Chapter 4.3, Problem 92E

RELATING CONCEPTS For Individual or Group Work (Exercises 91–94)

In 1935, Charles F. Richter devised a scale to compare the intensities of earthquakes. The intensity of an earthquake is measured relative to the intensity of a standard zero-level earthquake of intensity $I_0$. The relationship is equivalent to

$I=I_0\times {10}^R$, where R is the Richer scale measure.

For example, if an earthquake has magnitude 5.0 on the Richter scale, then its intensity is calculated as

$I=I_0\times {10}^{5.0}=I_0\times 100,000,$

which is 100,000 times as intense as a zero-level earthquake.

To compare two earthquakes, such as one that measures 8.0 to one that measures 5.0, calculate the ratio of their intensities.

$\frac{\text{intensity 8}\text{.0}}{\text{intensity 5}\text{.0}}=\frac{I_0\times {10}^{8.0}}{I_0\times {10}^{5.0}}=\frac{{10}^8}{{10}^5}={10}^3=1000$

An earthquake that measures 8.0 is 1000 time as intense as one that measures 5.0.

The table lists information for selected earthquakes with their years, locations, and magnitudes. Work Exercises 91–94 in order.

Year	Earthquake Location	Richter Scale Measurement
1960	Chile	9.5
1952	Kamchatka	9.0
2007	Southern Sumatra, Indonesia	8.5
2013	Obihoro, Japan	6.9
2002	Hindu Kush, Afghanistan	5.9
Source: earthquake.usgs.gov

Compare the intensity of the 2013 Obihoro earthquake with the 2002 Hindu Kush earthquake.