Measuring earthquake energy
Earthquakes are measured on a scale of 0 to 9, corresponding to how much energy they release. This is a log scale, so each whole number on the Richter scale represents a ten-fold increase in energy.
An earthquake hit Christchurch in New Zealand on 22 Feb 2011, measuring 6.3 on the Richter scale (tragically 185 people were killed). In 1928, an earthquake in Murchison NZ measured 7.3, leaving 173 dead. How much more energy was released in the Murchison earthquake?
(To make this problem interactive, turn on javascript!)
- I need a hint ... : Each point on the Richter scale multiplies the unlogged measurement of energy by 10.
- ...another hint ... : 7.3-6.3 = 1
I think I have the answer: 10 times as much.
In the example above, the logged numbers were exactly 1 unit apart, and the quick answer to how much more energy was released would be simply
101 = 10 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. In the real world, measurements are usually messier. But the principle is the same: find the difference between the two logged numbers, and "unlog" that difference.
The earthquake in Newcastle Australia in 1989 measured 5.6 on the Richter scale. How much more energy was released in the Christchurch earthquake (6.3) vs. the Newcastle earthquake?
(To make this problem interactive, turn on javascript!)
- I need a hint ... : 6.3 - 5.6 = 0.7
- ...another hint ... : The anti-log of 0.7 is 100.7
I think I have the answer: 100.7 = 0.5 times as much energy
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