Gutenberg–Richter law

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 ${\displaystyle N}$ and ${\displaystyle M}$.

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.