (2003) use the system specifications made available by the shallow depths from 1 to 100 m. manufacturer and statistical analysis to remove artifacts from For the signal to noise ratio is one of the key survey data. Measurements can be conducted in a large tank parameters for successful bottom detection. For receivers where the far-field beam pattern and sensitivity at different in SeaBat systems older than the T-series, moderate clip- gains of the MBES system are measured by application of ping, low dynamics in the analog to digital converter (ADC), either a standard target (Foote et al. 1988; Lanzoni and Weber non-linear gain characteristics that lead to saturation, as well 2012), or a distributed target (Heaton et al. 2017). Lanzoni as temperature-dependent amplifiers do not have a crucial and Weber (2011) perform a field calibration of a MBES impact on bathymetry performance. Meanwhile, these prop- using a setup that includes a target sphere and a split-beam erties are critical limitations, when the scattering strength of echosounder . Relative MBES calibration using reference the seafloor is required, and compensation of the MBES’s areas on a seafloor with a high degree of temporal stability influence on data is necessary. The successor, the SeaBat can be used to establish a common reference between differ- T50, has been designed for the acquisition of the seabed ent MBES systems (Weber et al. 2017; Roche et al. 2018); scattering strength, and it does to a far lesser extent suffer for a lone MBES system, a reference area can be applied from the aforementioned limitations. repeatedly in order to compare changes in Sb due to changes in, e.g., sonar settings, temperature or ageing. Absolute in situ calibration of an MBES can be conducted by the use * Gorm Wendelboe of a singlebeam echosounder (SBES) as reference (Ladroit [email protected] et al. 2017; Eleftherakis et al. 2018). This method does not require a temporal stable seabed, and calibrations can be con- 1 Teledyne RESON, Fabriksvangen 13, 3550 Slangerup, ducted frequently without large practical and time-consuming Denmark

Vol.:(0123456789)1 3 106 Marine Geophysical Research (2018) 39:105–120 limitations. For the work presented here, absolute calibra- e.g., (Jackson and Richardson 2007) Eq. 2.15 for the defini- tion was carried out in the RESON test tank. Separate tank tion and ideal case, and Eq. G.4 for a realistic application). measurements of the transmit sensitivity, the across-track Here, the scattering cross section for the MBES is directivity of the receiver elements, tone-burst durations, p 2 r4 and the relations between the digitized machine unit value = s k�� r 2 2⟨� 2� ⟩−4 w (1) and the sound pressure value in front of the receiver array p0 r0 BTxze A were conducted. A company proprietary model was applied 2 to estimate the far-field beam pattern. In the sea trials, sonar where ps is the mean square value of the backscattered setting tests served to validate that the scattering strength is sound ⟨�pressure� ⟩ originating from a large number of small independent of changes in tone-burst duration, source level patches within an insonified area A, measured at the distance and receive gain. Frequency dependence tests were also con- r. The transmit peak pressure at r0 = 1 m from the source is ducted, but they are complicated by the fact that the scatter- p0, BTxz is the normalized accros-track beam pattern of the ing strength may change with frequency depending on the transmitter, and kw is the exponential coefficient for absorp- sediment type. Therefore, the assessment included compari- tion in the water. The mean square value of the backscattered sons with Sb-values obtained by other measurements (Green- sound field is obtained from recorded data by law et al. 2004; Weber and Ward 2015; Williams et al. 2009). 2 Here, the tests were conducted over a sandy area 1 km outside 2 F ( a , f , G) ps = the harbor of Santa Barbara, CA, USA. B� 2� (2) ⟨� � ⟩ RCxz

where the function F converts the magnitude of the digital MBES for backscatter IQ-value1, |a|, into the corresponding magnitude of the com- plex sound pressure, ps , at the face of the receiver. Thus, The SeaBat MBES is designed as a Mills Cross array (Urick ps = ppeak is the peak pressure of the physical field which 1983). It consists of two highly directive, approximately is also required for Eq. 1 since p0 is a peak pressure. The 1D, arrays placed perpendicular to each other. The transmit conversion in Eq. 2 depends on the receive gain G as well array emits sound onto an area which is wide in the across- as the acoustic frequency f. The IQ-data are dimensionless, track direction and narrow in the along-track direction. The and ps is in Pascal. The conversion function is based on receiver operates with narrow steered beams in the across- measurements conducted in the RESON test tank at normal track direction and a much wider along-track opening angle. incidence; it is proprietary, but characteristic curves for f = As a result one obtains an effective insonification which is 300 kHz are shown in Fig. 15 (see “Measurements of the → limited to a small area around the receiver steering angle, see a ppeak relation” section). The normalized across-track Fig. 1a. Figure 1b shows the bracket-mounted SeaBat T50 beam pattern of the receiver, BRCxz, in Eq. 2 ensures that 2 transmit and receive arrays applied for the tests presented ps can be obtained for beams pointing away from normal here. For each receive beam a portion of the backscatter time ⟨�incidence.� ⟩ Beam pattern normalization is made with respect series around the bottom detection point is applied for the to normal incidence. estimation of the seabed backscattering cross section, [see, The insonified area depends on the tone-burst duration , the along-track beam pattern of the transmitter, BTyz and the across-track beam pattern of the beamformed receiver beams, BRxz . The equivalent beam widths (Lurton 2010) are derived from BTyz and BRxz , and they are used in the calcula- tion of the insonified area, A. For the current application the seabed is assumed flat in the along-track direction, whereas compensations for height variations are made for the across- track direction (Wendelboe et al. 2012). For the computation of the insonified area and the use of the zero-slope assump- tion see, e.g., the standard models (Lurton 2010; Amiri- Simkooei et al. 2009; Lurton and Lamarche 2015). The number of samples applied for the calculation of increases gradually with the steering angle . From the nadir Fig. 1 a Mills Cross effective beam pattern, andb the SeaBat T50 transmit array, the TC2181, the semi-cylindrical unit in the fore- 1 a a ia a a ground, and the EM7218 receive array the rectangular shaped receive = I + Q, where I is the in-phase component, Q is the quadra- unit in the background ture component and i is imaginary number (Papoulis 1984).

