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Larger earthquakes occur less frequently than smaller ones. The relationship is exponential, ie there are ten times as many magnitude 4 or larger earthquakes in a given time period than magnitude 5 or larger earthquakes. This can be expressed by the Gutenberg-Richter formula

log N = a - b M

where *N* is the number of earthquakes per year exceeding a given
magnitude *M*. The constant a reflects the absolute level of seismicity
in an area, and the value of b has generally been found to be
consistently close to 1.0.

The graph shows the relationship for the UK. A least-squares regression to this data gives the relationship

log N = 3.82 - 1.03 M

Also shown is an alternative doubly-truncated exponential model which gives a curved fit ot the data at the higher magnitude end.

On average, the UK may expect:

- an earthquake of 3.7 ML or larger every 1 year
- an earthquake of 4.7 ML or larger every 10 years
- an earthquake of 5.6 ML or larger every 100 years.

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