We have built a vertical traveltime difference (VTD) gather to image diffractions in the 3D time domain. This significantly improves detection of small-scale faults and heterogeneities in 3D seismic data. The VTD gather is obtained using 3D Kirchhoff prestack time migration based on the traveltime-related inline and crossline dip angles, which is closely related to the 2D dip-angle gather. In VTD gathers, diffraction events exhibit flattening, whereas reflection events have convex upward-sloping shapes. Different from the 2D dip-angle gather, Fresnel zone-related specular reflections are precisely focused on the given regions over all offsets and azimuths, thus leaving more diffraction energy after muting. To image linear diffractors, such as faults in three dimensions, the VTD gather can be extended into two dimensions by adding a dip-azimuth dimension. This makes it possible to correct phases of edge diffractions and detect the orientations of the linear diffractors. The memory requirement of the VTD or VTD plus azimuth gathers is much less than that of the 2D dip-angle gathers. We can store the gathers at each lateral position and then correct the phase and enhance the weak diffractions in 3D cases. Synthetic and field data tests demonstrate the effectiveness of our 3D diffraction imaging method.