We study seismic traveltime measurements acquired in the borehole, including vertical seismic profiling, seismic measurements while drilling, and drill-bit noise generated data. These traveltime data are used to assess informative parameters, including drill-bit position, distance to drilling target, and parameters of the velocity model. First, we analyze seismic traveltime data using a simple hyperbolic traveltime equation for rays between surface sampling locations and the drill bit. Second, we describe a model for estimating both the position of the drill bit and the relative distance to geologic interfaces ahead of the bit. Finally, we present a dynamic Bayesian strategy for real-time prediction of drill-bit positions, velocity parameters, and distances to geologic markers. Walk-away vertical seismic profiling data from the Norwegian Sea are used to demonstrate our methods. For this data set, we pick five key reflectors ahead of the drill bit. The deepest reflector is estimated to be ahead of the drill bit, using seismic traveltime data alone. The effects of aperture and surface sampling locations are large on our estimates and their associated uncertainties, and we observe that large offset is preferable to dense sampling in terms of positioning accuracy.