Displacement impedance for an internal wave at a velocity jump ($Z=U^{2}m$)

At a material velocity jump with continuous background mass density, vertical displacement $\eta$ and fluid pressure are continuous, while $w=ikU\eta$ need not be. For a stationary component, $p=U^2{\eta }_z$ and the signed upward-wave impedance is $Z=U^{2}m$. Reflection and vertical-displacement transmission are $R=(Z_1-Z_2)/(Z_1+Z_2)$ and $T=2Z_1/(Z_1+Z_2)$.