In seismology, the Gutenberg–Richter law (GR law) expresses the relationship between the magnitude and total number of earthquakes in any given region and time period of at least that magnitude.

${\displaystyle \!\,\log _{10}N=a-bM}$

or

${\displaystyle \!\,N=10^{a-bM}}$

where

• ${\displaystyle \!\,N}$ is the number of events having a magnitude ${\displaystyle \!\,\geq M}$,
• ${\displaystyle \!\,a}$ and ${\displaystyle \!\,b}$ are constants, i.e. they are the same for all values of N and M.

Since magnitude is logarithmic, this is an instance of the Pareto distribution.

The Gutenberg–Richter law is also widely used for acoustic emission analysis due to a close resemblance of acoustic emission phenomenon to seismogenesis.