Sound-exposure regulations for aquatic wildlife frequently cite specific sound thresholds of concern. Regions exposed by human activity to sound levels above these thresholds may require mitigation. Greeneridge Sciences offers this calculator to help educate practitioners on how the size of these regions may depend on source and transmission parameters.
To proceed, you must have an estimate of the received level at a known range from the source (for a source level, use the default range of 1 meter). You must also characterize the transmission loss (TL)
TL = B*log10(R) + C*Rby identifying B, the logarithmic (predominantly spreading) loss, and C, the linear (scattering and absorption) loss, where R is range from the source in meters.
Transmission-loss parameters vary with frequency, temperature, sea conditions, source depth, receiver depth, water depth, water chemistry, and bottom composition and topography. Logarithmic loss B is typically between 10 dB (cylindrical spreading) and 20 dB (spherical spreading) although in some circumstances it can rise to 40 dB. Linear loss C has several physical components, including absorption in seawater, absorption in the sub-bottom, scattering from inhomogeneities in the water column and from surface and bottom roughness, and (for RMS levels of transient pulses) temporal pulse-spreading. For frequencies below 3.5 kHz in very deep water, C may be below 0.0001; in very shallow water, however, C may be as much as 0.01 or more. Start with B=15 and C=0.003 and see how changing these parameters changes the radii.
If you are using B and C values gained from a simple least-squares regression to experimental data, these parameters may provide a numerical fit to the original results but may not have any physical interpretation in terms of spreading or absorption. Extrapolate using such parameters only with extreme care. For example, one regression on airgun sounds measured at 100 to 1500 m range yielded B=4.4 and C=0.02. Such a small B and such a large C are atypical of physical parameters and instead probably reflect mathematical optimization by the physics-blind regression algorithm. We would not use these parameters to predict received levels outside the 100-1500 m range covered by the regression.
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