Theory of interval traveltime parameter estimation in layered anisotropic media

Moveout approximations for reflection traveltimes are typically based on a truncated Taylor expansion of traveltime squared around the zero offset. The fourth-order Taylor expansion involves normal moveout velocities and quartic coefficients. We have derived general expressions for layer-stripping second- and fourth-order parameters in horizontally layered anisotropic strata and specified them for two important cases: horizontally stacked aligned orthorhombic layers and azimuthally rotated orthorhombic layers. In the first of these cases, the formula involving the out-of-symmetry-plane quartic coefficients has a simple functional form and possesses some similarity to the previously known formulas corresponding to the 2D in-symmetry-plane counterparts in vertically transversely isotropic (VTI) media. The error of approximating effective parameters by using approximate VTI formulas can be significant in comparison with the exact formulas that we have derived. We have proposed a framework for deriving Dix-type inversion formulas for interval parameter estimation from traveltime expansion coefficients in the general case and in the specific case of aligned orthorhombic layers. The averaging formulas for calculation of effective parameters and the layer-stripping formulas for interval parameter estimation are readily applicable to 3D seismic reflection processing in layered anisotropic media.