Volume attenuation

Volume attenuation in the ocean has a chemical nature, and it is induced by relaxation processes of salt constituents like MgSO$_4$, B(OH)$_3$ and MgCO$_3$.

The factor $\phi_V$ is given by the decaying exponential

$$\phi_V = \exp\left( -\alpha_Ts \right) ,$$ (4.4)

where $s$ is the ray arclength and $\alpha_T$ is the Thorpe (frequency dependent) attenuation coefficient in dB/m, given by[2]

$$\alpha_T = \frac {40f^2}{4100+f^2} + \frac {0.1f^2}{1+f^2} ,$$ (4.5)

with the frequency given in kHz.