Impact of anisotropic and inhomogeneous medium on measuring seismic shear-wave splitting

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Parameters of seismic shear-wave splitting are important basis for determining the features of anisotropy in earth medium. Significant scatters due to inaccuracy in measuring polarization and time delay of fast-slow shear waves were major obstacles in seismic anisotropy and shear-wave splitting study in the past decades. This paper analyses the following points: (1) difference of seismic wave propagation characteristics in anisotropic medium compared with isotropic medium; (2) non-orthogonal nature of S-waves in anisotropic medium; (3) non-orthogonal relationship of S- to P-waves due to different travel paths. Hereby it makes clear that the anisotropy and inhomogeneity of real earth medium can lead to differences in traveltime, polarization and phase sequence of observed seismogram in comparison to those of theoretical calculation that is based on isotropic medium assumption. Furthermore, velocity variations due to anisotropy and inhomogeneity, different travel paths due to different wave types can lead to observation of wave arrivals of different polarization within a very small time window, making non-orthogonality a common problem in a wide range of seismic recordings. In consequence, non-orthogonality due to either different polarization or/and different travel paths impedes the traditional orthogonal wave separation techniques from extracting accurate shear wave splitting parameters, particularly the travel time delay between fast and slow shears waves, from 3C seismic record, thus causing significant scatter of the measured results. This paper also analyses challenges in current techniques of seismic phase identification and parameter determination. Despite decade-long development, methods in shear wave analysis and parameter extraction are largely based on orthogonal wave separation techniques that are valid only for homogenous and isotropic medium. To reduce the scatter and improve the accuracy of measured shear wave splitting parameter, the vector nature of seismic phases and their non-orthogonal relationship must be taken into account. Using synthetic data, this paper illustrates: (1) non-uniqueness of orthogonal wave field separation; (2) ambiguity/uncertainty of waveform for vector phases on observed seismic records; (3) failure and/or error in identification of seismic phases by traditional seismic phase and waveform analysis methods. It proposes approaches to improve reliability in estimating shear wave splitting parameters. Here it introduces: (1) definition of polarization direction and number of seismic vector phases on 3C seismic record; (2) vector analysis method for non-orthogonal seismic vector phases. Using the above methodology, the paper uses an algorithm example to show how to extract complete waveform under certain assumptions. Hereby the formulas of wave field separation expressed in unit vector of the polarization direction are derived. The Fourier transform of the formulas and its projection on different coordinate axis can be used as rough estimates for directions of observed seismic vector phases. With the current methods, it is impossible to know whether a 3C seismic record is free from influences of anisotropy or inhomogeneity origins; neither can we determine quantitatively their respective influences. The paper stresses that non-orthogonality is an inherent nature of common 3C seismic recordings, and it is a significant factor for reliable determination of kinematic and dynamic parameters of seismic phases, including splitted shear waves, secondary and later weak arrivals. The non-orthogonal relationship among seismic phases is a complex expression, not only influenced by anisotropy and inhomogeneity, but also controlled by local geology under recording stations and by physical states like stress, deformation, temperature and pressure of the medium along wave paths. The successful separation of all different seismic phases should deal with their vector nature, thus improving our understanding of observed seismic waves.