= Flux-normalized elastic characteristic amplitudes
{title2=$\phi_\pm=(\sqrt Z\,v\mp\sigma/\sqrt Z)/2$}
These characteristic <wave amplitudes> split a one-dimensional <elastic wave> into forward and backward components. Their instantaneous net <elastic-wave energy flux> is $\phi_+^2-\phi_-^2$. For real-part harmonic phasors the mean flux is $(|\phi_+|^2-|\phi_-|^2)/2$. In a static graded medium with real positive <seismic impedance>, put $g=(\log Z)'/2$; then $\partial_x\phi_\pm\pm\beta^{-1}\partial_t\phi_\pm=g\phi_\mp$. <Seismic impedance> <gradients> couple the two directions while preserving net flux.
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