A downhole tool for gathering formation data from inside a borehole includes a substantially tubular housing adapted for axial connection to a drill string and multiple sensors coupled to the tubular housing. The sensors include a first pair of sensors aligned along a first axis and adapted to measure a spatial derivative along the first axis, a second pair of sensors aligned along a second axis and adapted to measure a spatial derivative along the second axis, and a third pair of sensors aligned along a third axis and adapted to measure a spatial derivative along the third axis. In selected embodiments, the spatial derivatives are used to differentiate seismic or sonic compression and shear waves measured in a downhole environment.