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?

1 Answer
Feb 1, 2018

Answer:

#~~ 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#