# How does the Richter scale measure magnitude?

Sep 17, 2015

It measures the maximum energy liberated from the earthquake, compares it to a reference value and then take the log of it

#### Explanation:

The formula is $M = \log \left(A\right) - \log \left({A}_{0}\right) = \log \left(\frac{A}{A} _ 0\right)$

There are tables for the value of ${A}_{0}$ based on the distance from the epicenter.

It's important to note that these values depend of the distance from the epicenter of the earthquake.

There's been advancements and alternate formulas though, still logarithmic, which take the distance as direct variable instead of a parameter. They're of the type

$M = {k}_{1} \log \left(A\right) + {k}_{2} \log \left(D\right) + {k}_{3}$

The most famous of which is the Lillie's Empirical Formula:
$M = \log \left(A\right) + 2.76 \log \left(D\right) - 2.48$,
with values based on empirical data, for D measured in km.