Chapter 8.5, Problem 18PPS

(a)

To determine

To find: The comparison between the intensity of earthquake that was on $1906$ than the $1979$ near San Francisco.

Answer to Problem 18PPS

The intensity of earthquake was on $1906$ is approximately $26$ times more intense than $1979$ .

Explanation of Solution

Given:

The given intensity of earthquakes are as:

In $1979$ , an earthquake near San Francisco registered approximately $5.9$ on the Richter scale.

And the famous San Francisco earthquake of $1906$ measured $8.3$ in magnitude.

Calculation:

Since the Richter scale is used to measure earthquake intensity and it’s rounded to the nearest tenth.

So every increase of $1$ is $10$ times. So here dealing is with natural log (log base $10$ ).

The intensity of earthquake registered in $1906$ is given as:

  ${\log }_{10}E=5.9$

Here $E$ is the energy released in earthquake.

The intensity of earthquake registered in $1979$ is given as:

  ${\log }_{10}E=8.3$

Suppose,

  $x=\text{number of times more intense}$ .

So

  ${\log }_{10}x=\frac{8.3}{5.9}$

Solve the above expression is as:

  $\begin{array}{c}{10}^{{}_{{\log }_{10}}x}={10}^{\frac{8.3}{5.9}}\\ x\approx 26\end{array}$

So the intensity of earthquake was on $1906$ is approximately $26$ times more intense than $1979$

(b)

To determine

To find: The difference in intensities in between Richter himself classified and more recent research.

Answer to Problem 18PPS

The $1906$ earthquake was revised downward $60.2\%$ in intensity.

Explanation of Solution

The more recent research indicates the earthquake was most likely a $7.9$ .

Calculate the amplitude seismic value ${10}^x$ , where $x=\text{the magnitude of the earthquake}$ is as:

  $\begin{array}{c}{10}^{7.9}=79,432,823\\ {10}^{8.3}=199,526,321\end{array}$

Take the ratio of the two numbers then subtract $1$ to measure the percent change.

  $\begin{array}{c}\frac{79,432,823}{199,526,321}-1=.398-1\\ =-0.602\\ =-60.2\%\end{array}$

Therefore the $1906$ earthquake was revised downward $60.2\%$ in intensity.