On the complex conjugate roots of the Rayleigh equation: The leaky surface wave

In recent experiments and numerical studies, a leaky surface wave has been observed at the surface of an isotropic homogeneous elastic solid. This paper gives a detailed description of this leaky surface wave and explains its origin from the fundamental differential equations. Theoretically, the leaky surface wave arises from the complex conjugate roots of the Rayleigh equation. The complex conjugate roots give rise to a wave that propagates along the surface and is coupled to a plane shear wave in the medium. Due to the coupling, the surface wave leaks energy into the medium and is highly inhomogeneous. Its particle motion at the surface is prograde in nature, distinguishing it from the well-known Rayleigh surface wave which causes a retrograde particle motion.