= Spherical elastic ray invariant
{title2=$p=r\sin i/\alpha(r)$}
For an <isotropic> radial <wave speed> $\alpha(r)$, the <elastic ray> equations imply conservation of $\mathbf x\times\mathbf y$, where $\mathbf y$ is the <slowness> vector. Indeed, its derivative is $\alpha\mathbf y\times\mathbf y+\mathbf x\times\nabla(1/\alpha)=0$. Thus each nonradial <elastic ray> lies in a fixed plane through the centre and $p=|\mathbf x\times\mathbf y|$ is constant. The angle $i$ is measured from the radial direction; tangential <slowness> continuity preserves $p$ across spherical interfaces.
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