A seismic data analysis system includes seismic receivers to collect seismic survey data, wherein the seismic survey data includes direct and reflected arrival data in response to at least one seismic source fired at different shot offsets. The system also includes memory that stores the collected seismic survey data. The system also includes a processing unit that extracts traveltimes for direct and reflected arrivals from the seismic survey data and performs an inversion using the direct and reflected arrival traveltimes simultaneously to determine anisotropy parameters, including Thomsen parameters, epsilon (ε) and delta (δ), for at least one layer of a vertical transversely isotropic (VTI) model.