Problem 207: In 1906, San Francisco experienced an intense earthquake with a magnitude of 7.8 on the Richter scale. Over 80% of the city was destroyed by the resulting fires. In 2014, Los Angeles experienced a moderate earthquake that measured 5.1 on the Richter scale and caused $108 million dollars of damage. Compare the intensities of the two earthquakes.
Solution: The magnitude of an earthquake is measured by , where is the intensity of its shock wave.
For the 1906 earthquake, the intensity is given by
(1)
For the 2014 earthquake, the intensity is given by
(2)
Then we can take their ratio to compare their intensity. Thus
(3)
This means that the intensity of the 1905 earthquake in San Francisco was 501 more than the earthquake in 2014 in Los Angeles.
Leave a Reply