 Anisotropic Love-wave dispersion

For an aligned anisotropic surface layer, $q^2=({\omega }^2-{\beta }_x^{\prime 2}{k}^2)/{\beta }_z^{\prime 2}$, while the isotropic substrate has ${\kappa }^2=k^2-{\omega }^2/{\beta }^2$. Zero top traction and welded displacement/traction continuity give the displayed dispersion relation. The horizontal speed sets the limiting phase velocity; the vertical speed sets rigid-base cutoff frequencies. The effective contrast for the high-contrast transition is ${\rho }^{\prime }{\beta }_x^{\prime }{\beta }_z^{\prime }/(\rho {\beta }^2)$.