(5) |
In equation 4, the parameters , , and are defined with respect to the zero-offset ray, whereas and are obtained from finite-offset rays (Sripanich et al., 2017). With these definitions, the parameters , , and are related to previously known time-processing parameters: simply denote the reciprocals of NMO velocities and govern the so-called NMO ellipse (Grechka and Tsvankin, 1998a). represent the quartic coefficients that govern the nonhyperbolicity of reflection traveltimes. A common approach to simplify and relate the quartic coefficients () to anisotropic parameters of the subsurface medium is done using the pseudoacoustic approximation, where can then be expressed in terms of (Alkhalifah, 2003; Sripanich and Fomel, 2016; Alkhalifah and Tsvankin, 1995; Sripanich et al., 2017; Stovas, 2015). With regard to this study, we keep the notation to maintain the generality of the proposed moveout inversion approach.
On the other hand, the and are designed to be dynamic and can vary with respect to different choices of finite-offset rays, which lead to better flexibility and accuracy of traveltime fitting. As a result, they cannot be directly related to medium parameters and one may expect that there are many possibilities of and that can lead to equally good approximation accuracy. Therefore, we expect that the non-uniqueness of and can lead also to the non-uniqueness in the final inverted models.