A method and a system for implementing the method are disclosed wherein the pre-stack seismic input data, an initial anellipticity anisotropy parameter, and a baseline normal moveout velocity from a non-flat surface, are sometimes mild or foothill topography as well as the shot and receiver lines might not necessarily be straight, and often curve to avoid obstacles on the land surface. In particular, the method and system disclosed, allows for updating the anisotropy parameters iteratively and when the stopping criteria is satisfied, the final estimated parameter can be directly used for time migration. This method and system are mainly used for time migration with the purpose of obtaining the high fidelity (accurate amplitude, i.e. not only travel-time correct but also amplitude correct) image gathers which are used for reservoir characterization and interpretation.