Volcanoes
Jamaica and the other islands of the Antilles evolved from an arc of ancient volcanoes that rose from the sea millions of years ago, however, it doesn't have any active volcanoes. Jamaica does have other well known mountain ranges. The Blue Mountains extend over the eastern part of the island. Jamaica's main mountain system contains two ranges. The northerly one includes Blue Mountain Peak, which rises to 2,256 meters (7,402 feet), the country's highest elevation. The second range, known as the Port Royal Mountains, extends south-eastward from the principal range, reaching elevations of up to about 1,219 meters (4,000 feet). The John Crow Mountains rise in the extreme northeast of the island, between the Rio Grande and the sea. Vestiges of volcanic activity occur in Jamaica in the form of lava cones and hot springs.

http://www.nationsencyclopedia.com/geography/Indonesia-to-Mongolia/Jamaica.html

Tsunami
Jamaica has a history of tsunamis that have affected the coastline since 1688 causing loss of life and destruction of property. Jamaica's geologic setting makes the coastline particularly vulnerable to both tsunami and storm surge hazards. The entire coastline of Jamaica is exposed to tsunami hazards. Since most of the urban population in Jamaica resides in coastal areas any future tsunami is likely to have a disastrous impact because of the development in the coastal areas. In Jamaica, The Office of Disaster Preparedness and Emergency Management (ODPEM) has determined, based on its research, that the Old Harbour Bay community is at risk to the threat of tsunamis. The organization has carried out a Tsunami Drill Exercise with more than 500 residents to evaluate the community’s tsunami response capacity. The exercise is also expected to increase tsunami preparedness and improve coordination for the tsunami hazard in Jamaica.


http://www.mona.uwi.edu/cardin/virtual_library/docs/1171/1171.pdf
http://www.jamaicaobserver.com/latestnews/Old-Harbour-Bay-at-risk-to-threat-of-tsunami---ODPEM

Earthquakes

About 200 earthquakes are located in and around Jamaica per year most of which are minor, having magnitudes less than 4.0. The most seismically active areas are the Blue Mountain block in eastern Jamaica and the Montpelier-Newmarket belt in western Jamaica. Other areas of notable seismicity include the near offshore southwest of Black River on the south coast, and offshore Buff Bay on the northeast coast. The United Nations Development Program says it is necessary to raise the level of awareness on Jamaica’s seismic potential and to find a way to make enhance preparedness. Unfortunately, Jamaica is not prepared. A February 7, 2014 story in the Jamaica Gleaner suggests that approximately 70% of designed buildings, are done without the input of building professionals. A push for stricter building codes could help Jamaica be more prepared for hazards. 

http://www.mona.uwi.edu/earthquake/jaequake.php

http://www.jm.undp.org/content/jamaica/en/home/presscenter/articles/2013/05/03/jamaica-must-prepare-for-large-earthquakes.html

Plate Tectonics
Tectonic plates are pieces of lithospheric plates that move relative to one another. There are three types of plate boundaries: divergent, convergent, and transform. Divergent boundaries occur where new lithosphere is being produced and neighboring parts of plates are moving away from each other. In contrast, convergent plates occur when plates collide. Lastly, transform boundaries (transform faults) occur when the edges of two plates slide past each other. Jamaica lies on a stretch of plate that connects to the Gon'ave-Caribbean Plate Boundary. On June 7 1692, there was a massive earthquake that rocked Port Royal, Jamaica. Fifty people were killed in a landslide. In all, about 3,000 people lost their lives that day. Thousands more died in the following weeks due to sickness and injury. Aftershocks discouraged the survivors from rebuilding Port Royal. Instead, the city of Kingston was built and remains to this day the largest city in Jamaica.

https://courses.washington.edu/tesc243/jamaica/index_files/page0007.htm