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The Ocean Drilling Program recently published results indicating that the 2011 Tohoku-Oki earthquake produced a maximum co-seismic slip of more than 50 meters near the Japan Trench. This is the largest fault displacement that has been measured for an observed earthquake. They also suggest that the displacement across the fault likely relieved nearly 100% of the preexisting shear stress across the fault in a matter of minutes.

What physical process could explain how the rock in the fault zone remained relatively strong for many decades and then suddenly become very weak?

This great earthquake is unprecedented for seismology because of its size and because it was possible to collect so much data about it. The details of the physical mechanism responsible for it is the subject of active research. The simple models of faults we learned in school are entirely applicable, but inadequate to entirely explain all the observations.

This paper is possible place to start for the technically advanced: The 2011 Magnitude 9.0 Tohoku-Oki Earthquake: Mosaicking the Megathrust from Seconds to Centuries

This article, for general scientific audience: Japan's 9.0 Tohoku-Oki Earthquake: Surprising Findings About Energy Distribution Over Fault Slip and Stress Accumulation which also contained the following:

For seismologist Hiroo Kanamori, Caltech's Smits Professor of Geophysics, Emeritus, who was in Japan at the time of the earthquake and has been studying the region for many years, the most significant finding was that a large slip occurred near the Japan Trench. While smaller earthquakes have happened in the area, it was believed that the relatively soft material of the seafloor would not support a large amount of stress. "The amount of strain associated with this large displacement is nearly five to 10 times larger than we normally see in large megathrust earthquakes," he notes. "It has been generally thought that rocks near the Japan Trench could not accommodate such a large elastic strain."

Mark Rovetta
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The rock didn't suddenly become weak. Over the last (according to the Wikipedia article you cite) 260 to 880 years the rocks have been deforming elastically, and 11 March 2011 the stress had built up to the yield stress of the rock and it fractured and sprang back.

Subduction

This is an illustration of what's happening off the Japanese coast (this is actually equatorial America but it's similar to the subduction off Japan - a Google image search will find many more such diagrams). The contact patch between (in this case) the Cocos plate and the Caribbean plate isn't as strong as rock because there is sediment between the two plates. Nevertheless it has a considerable yield stress so it takes a lot of force to make the plates slide over each other. As the Cocos plate slides downwards it elastically deforms the Caribbean plate and bends it downwards. You may not think of rock as elastic, but on the large scales involved it can bend just as large pieces of glass can bend (basalt and glass are not dissimilar).

Anyhow, as the deformation increases, the stress at the contact patch increases and eventually becomes big enough to break the plates free of each other. At this point the Caribbean plate will rebound upwards, which results in an earthquake. The figure of 50m you quote is the amount the upper plate had been deformed down and slipped back up along the subducting plate after the contact patch fractured.

Predicting when the fracture will occur is impossible since fractures invariably start at defects in the contact patch, and we have no way of knowing what those defects are. Nevertheless, as the Wikipedia article mentions, because the subduction rate is roughly constant there is some regularity to the earthquakes. The process of stress build up then fracture repeats on a timescale of some hundreds of years.

John Rennie
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Two years following the event, seismologists are making progress towards understanding the details of the physical mechanism responsible for this extraordinary earthquake.

The (May 2013) special issue of the BSSA is about the 2011 Tohoku Earthquake and Tsunami and reports on modern models of the earthquake rupture mechanism – including an online video of dynamic rupture simulations for this specific earthquake developed by Kozdon and Dunham.

Their paper explains that it was surprising that this earthquake’s coseismic rupture reached the seafloor rather than stop several tens of kilometers down-dip of the seafloor. One possible explanation to explain this would be a mechanism of dynamic weakening and stress release around shallow subducted seamounts (submarine volcanos.) The authors of this paper propose an alternative mechanism, supported by their 2D computer simulations and seismic surveys of the Japan Trench, which incorporates depth dependent material properties and the complex geometry of the fault, seafloor, and material interfaces. The rupture nucleates on a deeper, velocity-weakening, section of the fault and then propagates upwards, through a velocity-strengthening region, to the seafloor.

Mark Rovetta
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