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Like Japan, Taiwan is located on the Pacific Ring of Fire and is an exceptionally bad location for nuclear power stations. About 90% of the world’s earthquakes and 81% of the world’s largest earthquakes occur along the Ring of Fire. https://en.wikipedia.org/wiki/Ring_of_Fire
"This dynamic earth: the story of plate tectonics" 1996, Kious, W. Jacquelyne; Tilling, Robert I., USGS Unnumbered Series General Interest PublicationThe ‘Ring of Fire’, also called the Circum-Pacific belt, is the zone of earthquakes surrounding the Pacific Ocean- about 90% of the world’s earthquakes occur there. The next most seismic region (5-6% of earthquakes) is the Alpide belt (extends from Mediterranean region, eastward through Turkey, Iran, and northern India.” (“This dynamic earth: the story of plate tectonics” 1996, Kious, W. Jacquelyne; Tilling, Robert I., USGS Unnumbered Series General Interest Publication) http://pubs.er.usgs.gov/publication/7000097

Tuesday afternoon local time, Taiwan reported an offshore 7.2 M earthquake. The USGS calls it a 6.4 M. It was offshore from two of Taiwan’s nuclear power stations. Two of the four nuclear reactors were offline due to technical problems. There was no tsunami reported. The star and circles are from the USGS. The coordinate numbers are the position given by the Taiwan Government Central Weather Bureau.
USGS Map Taiwan earthquake 6.4; coordinates of Taiwan M 7.2
Nuclear Power Station coordinates exported from: https://en.wikipedia.org/wiki/Jinshan_Nuclear_Power_Plant https://en.wikipedia.org/wiki/Kuosheng_Nuclear_Power_Plant

Taiwan, like Japan, is located on the Pacific Rim seismic zone and frequently experiences earthquakes. All four nuclear plants in Taiwan are built near the coastline, with distances from the coastline ranging from 1.04 km to 3.37 km (Kuosheng, 1.04 km; Jinshan, 1.05 km; Longmen, 2.96 km; and Maanshan, 3.37 km). This places them within the reach of tsunamis similar to the one that hit Japan on 11 March, which traveled 3 km inland from the coast and flooded the Fukushima nuclear power plants. However, three of Taiwan’s nuclear power plants (Kuosheng, Jinshan, and Longmen) are located within 20–40 km from Taipei (population 6 million), the capital city, and the Maanshan nuclear power plant is only 67.4 km from Kaohsiung (population 2 million), Taiwan’s second largest city. By contrast, the Fukushima nuclear power plants are about 225 km away from Tokyo (population 20 million).” (“A Fukushima-Like Nuclear Crisis in Taiwan or a Nonnuclear Taiwan?” Chang-Chuan Chan Ya-Mei Chen. East Asian Science Technology and Society an International Journal 09/2011; 5(3):403-407.) (Longmen nuclear power station was apparently cancelled.)

The day before the earthquake, activists filed suit against reopening of Jihshan reactor number one: “Activists file suit over Jinshan reactor” By Chen Wei-han, 31 May 2016, Taipei Times: “The Jinshan plant’s No. 1 reactor is the most dangerous reactor in the world. Fuel rods inside the reactor cannot be removed and maintenance cannot be conducted. This situation cannot be found anywhere else in the world.https://web.archive.org/web/20160530182139/http://www.taipeitimes.com/News/taiwan/archives/2016/05/31/2003647555
 7.2 M offshore earthquake Taiwan Central Weather gov

One of the reactors of the Kuosheng power station restarted on “May 16, but half an hour later, it automatically shut down for reasons that are not yet clear.” and probably won’t restart until July: “Reactor at New Taipei nuclear power plant shuts down” 2016/05/30, Focus Taiwan, CNA: https://web.archive.org/web/20160531102521/http://focustaiwan.tw/news/asoc/201605300005.aspx

Magnitude-7.2 earthquake strikes off northern Taiwan coast“,
2016/05/31 13:47:51 Focus Taiwan CNA: https://web.archive.org/web/20160531215820/http://focustaiwan.tw/news/afav/201605310011.aspx


The discovery of cracked anchor bolts at one of the power plant’s reactors is the final warning,” said Green Consumers Foundation Chairman Jay Fang. https://nuclear-news.net/2012/04/21/call-to-close-north-taiwans-aging-degenerating-nuclear-power-plant/

On 28 December 2014, the number 1 reactor of the plant was shutdown and went out of service due to a component failurehttps://en.wikipedia.org/wiki/Jinshan_Nuclear_Power_Plant

For Kuosheng: “core shroud leakage + station blackout (SBO) / steamline break (loss of coolant accident, LOCA) transient caused the cladding temperature larger than 1088 K and affected the Kuosheng NPP safety“. http://www.nrc.gov/reading-rm/doc-collections/nuregs/agreement/ia0450/

The Maanshan Nuclear Power Station, to the south, was impacted by the Hengchu earthquake on 26 December 2006: “Because of the vigorous vibration, the alarm at Reactor #2 was activated, forcing the operators to carry out SCRAM immediately.“. https://en.wikipedia.org/wiki/Maanshan_Nuclear_Power_Plant. https://en.wikipedia.org/wiki/2006_Hengchun_earthquakes