Calculating catastrophe
On March 11, 2011, a magnitude 9.0 earthquake off the Sanriku coast of Japan generated a catastrophic tsunami. Waves reached run-up heights of 40 meters in some areas, inundating over 400 square kilometers of land along the Pacific coast. Amid the widespread destruction, geologists observed something curious: the water had moved immense boulders, some weighing tens of tons, for hundreds of meters. This presented a complex physics problem. By studying these displaced rocks, scientists can calculate the immense forces the wave unleashed, measuring the tsunami's force.
Researchers use a set of hydrodynamic equations to estimate the minimum flow velocity needed to move a coastal boulder. These calculations must account for multiple forces acting on the rock. The primary forces are drag, which is the force of the water flowing against the boulder, and lift, an upward pressure created by the moving fluid. Opposing these are the boulder's submerged weight and the friction between it and the ground. A boulder begins to slide when the hydrodynamic forces exceed the resisting forces. At Hoshiyama beach on the Sanriku coast, one large boulder with a long-axis of 7.35 meters was moved by the 2011 tsunami. Simulations suggest the water there reached a maximum velocity of 6.51 meters per second, just enough to initiate motion according to the equations.
Reading the rocks
The study of tsunami-displaced boulders is part of paleotsunamiology, the science of identifying and dating historic and prehistoric tsunamis. The Sanriku coast, with its long history of seismic activity, has a geological record of these events. Scientists can analyze sediment layers in coastal lowlands to find signs of past floods. For example, distinct layers of gravelly sand found far inland at Noda, a village on the Sanriku coast, record massive tsunamis in the region's deep past.
By analyzing the characteristics of gravel in these deposits, researchers can even estimate the scale of ancient tsunamis. One method involves tracking the "roundness" of gravel particles at different distances from the shore. The point where the roundness of sea-worn gravel gives way to the angularity of local inland rock—the "Tsunami Gravel Inflection Point"—consistently occurs at about 40% of the tsunami's total inundation distance. Applying this technique to ancient deposits helps scientists reconstruct the size of tsunamis that occurred thousands of years ago, long before human records existed. These geological clues show a timeline of catastrophe, estimating that tsunamis larger than the destructive 1896 Meiji Sanriku event strike the coast on average every 290-390 years.