Your typcial UHF TV antenna is infact a Yagi not a Log Periodic. A Log Periodic has all the elements connected, a Yagi does not.
The front elements of the Yagi are directors, they are electrically shorter than the wanted signal and they do not need to be connected conductively to the boom. As these directors are not terminated, ie nothing absorbs the energy they catch, they reradiate it. As they are effectively seen as capacitive (because they are shorter) and due to their relative location to the main dipole of the antenna their re radiated signal is recieved by the active dipole and add to the directly recieved signal at the dipole. The same applies to the reflector behind the main dipole, however being inductive (longer than the dipole/wanted signal) the phase of the reradiated signal also adds to the all the other signals seen at the dipole. Your typical UHF TV Yagi normally has a mesh corner reflector style reflector, this significantly improves rejection of signals from behind.
All DTT Terrestial transmissions in NZ will be in the UHF band. The DVB-T standard they use, uses COFDM as the modulation method. There is no intention to use BandI (45-69MHz) or BandIII(174-230MHz) as these are more prone to impulse noise, a major problem with COFDM. Australia uses BIII and BIV/V (UHF), however not BandI. However due to the terrain in Aus they needed to use the larger coverage VHF band to get effective coverage. I think the decision in NZ to use Satellite to perform overal coverage and UHF to cover the metro areas makes good sense.