6a. An earthquake of magnitude 7.0 on the Richter scale strikes. A few days late

Question

6a. An earthquake of magnitude 7.0 on the Richter scale strikes. A few days later another quake strikes, but it is of magnitude 7.3. How much stronger, in percentage terms, is the second quake? [The Richter is a log scale of seismic activity to the base 10. That is, the number reported for the quake is the log of seismic activity.]

6b. An earthquake off the coast of Chile in 2010 was reported to be an 8.8. The quake that hit Haiti earlier in the same year was a 7.0. On the Richter scale basis, what is the relative magnitude of the Chilean and Haitian quakes?

6c. The Richter scale measures seismic activity. Other measures of quake strength include the energy released by quakes. One of these other measures is given by the equation.(2/3) log10 y = x. Using this measure, find the relative strengths of the Chilean and the Haitian earthquakes.

Explanation / Answer

The Richter is a log scale of seismic activity to the base 10.

So that the secoond quake is (10^7.3/10^7)*100 = 199.53% stonger than the first one.

6b) Relative magnitudes are obtained by dividing one of the indexes by the others, which is taken as the basis of comparison

So that the relative magnitude of the Chilean and Haitian quakes = 8.8/7.0 = 1.257143

6c) the equation of the energy released by quakes is (2/3) log10 y = x.

so that y = (3/2)* 10^x

For Chile : the energy released by quakes is = (3/2)*10^8.8

For Haiti the energy released by quakes is = (3/2)*10^7.0

So the relative strengths of the Chilean and the Haitian earthquakes is {(3/2)*10^8.8 }/{(3/2)*10^7.0} = 63.10

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