Evaluations of prestack anisotropic Kirchhoff, Phase-shift-plus-interpolation and reverse-time depth migration methods for dipping TI media
Xiang Du, John C. Bancroft, Donald C. Lawton, Laurence R. Lines
Thick anisotropic sequences of dipping sandstones and shales often overlie the reservoir in fold and thrust belts, such as in the Canadian Foothills. In these cases, such an assumption, when anisotropy is negligible or only anisotropy with vertical symmetry axis (VTI) is considered, may result in imaging problems and mispositioning errors. Three prestack migration algorithms based on totally different principles, Kirchhoff, Phase-shift-plus-interpolation (PSPI), and reverse-time, are extended and presented for dipping TI media. Derived from the isotropic Kirchhoff, PSPI, and reverse-time migration methods, these three algorithms possess their own characteristics in accuracy and efficiency aspects. The ray-tracing algorithm used in 2-D prestack Kirchhoff depth migration is modified to calculate the traveltime in the presence of TI media with a tilted symmetry axis.
Based on an analytical solution of the quartic phase velocity equation for dipping TI media in the frequency-wavenumber domain, and an assumption for anisotropic parameters versus lateral velocities, the prestack anisotropic PSPI migration method can handle laterally variable anisotropic parameters and velocities. The prestack anisotropic reverse-time migration method employs the weak-anisotropy approximations to get the individual P-wave equation and implements depth migration with the pseudo-spectral method. Prestack anisotropic Kirchhoff depth migration still keeps its low cost isotropic algorithm advantage; however it suffers greatly from the difficulty of calculating the Green's function in media with both vertical and lateral variations in the space. Prestack anisotropic PSPI makes a good balance between computation efficiency and accuracy, but lacks the flexibility to deal with rapid spatial variation in the Thomsen parameters unless the reference wavefield is calculated for each pair of anisotropic parameters. The prestack anisotropic reverse-time method retains the isotropic algorithm's high cost character. The advantage of the method lies in the fact that it can handle arbitrary variable velocities and anisotropic parameters with excellent dipping angle imaging capability. Examples of migration on numerical and physical data with these three algorithms, shows imaging results can be improved by considering anisotropy parameters and the different characteristics of each method.