Tuesday, December 31, 2013

An Incident at Fukushima Daiichi, Part 3, The Earthquake

Foreshock  3-9-2011

   At 46 minutes after 2 o’clock in the afternoon of March 11, 2011, the Pacific Tectonic Plate (the Pacific Plate is an oceanic tectonic plate that lies beneath the Pacific Ocean. At 103 million square kilometers (3.9769e+7mi² square miles), it is the largest tectonic plate on the planet) subducted (moved under) what is probably the part of the North American Tectonic Plate that surrounds Japan (why would the North American Plate surround Japan? A small sliver of it just does... see the chart above), approximately 43 miles east of the Oshika Peninsula of Tōhoku, at a depth of 19.9 miles beneath the Earth’s surface. Most of the time, the two tectonic plates grind into each other storing up potential energy, but at some point that energy is released in the form of ground movement, some times in small amounts resulting in small earthquakes, or tremors, other times, such as in this instance, quite large amounts of energy are released, and a massive quake ensues. 
   The quake has been called the Great East Japan Earthquake, the 2011 Tōhoku Earthquake, and the 3.11 Earthquake, and it subducted a lot, creating a magnitude 9.0 (Mw) quake which lasted at least 6 minutes in duration, the most powerful known quake ever to have hit Japan, and the fifth most powerful earthquake in the  entire world, at least since 1900 when they began recording such events. 
   The earthquake released a surface energy (Me) of 1.9 ± 0.5×1017 joules, dissipating as ground movement and tsunamic energy, which was nearly double that of the 9.1-magnitude 2004 Indian Ocean earthquake and tsunami that killed 230,000 people. 1.9 ± 0.5×1017 joules is enough energy to power Los Angeles for an entire year, including that billboard sized television monitor up at Citywalk. The total amount of energy released by the quake, known as the seismic moment (MO) was more than 200,000 times the surface energy and was calculated by the US Geological Survey at 3.9×1022 joules, which is a heck of a lot of joules, yet a little less than that displayed during the Indian Ocean quake, but still equivalent to 9,320 gigatons of TNT, or approximately 600 million times the energy of the Little Boy atomic bomb which we discussed in the last post.
   The force of the earthquake moved the northern parts of Japan closest to the quake’s epicenter approximately  7.9 to 13 feet closer to the United States, or east if you prefer, it also made Japan wider. A 250-mile-long coastal section of Japan dropped in altitude by as much as 2 feet, which unfortunately allowed the waters of the upcoming tsunami to travel farther and faster inland.  
   Like other powerful earthquakes the 2011 Japanese quake shifted the planet’s axis by estimates of between 4 and 10 inches. That deviation led to a number of other small, hardly noticeable planetary changes, including the length of a day, the tilt of the Earth, and the old Chandler wobble.
   The axial shift was caused by the redistribution of mass on the Earth's surface due to earth movement, which changed the planet's moment of inertia. Now as every fourth grader knows, because of the conservation of angular momentum, such changes of inertia result in small changes to a spinning body’s rate of rotation, in this case the Earth’s. The speed of the planet’s rotation increased which of course shortened the day by about 1.8 microseconds (one millionth of a second, or if you prefer, 1800 nanoseconds), which really pisses me off as there’s simply not enough time in the day as it is. 
   The Chandler wobble (discovered by American amateur mathematician and former alcohol and drug intern at the Pasadena Adult Rehabilitation Center and part time airline stewardess, Michelle Chandler) is a small deviation in the Earth's axis of rotation relative to the solid earth, and an example of the kind of motion that can occur for a spinning object that is not a perfect sphere (the Earth bulges near the equator). The earthquake shifted about 6.5 inches where the figure axis intersects the surface of the planet. That figure axis is near, but does not quite align with, the rotational axis that the Earth spins around. The inherent implications of this are too obvious and horrible to mention.
   The Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) unintentionally became the first seismograph in orbit when it detected sound waves (acoustical energy) generated by the earthquake. 
   The closest major city to the quakes epicenter was Sendai (38° 16′ 0″ N, 140° 52′ 0″ E), “The City of Trees," and the capital of the Miyagi Prefecture, retail and services accounting for two thirds of it’s economy, with a population of about 1 million people, mostly Japanese. Sendai lies about 81 miles from the source of the earthquake. Coastal areas of the city suffered catastrophic damage from the quake and the tsunami that followed. 
