Sound absorption in sea. Thorp equation

Mathematical definition

$$\boxed{\alpha \left( f \right) = \frac{{0.1{f^2}}}{{1 + {f^2}}} + \frac{{40{f^2}}}{{4100 + {f^2}}}}$$

Notation	Description	Units	Limits	Conversion
$\alpha$	absorption	$\text{dB/km}$		$\alpha \left[ {{\rm{dB/km}}} \right] = \alpha \left[ {{\rm{dB/kyd}}} \right] \times 1.0936$
$f$	frequency	$\text{kHz}$	$f < 50$

Octave/Matlab implementation

function alpha = sound_absorption_sea_thorp(f)
% Inputs
%   f: frequency \ kHz
% Outputs
%   alpha: absorption of sound in seawater \ dB/km

    alpha = 1.0936*(0.1*(f.^2)./(1+f.^2) ...
          + 40*(f.^2)./(4100+f.^2));
end

Computational examples

References

Thorp, William H, "Analytic description of the low‐frequency attenuation coefficient", 1967
Etter, Paul C, "Underwater acoustic modeling and simulation", 2018