The Origin of the Earthquake Inter-Event Time Distribution

Sarah Touati, Mark Naylor, Ian Main

Why inter-event time distributions?

• They characterise the temporal behaviour of a seismic region

• Understanding them will afford insight into seismic patterns

• Recognising and understanding their features will allow validation of physical models of seismicity

Universal gamma distribution?

Corral, A., PHYSICAL REVIEW E 68, 035102(R) (2003)

Examples of IET distributions

ETAS model• Statistical point-process model for earthquake

occurrence• Inspired by population models in epidemiology

immigration birth death

spontaneous events

triggering of events

not used

ETAS model

)|( tHt

ttip

i

MM

i

i

ctteK

:

)(

)(

10

time

Magnitudes follow Gutenberg-Richter distribution and are independent of history

ETAS IET distributions

Origin of the IET distribution

time

correlated

uncorrelated

Origin of the IET distribution

μ = 0.0029 μ = 0.74 μ = 11

Rescaled ETAS IET distributions

Conclusions

• Earthquake inter-event times follow a mixture distribution, not a gamma distribution– Intervals between correlated events are gamma-

distributed– Intervals between uncorrelated events are

Poisson-distributed

• The distribution cannot be fully universal