= Refraction of a cylindrical SH wavefront
{title2=$a_T=C T_{\rm SH}/\sqrt{r_1+\beta_1q_1^2(t-t_1)/q_2^2}$}
Place a line source a distance $h$ above a plane welded interface and put $q_j=(\beta_j^{-2}-p^2)^{1/2}$, $t_1=h/(\beta_1^2q_1)$ and $r_1=h/(\beta_1q_1)$. The transmitted <elastic ray> is $x=hp/q_1+\beta_2^2p(t-t_1)$, $z=\beta_2^2q_2(t-t_1)$. <Elastic-interface boundary conditions> give $T_{\rm SH}=2\mu_1q_1/(\mu_1q_1+\mu_2q_2)$. Differentiating the ray positions across neighboring values of $p$ and applying <SH ray-tube amplitude transport> gives the displayed leading amplitude. Both $q_j$ must be positive; critical and evanescent incidence require different asymptotics.
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