Moment magnitude (Mw)
A measure of earthquake size derived from the seismic moment, meaning the fault area that ruptured and how far it slipped, which replaced the Richter scale because it does not saturate on great earthquakes.
Moment magnitude (Mw) is the measure of earthquake size computed from the seismic moment, the product of rock rigidity, ruptured fault area and average slip. March 11, 2011, off Tōhoku: the Japan Meteorological Agency (JMA) first announced a magnitude of 7.9, then raised it in steps to 9.0. The first tsunami warnings had been calibrated on the low number. The gap comes from method. Charles Richter's local magnitude, published in 1935, reads the amplitude of one wave on a seismograph and saturates around 7: a 500-kilometer rupture and a 100-kilometer rupture end up giving the same reading. Hiroo Kanamori proposed moment magnitude in 1977, and the Hanks and Kanamori formula of 1979 tied it to the older scales over the range where they work. The scale is logarithmic. One unit up means roughly 32 times more energy; two units, roughly 1,000 times. Newspapers still say "Richter" for any number, while the United States Geological Survey (USGS) publishes Mw for large events. In a cat model, magnitude drives the stochastic catalog: a Gutenberg-Richter law sets frequency by magnitude, truncated at a maximum magnitude per fault or source zone. Cat bonds and parametric earthquake covers often trigger on the magnitude published by the USGS, combined with depth and a geographic box. A practitioner's caveat: magnitude measures the source, and damage depends on depth, distance and soil. A shallow Mw 6.5 under a city costs more than an Mw 8 at 600 kilometers depth, and a parametric contract that reads only Mw carries that basis risk.
Textbook case, made-up figures: a 100 million dollar parametric cover pays 50% if the USGS publishes an Mw of at least 7.5 inside the capital's box, shallower than 70 kilometers, and 100% from 8.0. The stochastic catalog gives 1.2% a year above 7.5 in the box and 0.3% above 8.0. Expected loss: 50 × 1.2% + 50 × 0.3% = 0.75 million dollars a year. A quake published at 7.4 on day one and revised to 7.6 the following week pays 50 million if the contract reads magnitude at day 10, nothing if it reads it at day 1.
moment magnitude scale, Mw, MMS, moment magnitude
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