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Table 1 Overview of the Name Obtained by Symbol calibration Transmitter (TC2181) Peak sound pressure @ 1 m from the source (derived from the Measurement p0 measured source level ) Tone-burst duration Measurement Along-track beam pattern Numerical model BTyz Across-track beam pattern Numerical model BTxz Receiver (EM7218) → Receiver a ppeak relations Measurement F Across-track beam pattern of the beamformer Numerical model BRxz Across-track beam pattern of the receiver ceramics Measurement BRCxz

◦ beam 2 samples are collected, about 7 samples around 30 , and peak sound pressure relations, and the across-track beam ◦ and finally, approximately 13 samples at60 are collected. pattern of the receiver elements, see Table 1. The calibra- For most types of sea floor the depends on the grazing tions in the tank have been conducted for center frequencies angle between the incoming field and the seafloor, g . In between 190 and 400 kHz in steps of 10 kHz. addition it has been shown that depends on the frequency (Greenlaw et al. 2004; Weber and Ward 2015; Williams et al. Calibration transducers 2009), hence: The calibrations in the tank are based on the use of quasi- = (g, f ) (3) omnidirectional projectors (transmitting transducers) and Finally, results are evaluated in terms of the scattering quasi-omnidirectional (receiving transduc- strength ers). Two hydrophones are used: the RESON TC4034 (Teledyne-RESON 2018b) and the RESON TC4014-5 Sb = 10 log10( ) (4) (Teledyne-RESON 2018a). The TC4034 can be used as To summarize, estimation of the insonified area A includes 2 either or projector. The TC4014-5 is a TC4034 , BTyz and BRxz, the estimation of ps includes BRCxz and with a built-in preamplifier, which increases the receive F, and finally, the sound pressure⟨� variations� ⟩ of the incom- sensitivity by about 40 dB. This is advantageous for the ing field along the across-track direction is accounted for by measurements of sound pressure levels close to the noise using p0 and BTxz . In order to obtain the scattering strength, floor. The TC4014-5 can only be used as a hydrophone. these parameters must be estimated, which is the purpose of Figure 2 is a sketch of the angle definitions used for the MBES calibration presented in the next section. describing the beam pattern of the hydrophones. The origin of the TC4034 or TC4014-5 is the point on the units where the serial number is engraved. The sensitivity of the hydro- Calibration phone or projector is measured by a sound field which is, respectively, directed towards or away from the origin in ◦ The calibration was carried out in the RESON test tank, 4.5 the horizontal plane. This direction is defined as 0 in the m long, 2.5 m wide, and 3.0 m deep. The official uncertainty and accuracy in the test tank is ± 0.7 dB for frequencies between 70 and 420 kHz (Teledyne-RESON 2018c). The -90° Serial dimensions of the test tank do not allow for far-field meas- number urements of the transmit beam pattern. Therefore, the along- a Serial number track beam pattern as well as the across-track beam pattern sound of the transmitter will be obtained from a company propri- 0° Incoming -90° etary transducer model. The receive beam pattern generated sound by the beamformer is also obtained from a model (Murino 0° and Trucco 2000). The tank calibrations include measure- 90° ments of the transmitted tone-burst duration and measure- (a) (b) ments of the source level from which the peak sound pres- sure @ 1 m from the source is obtained. For the receiver, the Fig. 2 Definition of the origin of TC4034 and TC4014-5. Angles tank calibrations include measurements of the IQ-magnitude defined fora the horizontal plane, and b the vertical plane

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TC4034 (SN-1611293) TC4014-5 (SN-3411076) TC4014-5 (SN-3411076) -178 145 0.5 200 kHz 250 kHz 300 kHz 350 kHz 400 kHz Pa

140 -180 0 dB Pa/ Vrms @ 1 m 135 -182

130 dB re 1 Vrms/

dB re 1 -184 -0.5 200 250 300 350 400 200250 300350 400 Frequency (kHz) Frequency (kHz) -10 -8 -6 -4 -2 0246810 (a) (b) Angle in the horizontal plane (°)

0.5 200 kHz 250 kHz 300 kHz 350 kHz 400 kHz Fig. 3 a TC4034 transmit sensitivity, and b TC4014-5 receive sensi- tivity 0 dB TC4034 (SN-1611293) 0.5 200 kHz 250 kHz 300 kHz 350 kHz 400 kHz -0.5 -96 -94 -92-90 -88 -86 -84 0 Angle in the vertical plane (°) dB

Fig. 5 -0.5 TC4014-5 beam patterns in horizontal and vertical planes -10 -8 -6 -4 -2 0246810 Angle in the horizontal plane (°) ◦ ◦ by ± 0.1 dB. In the angle range of − 90 ±7 the vertical 0.5 beam patterns vary by ± 0.4 dB. The horizontal and vertical beam patterns of the TC4014-5 (SN-3411076) are shown in Fig. 5. The vertical dashed lines represent bearings to the 0 dB → TC4034 (SN-1611293) for the ( a ppeak ) relation meas- ◦ urements. In the angle range ± 11 the horizontal beam pat- 200 kHz 250 kHz 300 kHz 350 kHz 400 kHz ◦ ◦ -0.5 terns vary by ± 0.5 dB. In the angle range of − 90 ±7 the -96 -94 -92 -90-88 -86-84 vertical beam patterns vary by ± 0.5 dB. Angle in the vertical plane (°) For the source level measurements described in “Source level” section and the across-track directivity of the receiver Fig. 4 TC4034 beam patterns in horizontal and vertical planes elements described in “Across-track beam pattern of the receiver element, BRCxz” section, two other calibrated ◦ TC4034 hydrophones are used as a hydrophone and projec- horizontal plane and − 90 in the vertical plane. Figure 3a tor respectively. shows the transmit sensitivity of a TC4034 (SN-1611293) in the frequency range from 190 kHz up to 410 kHz. The Transmitter transmit sensitivity is between 131 and 146 dB re 1 Pa/ Vrms @ 1 m with maximum at the resonance frequency at Source level around 320 kHz. The receive sensitivity of a TC4014-5 (SN-3411076) is shown in Fig. 3b; it ranges from about Source levels are estimated from tank measurements where ∕ − 183 to − 179 dB re 1 V rms Pa. The receive resonance the TC4034 has been positioned in the center-line of the TM frequency is about 360 kHz. TC2181 at a distance of 3 m, see Fig. 6. LabView is used The horizontal and vertical beam patterns of the TC4034 to control the T50 source level, tone-burst duration, center (SN-1611293) are shown in Fig. 4, but only for angles rele- frequency, and a trigger signal for transmission of the tone- a → p vant for the measurements of the ( peak ) relation of the burst. The signal received by the hydrophone is sampled a → p TM receiver presented in “Measurements of the peak rela- and stored by an NI PXI scope, and data is analyzed in TM tion” section). Although the beam patterns have been meas- Matlab . The source level is given in dB rms re 1 Pa, i.e., ured for all frequencies from 190 kHz in steps of 10 kHz up to 400 kHz, they are only shown for five selected frequen- p0 SL = 20 log10 � �, cies, that is, 200, 250, 300, 350, and 400 kHz. The vertical 2 p (5) √ ref dashed lines represent bearing angles to the TC4014-5 (SN- → 3411076) for the measurements of the ( a ppeak ) relation. p r = 1 ◦ where 0 is the acoustic peak pressure in Pascal at 0 In the angle range ± 11 the horizontal beam patterns vary meter away from an equivalent point source, and where

