P-SV displacement potentials (source code)

= P-SV displacement potentials
{c}
{title2=$u_x=\phi_x-\psi_z,\quad u_z=\phi_z+\psi_x$}

= P-SV potentials
{c}
{synonym}

In a uniform isotropic material, these scalar <P-SV displacement potentials> separate longitudinal <P waves> from vertically polarized <SV-waves> in an $x,z$ plane. They satisfy $\phi_{tt}=\alpha^2\Delta\phi$ and $\psi_{tt}=\beta^2\Delta\psi$, with compressional and shear speeds $\alpha,\beta$. Reversing the sign convention for $\psi$ changes its polarization column but not the physical <P-SV directional impedance matrix> or the separate modal <energy> fluxes.