The density $\rho$ of water of bulk modulus B at a depth y in the ocean is related to the density at surface ${\rho }_0$ by the relation

Bulk modulus, $\mathrm{B}=-\frac{∆\mathrm{P}}{{\displaystyle \frac{∆\mathrm{V}}{{\mathrm{V}}_0}}}\Rightarrow ∆\mathrm{V}=-{\mathrm{V}}_0\frac{∆\mathrm{P}}{\mathrm{B}}\Rightarrow \mathrm{V}={\mathrm{V}}_0\left[1-\frac{∆\mathrm{P}}{\mathrm{B}}\right]$

Since density=mass/volume

Density, $\mathrm{\rho }={\mathrm{\rho }}_0{\left[1-\frac{∆\mathrm{P}}{\mathrm{B}}\right]}^{-1}={\mathrm{\rho }}_0\left[1+\frac{∆\mathrm{P}}{\mathrm{B}}\right]$ Where $∆\mathrm{P}=\mathrm{P}-{\mathrm{P}}_0={\mathrm{h\rho }}_0\mathrm{g}$

 = pressure difference between depth and surface of ocean

$\therefore \mathrm{\rho }={\mathrm{\rho }}_0\left[1+\frac{{\mathrm{\rho }}_0\mathrm{gy}}{\mathrm{B}}\right] (\because \mathrm{h}=\mathrm{y})$