As used in Scripture, the purpose of all earthquakes, regardless of the cause, is to warn or administer judgment to individuals in history for apostasy, reversionism, and evil.
One aspect of of the Haitian nation which seems to be avoided, is their past history and trends as an enemy of the US. Our expenditure of Billions of dollars there protecting ourselves defensively from many threats being fostered there is being ignored. There have been many a nation with far less, who turned to God with far more growth, than exhibited by Haiti.
Considering the number of antiterrorist special forces sent there over the last decade might indicate things were going on there which haven’t been so publicly revealed.
IMHO, I don’t rule out that God Himself might have been administering either judgment on evil in that nation, and/or warning others that such enterprises do not escape His view or judgment.
All history is His Story, and there are reasons for all things, for believers and unbelievers alike, although rewards are predestined for those who persevere through faith in Him.
Name a single earthquake or natural disaster of any consequence in Germany from 1933 to 1945.
Sometime in the next 30 years; could be five minutes from now, could be two decades from now. a 6.7-7.2 magnitude quake is going to occur on the Hayward Fault along the Eastern San Franscisco Bay. It's going to do several hundred billion dollars of damage, and, depending on the time of day it occurs, kill hundreds to thousands of people.
It will instantly be proclaimed by many (with great relish) to be a judgement against all the homosexuals in the Bay area, or the radical leftists of Berkeley, or the fact abortion is legal in the US, etc. etc.
The reality, of course, is that it was a result of the slow movement of the Pacific Plate northwest along the margin of the North American Plate; there was the historical Hayward quake of 1868, and paleoseismic trenching studies have found a repeated pattern of such quakes every 100-200 years or so going back thousands of years, to when there was only a smattering of Indians in the area for the quake to administer a "judgment" to.