- Gutenberg–Richter law
seismology, the Gutenberg–Richter law [ B. Gutenberg and C.F. Richter, "Seismicity of the Earth and Associated Phenomena", 2nd ed. (Princeton, N.J.: Princeton University Press, 1954), pages 17-19 ("Frequency and energy of earthquakes").] expresses the relationship between the magnitude and total number of earthquakes in any given region and time period. : or:
* is the number of events in a given magnitude range
* is a magnitude range
* and are constants
The relationship was first proposed by
Charles Francis Richterand Beno Gutenberg. The relationship is surprisingly robust and does not vary significantly from region to region or over time.
The constant "b" is typically equal to 1.0. This means that for every magnitude 4.0 event there will be 10 magnitude 3.0 quakes and 100 magnitude 2.0 quakes. A notable exception is during earthquake swarms when the
b-valuecan become as high as 2.5 indicating an even larger proportion of small quakes to large ones. A b-valuesignificantly different from 1.0 may suggest a problem with the data set; e.g. it is incomplete or contains errors in calculating magnitude. The "roll off" of the b-valueis an indicator of the completeness of the data set at the low magnitude end.
The "a-value" is of less scientific interest and simply indicates the total seismicity rate of the region.
Modern attempts to understand the law involve theories of
self-organized criticalityor self similarity.
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