Earthquake

cmartinez

Joined Jan 17, 2007
8,253
upload_2017-9-21_11-35-37.png

Caption reads: International aid for earthquake victims has arrived. Specialized teams from the U.S., Israel, Japan and France arrive in Mexico City to collaborate in search and rescue activities after the earthquake.
 

cmartinez

Joined Jan 17, 2007
8,253
This conversation has left me thinking. Why did the scientists choose a logarithmic scale to describe the strength of an earthquake? Why not linear instead? Is it a matter of perception, or something else?
 

nsaspook

Joined Aug 27, 2009
13,277
This conversation has left me thinking. Why did the scientists choose a logarithmic scale to describe the strength of an earthquake? Why not linear instead? Is it a matter of perception, or something else?
You must know the answer to that already, exponentials. It makes calculations easier.
http://www.montereyinstitute.org/co...P-1-19_RESOURCE/U18_L4_T2_text_container.html
Power (strength of an earthquake) is proportional to amplitude squared with inverse square law for distance.




The monster looks like an 8 on the bad mofo scale.
 
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nsaspook

Joined Aug 27, 2009
13,277
I wish I was better at math. :(
My math skills are poor when compared to some here. Sure, a bit of math is necessary but what you need is a good understanding of physics basics so you can use the first principles method for a qualitative understanding. If you understand the simple basics of area power laws, earthquake waves, earthquake wave transmission and the seismograph from first principles, it's completely logical to use log scales because it's the same reason we use log scales in electronics when we talk about power transmission, gains and losses from sources.

Reason:
It is the only way to get a graph to fit on the paper.
 
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Glenn Holland

Joined Dec 26, 2014
703
This conversation has left me thinking. Why did the scientists choose a logarithmic scale to describe the strength of an earthquake? Why not linear instead? Is it a matter of perception, or something else?
The energy released in an earthquake is related to something called the "moment" which represents the total area of the displacement along the fault line.

A similar analogy is the total heat present in a cup of hot coffee VS the total heat in a 200 gallon hot tub. Accordingly, the ratio of the heat in the tub and the cup would need to be expressed on a logarithmic scale and a thermometer with a linear temperature scale cannot be used to measure the total heat content. Therefore, in addition to the simply measuring the temperature of the water, the total mass of the water must be taken into account.

Likewise, a seismograph using a linear transducer and amplifier cannot directly measure the moment of the fault displacement and the total energy of an earthquake. However, Charles Richter (and others) developed a mathematical relationship between the trace on a seismogram (the vector sum of the ground displacement in the "Far Field") and the actual moment of the fault displacement.

This was a long and tedious empirical process involving a statistical analysis of 1000s of earthquakes in California and Japan. The result was that the total ground displacement measured at a very remote site from a fault has a definite relationship to the total moment of the displacement at the fault itself and it is a logarithmic function rather than a simple linear function.
 
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