Migration Velocity Analysis for TI Media in the Presence of Quadratic Lateral Velocity Variation

One of the most serious problems in anisotropic velocity analysis is the trade-off between anisotropy and lateral heterogeneity, especially if velocity varies on a scale smaller than spreadlength. Here, we develop a P-wave MVA (migration velocity analysis) algorithm for transversely isotropic (TI) models that include layers or blocks with small-scale lateral heterogeneity. Each layer is described by constant anisotropy parameters epsilon and delta and the symmetry-direction velocity V0 that varies as a quadratic function of the distance along the layer boundaries. For tilted TI (TTI) media, the symmetry axis is taken orthogonal to the reflectors. We analyze the influence of lateral heterogeneity on image gathers obtained after prestack depth migration (PSDM) and show that quadratic lateral velocity variation in the overburden can significantly distort the moveout of the target reflection and the estimated parameters of the deeper part of the section. Since residual moveout is highly sensitive to lateral heterogeneity in the overburden, our algorithm simultaneously inverts for the parameters of all layers or blocks. Synthetic tests demonstrate that if the vertical profile of the velocity V0 is known at one location, the algorithm can reconstruct the other relevant parameters throughout the medium.