We are developing a laterally variable velocity model of the crust and upper mantle across Eurasia and North Africa to reduce event location error by improving regional travel-time prediction accuracy. The model includes both P and S velocities and we describe methods to compute travel-times for Pn, Sn, Pg, and Lg phases. For crustal phases Pg and Lg we assume that the waves travel laterally at mid-crustal depths, with added ray segments from the event and station to the mid crustal layer. Our work on Pn and Sn travel-times extends the methods described by Zhao and Xie (1993). With consideration for a continent scale model and application to seismic location, we extend the model parameterization of Zhao and Xie (1993) by allowing the upper-mantle velocity gradient to vary laterally. This extension is needed to accommodate the large variation in gradient that is known to exist across Eurasia and North African. Further, we extend the linear travel-time calculation method to mantle-depth events, which is needed for seismic locators that test many epicenters and depths. Using these methods, regional travel times are computed on-the-fly from the velocity model in milliseconds, forming the basis of a flexible travel time facility that may be implemented in an interactive locator. We use a tomographic technique to improve upon a laterally variable starting velocity model that is based on Lawrence Livermore and Los Alamos National Laboratory model compilation efforts. Our tomographic data set consists of approximately 50 million regional arrivals from events that meet the ground truth (GT) criteria of Bondar et al. (2004) and other non-seismic constraints. Each datum is tested to meet strict quality control standards that include comparison with established distance-dependent travel-time residual populations relative to the IASPIE91 model. In addition to bulletin measurements, nearly 50 thousand arrival measurements were made at the national laboratories. The tomographic method adjusts Pn velocity, mantle gradient, and a node-specific crustal slowness correction for optimized travel-time prediction
