Question

The intensities of earthquakes are measured with seismographs all over the world at different distances from the epicenter. Suppose that the intensity of amedium earthquake is originally reported as 10 times I. Later this value is revised as 10 times I. The local magnitude M (on the Richter scale) of anearthquake of intensity I is given by log(a) Determine the magnitude of the earthquake using the original estimate for Intensity.b) Determine the magnitude for the revised estimate for intensityc) How many times more intense was the earthquake than originally thought? Round to 1 decimal place

Answer 1

a) We have to calculate the magnitude M of the earthquake.

We will use the first intensity measure, that is I = 10^5.4*I₀.

We then can calculate the magnitude M as:

$\begin{gathered} M=\log(\frac{I}{I_0}) \\ M=\log(\frac{10^{5.4}*I_0}{I_0}) \\ M=\log(10^{5.4}) \\ M=5.4*\log(10) \\ M=5.4*1 \\ M=5.4 \end{gathered}$

b) Now we will use the revised measure of I = 10^6.2*I₀ to calculate the magnitude:

$\begin{gathered} M=\log(\frac{I}{I_0}) \\ M=\log(\frac{10^{6.2}*I_0}{I_0}) \\ M=\log(10^{6.2}) \\ M=6.2 \end{gathered}$

c) We have to calculate how many more intense was the earthquake than originally thought. We can calculate this as the ratio between the actual magnitude (revised) and the original:

$\frac{M_{actual}}{M_{original}}=\frac{6.2}{5.4}\approx1.1$

It was 1.1 times more intense (about 10% more intense).

Answer:

a) M = 5.4

b) M = 6.2

c) 1.1 times