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NITM T50 PC Fc = 300 kHz. UI: = 100 s, Power = 220 dB rms re 1 Pa LabViewTM PC 500 PXI scope Transmit generator

250

Transmitter TC2181 0 Hydrophone TC4034 Voltage (mV)

R = 3 meter -250

-500 Fig. 6 Source level measurement 145 249 Time ( s) −6 pref = 10 Pa is the reference pressure. Since the measure- Fig. 7 ment point is within the near-field of the TC2181 transmit- Example of a tone-burst where source level and duration is estimated. The time difference between the vertical lines represents ter, the field is not fully developed, and the pressure meas- the estimated duration and the interval of DFT analysis ured by the hydrophone, ph, is lower than p0 . The acoustic pressure measured by the hydrophone can be expressed as

− r 220 SL = 218.7 dB rms re 1 Pa r0(1 − e ) ph(r)=p0 (6) r 210 −1 where ([m ]) has been estimated from a proprietary com- 200 Pa) pany model of the TC2181. Thus, 190 rp (r) p = h 0 − r (7) 180 r0(1 − e ) (dB rms re 1 p 170 The sensitivity of the hydrophone, Ls, is given in dB re 1 L Vrms∕ Pa, i.e., 160

Up∕ph 150 Ls = 20 log10  (8) 1Vrms∕pref 0 200 400600 800 1000 Frequency (kHz) where Up is the peak voltage measured by the hydrophone. Thus, for a given Up-value the pressure at the hydrophone is Fig. 8 One-sided amplitude spectrum of the tone-burst in Fig. 7. There is a difference of 1.3 dB between the nominal value (220 dB re Uppref Pa (−Ls∕20) 1 ), and the actual value, which is compensated for ph = 10  (9) 1Vrms Figure 7 shows a tone-burst with a center frequency of Eq. 9 is inserted into Eq. 7 and rearranged so that 300 kHz, a sonar commanded pulse duration of 100 s, and

(−Ls∕20) a sonar commanded sound pressure level of 220 dB re 1 p0 r 10 (Up∕1Vrms) = Pa (denoted “Power” in the sonar User Interface (UI)). The p r (1 − e− r) (10) ref 0 signal has been sampled at 3 MHz. The red dashed verti- cal lines have been obtained from a company proprietary By combining Eqs. 10 and 5 the source level can be algorithm that detects the beginning and end of the signal. expressed as The part of the signal within the detected limits is used to

Up estimate the source level using a DFT. Figure 8 shows the SL = 20 log10 � �−Ls + 20 log10(r∕r0) one-sided spectrum obtained by weighting the time-signal 1V 2 rms√ (11) with a Flattop window (D’Antona and Ferrero 2006). A − r −20 log10(1 − e ) source level of 218.7 dB rms re 1 Pa is estimated, and the

1 3 110 Marine Geophysical Research (2018) 39:105–120 difference of − 1.3 dB—with respect to the UI-Power value to the insonified area (Lurton and Lamarche 2015), a lack of of 220 dB rms re 1 Pa—is being compensated for when the compensation will lead to an error estimate of Sb of approxi- scattering strength is estimated. mately − 0.6 dB. The tone-burst duration estimate based on the detected Tone‑burst duration times of the beginning and end of the signal shown in Fig. 7 is 104 s. It corresponds to a difference of 0.17 dB. The transmitted signal uses a trapezoidal window as an Although the uncertainty of the edge detection method has approximation to the Tukey window (Bloomfield 2000). not been quantified, an error of % 4 is believed to be within The tapering parameter the uncertainty of the edge detection performance. Thus, the nominal -value is maintained as the duration of the 2tT = , tone-burst.  (12)

2tT , is the ratio of total taper-time, to the total duration, Along‑track beam pattern, BTyz . The computation of the insonified area is based on the assumption that the envelope is rectangular. The transient For the TC2181 transmitter the opening angle in the along- part is taken into account by estimating the energy-equiv- track direction depends on frequency. For example, in the ◦ ◦ alent rectangular-shaped tone-burst. In Fig. 9a the blue far-field it is about2 at 200 kHz and 1 at 400 kHz. The and solid curve represents the trapezoidal tapering func- near-field of the TC2181 transmitter extends about 20 meters Λ=0 t = 0 tion which increases in amplitude from at up depending on frequency. Figure 10 shows how the along- Λ=Λ t = t to 0 at T . Within the rising time the energy of the track main beam increases with decreasing range. Thus, trapezoidal envelope is when computing the scattering cross section the influence 2 from depth and frequency on the along-track beam pattern tT Λ t 2 Λ t 0 0 T is taken into account. The transmit beam patterns predicted ET =  dt = , (13) 0 tT 3 by the company proprietary model have regularly been com- pared with measured values in the near field (3 m) and on and of the energy-equivalent it is a single occasion in the far field (20 m) in a large tank at 2 an external facility. Around the main lobes the predictions ER =Λ0tR , (14) match well with the measurements, which supports the use where tR is time required for the rectangular envelope to of the model at other ranges. have ER = ET (Fig. 9b). Thus, tR = tT ∕3.Consequently, the duration of the energy-equivalent envelope is

e = − 2tT + 2tR (15) which yields

e = (1 − 2∕3) (16) 200 Hz 400 kHz dB The tone-burst applied here has = 0.2, which means that 0 e ≈ 0.87 . For small grazing angles where is proportional 35 -5 30

25 -10

20 -15 Range (m) 15 -20 10 -25 5

-30 -100 10 -10 010 Fig. 9 a Trapezoidal tapering of the tone-burst (blue solid line) and Along-track angle (° ) Along-track angle (° ) the energy-equivalent rectangular envelope (red solid-dotted line) as a function of time. b The energy as a function of time for the two envelope types Fig. 10 Model-based along-track transmit beam pattern BTyz

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1 LabViewTM PC

0 NITM PXI T50 PC Trigger signal Signal generator Transmit generator -1 and scope Hydrophone signal -2 data dB -3 50 dB amplifier l IQ Channe -4 Receiver (EM7218) -5 200 kHz 400 kHz Spherical -6 transducer Receive (TC4014-5) -80 -60 -40 -20 020406080 (TC-4034) (° ) R = 2.75 m

