Efficient anisotropic wavefield extrapolation using effective isotropic models

Isotropic wavefield extrapolation is more efficient than anisotropic extrapolation, and this is especially true when the anisotropy of the medium is tilted (from the vertical). We use the kinematics of the wavefield, appropriately represented in the high-frequency asymptotic approximation by the eikonal equation, to develop effective isotropic models, which are used to efficiently and approximately extrapolate anisotropic wavefields using the isotropic, relatively cheaper, operators. These effective velocity models are source dependent and tend to embed the anisotropy in the inhomogeneity. Though this isotropically generated wavefield theoretically shares the same kinematic behavior as that of the first arrival anisotropic wavefield, it also has the ability to include all the arrivals resulting from a complex wavefield propagation. In fact, the effective models reduce to the original isotropic model in the limit of isotropy, and thus, the difference between the effective model and, for example, the vertical velocity depends on the strength of anisotropy. For reverse time migration (RTM), effective models are developed for the source and receiver fields by computing the traveltime for a plane wave source stretching along our source and receiver lines in a delayed shot migration implementation. Applications to the BP TTI model demonstrates the effectiveness of the approach.