Shear wave splitting in three-dimensional anisotropic media

TLDR: In this article, a numerical study of elastic wave propagation in weakly anisotropic het- erogeneous media was conducted to investigate the validity of different assumptions made in the derivation of these kernels.

Abstract: SUMMARY Splitting intensity, a new seismic observable that characterizes seismic anisotropy, can be ex- pressed as linear combinations of elastic perturbations involving 3-D sensitivity (or Frechet) kernels. We conduct a numerical study of elastic wave propagation in weakly anisotropic het- erogeneous media in order to investigate the validity of the different assumptions made in the derivation of these kernels. For characteristic periods larger than 6 s, the splitting parame- ters obtained from the analysis of synthetic seismograms calculated using a spectral-element method (SEM) are in excellent agreement with predictions based upon the 3-D kernels. This suggests that the kernels fully capture the complexity of shear wave splitting in heterogeneous anisotropic media and can be used for tomography. In addition, they can be used to calculate synthetic splitting parameters in 3-D anisotropic media, which represents a very small amount of computation compared with finite-difference or finite-element modelling. 3-D kernels dis- tribute sensitivity off of the reference ray given by the laws of geometrical optics. This has important consequences for the interpretation of apparent splitting parameters, which usually relies on ray theory. Apparent splitting parameters estimated at the surface can differ signif- icantly from the anisotropic properties in the underlying medium wherever heterogeneities occur with a characteristic wavelength smaller than approximately 0.75 times the width of the first Fresnel zone √ λz, with λ the wavelength and z the depth.