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

Abstract

A space–frequency domain 2D depth‐migration scheme is generalized for imaging in the presence of anisotropy. The anisotropy model used is that of a transversely isotropic (TI) medium with a symmetry axis that can be either vertical or tilted. In the proposed scheme the anisotropy is described in terms of Thomsen parameters; however, the scheme can accommodate a wide range of anisotropy rather than only weak anisotropy. Short spatial convolution operators are used to extrapolate the wavefields recursively in the space–frequency domain for both qP‐ and qSV‐waves. The weighted least‐squares method for designing isotropic optimum operators is extended to asymmetric optimum explicit extrapolation operators in the presence of TI media with a tilted symmetry axis. Additionally, an efficient weighted quadratic‐programming design method is developed. The short spatial length of the derived operators makes it possible for the proposed scheme to handle lateral inhomogeneities. The performance of the operators, designed by combining the weighted least‐squares and weighted quadratic‐programming methods, is demonstrated by 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 illustrated for finite‐difference modelled shot records in TI media.