Tuesday, December 27, 2011

The Richter Scale

I'm sure most of you have heard what the Richter scale is, but how much do you really know? The Richter scale is a way to rank the magnitude of earthquakes, specifically, it takes the log of the amplitude of the waves measured by a seismograph. All this means is that the Richter scale is actually a base 10 logarithmic scale. A computer (or a person) will take the highest point on a graph of the wave created by an earthquake, and then find its log.
The Richter scale works by taking the log of the highest point (magnitude) of a graph like this.

A seismograph is a simple machine, all it does is move a needle when it feels a vibration. As simple as it is, most seismographs are surprisingly accurate, able to give precise measurements of even the smallest earthquake. The Richter scale has no upper or lower limit, but there are some useful markers to help you get a feel for how the scale is ranked. Anything with a magnitude 2.0 or less is considered a microearthquake, an earthquake so small that you usually wouldn't be able to feel it. Magnitudes of 4.6 or higher are detectable to a seismograph anywhere in the world, and 10+ has never been recorded, but would be catastrophic if it ever did occur. The way the Richter scale is set up, a plus one increase in magnitude corresponds to approximately a 31 fold increase in energy. This means that a magnitude 5 earthquake is much more powerful than a magnitude 4.
The general equation for magnitude of an earthquake is as follows:
M_\mathrm{L} = \log_{10} A - \log_{10} A_\mathrm{0}(\delta) = \log_{10} [A / A_\mathrm{0}(\delta)],\
Where A is the maximum excursion of the Woody-Anderson seismograph, and A0 is based on epicentral distance delta. 

Earthquakes can be extremely destructive.

Though most people are familiar with the Richter scale, it isn't actually the most common scale used to classify earthquakes. Currently, the moment magnitude scale (MMS) is the most common scale. This scale was devised after the Richter scale with the intention of being more accurate, and it is. Like the Richter scale, this scale also measures energy, but it does it differently. MMS measures the seismic moment of an earthquake, basically the rigidity of the earth multiplied by the average amount of slip and the area slipped. The equation for conversion to MMS looks like this:
M_\mathrm{w} = {\frac{2}{3}}\log_{10}M_0 - 10.7,
Where M0 is the magnitude of the seismic moment.

Yet one more earthquake scale still exists, and this one isn't nearly so technical. The Mercalli intensity scale ranks earthquakes based on their effect. This scale ranges from detectable to instruments all the way to catastrophic. While the other scales measure the motion of the earth, the Mercalli scale measures the damage caused, how many building went down, how many live lost, that sort of thing. While this scale isn't very useful to scientists, it certainly has a strong human aspect to it.

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