4 Sound propagation modelling methodology

There are several methods available for modelling the propagation of sound between a source and receiver ranging from very simple models which simply assume spreading effects according to a 10 log (R) or 20 log (R) relationship (as discussed above, and where R is the range from source) to full acoustic models (e.g. ray tracing, normal mode, parabolic equation, wavenumber integration and energy flux models). In addition, semi-empirical models are available, whose complexity and accuracy are somewhere in between these two extremes.

In choosing the correct propagation model to employ, it is important to ensure that it is fit for purpose and produces results with a suitable degree of accuracy for the application in question, taking into account the context, as detailed in “Monitoring Guidance for Underwater Noise in European Seas Part III”, NPL Guidance, (Dekeling et al., 2014) and in Farcas et al. (2016). Thus, in some situations (e.g. low risk of auditory injury due to underwater sound, where range dependent bathymetry is not an issue, i.e. for non-impulsive sound) a simple (N log R) model might be sufficient, particularly where other uncertainties (such as uncertainties in source level or the impact thresholds) outweigh the uncertainties due to modelling. On the other hand, some situations (e.g. very high source levels, impulsive sound, complex source and propagation path characteristics, highly sensitive receivers, and low uncertainties in assessment criteria) warrant a more complex modelling methodology.

The first step in choosing a propagation model is therefore to examine these various factors, such as:

• Balancing of errors/uncertainties;
• Range dependant bathymetry;
• Frequency dependence; and
• Source characteristics.

For the sound field model, relevant geo-acoustic data, physical parameters and bathymetry will be developed based on a combination of data provided by the Applicant combined with the information gathered from the publicly available literature. These parameters will be fed into an appropriate propagation model routine, in this case the Weston Energy Flux model (for more information see Weston, 1971; 1980a; 1980b), suited to the region and the frequencies of interest. The frequency-dependent loss of acoustic energy with distance (TL) values will then be evaluated along different transects around the chosen source points.

The propagation loss is calculated using one for the four formulae detailed in  Table 4.1, depending on the distance of the receiver location from the source, and related to the frequency and the seafloor conditions such as depth and its composition.

Table 4.1:  Regions of transmission loss derived by Weston (1971).

In Table 4.1, is the depth at the source, is the depth at the receiver, is the minimum depth along the bathymetry profile (between the source and the receiver), is the critical grazing angle (related to the speed of sound in both seawater and the seafloor material), and are the wavelength and wavenumber as usual, and is the seabed reflection loss gradient, empirically derived to be 12.4 dB/rad in Weston (1971).

The spherical spreading region exists in the immediate vicinity of the source, which is followed by a region where the propagation follows a cylindrical spread out until the grazing angle is equal to the critical grazing angle . Above the critical grazing angle in the mode stripping region an additional loss factor is introduced which is due to seafloor reflection loss, where higher modes are attenuated faster due to their larger grazing angles. In the final region, the single-mode region, all modes but the lowest have been fully attenuated.

For estimation of propagation loss of acoustic energy at different distances away from the sound source location (in different directions), the following steps were considered:

• The bathymetry information around this chosen source points will be extracted from the GEBCO database in 72 different transects.
• A geoacoustic model of the different seafloor layers in the survey region will be calculated.
• A calibrated Weston Energy model will be employed to estimate the TL matrices for different frequencies of interest (from 25 Hz to 80 kHz) along the 72 different transects.
• The calculated source level values will be combined with the TL results to achieve a frequency and range dependant RL of acoustic energy around the chosen source position.
• The TTS and PTS potential impact distances for different marine mammal groups will be calculated using relevant metrics and weighting functions (from Southall et al., 2019) and by employing a simplistic animal movement model (directly away from the sound source) where appropriate.
• The Weston model will be calibrated against Parabolic Equation and Normal Mode models.