= SH impedance Riccati equation
{c}
{title2=$Z'=-i\omega(Z^2/\mu-\mu p_\beta^2)$}
With $e^{ikx-i\omega t}$ phasors, positive depth $z$, <shear modulus> $\mu=\rho\beta^2$, vertical <traction> $T$ and particle <velocity> $V$, the shear-wave equations give $V'=-i\omega T/\mu$ and $T'=-i\omega\mu p_\beta^2V$, where $p_\beta^2=\beta^{-2}-k^2/\omega^2$. Define $Z=-T/V$ wherever $V\ne0$. Differentiation gives the displayed <Riccati equation> and $V'=i\omega ZV/\mu$. A pole of $Z$ can be an ordinary zero of $V$, not a singular physical wavefield.
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