Processing of seismic data is often performed under the assumption that the velocity distribution in the subsurface can be approximated by a macromodel composed of isotropic homogeneous layers or blocks. Despite being physically unrealistic, such models are believed to be sufficient for describing the kinematics of reflection arrivals.
In this paper, we examine the distortions in normal-moveout (NMO) velocities caused by the intralayer vertical heterogeneity unaccounted for in velocity analysis. To match P-wave moveout measurements from a horizontal or a dipping reflector overlaid by a vertically heterogeneous isotropic medium, the effective homogeneous overburden has to be anisotropic. This apparent anisotropy is caused not only by velocity monotonically increasing with depth, but also by random velocity variations similar to those routinely observed in well logs.
Assuming that the effective homogeneous medium is transversely isotropic with a vertical symmetry axis (VTI), we express the VTI parameters through the actual depth-dependent isotropic velocity function. If the reflector is horizontal, combining the NMO and vertical velocities always results in nonnegative values of Thomsen's coefficient δ. For a dipping reflector, the inversion of the P-wave NMO ellipse yields a nonnegative Alkhalifah-Tsvankin coefficient η that increases with dip. The values of η obtained by two other methods (2-D dip-moveout inversion and nonhyperbolic moveout analysis) are also nonnegative but generally differ from that needed to fit the NMO ellipse. For truly anisotropic (VTI) media, the influence of vertical heterogeneity above the reflector can lead to a bias toward positive δ and η estimates in velocity analysis.