Question

Alaska experienced an earthquake of magnitude `8.7` on the Richter scale in February 1965. The earthquake in Indonesia in 2004 was `4` times as strong as the Alaskan one. So what was its approximate magnitude on the Richter scale?

Answer 1

`~~ 9.1`

Explanation:

Assuming that `4` times as strong means releasing about `4` times the energy, note that the energy release is the `3/2` power of the amplitude and the magnitude (as measured on the Richter scale) is based on the common (base `10`) logarithm of the amplitude.

Hence the magnitude we are looking for is:

`8.7 + log(4^(2/3)) = 8.7 + 2/3 log(4) = 8.7 + 4/3 log(2) ~~ 8.7 + 4/3 * 0.3 = 9.1`