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Absorption of the sound by the sea water and the seabed; The geometrical spreading of the sound away from the source; and Relative source and receiver depth.


180. One common approach is to use a method of normal modes, often applied in cases where the sound speed is stratified (changes vertically with depth but not horizontally with range). The normal mode method is useful to calculate the field in shallow water where the water column acts as a waveguide for a limited number of propagating modes. The theory can be expanded to account for different types of seabed (assuming the properties are known), and variations in sound speed gradients. The problem of solving the wave equation for range dependent conditions such as sloping or irregular bottoms and range-varying sound speed profiles has been overcome by an approximation called the parabolic equation. Here, small incremental changes in range and depth are used to accommodate changes in propagation parameters without the occurrence of large errors. However, in deep water with large numbers of modes propagating, the method is computationally demanding (Lurton 2003; Richardson et al. 1995). The Parabolic Equation method provides a frequency domain solution for transmission loss and can provide distance and depth dependent transmission loss predictions. An alternative approach which can prove useful for broadband impulsive sounds is to use a time-domain approach such as a finite-difference method. This method has been used extensively in the geophysical surveying industry.


181.


In water deep enough for propagation of ten or more modes, ray theory may be used. This requires that the sound speed changes slowly, with little change over a distance of one acoustic wavelength, making it best suited to the higher frequencies (and thus smaller wavelengths). The sound field is calculated by tracing ray paths, starting from the source, at uniformly spaced angular intervals. For each increment in range, the ray direction is determined from the ray equations and the local gradient of sound speed versus depth. This method is useful in deep water, where a small number of rays transmit most of the acoustic energy from source to receiver, where there is a direct path from source to receiver, and where only a limited number of surface and bottom reflections contribute. For shallow water, the large number of reflected paths makes the method somewhat impractical (Lurton 2003; Richardson et al. 1995).


182.


In simple cases, acceptable accuracy may be obtained by use of relatively simple geometrical spreading models. Commonly used models include spherical spreading (in decibel notation, this corresponds to a reduction in received level with range, r, of


Preliminary Environmental Information May 2014


East Anglia THREE Offshore Windfarm Appendix 9.1 Underwater Noise Modelling 88


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