Logarithms -- The Wonder of Logarithms: The Richter Scale

Now we are on to the use of logarithms! Logarithms isn't hard, right?

The Richter Scale is a logarithm scale that is used to calculate the magnitude of earthquakes.

The Richter Scale refers the measure of the amount of energy contained in an earthquake.

Cool Fact:

There is often a misconception that an earthquake that measure 5.0 on the Richter scale is just 1.0 larger than that of an earthquake of 4.0. This is WRONG.

An earthquake that measure 5.0 has an amplitude of 10 times larger than an earthquake that measures 4.0.

And 6.0 releases 100 times the energy of 4.0.

So, a magnitude of 9.0 is SCARY, isn't it?

And the secret formula is...

$M_\mathrm{L} = \log_{10} A - \log_{10} A_\mathrm{0}(\delta) = \log_{10} [A / A_\mathrm{0}(\delta)],\$

http://upload.wikimedia.org/math/1/3/e/13e5e0759d863fbb88d35d2ca1421b7b.png

We will go into more detail in the later postings...

Why is Logarithm needed?

Earthquake magnitudes and calculations are of a very large range. Thus Logarithm comes to the rescue! Logarithms are used to deal with numbers that span a very large range by using exponents of ten.

Here's the relation between Magnitude and Ground Amplitude before we end today's post.