Surface waves in layered anisotropic structures

We report a method to calculate surface waves in layered anisotropic media using a reflectivity algorithm. The method posits a finite stack of constant anisotropic layers over an isotropic half-space. The parametrization within each layer allows for anisotropy with an arbitrarily oriented axis of symmetry ŵ, with magnitude scaled by three constants related to wave-speed variations of P and S waves with respect to the azimuth relative to ŵ. Within each layer, eigensolutions to the equations of motion can be expressed as upgoing and downgoing oscillatory and/or evanescent plane waves, except possibly within narrow intervals of horizontal slowness p where the governing matrix becomes near-defective and an alternative set of eigensolutions is used to avoid numerical instability. Synthetic seismograms for simple anisotropic crustal models demonstrate that significant Love–Rayleigh coupling occurs between adjacent overtone branches, leading to significant ‘scattering’ in the absence of 3-D velocity structure. The dependence of this scattering on azimuth relative to ŵ can cause the Love-Rayleigh scattering to appear to be related to a spurious component of the source mechanism.