Removing the Depth Dependence

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If we have a problem in which the water depth is of constant depth [math]\displaystyle{ z=-d/math\gt (we are assuming the free surface is at \lt math\gt z=0 }[/math]) and all the scatters are also constant with respect to the depth then we can remove the depth dependence by assuming that the dependence on depth is given by

[math]\displaystyle{ \phi(x,y,z) = \cosh \big( k (z+d) \big), \quad m \geq 0. }[/math]