Question

An earthquake registered a magnitude of 7.8. It was followed by an aftershock with a magnitude of 6.9. How many times more intense was the initial earthquake than the aftershock?

Answer 1

The initial earthquake was approximately 31.6 times more intense than the aftershock.

Step-by-step explanation:

The intensity of an earthquake is related to its magnitude on the Richter scale. The Richter scale is logarithmic, meaning that each whole number increase on the scale represents an earthquake that is 10 times stronger in terms of energy release.

So, in this case, we can calculate the difference in intensity between the initial earthquake (magnitude 7.8) and the aftershock (magnitude 6.9) by finding the ratio of their energy releases.

To do this, we can use the following equation:

Intensity ratio = 10^((magnitude1 - magnitude2) * 1.5)

Plugging in the values, we get:

Intensity ratio = 10^((7.8 - 6.9) * 1.5) = 31.6227766 times

Therefore, the initial earthquake was approximately 31.6 times more intense than the aftershock.

Answer 2

The initial earthquake was approximately
`10^(0.9)` times more intense than the aftershock, which is equivalent to about 7.94 times more intense.

How to find the more intense the shock will be

The magnitude scale for earthquakes is logarithmic, meaning that each whole number increase represents a tenfold increase in amplitude.

Therefore, the initial earthquake with a magnitude of 7.8 is 10 times more intense than the aftershock with a magnitude of 6.9.

To calculate how many times more intense the initial earthquake was than the aftershock:

`\[ 10^((7.8 - 6.9)) = 10^(0.9) \]`