In this project, we develop new theories and methods for multi-domain one-way wave-equation based propagators, and apply these techniques to seismic modeling, seismic imaging, seismic illumination and model parameter estimation in 3D complex environments. The major progress of this project includes: (1) The development of the dual-domain wave propagators. We continue to improve the one-way wave-equation based propagators. Our target is making propagators capable of handling more realistic velocity models. A wide-angle propagator for transversely isotropic media with vertically symmetric axis (VTI) has been developed for P-wave modeling and imaging. The resulting propagator is accurate for large velocity perturbations and wide propagation angles. The thin-slab propagator for one-way elastic-wave propagation is further improved. With the introduction of complex velocities, the quality factors Qp and Qs have been incorporated into the thin-slab propagator. The resulting viscoelastic thin-slab propagator can handle elastic-wave propagation in models with intrinsic attenuations. We apply this method to complex models for AVO modeling, random media characterization and frequency-dependent reflectivity simulation. (2) Exploring the Information in the Local Angle Domain. Traditionally, the local angle information can only be extracted using the ray-based method. We develop a wave-equation based technique to process the local angle domain information. The approach …