= Reflection from a layered SH impedance
{title2=$R=(q_a-Z_{\rm in})/(q_a+Z_{\rm in})$}
Set the lower <half-space> load to $q_b=\mu_bp_{\beta,b}$ using the <causal vertical wavenumber branch>, which excludes a wave arriving from depth infinity. Apply the <uniform-layer SH impedance update> upwards through every layer, keeping particle <velocity> and <traction> continuous. For upper <half-space> impedance $q_a$, incident <velocity> $V_0$ and reflected <velocity> $RV_0$, the top values are $V=V_0(1+R)$ and $T=-q_aV_0(1-R)$. Their ratio gives the displayed <reflection coefficient>, incorporating every underlying interface and multiple reflection.
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