Richter magnitude scale

The Richter magnitude test scale (or more correctly local magnitude ML scale) assigns a single number to quantify the size of an earthquake. It is a base-10 logarithmic scale obtained by calculating the logarithm of the combined horizontal amplitude of the largest displacement from zero on a seismogram. So, for example, an earthquake of magnitude 5 is ten times greater than one of magnitude 4 and an earthquake of magnitude 8 is 10(8-4) or 10000 times greater than one of magnitude 4.

Related Topics:
Earthquake - Logarithmic scale - Amplitude - Seismogram

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However, the energy of an earthquake is proportional to the square root of the cube of the amplitude. So each step of the Richter scales has an energy 103/2 (~ 31.6) times that of the previous step. So a magnitude 9 has 10,000 times the amplitude of a magnitude 5, but a million times more energy.

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The diminution of amplitude due to distance between the earthquake epicenter and the seismometer is corrected for by subtracting the common logarithm of the expected amplitude of a magnitude 0 event at that distance. This correction for distance is intended to make the local magnitude an absolute measure of earthquake size.

Related Topics:
Epicenter - Common logarithm

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:M = log_{10}A + 3 log_{10}(8 Delta t - 2.92) where A is amplitude in millimeters and t is time in seconds.

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