= SH-wave travel times in a crustal waveguide
{c}
{title2=$t_m(x)=\sqrt{x^2+(2mh)^2}/\beta_1$}
For a flat layer of thickness $h$ and shear <speed> $\beta_1$ above a faster half-space of <speed> $\beta_2$, unfolding $m$ down-and-up traversals gives the displayed reflected-ray <travel time>. Its slope is the horizontal ray <slowness>. At $x=2mh\tan i_c$, with $\sin i_c=\beta_1/\beta_2$, the corresponding head-wave branch $t=x/\beta_2+2mh\sqrt{\beta_1^{-2}-\beta_2^{-2}}$ is tangent to this curve.
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