Local tomography is interactive, ray-based, residual-interval-parameter analysis for updating background anisotropic velocity parameters. The method operates directly on image gathers generated by anisotropic curved-ray Kirchhoff time migration. A locally 1D, spatially varying, vertical transversely isotropic model is assumed. The background anisotropy parameters are the instantaneous (interval) vertical compression velocity VP and the two Thomsen anisotropy parameters, δ and ε. The interval velocity δ is updated from short-offset reflection events, and δ is updated from available long-offset data. The medium parameters are updated from the top down both vertically and by layers, one parameter at a time. The picked residual-anisotropy parameters correspond to the residual-moveout (RMO) curves that best fit the migrated reflection events. The method is based on splitting the contribution to the computed RMO at a given point into two parts: from overburden residual parameters and from the actual picked residual parameter. This approach allows for direct residual-interval-parameter analysis to be applied in the same way we perform the commonly used residual-effective-parameter analysis. The local tomography enables a controlled interactive estimation of the long-wavelength anisotropy parameters. The reliable anisotropy parameters estimated by the local approach are used as a background (guiding) model for a global tomography. This makes it possible to successfully apply a global constrained inversion that is performed simultaneously for all parameters of all output intervals using detailed RMO information.