 Rayleigh wave

A Rayleigh wave propagates along a stress-free boundary of an isotropic elastic half-space and decays into its interior. It combines an evanescent longitudinal wave with an evanescent vertically polarized shear wave. If its speed is $0<c<c_S<c_P$, the decay factors are $\alpha =\sqrt{1-c^2/c_P^2}$ and $\beta =\sqrt{1-c^2/c_S^2}$. Vanishing shear and normal traction gives the displayed determinant condition.

A Rayleigh wave is a type of surface wave that travels along the surface of a solid medium, such as the Earth. Named after the British scientist Lord Rayleigh, who studied these waves in the 19th century, Rayleigh waves are one of the three primary types of seismic waves generated by earthquakes, the other two being P-waves (primary or compressional waves) and S-waves (secondary or shear waves).