Course:MATH110/Archive/2010-2011/003/Teams/Basel/homework 13

Homework 13

The Richter Scale

The Richter scale came into place in order to measure the magnitude, or intensity of an earthquake. Maginitude is measured in units of whole numbers and decimals such as 5.1 or 6.1 (USGS 2009). Due to the logarithmic nature of the Richter Scale, each whole number increase is 10 times the magnitude (Richter 1935).

"...each whole number step in the magnitude scale corresponds to the release of about 31 times more energy than the amount associated with the preceding whole number value." (USGS 2009).

According to Richter (1935), a scale was put into place to measure such amplitudes of an earthquake, and in order to dreive this scale, they had to look at everything from shocks, and the logarithms to which the amplitudes were plotted over a distance.

As Richter (1935) states,

"Curves were drawn through the several points referring to each shock, and were seen to be roughly parallel, as the hypothesis of proportional amplitudes requires. These were then combined into a single curve, parallel to the indi-ddual shock curves, andpassing through an arbitrarily selected point." (Richter 1935).

The journal article then shows charts to back up Richter's hypothesis.

Now lets talk logarithms.

Because when each whole number increases by one, and the magnitude is 10 fold that of the previous, this makes it a log₁₀.

The original equation to measure magnitude of earthquakes according to Richter (1935) was as follows:

$M_{\mathrm {L} }=\log _{10}A-\log _{10}A_{\mathrm {0} }(\delta ),\$

A = the max excursion of the seismograph,
the empirical function A₀ is dependent on the epicentral distance
to obtain M_L value the readings rom all the stations observing the earthquake are averaged out.

(Richter 1935)

Listed Citations

Richter C.F. 1935. An Instrumental Earthequake Magnitude Scale. Bulletin of the Seismological Society of America. Vol. 25.

U. S. Geological Survey General Interest Publication (USGS). 1989-288-913. Available at http://earthquake.usgs.gov/learn/topics/richter.php. [cited on February 3, 2011].