Fig. 11 Across-track beam pattern BTxz

Fig. 12 Measurement of the EM7218 receiver sensitivity. The TC4034 works as a transducer with an approximately omnidirectional Across‑track beam pattern, BTxz directivity and it insonifies the receiver array. A TC4014-5 hydro- phone is mounted next to the EM7218, and it measures the sound pressure level, while the EM7218 acquires raw IQ data The across-track beam pattern of the TC2181, BTxz, is based on results obtained from the transducer model. It is approxi- mately range independent, and consequently, only depends stretched to its upper voltage limit where the transmit sen- ◦ on frequency. The − 3 dB opening angle is about ±75 for sitivity might change, and in addition, the 50 dB amplifier all frequencies (Fig. 11) with a deviation of about ± 0.5 for is not calibrated. Instead each acoustic tone-burst is meas- ◦ ured by the TC4014-5 (SN-3411076) mounted next to the angles above approximately 55 . TM EM7218 and the signal is digitized by the NI PXI and TM SeaBat T50 receiver (EM7218) stored on the LabView PC. Figure 13 shows the receiver in a bracket together with the TC4014-5 hydrophone with → Measurements of the a ppeak relation the housing for a preamplifier. Another TC4034, which is not the SN-1611293, is used as an extra reference hydro- The setup used for measuring the relation between the mag- phone as a safety validation that the sound pressure levels nitude of the digital IQ-signal, |a|, and the corresponding measured by TC4014-5 levels are correct. The advantage peak sound pressure at the face of the receive array, ppeak, is of using a TC4034 as sound source is its nearly omnidi- sketched in Fig 12. The TC4034 (SN-1611293) transmitter rectional property, which should lead to a uniform sound is positioned 2.75 m from the center of the receiver along pressure level across all receiver channels as well as on a line perpendicular to the receiver surface. The measure- the receiving element on the TC4014-5. Meanwhile, as it ment includes a sequence of tone-bursts, where the input was shown in “Calibration transducers” section, the beam voltages to the TC4034 vary in order to generate different patterns of the TC4034 (Fig. 4) and TC4014-5 (Fig. 5) are sound pressure levels in front of the receiver array. The not perfectly omnidirectional. Figure 14a shows the verti- TM TM sequence is controlled by LabView . An NI PXI gen- cal (left) and horizontal (right) offsets between the TC4034 erates the requested tone-burst and transmits the signal to and TC4014-5. The resulting deviations from the omni- the TC4034. To obtain the highest possible source levels, directional assumption are shown in Fig. 14b, and vary ±0.4 a 50 dB amplifier is used. The maximum sound pressure approximately dB. Thus, the estimated calibration level is governed by the maximum allowed input voltage errors are within the tank uncertainty of ± 0.7 dB, and of 100 V to the TC4034. For each sound pressure level the therefore, the experimental setup is considered acceptable. EM7218 records the in-phase and quadrature signals for Figure 15 shows, for a single receiver channel, |a| given p all 256 channels and for all receive gains from 0 to 83 dB. in EM7218 machine units as a function of peak measured Five pings are collected at each setting for averaging. The by the TC4014-5 and given in dB re 1 Pa. The curves cor- transmit sensitivity of TC4034 sound source is not being respond to 6 different values of the receive gain G. The fre- applied in the computations; the TC4034 transmitter is quency of the incoming field is 300 kHz. The maximum

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300 kHz 105

104

103

102 G = 10 |a| (Machine Units) G = 20 G = 30 1 10 G = 40 G = 50 G = 60 100 110 120 130 140 150160 170 p (dB re 1 Pa) peak Fig. 13 The EM7218 and the TC4014-5 hydrophone (to the right in the image) with the characteristic bronze housing. The TC4034 hydrophone (to the left in the image) is an extra reference hydrophone Fig. 15 Relations between the magnitude of the IQ-signal and the only applied prior to measurement peak sound pressure at the face of the EM7218 receiver at 300 kHz

Vertical plane Horizontal plane Trigger signal 275 cm 275 cm Signal generator T50 PC 15 Test PC Channel IQ data 30

cm 6° Channe cm -90°+3° Actuator signal to rotor -90°-3° 6° l IQ data

Receiver (a) Angles between TC4034and TC4014-5invertical and horizon- EM7218 talplanes.

Spherical 0.4 transducer 0.2 (TC-4034) 0 R = 3 m dB -0.2 -0.4 200 220 240260 280300 320 340 360380 400 Frequency (kHz) Fig. 16 Measurement of the across-track directivity of the receiver B ◦ (b) Theresulting errors causedbythe combined beam pattern vari- ceramics, RCxz . The T50 receiver is rotated in steps of 1 from =−90◦ = 90◦ ations of the TC4034and TC4014-5. to

Fig. 14 Estimated calibration errors caused by beam pattern varia- A spherical sound source (TC4034) is positioned 3 m from tions of the TC4034 and TC4014-5 the pole and it is used to insonify the array at angles from ◦ ◦ ◦ =−90 to = 90 in steps of 1 . For each angle raw IQ 15 value of |a| is 2 = 32768 indicated by the black, solid, data is recorded, and the median value of the IQ-magnitude, horizontal line. The peak sound pressure level at the face of a , across the 256 channels is found. This procedure results the receiver ranges between 115 dB re 1 Pa to about 165 in a vector where each element is the a -value associated dB re 1 Pa. with a discrete -angle. Subsequently, this vector is normal- ized by its maximum value, and BRCxz is obtained. This is Across‑track beam pattern of the receiver element, BRCxz repeated for each frequency. Figure 17 shows two examples of BRCxz obtained at 220 and 360 kHz. The part of the tank The across-track beam pattern of the individual receiver ele- calibration that involves the measurement of BRCxz was con- ◦ ments must be compensated for. Figure 16 shows the meas- ducted at 23 C, whereas the sea tests were conducted at ◦ urement applied in the RESON test tank. The receiver array 15 C. There is some degree of concern that the shape of is mounted on a pole and can rotate around the vertical axis. BRCxz will change with temperature. As water temperature

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0 0

-10 -10 dB dB -20 -20

-30 -30

-4 -2 024 46 48 50 52 54 (a) (° ) (b) (° )

