Course:MATH110/Archive/2010-2011/003/Teams/Jura/Homework/13 Part3
Jura Corporation: We used to make fine Swiss cheese... until the earthquake.
Our recent expansion into the fine art of cheese making was doing extremely well. It wasn't surprising! We had thousands of orders and even the rats in the city were congregating in our warehouse! Luckily, our mathematical prowess convinced our CEO, the one who shall not be named, to invoke extreme prejudice on those nasty critters. With the business saved, all was good... until the earthquake. Yes... the earthquake! Our warehouse could not handle the force of the earthquake and the unfortunate event brought our cheese business to an halt. Although our CEO is quite angry, he has re-mortgaged his house to pay for our new warehouse, but he wants to ensure that our next warehouse can actually withstand a future earthquake. Enough of this, it's time to suit up and do some math!
An Introduction to the Richter Magnitude Scale
Seismic waves are defined as the vibrations from earthquakes that travel through the Earth [1]. With the definition of what seismic waves are, it was interesting to discuss the possibility of a method to accurately compare different earthquakes with each other. Charles Richter, a Physicist, found this to be a topic of fascination. It was such a great topic of interest for him that in 1935, Richter was able to accurately measure the magnitude of an earthquake [2].
Richter described his scale in the following way: 1) The magnitude of an earthquake is determined from the logarithm of the amplitude of waves recorded by seismographs [3]. 2) The magnitude is represented by real numbers. For example, the real number, 6.5, would describe the magnitude of a particular earthquake. With what we know about Logarithms, we know that whenever there is an increase in the whole number (e.g., 4.5 to 5.5) there will be a tenfold increase in magnitude. A more mathematical explanation will be detailed in the next section.
Listed below is a graph outlining the effects of different magnitudes of earthquakes [4].
The Richter Magnitude Scale: How it Works on a Logarithmic Scale of Log Base 2
Let's start by defining:
Base 10: Is a logarithmic with 10 as its base and is commonly seen in Roman Numerals or you guessed it, the Richter Magnitude Scale.
Logarithmic Scale: A scaled measurement. Logarithmic scales use logs to represent a quantity instead of using the actual quantity.
An example from the Wiki:
1, 10, 100, and 1000 instead of 1, 2, 3, and 4. This is also an example of how logarithmic scales are used with the Richter Magnitude scale.
Description:
For the Richter's scale, log base 10 denotes the amount of seismic energy released by an earthquake. The number equated for the earthquake represents its strength and increases as the number becomes larger. A 6.0 magnitude earthquake is 10 times larger than a 5.0 magnitude earthquake. This is so because each whole number increases are broken up into ten 0.1 increments; from 5.1 to 6.0. The final quantity, the magnitude, is found by deriving the logarithm of the wave amplitude recorded on a seismograph. The equation is:
M2= log10A - log10A0(S)
A= maximum excursion of the needle on the "Wood-Anderson" seismograph
A0= the distance from the epicenter to the station(S)
Gentlemen, we can rebuild it. We have the technology. We have the capability to build an earthquake resistant building. Jura Corporation will be that building. Better than it was before. Better, stronger, classier.
With a better understanding with how to measure the magnitude of earthquakes, Jura Corporation can use this information in developing a stronger infrastructure for our new warehouse. To the untrained person, an earthquake magnitude of 5.0 when compared to a magnitude of 6.0 might not seem drastically different, but from what we have explained, we know that the difference is actually quite large. This understanding will help us ensure that our engineers can build a proper warehouse.
