Backscatter strength

$BS$ (in dB re 1 m per m

${}^{2}$) is dependent on the composition of the seafloor, the angle of incidence

$\varphi $ on the seabed, and the acoustic frequency

f [

3]. Thus, the backscatter strength provides an indication of the seafloor properties [

26]. However, before any useful information can be extracted from the received acoustic echo level

$EL$ at the MBES, an appropriate processing is necessary to account for the measurement configuration, seawater properties and the hardware and software settings of the sonar. The terms affecting

$B{S}_{f}\left(\varphi \right)$ are expressed by the sonar equation (modified from [

27,

28])

where

$SL$ is the source level (in dB re 1

$\mathsf{\mu}$Pa at 1 m), modulated by the transmission directivity pattern

$B{P}_{T}$ as a function of

f and the transmission angle

${\theta}_{T}$ with respect to the sonar axis.

$PG$ (in dB) is the receiver gain applied by the receiver electronics,

$SH$ (in dB re 1 V/

$\mathsf{\mu}$Pa) is the transducer sensitivity with respect to

f, and

$B{P}_{R}$ is the directivity pattern at reception expressed as a function of

f and the receiving angle

${\theta}_{R}$ with respect to the sonar axis.

$B{S}_{f}$ is defined per m

${}^{2}$ and derived from the target strength

$TS=B{S}_{f}+10log\left(A\right)$ (in dB re 1 m

^{2}) via the ensonified footprint area

A. The transmission loss

$TL$ depends on the water conditions and the travel distance

R of the signal to the seabed. It can be written as

where

$\alpha $ is the absorption coefficient depending on the temperature, salinity, acidity, pressure, and

f. The second term in Equation (

2) accounts for the energy loss of the signal due to geometrical spreading.

A is affected not only by the sonar characteristics but also by the seabed morphology, i.e., the across-track slope

${\u03f5}_{y}$ and along-track slope

${\u03f5}_{x}$ (radians). The ensonified footprint area in the pulse limited regime

${A}_{p}$ and in the beam limited regime

${A}_{b}$, respectively, are expressed by [

29]

and

where

c is the sound speed in water,

${\tau}_{eff}$ is the effective pulse length, and

${\varphi}_{fl}$ is the incident angle with respect to nadir and a flat seabed.

${\mathsf{\Omega}}_{tx}$ and

${\mathsf{\Omega}}_{rx}$ are the beam opening angles (representing the

$-3$ dB width of the main lobe) for transmission and reception and can be approximated for a continuous line array with length

L and equally spaced transducer elements by [

30]

where

$\lambda $ is the wavelength of the transmitted signal given by

$\lambda =c/f$. The term

$1/cos\left({\theta}_{R,T}\right)$ in Equation (

5) describes the increase of the beam opening angle with increasing steering angle

$\theta $ due to the reduced projected line array length. Considering a constant array length, the beam width changes with varying frequency. Furthermore, the incident angle with respect to the actual seabed

$\varphi $ can be calculated from

${\varphi}_{fl}$ (degrees) according to [

29]

The incident angle correction assigns to each backscatter measurement the true incident angle. In environments with a rough seabed morphology, this correction is essential for seabed classification using backscatter data.

The sonar equation (Equation (

1)) allows for the theoretical extraction of the absolute backscatter strength from the received signal of the MBES. However, the necessary variables and parameters might not be available from the sonar producer or measured sufficiently accurately. Even though all variables are properly documented, the conversion from analog to digital data and vice versa at reception and transmission often exhibits a discrepancy between the design and actual hardware implementation. In addition, aging of the MBES components might change the sensitivity of the system hardware over time [

28]. In such a case frequently performed relative or absolute calibrations of the MBES systems using natural reference areas or a calibrated singlebeam echosounder can be conducted [

31,

32]. If no calibration is performed, the backscatter data is considered as uncalibrated data. Still, as long as the relative variation of backscatter strength with respect to varying sediment types and incident angles are preserved within the processing, seabed classification can also be applied.