We present an a priori three-dimensional 'tomographic' model of the upper mantle. We construct this model (called 3SMAC - three-dimensional seismological model a priori constrained) in four steps: we compile information on the thickness of 'chemical' layers in the Earth (water, sediments, upper and lower crust, etc); we get a 3D temperature distribution from thermal plate models applied to the oceans and continents; we deduce the mineralogy in the mantle from pressure and temperature and we finally get a three-dimensional model of density, seismic velocities, and attenuation by introducing laboratory measurements of these quantities as a function of pressure and temperature. The model is thus consistent with various geophysical data, such as ocean bathymetry, and surface heat flux. We use this model to compute synthetic travel-times of body waves, and we compare them with observations. A similar exercise is performed for surface waves and normal modes in a companion paper (Ricard et al., 1996, J. Geophys. Res., in press). We find that our model predicts the bulk of the observed travel-time variations. Both the amplitude and general pattern are well recovered. The discrepancies suggest that tomography can provide useful regional information on the thermal state of the continents. In the oceans, the flattening of the sea-floor beyond 70 Ma seems difficult to reconcile with the seismic observations. Overall, our 3SMAC model is both a realistic model, which can be used to test various tomographic methods, and a model of the minimum heterogeneities to be expected from geodynamical modeling. Therefore, it should be a useful a priori model to be used in tomographic inversions, in order to retrieve reliable images of heterogeneities in the transition zone, which should, in turn, greatly improve our understanding of geodynamical processes in the deep Earth. 3SMAC and accompanying software can be retrieved by anonymous ftp at geoscope.ipgp.jussieu.fr.