*3.3. Processing of Undewater Noise*

The signals were processed to obtain information on the frequency domain as well as the time-frequency domain.

For the frequency information, each 5 min recording was filtered in each third octave band with center frequencies from 10 Hz to 100 kHz. The average and standard deviation of the sound pressure level (SPL) was calculated from the signals obtained by windowing the filtered signals in 10 s sections. The average was calculated from *prms* = <sup>1</sup> *N <sup>N</sup> <sup>i</sup>*=<sup>1</sup> *pi*,*rms* and the standard deviation from δ*prms* = <sup>1</sup> *N <sup>N</sup> <sup>i</sup>*=1(*pi*,*rms* − *prms*) 2 , where *pi*,*rms* is the root mean square pressure of each windowed signal. From the resulting values, the *SPL* was calculated according to its usual definition [24], *SPL* = 20 log *prms*/*pre f* and δ*SPL* = 20 log δ*prms*/*pre f* , where *pre f* = 1 μ*Pa*. Although the variability of the SPL may change according to the window used, this calculation provided an approximation of the error involved in quantifying the SPL.

A spectrogram with a rectangular window able to identify the variations of SPL with respect to the background was used for the time-frequency domain.

### *3.4. Underwater Sound Propagation Model*

Several mathematical models can be used to study the underwater acoustic propagation (parabolic equation model, the based on normal modes, the spectral integration model, among others). In each case, the implementation of these mathematical models required several parameters whose exact value was not always known, which could lead to unreliable results. In order to simplify this problem, several semi-empirical models can be found that distinguish different types of analytical propagation phenomena [25].

The depth of water in the Port of Cartagena (~12 m) is such that there are multiple rebounds of the signal between the surface and the seabed, which leads to a considerable level of interaction between the propagated and reflected acoustic signals. This interaction is quite complex, as it is necessary to take into account the type of seabed, type of sediment, how it is distributed, and possible depth variations, among others. This behavior means that there is a shallow-water propagation channel.

The transmission loss of sound propagation in shallow water depends upon many natural variables of the sea surface, water medium, and bottom. Because of its sensitivity to these variables, the transmission loss in shallow water is only approximately predictable in the absence of precise values for the variables. The semi-empirical Marsh–Schulkin expressions based on the Colossus models are useful for rough prediction purposes [24,26]. This model can be used for simulations between 0.1 and 10 kHz. From this model, the transmission losses are obtained according to the equations given in:

$$TL = \begin{cases} 20\log(R) + aR + 60 - k\_L & R < H \\ 15\log(R) + aR + a\_T\left(\frac{R}{H} - 1\right) + 5\log(H) + 60 - k\_L & H < R < 8H \\ 10\log(R) + aR + a\_T\left(\frac{R}{H} - 1\right) + 10\log(H) + 64.5 - k\_L & R > 8H \end{cases} \tag{1}$$

where *R* is the distance from the source; α is the absorption coefficient of the water; *kL* is a parameter called *near-field1 anomaly*, which measures the gain due to rebounds between the background and the surface; α*<sup>T</sup>* is the so-called effective attenuation coefficient, which takes into account the losses due to the energy coupling between the surface and the bottom [26]; and *H* is the *distance of jump* or *transmission*, defined as that maximum distance at which a ray contacts the surface or the background, whose shape depends on the depth of the water column, *D*, and is given by the following equation:

$$H = \sqrt{\frac{L+D}{3}}\tag{2}$$

In the study, the model was applied to the port considering 1 kHz, a calm sea, and a sandy bottom: *kL* = 6 dB/bounce and α*<sup>T</sup>* = 1.8 dB/bounce.

It should be noted that this model was simplified and did not account for a large number of effects that should be taken into account in a more detailed propagation study. Some of these effects consider a reflection coefficient at the port perimeter and variations in depth, among others. Therefore, the numerical results of the calculations should be taken with caution. However, our intention of using a simplified propagation model here was to determine the approximate acoustic behavior of the complex propagation processes in a port environment.

### **4. Results and Discussion**

### *4.1. The Submarine Seabed*

The fundamental properties of the water column and the seabed were characterized by two different methods:

1. Visual inspections by an underwater ROV to obtain photographic and video reports. Figure 5 shows the robot deployed from the boat (left) and an image of the bottom at a depth of 9 m (right). The bottom was found to be soft (composed of sand, mud, small stones, and gravel) and shelved slightly with a distance from the jetty.

2. A bathymetric survey, which obtained information on the depth and types of material below the seabed, plus an updated isopach map, was carried out by a sub-bottom profiler (SBP) coupled to the stern of an ASV. The autonomous vessel was programmed to cover Cartagena Bay following parallel paths. Figure 6 shows the ASV's control, communication, and command software, which included an initial isopach layer of the bay provided by the Cartagena Port Authority.

**Figure 5.** Robot on deployment (**left**) and an image of the seabed (**right**).

**Figure 6.** ASV control software.

A screenshot of the sub-bottom profile can be seen in Figure 7. The SBP emits a 20 kHz low frequency pulse into the seabed and highlights seismic structures and layers. The operator can view the raw high frequency profile on the screen.

The survey found a structural change at a depth of around 5 m under the seabed at certain points due to rock formations and possible sunken objects.

**Figure 7.** Sub-bottom profile image obtained.
