Several prestack depth wave-equation-based migration algorithms are investigated in this thesis. The algorithms fall into two categories - those based on two-way (reverse-time) wave equations and those based on one-way wave equations (downward-continuation migration methods, such as phase-shift-plus-interpolation (PSPI), split-step Fourier method (SSF), and implicit finite-difference (IFD)). Some improvements on these methods are presented and their corresponding anisotropic depth migration algorithms are designed, analyzed and evaluated.
An operator based on finite-element and finite-difference methods is presented and analyzed for seismic modelling and reverse-time migration, which has looser stability constraints and allows irregular grids to improve the efficiency and resolution of wavefield extrapolation.
A technique is formulated for downward-continuation Fourier methods (PSPI, SSF and IFD) to implement migration from near-surface topography. These three depth migration methods are analyzed in their performance with regard to speed and resolution through numerical and field examples.
The migration methods (reverse-time, PSPI, IFD and SSF) are extended to handle transversely isotropic media (TI). Anisotropic reverse-time migration and PSPI successfully deal with tilted TI media, whereas anisotropic IFD can only process VTI media and anisotropic SSF is only suitable in simple anisotropic cases. Many numerical and physical examples are applied to validate the anisotropic migration algorithms and illustrate the characteristics of each method in terms of efficiency and resolution.
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