We introduce a new method to measure differential travel times and attenuation of seismic body waves. The problem is formulated as a nonlinear inverse problem, which is solved by simulated annealing. Using this technique, we have analyzed triplicated PKP waves recorded by the temporary Eifel array in central Europe. These examples demonstrate the potential of the technique, which is able to determine differential travel times and waveforms of the core phases, even when they interfere on the seismograms or when additional depth phases are present. The PKP differential travel times reveal the presence of large-amplitude and small-scale heterogeneities along the PKP(AB) ray paths and favor a local radial inner core model with ~0.9% velocity perturbation in its top 150 km and small velocity perturbations below. The quality factor in the top 300 km of this inner core region is estimated from PKP differential attenuation. Its preferred value is 330 with a lower bound of 75.