= Love-wave interface reflection phase
{c}
{title2=$R_h=\frac{\mu_0q-i\mu p}{\mu_0q+i\mu p}$}
For a slower surface layer supporting propagating <SH-waves> with vertical <wavenumber> $q>0$ above an <evanescent> half-space with decay exponent $p>0$, continuity of <displacement field> and <traction> gives the displayed <reflection coefficient> for a downward incident <displacement field> wave. Its modulus is one and its <wave phase> is $-2\arctan(\mu p/(\mu_0q))$. A traction-free top reflects <displacement field> with coefficient $+1$. The round-trip condition $R_he^{2iqh}=1$ then gives $\tan(qh)=\mu p/(\mu_0q)$, equivalent to direct <Love wave> mode matching.
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