= Core-reflected travel time
{title2=$T=2\sqrt{R^2+a^2-2Ra\cos(\Delta/2)}/c$}
In a constant-speed spherical shell with outer radius $R$ and inner radius $a$, a symmetric single reflection from the inner boundary has the displayed <travel time>. The boundary lies on the angular bisector of source and receiver. The branch exists only for $0\leq\Delta\leq2\arccos(a/R)$, since the incident line must remain in the shell. At the endpoint it joins the mantle-only chord branch with the same slope $a/c$. Continuing the formula beyond that endpoint would make the line intersect the inner boundary before its supposed reflection point.
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