= Uniform-layer SH impedance update
{title2=$Z(z)=\frac{Z_r\cos\kappa d+iq\sin\kappa d}{\cos\kappa d+i(Z_r/q)\sin\kappa d}$}
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.
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