Fig. 18 Two examples of the beam pattern BRxz at 400 kHz

Fig. 17 Across-track beam pattern of the receiver ceramics, BRCxz , for 220 kHz (red dotted line) and 360 kHz (blue solid line) beamforming is conducted using floating point numbers. For large amplitudes the beamformer may clip the signals which typically occurs in the center beam at normal incidence. The decreases, the impedance contrast between the water and the T50 user interface sets up a warning if the beamformer is receiver front layer increases, and thus, the beam pattern will clipping, so the operator can reduce either the source level or pull back. A rough estimate provided by the array designer ◦ ◦ the receive gain. The time variant gain (TVG) delivers gain suggests that a temperature change from 23 C down to 15 C ◦ values with the same gain precision as the fixed gain. The may result in a reduction of BRCxz from 0 dB at 50 steering ◦ TVG curve is an inherent part of the Sb-calculation. angle down to − 1.5 dB at 70 . However, it is still uncertain by how much BRCxz will decrease, and therefore, a tempera- ture compensation cannot be included before further inves- tigations have been carried out. Fortunately, the pull back of Experimental site BRCxz is not frequency dependent. The T50 field tests have been conducted 1 km offshore from Beamformer the harbor of Santa Barbara, California, see Fig. 19. Sb-invari- ance tests with respect to changes in the receive gain and the With 256 receiver channels the EM7218 has an aperture size tone-burst duration were conducted at 15 m depths. Due to a of approximately 40 cm. At 400 kHz the center beam, i.e., setting error no GPS data were recorded for the receive gain the beam with the steering angle = 0, has a − 3 dB beam and the tone-burst duration tests, and consequently, their loca- ◦ width of 0.5 . As the steering angle increases, the width of tions are not marked in Fig. 19. Fortunately, GPS data were the main lobe increases as 1∕ cos( ) due to a reduced effec- recorded for the source level invariance test and the frequency tive aperture size. The beamformer uses a -30 dB Chebyshev dependence measurements. The source level invariance test window (Harris 2004) to suppress side lobes. Auto-focusing was conducted at a depth of 10 m along a 195 m line, with a ensures that the main-lobe width is approximately constant vessel speed of 2 knots. The frequency dependence measure- for all ranges. Figures 18a and b show the beam pattern for ments were conducted along four different lines within a sector two steering angles at 400 kHz. Approximations are made of 356×471 m. The average vessel speed was approximately when using fixed-point numbers on Field-Programmable 0.33 knots, so the boat was almost drifting. The lengths of the Gate Array (FPGA); however, this is not expected to produce lines vary between 30 and 100 m, and the lengths are governed any significant errors. A tank measurement, equivalent to the by the ping rate as well as the number of pings per frequency, one sketched in Fig. 16, has shown that at normal incidence, which varies between 100 and 300 pings. The average depth the magnitude level over all channels approximately follows within the sector is approximately 16 m. Figure 20a shows the a normal distribution, with 68% of the data within 0.36 dB bathymetric map obtained from Line 1 ( L1 ), and Fig. 20b the of the median value, and a coefficient of variation ofa | | of corresponding backscatter mosaic.The backscatter values in about 5% . The phase error has been estimated by acknowl- the mosaic are a result of a processing method, where the angle edging that the incoming field is spherical, and a standard dependency on Sb-values, has been filtered out. The mosaic ◦ deviation of the phase of about 5 has been found. For an is based on data obtained from a sequence beginning at 190 ◦ incoming field with an angle of = 70 the magnitude level kHz in steps of 10 kHz up to 400 kHz; preferably, it should follows approximately a normal distribution with 68% of have been made on a data set where the frequency is constant the data within 0.80 dB of the median, and a coefficient along the line, but such a data set was, unfortunately, never of variation of |a| of about 10% ; the standard deviation of obtained. Meanwhile, the mosaic shows no dramatic changes ◦ the estimated phase is about 5 . For both cases this will in the backscattering level along the line, indicating that the yield a beamformer error of less than 0.05 dB provided that seabed is homogeneous. No environmental characterization

1 3 114 Marine Geophysical Research (2018) 39:105–120

Table 2 Environmental parameters, Santa Barbara, 2016

34.41 Name Symbol Value Units

Measured parameters ◦ Water temperature T 15.5 C ) ° Sound speed at MBES cw 1506.8 m/s 34.405 Estimated parameters pH value of seawater pH 8 Latitude ( Derived parameters L 4 Water salinity S 33.6 PPT L 1 356m 1 k − L Absorption @200 kHz w 0.0074 m 34.4 L 2 3 −1 Absorption @400 kHz kw 0.0121 m 471m -119.682 -119.674 Longitude (° ) 2001). For the experimental site sonar images did not show any signs of bubbles. The water sound speed cw is measured Fig. 19 Survey lines 1 km outside Santa Barbara harbor, CA (Google □ with a (SVP) mounted next to the MBES. Earth). L1 L4 : Frequency dependence test with the four lines - and T ◊ : Source level test. No GPS-data were recorded during the receive The water temperature is measured with a thermometer gain and tone-burst tests, but they have been conducted within the inside the housing of the SVP. The temperature is not assumed area shown on the map very different from that of the ambient water. The MBES is mounted on a pole to the port side of vessel at a depth of about D = 1.5 m. Given D, cw, and T, the salinity S can be Depth (m) Backscatter (dB) estimated [(Medwin 1975), Eq. 1 ]. Subsequently, by assum- ing a pH value of 8, the acoustic absorption in the seawater is estimated (Jackson and Richardson 2007; Francois and Gar-

120 rison 1982a, b), see Table 2.The sonar settings are changed by remote commands from a separate PC, which enables the use 105 of numerous different settings over a short period of time. For each beam recorded Sb-values are stored as time series around 90 the time of the bottom detection. The Sb-values are converted

75 from the logarithmic domain into the absolute domain in order to obtain the corresponding -values. For each ping the mean

(m) 60 -value is found within each beam, where it will be linked to the estimated grazing angle around the bottom detection point. ◦ 45 All ( , ) pairs obtained from a ping are sorted into bins of 1 ◦ ◦ width ranging from 20 up to 90 . Next, the mean and standard 30 deviations of all the pings are found. 15

0 14 28 42 56 70 0 14 28 42 56 70 Results (m) (m) (a) (b) The seafloor echo signals processed by the sonar have been beamformed in the equidistant mode, i.e., a beamforming Fig. 20 a Bathymetric map obtained from line L1, where the white mode with a constant ground range distance between the bot- arrow marks the travel direction of the vessel. b The corresponding TM tom detection points. backscatter mosaic along L1 . The maps have been produced in QPS Sonar settings invariance test was made in connection with the test. However, back in 2009 the U.S. Geological Survey reported that the mean grain size The purpose of the Sonar Settings Invariance Tests is to over this area is 0.26 mm, i.e., medium-fine sand (Barnard validate that the estimated scattering strengths are invariant et al. 2009). About 10 km west of Santa Barbara harbor, close according to changes in source level, receive gain and the to the university (UCSB), the inner continental shelf has a high tone-burst duration. These tests have been conducted at 400 density of naturally occurring gas and oil seeps (Fleischer et al. kHz. The source level settings is varied from 210 to 220 dB re

1 3 Marine Geophysical Research (2018) 39:105–120 115

-6 14o - 20o 20o - 30o -20 -15 210 dB re 1 Pa -8 211 .. -23 -18 (dB)

