The Magic Formulas (Richter Scale)

In the previous post, we introduced a formula for calculating the magnitude of earthquakes. The formula is

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

WOW! You may be shocked and at a loss because this is one large chunk of logarithms and funny symbols! Do not worry. We will try to explain this formula so that it's easier for everyone to understand.

Before we start, let me introduce you to another formula very similar to the first one:

M = log₁₀ (A / A_zero)

A = A_zero 10^M

Don't understand? We will start with this formula first because it's simpler to understand and because you must be able to understand this formula before moving on to the original formula. (The original formula is derived from a few equations, including the ones we just introduced)

M = log₁₀ (A / A_zero)

Definitions:

M is the magnitude

A is the maximum excursion of the seismograph

A₀ is the empirical function depending on the epicenter distance

So as the for every 1 unit the magnitude increases, the amplitude increases by a factor of 10. The same 1 unit of increase in magnitude would give you an approximate of 32 times the earthquake's energy! Scary, isn't it?

So, by inserting the variables A and A_{0, you will get the magnitude of the earthquake and then you can find out the energy of the earthquake.}

_{Now you may ask, "How do we find the epicenter distance?"}

_{During an earthquake, seismic waves are spread spherically out from the hypo-center. You can find the epicenter distance by measuring the time difference on the seismograph and the distance on a travel-time graph at which the P-wave and S-wave have the same separation.}

_{A picture worth a thousand words. So let's let the animation tell you something about the P-wave and the S-wave.}

http://upload.wikimedia.org/wikipedia/commons/6/62/Onde_compression_impulsion_1d_30_petit.gif

http://upload.wikimedia.org/wikipedia/commons/6/6d/Onde_cisaillement_impulsion_1d_30_petit.gif

Left to right: P-wave (Primary Wave), S-wave (Secondary Wave)

And you on to the magic formula!

It is the same logic as the previous formulas we have just mentioned. While M is the magnitude and A is the amplitude. There's something new -- δ.δ the epicenter distance of the station, which is where the earthquake takes place. This formula is derived from the previous formulas.

Note: Magnitude greater than 4.6 are strong enough to be recorded b a seismograph. Any figures below 4.6 are not considered strong enough to be considered an earthquake.

And TADAAAA. You have your Richter Scale!

http://en.wikipedia.org/wiki/Epicentral_distance#Epicentral_distance

_{http://en.wikipedia.org/wiki/P-wave}

_{http://en.wikipedia.org/wiki/S-wave}

_{http://www.vibrationdata.com/earthquakes/magnitude.html}