Precalculus question

Question

The 1906 San Francisco earthquake had a magnitude of 7.9 on the MMS scale. Around the same time there was an earthquake in South America with magnitude 4.6 that caused only minor damage. How many times more intense was the earth movement in San Francisco earthquake than the South American one? 

Answer 1

The MMS value of an earthquake is calculated with the formula M = (2/3)log(S₁/S₀).

7.9 = (2/3)log(S₁/S₀)

(7.9)/(2/3) = log(S₁/S₀)

10^(7.9)/(2/3) = S₁/S₀

S₁/S₀ ≈ 7.08*10¹¹

This tells us the San Francisco earthquake has about 7.08*10¹¹ times more earth movement than the baseline measure of S₀ = 10¹⁶.

4.6 = (2/3)log(S₂/S₀)

(4.6)/(2/3) = log(S₂/S₀)

10^(4.6)/(2/3) = S₂/S₀

S₂/S₀ ≈ 7.94*10⁶

This tells us the South American earthquake has about 7.94*10⁶ times more earth movement than the baseline measure.

S₂/S₁ = 7.08*10¹¹/7.94*10⁶ ≈ 89169

Therefore, the earth movement in the San Francisco earthquake was about 89169 times more intense than in the South American earthquake.

Hope this helped!