The weathering layer may be the most variable of all layers; yet in seismic processing, it is routinely taken to be uniform either in thickness or velocity. Datuming through an incorrect weathering model can corrupt the stack, possibly introducing false structure into deep reflectors. Recognizing that direct measurements of the weathering properties may not, in practice, be readily available, this paper investigates the feasibility of computing the weathering model from the traveltimes of refracted first arrivals. The problem is formulated in terms of the difference in arrival time at adjacent receivers, resulting in a much sparser matrix for inversion. Lateral variations in both the weathering thickness and velocity are sought; however, analysis indicates a fundamental long wavelength ambiguity in the solution, with gradual changes in velocity trading-off with gradual changes in thickness. In most cases, it is necessary to include a small number of constraints to obtain the true weathering model. Any roughness in the solution that is not required to fit the data is most effectively removed using a second difference smoothing technique.