212 .. b

213 .. S -10 214 .. -26 -21 215 .. 30 100 200300 30 100 200 300 216 .. 30o - 40o 40o - 50o -12 217 .. -14 -12 218 .. 219 .. -17 -15 220 .. (dB)

-14 b (dB)

Mean curve S b S -20 -18 -16 30 100 200300 30 100 200 300 50o - 60o 60o - 70o -10 -8 -18 -13 -11 (dB) b -20 S -16 -14 30 100 200300 30 100 200 300 -22 70o - 80o 80o - 90o 10 20 30 40 50 60 70 80 90 -5 -5 Grazing angle (° ) -8 -8 (dB) b S Fig. 21 -11 -11 AR-curves from ten different source level settings 30 100 200300 30 100 200 300 ( s) ( s) -10 2 dB 4 .. Fig. 23 The scattering strength as a function of tone-burst duration -12 6 .. 8 .. for different grazing angle intervals 10 .. -14 12 .. 14 .. ◦ 16 .. strength taken from a 10 angle interval, except at the lowest -16 18 .. ◦ 20 .. grazing angle, where it is 6 . About 100 pings were applied -18 22 .. 24 .. in the averages. The overall result is a random fluctuation

(dB) 26 .. b 28 .. around a mean value of about ± 1.5–2 dB. No trends as func- S -20 30 .. s 32 .. tion of pulse duration are observed. The drop around 240 -22 34 .. Mean can probably be explained by a sudden change in the seafloor -24 properties. The fluctuations are largest near normal incidence.

-26 Frequency dependence test

-28 10 20 30 40 50 60 70 80 90 The multifrequency measurements conducted along the lines Grazing angle (° ) L1-L4, shown in Fig. 19, range from 190 kHz in steps of 10 kHz up to 400 kHz. Sb-estimates are divided into 14 grazing angle Fig. 22 ◦ ◦ ◦ AR-curves from 17 different receive gains bins of 5 width from 20 up to 90 . Figure 24 shows the Sb -estimates obtained from L1 . The blue curves are the estimated mean Sb-values with the corresponding standard deviations on 1 Pa in 1 dB steps, while all the other sonar settings are kept the error bars. The general picture shows a scattering strength constant. To each source level setting 300 pings have been that increases with increasing frequency. At 350 kHz a tran- recorded. Figure 21 shows the angular response (AR) curves sition occurs, above which the scattering strength increases obtained from the 11 measurements. For grazing angles below ◦ with frequency at a higher rate. For each grazing angle bin the 50 the variation is ± 1–2 dB, and above it is ± 0.5–1 dB. Fig- scattering cross section as a function of frequency is fitted to ure 22 shows the AR-curves obtained at the receive gain test. a power function of the form The gain was varied in steps of 2 dB between 2 and 34 dB, =  ⋅ f i ⋅ 10−6i , i = 1, 2. while all other settings were constant. Data obtained at gain i (17) settings above 34 dB resulted in clipping and are not included where f is the frequency [Hz], and where the parameter set, here. Each curve represents an average of 100 pings. For each ( 1, 1), is applied in the frequency range from 190 kHz up angle value the Sb-estimates vary by approximately ± 1–2 dB. to a transition frequency ft, which will be defined below, and Figure 23 shows the scattering strengths obtained when the where finally( 2, 2) is applied between ft and 400 kHz. The tone-burst durations vary between 30 and 300 s in 10 s power function estimations are carried out in the logarithmic increments. Each sub-figure represents the average scattering domain by the use of the classical unweighted linear least

1 3 116 Marine Geophysical Research (2018) 39:105–120

20° < 25° 25° < 30° square (LS) method. The chosen limit frequency between g g the low and high frequency LS-estimation is 350 kHz. The -15 -15

ft (dB) -20 -20 transition frequency is the frequency, where the two power b S functions are equal. If they do not become equal between -25 -25 190 and 400 kHz, ft will be set equal to 350 kHz. The green 200 250 300 350 400 200 250 300 350 400 30° < 35° 35° < 40° and red curves in Fig. 24 represent the estimated power laws g g -15 -15 below and above 350 kHz respectively. The two sets of esti-

(dB) -20 -20 mated power function parameters, ( 1, 1 ) and ( 2, 2 ), are b S shown in Fig. 25 for all grazing angles, and for all four sur- -25 -25 200 250 300 350 400 200 250 300 350 400 vey lines, L1-L4.Considered from an average point of view, 40° < 45° 45° < 50° g g the 1-values, the exponents for the low frequency regime, ◦ -15 -15 vary between 1 and 1.3 for angles below 30 ; as the graz-

(dB) -20 -20 b

ing angle increases they decay approximately monotonically S ◦ down to a common value of about − 0.1 at 90 . For the high -25 -25 200 250 300 350 400 200 250 300 350 400 frequency regime the 2-exponents increase from values of 50° < 55° 55° < 60° ◦ ◦ g g 1.3 to 2.3 at 22.5 up to a value of about 5 between 60 and ◦ -12 -12 90 . Plots of the scaling factors 1 and 2 are included for

(dB) -17 -17 b completeness. S -22 -22 Figure 26 shows the residuals between the Sb-values and 200 250 300 350 400 200 250 300 350 400 60° < 65° 65° < 70° the estimated power functions from the four lines. If one g g leaves out the 210 kHz component, the residuals do not -10 -10 ◦ exceed ± 1.5 dB for grazing angles below 50 , and they all

(dB) -15 -15 b appear very coincident. It is unlikely that these coincident S -20 -20 residuals can be explained by the same sudden local change 200 250 300 350 400 200 250 300 350 400 70° < 75° 75° < 80° in seafloor properties in all four measurements. It is unclear g g whether the constant residual levels can be explained by -8 -8

scattering mechanisms in the sediment or if they are caused (dB) -13 -13 ◦ b 50 , S by calibration errors. Above the degree of correlation -18 -18 between the residuals drops slightly as the grazing angle 200 250 300 350 400 200 250 300 350 400 ◦ 80° < 85° 85° < 90° approach 90 . The 210 kHz component is deviating about g g 1.5–2 dB at all angles, and this is most likely caused by an -6 -6

