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The Math Behind the Richter Scale

Earthquakes… in Arizona?

While this “arid zone” is not known for earthquakes, they do happen at a frequency that might surprise you. In fact, hundreds of small earthquakes occur every year in Arizona. Faults in the hot dry state, and neighboring states like California, do have the potential to deliver large magnitude earthquakes which can be felt all over the Southwest. The Arizona Geologic Survey reports the most recent larger quake to be of 5.3 magnitude, occurring near Duncan, AZ in 2014. Despite it not being a “destructive”, the Duncan quake could be felt all the way from Phoenix to Alamogordo, N.M. and was followed by literally thousands of aftershocks.

While a 5.3 earthquake is somewhat powerful, it is not generally a magnitude that is going to cause a lot of destruction. However, with each notch up on the Richter Scale, earthquakes truly ramp up in force. For example, a 6.0 earthquake is ten times more powerful than a 5.0. Moving up to a 7.0, the math reveals that this magnitude is 10 x 10 (or 10 to the second) = 100 times more powerful than the 5.0! And yes, an 8.0 is literally 1000 times (or 10 to the third) as powerful as the 5.0! Can you imagine how the crazy the 1964 Alaskan quake must have felt at a 9.2, more than 10,000 times as strong as the one in Duncan, AZ in 2014?

The math behind the Richter Scale is not entirely straightforward. For a more complete explanation of the Richter Scale, check out the following link.[1] At the same time, I believe the Richter Scale offers a great case study for applying the mathematical concept of exponents to the physical science field of geology.

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