Wave amplitudes and contour profiles of surface Rayleigh waves in a layered half-space with transversely isotropic materials

We present field solutions for the surface Rayleigh wave fields in a layered half-space with transversely isotropic symmetry generated by a time-harmonic point load. The objective of this work is to provide a theoretical algorithm and numerical implementation for the solutions of surface Rayleigh wave fields for a layered half-space, so that it can be utilized as a tool in comparison with experimental tests and finite element simulations for seismic metamaterials. Our main focus will be the wave amplitudes and contour profiles affected by the anisotropic material parameters of the top layer. The top layer can be considered as a homogenized layer of an array of seismic resonators or simply can be utilized to reflect the geological feature of the Earth for possible wave attenuation. Field solutions of Rayleigh waves and the dispersion curves of a layered half-space are theoretically derived and numerically exemplified based on the dynamic reciprocity theorem. Simplified solutions for a homogeneous half-space with isotropic or transversely isotropic properties are verified with the existing known solutions. We demonstrate numerically how the amplitude of the surface Rayleigh waves will be affected by the anisotropic material parameters of the top-layer. Our study on the effect of top-layer material anisotropy could provide guidelines in the assessment of wave amplitudes of Rayleigh waves.