(dB) -11 -11

error within the MBES-system. b S Next, the Sb-estimates represented by the four power -16 -16 function fits will be compared with results obtained by 200 250 300 350 400 200 250 300 350 400 other authors. Greenlaw et al. (2004) present data obtained Frequency (kHz) Frequency (kHz) from a sandy sediment with an average grain size of 0.41 Fig. 24 Result from Line 1 in Fig. 19. The blue curves are the esti- mm (medium sand). The grazing angle was approximately S = 20◦ = 1.4 mated mean b-values with the corresponding standard deviations on g . They obtained a spectral exponent of the error bars. The green curves are the power law fits for f ≤ 350 between 265 and 400 kHz. Here, the estimated power-law f > 350 ◦ kHz, and the red curves for kHz parameters for g = 22.5 are listed in Table 3. The estimated transition frequencies range from 291 to 333 kHz. Param- eters estimated for the entire frequency range from 190 to value found by Greenlaw et al. Finally, the Sb-estimates 400 kHz, ( ,  ), are also included in order to compare with obtained here are about 1–2 dB higher than their values. the results from Greenlaw et al. (2004). Figure 27 shows the Weber and Ward (2015) measured the scattering strengths 45◦ Sb-values as obtained from the estimated power functions for at a grazing angle of at frequencies between 170 and ◦ lines 1–4 for g = 22.5 . The results are presented in terms 250 kHz; the sediment was sand with a mean grain size of of the Lambert parameter (Williams et al. 2009) given as 0.25–0.35 mm. They found spectral exponents of =−0.09 and = 0.32 at two different sites. At SAX04 (Williams = S − 10 ⋅ log (sin2( )) . et al. 2009) scattering strengths were obtained for grazing b 10 g (18) ◦ ◦ angles between 25 and 48 in the frequency range from 200 to 500 kHz. The average grain size of the sand at SAX04 The mean value of the exponent of the four lines for the was 0.36 mm, but the sediment was a mixed composition entire frequency range is = 1.31, which is close to the of sand in mud. Table 4 shows the estimated power law

1 3 Marine Geophysical Research (2018) 39:105–120 117

20° < 25° 25° < 30° 30° < 35° 35° < 40° Line 1 Line 2 Line 3 Line 4 g g g g (a) (b) 2 2 2 2 0.06 1.5 0.05 0 0 0 0

0.04 1 (dB) -2 -2 -2 -2 0.03 0.5 1 1 200 300 400 200 300 400 200300 400 200 300 400 0.02 0 40° < 45° 45° < 50° 50° < 55° 55° < 60° g g g g -0.5 2 2 2 2

0.01 -1 0 0 0 0

20 30 40 50 60 70 80 90 20 30 40 50 60 70 80 90 (dB) Grazing angle ( ) Grazing angle ( ) g ° g ° -2 -2 -2 -2 (c) (d) 200 300 400 200 300 400 200300 400 200 300 400 102 7 60° < 65° 65° < 70° 70° < 75° 75° < 80° 6 g g g g 1 10 2 2 2 2 5 2 100 2 4 0 0 0 0 (dB) 3 -2 -2 -2 -2 10-1 2 200 300 400 200 300 400 200300 400 200 300 400 Frequency (kHz) Frequency (kHz) 10-2 1 80° < 85° 85° < 90° 20 30 40 50 60 70 80 90 20 30 40 50 60 70 80 90 g g Grazing angle ( ) Grazing angle ( ) 2 2 g ° g ° Line 1 Line 2 0 0

(dB) Line 3 , Line 4 Fig. 25 Estimated pairs of scaling factors and exponents ( 1 1 ) (a, -2 -2 , b), and ( 2 2 ) (c, d) 200 300 400 200 300 400 Frequency (kHz) Frequency (kHz)

◦ parameters at g = 42.5 obtained here. Figure 28 shows Fig. 26 S ◦ Residuals between b-data and estimated power functions for the estimated power law fit for g = 42.5 for lines L1–L4, the four lines together with the Sb-values acquired by Weber and Ward (2015), Fig. 7), and finally, from SAX04 the mean values ◦ ◦ ◦ Table 3 Power function parameters at g = 22.5 of Sb between g = 39.4 and 44.7 [(Williams et al. 2009), Fig. 8]. The spectral slopes found by Weber et al. 2017 are Parameter L1 L2 L3 L4 significantly weaker than the ones estimated here. The scat- 1 0.0392 0.0251 0.0294 0.0256 tering strengths obtained at L1-L4 are 2–3 dB lower than the 2 0.0604 0.0831 0.0488 0.1002 values obtained at the site with =−0.09 ; they are about 0.0479 0.0337 0.0370 0.0359 1 dB higher than the Sb-values from the site with = 0.32 . 1 1.31 1.04 1.06 1.09 The scattering strengths obtained at L1–L4 are about 4 dB 2 1.66 2.13 1.47 2.33 higher than the ones obtained at SAX04, but in terms of the 1.45 1.25 1.22 1.33 spectral slope the SAX04 data do also show a change in the ft [kHz] 291 333 291 333 spectral slope between 300 and 350 kHz. The author has not been able to find any results published on the scattering strength at normal incidence in the fre- quency range 190–400 kHz from a sandy seabed. However, (2008), Fig. 6, top-left] are shown in Fig. 29. Table 5 shows ◦ Sessarego et al. (2008) have conducted normal incidence the estimated power law parameters at g = 87.5 obtained reflection measurements in a laboratory over flattened here. There is a drop in reflection loss of about 3 dB between medium sand with a mean grain size of 0.25 mm. Unlike the 250 and 330 kHz, where a similar increase is not observed laboratory measurement, the scattering strengths from L1–L4 in the scattering strengths from L1–L4, see e.g., Fig. 24 for ◦ ◦ are obtained over a rough seabed, where the coherent reflec- the case where 85 <𝜃g ≤ 85 .Above 330 kHz the reflection tion most likely is insignificant compared to the incoherent. loss decreases to − 10.5 dB at 400 kHz with the same rate Hence, the reflection loss based on the incoherent intensity as the Sb-estimates from L1–L4 increase. is considered here, and data taken from [Sessarego et al.

1 3 118 Marine Geophysical Research (2018) 39:105–120

20° < 25° Table 5 = 87.5◦ g Power function parameters at g -8 Greenlaw et. al. L1 L2 L3 L4 Parameter L1 L2 L3 L4 -10 1 0.0379 0.0427 0.0496 0.0359 2 14.1005 2.6231 6.4942 7.5047 1 − 0.10 − 0.06 − 0.01 − 0.33 -12 2 5.34 3.65 4.43 4.54 ft [kHz] 336.9 329.6 333.6 333.9 -14

Lambert Parameter (dB) 85° < 90° g -16 -8 -29 L1 L2 L3 L4 Sessarego et al.

