Relationship between phase velocities and polarization in transversely isotropic media

Abstract

Most techniques used to estimate anisotropy from multiple‐source offset VSP data assume angles measured from particle motion as an incidence angle. However, the difference between P‐wave polarization and the propagation direction for an anisotropic medium can be higher than 8 degrees. This difference provides a nonnegligible error in the estimation of anisotropy parameters from phase velocities. An exact model, proposed to describe P‐ and SV‐phase velocity variations for a transversely isotropic medium (TIM), takes into account the polarization angles. This model is a function of two anisotropy parameters (η and τ), of the vertical P‐ and SV‐wave phase velocities and of the polarization angle γ. However, η and τ can be used to express the polarization angle equation in a much simpler way. To quantify the error in estimated anisotropy parameters due to the assumption that the polarization angle is equal to the incidence angle, I study five TIMs. Each medium has an anisotropy that is representative of those observed in seismic surveying. The anisotropy parameters are recovered by inverting the P‐ and SV‐wave phase velocities for different incidence angles, and these incidence angles are assumed to be equal to the corresponding polarization angles. The mean error in estimated parameters is about 10 percent. This error is about the same as the one that would be obtained for velocities with uncertainties in their measurements. Unfortunately, the inversion of phase velocities measured from a real multiple‐source offset VSP to estimate anisotropy parameters needs, for calculating the misfit function, to add both errors in velocities due to hypothesis for angles and errors in velocity measurements due to uncertainties in data. In this case an exact model eliminates errors due to the assumption for the model and provides a more accurate estimation of anisotropy parameters.