Travel times or time fields contain informations on wave field properties of seismic waves. The wavefront cur- vature corresponds to one of the most important wave field properties. It is related to the normal moveout and the geometrical spreading and therefore leads to many important applications in seismic data processing, e.g., computation of migration weights, NMO corrections, Fresnel zones as well as an accurate and economical interpolation of traveltimes. We present a technique, which is based on the assumption that any arbitrarily shaped wavefront can locally be approximated by a sphere. No particular type of model is assumed. This corresponds to a hyperbolic expansion of traveltimes and leads to traveltime hyperbolae. If an isotropic horizontally stratified medium is assumed, the obtained relations reduce to the well known NMO relation. This relation is used in the T2 - X2 method to determine the NMO velocity for this particular type of model. Therefore, the described technique can be understood as an extension of the T2 - X2 method to arbitrary 3-D heterogeneous (and even anisotropic) media. A Dumerical example demonstrates the efficiency and accuracy of the application of the technique to traveltime interpolation. Further applications of the method are, e.g., in amplitude preserving migration where all required quantities are determined alone from coarse gridded traveltime tables.