Earthquake intensity

Question

How much more energy (intensity) does a 8.5 M earthquake have compared to I₀

m=log (I/I₀)

Answer 1

The magnitude is given as 8.5.

Plugging that intensity into the intensity equation, we get

m = log (I/I₀)

(8.5) = log (I/I₀)

Since we eventually want to solve for I/I₀, reverse the equation and place the ratio on the left-hand side

log (I/I₀) = 8.5

Now, we need to get rid of the log function on the I/I₀ ratio on the left-hand side. We do this by using the logs as exponents on a base of 10...

10^log(I/I₀⁾ = 10^8.5

I/I₀ = 316,227,766

meaning that a 8.5 M earthquake is 316-million times more powerful than the reference earthquake of intensity I₀ .