   Tokyo (35° 41′ 22.22″ N, 139° 41′ 30.12″ E), Japan’s capital, with a population of over 13 million, lies approximately 232 miles from the epicenter. 
   Tokyo enjoys earthquake resistant infrastructure (because the city and country have suffered a lot of past earthquakes), something I hope we have here in Los Angeles. Due to this, damage in Tokyo was minimal, relatively speaking, although the quake was felt and normal activity halted. The Bōsō Peninsula shielded the city from the worst effects of the tsunami, and the subsequent nuclear crisis caused by the tsunami initially left Tokyo mostly unaffected, although there were intermittent spikes in radiation levels (one minute before the earthquake was felt in Tokyo, the Earthquake Early Warning system, which includes more than 1,000 seismometers around the country, sent out warnings of impending strong shaking to millions of citizens. It is believed that this warning by the Japan Meteorological Agency (JMA) saved an untold amount of lives). 
   There were foreshocks to the March 11th quake. A foreshock is a separate earthquake that occurs before a bigger one (the mainshock) and is related to the larger quake in both time and space. As far as I know this phenomena did not present itself before the Sylmar and Northridge quakes.
   Of course Japanese officials did not realize it at the time, but the first foreshock occurred 2 days before the “mainshock,” at 1:54PM on March 9th, a 7.2 Mw event, a huge earthquake in itself. It centered approximately 105 miles from Sendai, at a depth of 8.5 miles, about 24 miles from the epicenter of the March 11th quake. 
   A tsunami warning was issued, although the expected height of the wave was only a half meter, or one and a half feet. This quake lasted at least 3 minutes, and prompted the CNN news story above. 
   A 2 foot wave was first reported at Ofunato port half an hour after the quake without causing any damage.
   "We have confirmed that small tsunami have come up on the shores, but we have no reports of damage at this point," said Shinobu Nagano, an emergency and disaster response official in Iwate prefecture.
   Daniel Jaksa, senior duty seismologist at Geoscience Australia, said the earthquake would have been felt in Japan, "but it's not likely to cause any great distress".
   "7.2 earthquakes are quite common in the northern part of the Honshu. They get one of these every couple of years."
   Tohoku Electric Power said its Onagawa nuclear plant was operating normally after the quake. Tokyo Electric Power Company (TEPCO) owner and operator of Fukushima Daiichi, also said there was no impact on its power plants in the region.
   That day, March 9th, another three quakes occurred that were in excess of 6.0 Mw. Those aren’t exactly what you would call minor events.
   Hundreds of aftershocks were reported after the main March 11th quake (this phenomena I have experienced here in Los Angeles, although not to this degree of severity), many of them extreme events in themselves. 
   A 7.0 Mw aftershock was reported at 3:06PM local time, after which a 7.4  Mw manifested 9 minutes later at 3:15, and a 7.2  Mw at 3:26. Over 800 aftershocks of magnitude 4.5  Mw or more occurred after the initial quake, including one on October 26th, this year (it being the last day of 2013... Happy New Year everyone!) of magnitude 7.3. 
   Back in 1894 seismologist Fusakichi Omori  published his work on the aftershocks of earthquakes, in which he stated that aftershock frequency decreases by roughly the reciprocal of time after the main shock, or as every fourth grader knows, n(t) =  K over c+t, where: n(t) is the rate of earthquakes measured in a certain time t after the main shock, K is the amplitude, and c is the "time offset" parameter. 
   Of course the modified version of Omori's law, which is now more commonly in use, was proposed by Prof. Tokuji Utsu in 1961, states n(t) = k over c+t)^p, where p modifies the decay rate and typically falls in the range 0.7–1.5. According to these equations, the rate of aftershocks decreases quickly with time. The rate of aftershocks is proportional to the inverse of time since the mainshock and this relationship can be used to estimate the probability of future aftershock occurrence. Thus whatever the probability of an aftershock is on the first day, the second day will have 1/2 the probability of the first day and the tenth day will have approximately 1/10 the probability of the first day (when p is of course equal to 1)
   So Japan has nothing to worry about... except major aftershocks that still occur several years after the initial quake and that don’t seem to follow Omori's law. 
   Other than those everything seems to be okay.
   In this post we’ve taken a quick look at the March 11th 9.0 Mw earthquake. In the next post we’ll examine the deadly tsunami (and the damage it caused) that followed about 30 minutes to an hour later.

To be continued. 

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