Keep in mind that this "special" "supermoon" is only about 0.5% closer this month than it was last month, or will be next month. And now is only 0.1% closer away at last year's minimum (and in fact, the minimum distance each year of the past 20 is only separated by 0.3% variation)
Makes it a little less exciting, eh? [source for data: timeanddate.com]
And likewise this article from space.com suggests that tide differences between a supermoon and a typical full moon are likely fairly small.
I'm certainly no expert on any of these topics in question, and am hopeful we'll see more precise calculations and details from someone more plugged into these fields. But that information at least suggests that it is dubious to credit the earthquakes to the exceptional proximity of THIS particular "supermoon".
Now do supermoons, or for that matter, full moons in general, cause earthquakes? I have no expertise in any of these topics areas (you can see that with my related question that I happened to post earlier this week asking about seasonal\temperature influences). But I decided to do a quick rough study because it was an interesting question that I had as well.
Applying the EMSC-CSEM earthquake search, I found that 7.9 and greater magnitude quakes gave me a good manageable set to work with from their database (dating to October 2004). I did not look at potential results when choosing the set size. But found it was a fair size to put together, and would at least give a potential taste.
So here are all >= 7.9s in the past 12ish years, as well as their moon phase and earth-moon distance (which appears to vary from about 356500-407000 km, completing 1-2 cycles a year):
- Mag | Moon | Moon Dist | Event
- 9.3 | 100% | 405266 km | 2004 Indian Ocean Earthquake (12-26-04)
- 9.0 | 33.% | 395992 km | 2011 Japan Earthquake (03-11-11)
- 8.8 | 97.% | 357971 km | 2010 Chile Earthquake (02-27-10)
- 8.6 | 92.% | 380842 km | 2005 Sumatra Earthquake (03-28-05)
- 8.4 | 01.% | 400497 km | 2007 Sumatra Earthquake (09-12-07)
- 8.4 | 72.% | 368806 km | 2012 Sumatra Earthquake (04-11-12)
- 8.3 | 25.% | 405266 km | 2006 Kuril Islands [NE of Japan] Earthquake (11-15-06)
- 8.3 | 99.% | 361064 km | 2013 Sea Okhotsk Earthquake [NE of Japan] Earthquake (05-24-13)
- 8.3 | 12.% | 404185 km | 2015 Chile Earthquake (09-16-25)
- 8.2 | 35.% | 400532 km | 2007 Kuril Islands [NE of Japan] Earthquake (01-13-07)
- 8.1 | 99.% | 405537 km | 2007 Solomon Islands Earthquake (04-01-07)
- 8.1 | 81.% | 403548 km | 2009 Samoa Islands Earthquake (09-29-09)
- 8.1 | 06.% | 381485 km | 2014 Chile Earthquake (04-01-14)
- 7.9 | 09.% | 399204 km | 2007 Peru Earthquake (08-15-07)
- 7.9 | 51.% | 382561 km | 2008 China Earthquake (05-12-08)
- 7.9 | 41.% | 402219 km | 2009 Tonga Earthquake (03-19-09)
- 7.9 | 33.% | 395899 km | 2011 Japan Earthquake Aftershock (03-11-11)
- 7.9 | 23.% | 365928 km | 2013 Solomon Islands Earthquake (02-06-13)
- 7.9 | 12.% | 390858 km | 2014 Alaska (Aleutians) Earthquake (06-23-14)
- 7.9 | 98.% | 357791 km | 2016 New Zealand Earthquake (focus of this post)
(Moon phases from USNO, distances from satellite-calculations.com)
Breaking it down (after removing the Japan aftershock), seems a bit of a predilection for full moons:
(6 of the 19 were 90+% full).
And just maybe a slight increase near new moon as well, which would match the way that earlier article described that tides work:
(5 of 19 <= 12%).
Here's a histogram of the spread [made at wessa.net]:

But it doesn't seem there's as much of a trend in distances:

It's almost certainly not enough data to draw a rock solid conclusion, but interesting that it seems hints at favoring full moons. I'm not sure what statistical calculations to do to prove it... the mean is only 51%, so it'd need more than just a mean test to prove that it's bi-modal (favoring full/new moons).
But this quick look certainly seems to suggest at least that there isn't obvious trends in earth-moon distance impacting earthquakes (R^2 = 0.14).
The real connections may be much more complex (varying by location\geology, only affecting certain types of earthquakes, more significant for weaker earthquakes, etc). But hopefully this try using big data from about the last decade is at least a help!
Hope the cleanup goes well AnonDCX!