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
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
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: