Thick anisotropic sequences of dipping sandstones and shales often overlie reservoirs in fold and thrust belts, such as 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 anisotropic migration algorithms based on totally different principles, Kirchhoff, phase-shift-plusinterpolation (PSPI) and reverse-time (RT), are presented for dipping TI media. Derived from the isotropic Kirchhoff, PSPI and reverse-time migration methods, these three algorithms each inherit different characteristics of accuracy and efficiency. 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 vertical wavenumber for dipping TI media and an assumption for the relationship between anisotropic parameters versus lateral velocities, the prestack anisotropic PSPI migration can handle lateral variable anisotropic parameters and velocities. The prestack anisotropic reverse-time algorithm employs the weak-anisotropy approximation to obtain the individual P wave equation and implements depth migration with the pseudo-spectral method. An example of migration on physical data with these three algorithms shows improved imaging results from considering anisotropy parameters and different characteristics for each method.
Hydrocarbon resource exploration and development projects are in areas containing dipping anisotropic sequences, such as in the Canadian Foothills (Isaac and Lawton, 1999). In these cases, depth migrations with either an isotropic migration algorithm or a vertical axis of symmetry (VTI) assumption will result in imaging problems and mispositioning errors. Anisotropic depth migration is required to correctly locate images when dipping transversely isotropic (TI) strata are present. Some advanced migration methods have been extended from isotropic to anisotropic media. Anisotropic depth migration methods, as with isotropic methods, can be based on various approaches such as ray-tracing, one-way equation, and full-wave equation. The prestack anisotropic Kirchhoff migration method presented in this paper is based on the ray-tracing theory. The prestack anisotropic PSPI starts from the one-way wave equation and carried out downward-continued wavefield extrapolation. Prestack anisotropic reverse-time migration achieves recursive extrapolation backward in time with the full wave equation. Three representative methods are chosen to demonstrate the characteristics of Kirchhoff, PSPI and reverse-time migration for dipping TI media in terms of performance, accuracy and efficiency. In this paper, we will first introduce the theory of three anisotropic migration methods, give certain analysis for each algorithm, and take into account the increase in calculation time between each anisotropic migration algorithm and the corresponding isotropic case. Through a physical model example, we demonstrate the performance of anisotropic migration algorithms and give some evaluations of these three anisotropic migration methods.
To illustrate the difference among anisotropic Kirchhoff, PSPI and reverse-time migration algorithms, we focus on the core techniques for each anisotropic algorithm. Anisotropic Kirchhoff depth migration The difference between the anisotropic and isotropic Kirchhoff migration algorithms lies in the traveltime calculation without changing the Kirchhoff algorithm itself.
