= Elastic mode classification by vertical energy flux
{title2=$J_3=\frac{\omega^2}{2}\operatorname{Re}[a^*(Tq+R)a]$}
For a mode $u=a e^{i\omega(p_\alpha x_\alpha+qx_3-t)}$ with $x_3$ positive downwards, the reduced <traction> is $(Tq+R)a$. Its mean vertical <acoustic energy flux> is the displayed expression. Propagating modes are downgoing for positive flux and upgoing for negative flux; phase-slowness sign need not agree in <anisotropy>. Depth-decaying evanescent modes have $\operatorname{Im}q>0$. At grazing or repeated roots use limiting radiation modes.
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