In recent times, seismic imaging efforts around the world have focused on increasingly complex earth models that are not only heterogeneous, but anisotropic as well. Focusing my investigation on the simplest realistic heterogeneous anisotropic model --- factorized VTI (transversely isotropic with a vertical symmetry axis) medium with constant vertical and lateral gradients in vertical velocity, I develop insights into how anisotropy and heterogeneity are coupled, and determine what parameters can be estimated uniquely from surface seismic data. I then outline a robust parameter estimation algorithm that is suitable for building a spatially varying anisotropic velocity field for depth imaging. Application of my algorithm to two field lines from West Africa confirms the presence of anisotropy and lateral heterogeneity and results in better images than those previously obtained. The analysis should help towards increasing our understanding of seismic imaging and tomography, and should be useful to Geoscientists studying seismic images, or anyone else interested in wave propagation in the earth.