With the exception of shear-wave splitting and receiver function analyses, the phase or amplitude anomaly of a particular arrival is usually measured on only one of the three-component seismic records. Perfectly good waveforms on the other components are often unused. In this article we show that the different components of the same arrival at the same receiver have different travel-time and amplitude sensitivities to variations in the velocity structure. This is a finite-frequency phenomenon for measurements derived from waveforms. It is important where the scales of velocity heterogeneities are comparable or smaller than the width of the Fresnel zone. We calculate the Fréchet sensitivity kernels using the scattering-integral method in conjunction with finite-difference wave simulation in three-dimensional media. The differences in the sensitivity kernels for the different components vary with the wave type, source-receiver geometry, and source mechanism. They are attributed to scattered waves that affect the waveforms on the different components by various amounts. Thus, the differential kernels between the different components of the same arrival may enable us to use the corresponding phase and amplitude measurements, which are relatively accurate observations unaffected by uncertainties in source origin time and location, to image the Earth structure, particularly fine structures near receivers.