Ground level events (GLEs) occupy the high-energy end of gradual solar energetic particle (SEP) events. They are associated with coronal mass ejections (CMEs) and solar flares, but we still do not clearly understand the special conditions that produce these rare events. During Solar Cycle 23, a total of 16 GLEs were registered, using ground-based neutron monitor data. We first ask if these GLEs are clearly distinguishable from other SEP events observed from space. Setting aside possible difficulties in identifying all GLEs consistently, we then try to find observables which may unmistakably isolate these GLEs by studying the basic properties of the associated eruptions and the active regions (ARs) that produced them. It is found that neither the magnitudes of the CMEs and flares nor the complexities of the ARs give sufficient conditions for GLEs. It is possible to find CMEs, flares or ARs that are not associated with GLEs but that have more extreme properties than those associated with GLEs. We also try to evaluate the importance of magnetic field connection of the AR with Earth on the detection of GLEs and their onset times. Using the potential field source surface (PFSS) model, a half of the GLEs are found to be well-connected. However, the GLE onset time with respect to the onset of the associated flare and CME does not strongly depend on how well-connected the AR is. The GLE onset behavior may be largely determined by when and where the CME-driven shock develops. We could not relate the shocks responsible for the onsets of past GLEs with features in solar images, but the combined data from the Solar TErrestrial RElations Observatory (STEREO) and the Solar Dynamics Observatory (SDO) have the potential to change this for GLEs that may occur in the rising phase of Solar Cycle 24.
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