The objective of this research is to develop forward modeling, velocity analysis, and migration methods in anisotropic media. The methodology and algorithms developed by this project will improve the quality and resolution of seismic images that are critical to the economic exploration for hydrocarbons. In addition, this project provides critical understanding of the fundamental physics of wave propagation in anisotropic media, which is necessary for the design of optimal seismic surveys used in hydrocarbons exploration.