*4.4. Propagation of Underwater Noise*

In these impulse noise source monitoring studies, we were interested in estimating the noise levels at various distances outside the port, as well as applying acoustic propagation models taking into account the characteristics of the water column and the soil.

Here, we applied the simplified model described in Section 3.3 to estimate the propagation range of a source with characteristics similar to the one described in Section 4.3. In addition, a ray tracing algorithm, specifically created by the Centro Tecnológico Naval y del Mar (CTN), was implemented that considered the topography of the Bay of Cartagena.

The ray trace was generated from the position of the detected impulsive noise source within the geometry of the port. Figure 11 shows, on the left, two examples of ray trajectories up to 5 km from the source. It should be noted that one ray leaves the port while the other remains inside the limits, which affected the final propagation levels. Figure 10 shows ray traces for different emission angles.

**Figure 11. (left**) Example of two ray traces. (**right**) All the rays traced. The red dot indicates the source.

Figure 12 shows, on the left, the percentage of rays that left the port, according to their emission point. It can be seen that this position is quite independent of the number of rays that left the port, that is, the port geometry influenced whether or not they exited. Only 10% of the rays travelled up to 5 km and 20% travelled up to 7.5 km. As explained below, these distances were enough to reduce the generated impulsive noise level.

**Figure 12.** (**left**) Percentage of rays that left the port. (**right**) Comparison of transmission losses with different propagation models.

In order to detect the effect of the resulting underwater acoustic propagation along these rays, we first compared the transmission losses due only to cylindrical geometrical divergence and absorption with the transmission losses of the semi-empirical model given in Section 3.3. Figure 12 right shows the results. It can be seen that both models had the same losses within a few meters of the emission. At closer distances, the semi-empirical model presented fewer losses because, in this region, the sound propagated under a spherical divergence. For longer distances, the large number of reflections led to a sharp increase in losses that limited propagation. Specifically, for 1 kHz, there were reductions of 35 dB in 100 m and 55 dB in 1000 m, much greater than those foreseen by divergence and absorption only.

From the above results we can estimate that a source of impulsive noise with an SPL of, typically, 120 dB re 1 μPaat 1 kHz inside the port, can generate a sound wave that could travel approximately 5 km to reach the background level shown above (70 dB re 1 μPa, see Figure 12). This means the sound could travel outside the port with a level below the background noise. Nevertheless, the real losses would be smaller, as the propagation model does not consider the lost reflections, which could be of about 4 to 7 dB per collision, so that this range would decrease.
