MathBench > Measurement

Logs and pH

Measuring earthquake energy

Here's another example you probably won't see in your biology class (unless you get your TA really mad, maybe), but you've probably heard of it. Earthquakes are measured on a scale of 0 to 9, corresponding to how much energy they release. This is a log scale, so each point on the Richter scale represents a ten-fold increase in energy.

Two earthquakes hit the Twin Cities ( St. Paul and Minneapolis , both of which are my hometowns and neither of which ever get earthquakes. oh well.) The St. Paul earthquake measures 1.0 on the Richter scale, the Minneapolis earthquake measures 3.0. How much MORE energy was released in Minneapolis?

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I think I have the answer: 100 times as much.

san francisco earthquake of 1906

In the example above, the logged numbers were exactly 2 units apart, and the quick answer to how much more energy was released would be simply

102 = 100 times as much.

Likewise, if the earthquakes measured 2 and 6 on the Richter scale, that's a difference of 4 points, and the difference in actual energy is

104 = 10,000 times as much.

Of course the logged number you encounter will not usually increase by exactly 1 unit (hence the fictional example above!) In the real world, measurements are more messy. But the principle is the same: find the difference between the two logged numbers, and "unlog" that difference.

The tsunami at Christmas 2004 measured 9.3 on the Richter scale, while the San Francisco earthquake of 1906 measured 8.0. How much more energy was released in the Christmas tsunami vs. the San Francisco earthquake?

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I think I have the answer: 101.3 = 19.5 times more energy