= Love-wave cutoff frequencies
{c}
{title2=$|\omega_n|=n\pi/[h\sqrt{\beta_0^{-2}-\beta^{-2}}]$}
For a slow uniform layer over a faster half-space, the nth <Love wave> branch reaches the half-space shear <wave speed> at the displayed threshold. Its half-space decay exponent then vanishes, so the threshold is a limiting nonlocalized state, not a trapped finite-energy mode. The fundamental has zero threshold and exists at every positive <frequency>; overtones require <frequency> strictly above their positive threshold. At high <frequency> each fixed branch approaches the layer shear <wave speed> from above.
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