You’ve raised an important point that might require clarification. On both the Richter scale and the preferred moment magnitude scale (or simply "the magnitude"), the amplitude - that is the shaking – goes as factors of 10. So in terms of the way people experience an earthquake, it is correct to say that a magnitude of a 9.0 earthquake is ten times greater than the magnitude of an 8.0 earthquake. The amplitude of a 9.0 earthquake is ten times greater than the amplitude of an 8.0 earthquake.
The amplitude and moment are easily quantified. The moment is the fault area multiplied by the displacement on the fault (times a number that is treated more-or-less as a constant). The area of the rupture and the displacement are easily quantified by seismologists using global data sets. This makes moment magnitude and amplitude easy to quantify. And they relate directly to the experience of people on the ground.
You are correct that the energy goes as ~32. Energy is a bit tricky to quantify because it can be released via different mechanisms (heat, motion etc...). The energy released by a quake may be experienced quite differently in different earthquakes; again, it is a much harder number to quantify.
In the video, I discuss these two quantities (magnitude and energy) in adjacent sentences and in retrospect this was confusing. It would have been clearer had I said: “A magnitude 9 earthquake is 10 times bigger--an order of magnitude bigger--than a magnitude 8 earthquake. This earthquake off the coast of Japan released 1000 times more energy than the recent earthquake in Haiti in 2010.”
-Submitted by Dr. Elizabeth Cottrell, Geologist, Smithsonian Institution
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