Depth migration of shot records in heterogeneous, transversely isotropic media using optimum explicit operators

A space-frequency domain 2D depth-migration scheme is generalized for imagi ng in the presence of anisotropy. The anisotropy model used is that of a tr ansversely isotropic (TI) medium with a symmetry axis that can be either ve rtical or tilted. In the proposed scheme the anisotropy is described in ter ms of Thomsen parameters; however, the scheme can accommodate a wide range of anisotropy rather than only weak anisotropy. Short spatial convolution o perators are used to extrapolate the wavefields recursively in the space-fr equency domain for both qP- and qSV-waves. The weighted least-squares metho d for designing isotropic optimum operators is extended to asymmetric optim um explicit extrapolation operators in the presence of TI media with a tilt ed symmetry axis. Additionally, an efficient weighted quadratic-programming design method is developed. The short spatial length of the derived operat ors makes it possible for the proposed scheme to handle lateral inhomogenei ties. The performance of the operators, designed by combining the weighted least-squares and weighted quadratic-programming methods, is demonstrated b y migration impulse responses of qP and qSV propagation modes for the weak and strong TI models with both vertical and tilted symmetry axes. Finally, a table-driven shot-record depth-migration scheme is proposed, which is ill ustrated for finite-difference modelled shot records in TI media.