 Uniform-layer SH impedance update

In a uniform layer, put $q=\mu p_{\beta }$, $\kappa =\omega p_{\beta }$ and $d=z-z_r$. Initial impedance $Z_r$ gives the displayed fractional-linear solution and $V(z)=V_r[\cos \kappa d+i(Z_r/q)\sin \kappa d]$. Expanding into exponentials yields forward and backward shear-horizontal waves. Negative $d$ propagates a bottom load upward. If the denominator vanishes, the nonsingular pair $(V,T)$ must be propagated through the impedance pole.