There are focal mechanisms on the larger two, and they are strike-slip. They are near the subduction zone, which is presumably capable of great thrust quakes. New Zealand farther south has a mix of thrust and right lateral. There is a zone of active right-lateral faults in the northeast part of the South Island. The main plate boundary on the South Island (and offshore of it to the south) is the Alpine Fault, which has oblique reverse right-lateral on it. I suppose a good question is whether this fault always breaks with this oblique motion, of if on the same place on the same fault you can have anywhere from major right-lateral quakes to major to great reverse quakes (reverse same as thrust except on steeper faults). I recall that this fault offshore of the southern part of South Island had a near M8 reverse or thrust quake in the last couple of years.

I may be wrong on the following, but I think the motion across the plate boundary has less strike-slip to the north. I'm curious if it still has a substantial right-lateral motion this far north. Today's quakes could be right-lateral parallel to the subduction zone, or left-lateral nearly perpendicular (fault strike) to it.

Chris