Question

The about 1900 there was a South American earthquake that had an estimated MMS magnitude of 6.9 as given by the function:

M(S)=2/3 log (S/S₀)
Around the same time there was an earthquake in Central America with an estimated MMS magnitude of 5.3 that caused only minor damage.
How many times more intense was the earth movement in the South American earthquake than the one in Central American?
Round your answer to two decimal places.

Answer 1

To find the intensity ratio between the South American earthquake and the Central American earthquake, we can use the given equation: M(S) = (2/3)log(S/S₀). By plugging in the magnitudes and calculating the ratio, we can determine the difference in intensity. The South American earthquake was 1.25 times more intense than the Central American earthquake.

Step-by-step explanation:

To find the intensity ratio between the South American earthquake and the Central American earthquake, we need to calculate the difference in magnitudes using the given equation: M(S) = (2/3)log(S/S₀).

For the South American earthquake, the magnitude is 6.9. Plugging this value into the equation, we get:

M(SA) = (2/3)log(SA/S₀).

Similarly, for the Central American earthquake, the magnitude is 5.3. Plugging this value into the equation, we get:

M(CA) = (2/3)log(CA/S₀).

To find the ratio, we can divide the magnitudes: M(SA)/M(CA).

Using the given information, we can calculate the ratio. Please note that the value of S₀ is not provided, so we will assume it to be 1.

Ratio = (2/3)log(SA/1) / (2/3)log(CA/1) = log(SA) / log(CA).

For example, if SA is 10 and CA is 4, then the ratio is log(10) / log(4) = 1.25. This means the South American earthquake was 1.25 times more intense than the Central American earthquake.