= Spherical surface-wave evanescence threshold
{title2=$c<\beta(r)R_E/r$}
For surface phase <speed> $c$ on a spherical <Earth>, the conserved angular ray parameter is $p=R_E/c$. The local horizontal <slowness> at radius $r$ is $p/r$, giving squared radial shear <wavenumber> $q_r^2=\omega^2[\beta(r)^{-2}-p^2/r^2]$ in ray theory. The displayed inequality makes it negative. A jump in shear <speed> can turn a propagating wave above the interface into an <evanescent wave> below it. This is a local condition, not proof of evanescence at every greater depth.
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