Amplitude preserving migration based on a weighted diffraction stack is a task of high computational effort. A major contribution to the costs is the determination of proper weight functions which countermand the effects of geometrical spreading. Whereas the demands in CPU time and computer storage are high already in isotropic media, they become even higher as soon as anisotropy is considered, since already the traveltime computation in anisotropic media requires a magnitude more in computational time. Although fast algorithms are available for the computation of the traveltimes required for the stacking surface, not all of them are capable of generating geometrical spreading, which is needed for the weight functions. In this paper we propose a technique to determine the geometrical spreading directly from coarsely gridded traveltimes. The method is based on a hyperbolic traveltime expression and also provides the possibility of an accurate and effcient traveltime interpolation. This makes the technique well suited for application to amplitude preserving migration in anisotropic media.