Question

On April 11, 2012, two earthquakes were measured off the northwest coast of Sumatra. The first had a magnitude of

8.6. The second had a magnitude of 8.2. By what approximate factor was the intensity of the first earthquake greater
than the intensity of the second earthquake?
M-log
M = the magnitude of an earthquake
/= the intensity of an earthquake
lo=
= the smallest seismic activity that can be measured, which is 1

Answer 1

Explanation:

The relationship between magnitude (M) and intensity (I) of an earthquake is given by:

I ~ 10^(1.5M + 4.8)

We can use this relationship to compare the intensities of the two earthquakes:

I1/I2 = (10^(1.5M1 + 4.8))/(10^(1.5M2 + 4.8))

= 10^(1.5(M1 - M2))

Substituting the given magnitudes, we get:

I1/I2 = 10^(1.5(8.6 - 8.2))

= 10^(1.5(0.4))

≈ 2.24

Therefore, the intensity of the first earthquake was approximately 2.24 times greater than the intensity of the second earthquake.

Answer 2

The relationship between earthquake magnitude and intensity is given by the Richter scale formula:

I = 10^(1.5M + 4.8)

where I is the intensity of the earthquake and M is its magnitude.

To compare the intensities of the two earthquakes, we can take the ratio of their intensities:

I1/I2 = 10^(1.5M1 + 4.8) / 10^(1.5M2 + 4.8)

Using the given values of M1 = 8.6 and M2 = 8.2, we get:

I1/I2 = 10^(1.5*8.6 + 4.8) / 10^(1.5*8.2 + 4.8)
= 10^(13.02) / 10^(12.72)
= 10^0.3
≈ 2.0

Therefore, the intensity of the first earthquake was approximately 2 times greater than the intensity of the second earthquake.