Chapter 4.5, Problem 82E

(a)

To determine

To calculate: The magnitude of an earthquake with an intensity of $39,811,000$ if the magnitude of earthquake and intensity are correlated by $R=\frac{\ln I-\ln I_0}{\ln 10}$ and it is assumed that $I_0=1$.

(b)

To determine

To calculate: The intensity of an earthquake in Vanuatu in which magnitude of the earthquake is $R=6.8$ and the magnitude of earthquake and intensity are correlated by $R=\frac{\ln I-\ln I_0}{\ln 10}$ and it is assumed that $I_0=1$.

(c)

To determine

To calculate: The intensity of an earthquake in Chile in which magnitude of an earthquake is $R=8.2$ and the magnitude of earthquake and intensity is correlated by $R=\frac{\ln I-\ln I_0}{\ln 10}$ and it is assumed that $I_0=1$.

(d)

To determine

To calculate: The amount of intensity increased of an earthquake if the magnitude of an earthquake $R$ is doubled and the magnitude of earthquake and intensity are approximated by the equation, $R=\frac{\ln I-\ln I_0}{\ln 10}$ and it is assumed that $I_0=1$.

(e)

To determine

To calculate: The value of $\frac{dR}{dI}$ if the amount of intensity and magnitude of an earthquake are correlated by $R=\frac{\ln I-\ln I_0}{\ln 10}$ and it is assumed that $I_0=1$.