-18 200 250 300 350 400 450 -10 -31 Frequency (kHz)

◦ -12 -33 Fig. 27 g = 22.5 (dB) The Lambert parameters for sand at . A straight- b line fit to the five data points by Greenlaw et al. (2004) is also S included (the thin dashed line). The Lambert-values from L1–L4 are obtained from the power law model in Eq. 17, and by the use of the -14 -35 input parameters sets ( 1, 2, 1, 2, ft) from Table 3 Incoherent reflection loss (dB)

-16 -37 200 250 300 350 400 450 42.5◦ Table 4 Power function parameters at g = Frequency (kHz)

Parameter L1 L2 L3 L4 ◦ Fig. 29 The scattering strength for sand at g = 87.5 . Included 1 0.0341 0.0200 0.0387 0.0250 is also the incoherent reflection loss from flattened medium sand 2 1.3740 1.2424 0.9422 0.9303 obtained in a laboratory (Sessarego et al. 2008) 1 1.06 0.67 0.98 0.81 2 4.39 4.40 3.81 4.03 Discussion ft [kHz] 330 331 324 325

The angular response curves obtained at the different source levels gain settings all lie within a band ΔSb ≈±1 dB. The 40° < 45° g fluctuations are attributed to the random nature of the acous- -14 tic interaction with the seabed. The tone-burst duration test Weber et al. SAX04 L1 L2 L3 L4 results in ΔSb-values fluctuating about 2–3 dB around the -16 mean scattering strength at each grazing angle interval. Near f -0.09 normal incidence, however, the variations can be up to 4 dB -18 for tone-burst durations above 100 s. In general, no trends as a function of either source level, receive gain, or tone- f 0.32

(dB) -20 b burst duration are observed. S For the frequency dependence test, in general the power -22 law estimations lead to residuals that are within ±1.5 dB (when the 210 kHz is not included). Provided the sedi- -24 ment is still medium sand as reported almost 10 years ago (Barnard et al. 2009) the scattering strengths obtained here -26 200 250 300 350 400 450 are close to what researchers have found on medium sand ◦ ◦ Frequency (kHz) for grazing angles of 22 and 45 . The SAX04 data also seem to be described by two different regimes with a transi- 42.5◦ Fig. 28 The scattering strength for sand at g = . Included tion frequency very close to ones found here, i.e, at about are also Sb-data from two sandy sites obtained by Weber and Ward 324–330 kHz. The resemblance is striking, and hence, the (2015), and data from SAX04 (Williams et al. 2009). The Sb-values sediment here seems to have a scattering characteristics from L1–L4 are obtained from the power law model in Eq. 17, and by the use of the input parameters in Table 4 similar to the sediment at SAX04. One can only speculate

1 3 Marine Geophysical Research (2018) 39:105–120 119 about the causes: gas bubbles, shells in the sediment, bio- Bloomfield P (2000) Fourier analysis of time series: an introduction. turbations, and mud mixed with sand as at SAX04. Nev- Wiley, New York D’Antona G, Ferrero A (2006) Digital signal processing for measure- ertheless, Hefner et al. (2010) conducted experiments in a ment systems. Theory and applications. Springer, Milano large fresh water pool over a diver-smoothed sand bottom at Eleftherakis D, Berger L, Bouffant NL, Pacault A, Augustin JM, Lur- frequencies between 200 and 500 kHz, and at grazing angles ton X (2018) Backscatter calibration of high-frequency multibeam ◦ ◦ between 10 –60 . Measurements with shell fragments dis- echosounder using a reference single-beam system, on natural sea- floor. In: G Lamarche , X Lurton (eds) Marine geophysical research, tributed over the flat sand were also made. The results indi- seafloor backscatter from swath mapping echosounders: from tech- cate that for sand, as well as for sand with shell fragments nological development to novel applications, Springer, New York on top, a change in spectral slope occurs between 300 and Fleischer P, Orsi TH, Richardson MD, Anderson AL (2001) Distribu- 400 kHz ((Hefner et al. 2010), Fig. 4). Thus, it seems pos- tion of free gas in marine sediments: a global overview. Geo-Mar Lett 21:103–122. https​://doi.org/10.1007/s0036​70100​072 sible that for medium sand a transition between two different Foote KG, Zhu D, Hammar TR, Baldwin KC, Mayer LA, Hufna- regimes occur around 320–340 kHz. At normal incidence gle LC, Jech JM (1988) Protocols for calibrating multibeam the reflection loss decays and the scattering strength rises sonar. J Acoust Soc Am 117(4):2013–2027. https​://doi. with the same rate above approximately 330 kHz. However, org/10.1121/1.18690​73 Francois RE, Garrison GR (1982a) Sound absorption based on the reduced reflection loss between 250 and 330 kHz is not ocean measurements: Part I: Pure water magnesium sul- supported by similar increase in the scattering strength, and fate contributions. J Acoust Soc Am 72:896–907. https​://doi. a reason for this disagreement is not possible to provide here. org/10.1121/1.38817​0 Surveys over the test lines with fixed sonar settings, Francois RE, Garrison GR (1982b) Sound absorption based on ocean measurements: Part II: Boric acid contributions and equation for including the frequency, have unfortunately not been total absorption. J Acoust Soc Am 72:1879–1890. https​://doi. obtained; bathymetric maps and mosaics would have pro- org/10.1121/1.38867​3 vided the investigation with essential information about the Greenlaw CF, Holliday DV, McGehee DE (2004) High-frequency degree of homogeneity of the sediment. As already stated scattering from saturated sand sediments. J Acoust Soc Am 115(6):2818–2823. https​://doi.org/10.1121/1.17070​85 the residuals in Fig. 26 from L1–L4 are almost the same (at ◦ Harris FJ (2004) Multirate signal processing for communication sys- least for 𝜃g < 50 ), and so are the estimated power laws. tems, 1st edn. Prentice Hall PTR, London Therefore, a sudden significant change in seafloor properties Heaton JL, Rice G, Weber TC (2017) An extended surface target for at all four lines is considered unlikely. high-frequency multibeam echo sounder calibration. J Acoust Soc Am 141(4):388–954. https​://doi.org/10.1121/1.49800​06 Acknowledgements Hefner BT, Jackson DR, Ivakin AN, Tang D (2010) High frequency The Innovation Fund Denmark partly sponsored measurements of backscattering from heterogeneities and discrete the development of the T50 system. The author would like to thank col- scatteres in sand sediments. Proc Eur Conf Underwater Acoust leagues at Teledyne RESON: Henrik Dahl for building the calibration 3:1386–1390 arrangement in the test tank, and Jesper T. Christoffersen for helpful Hellequin L, Boucher J, Lurton X (2003) Processing of high-frequency discussions and input related to the T50 system. The author would multibeam echo sounder data for seafloor characterization. IEEE J also like to thank former colleagues James Coleman, the vessel opera- Ocean Eng 28(10):1–12. https://doi.org/10.1109/JOE.2002.80820​ ​ tor, for providing expert support on the sea and for building the data 5 acquisition software, and finally, Eric Maillard for contributing with Jackson DR, Richardson MD (2007) High-frequency seafloor acous- algorithms, knowledge, and guidance during the work. tics. Springer, New York

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