Thursday, February 4, 2010

A Simple Markov Process for Earthquakes

There is a simple Markov process which agrees very well with the linear fit for the 2009 earthquake data. The states in the transition diagram below are labeled 1 through 3. In a given interval of time a fraction of the states, r, will produce earthquakes while the remainder will undergo transition to the next higher state. The exceptions are the initial and final states. The first state will return to itself while all of the last will return to the original state. The transition matirx for the process is T. If one knows the numbers for each state one can then calculate what the changes will be.

The length of the chain can be extended to any number of states. If one chooses 15 states to correspond to the histogram intervals in the table computed for the fit to the 2009 earthquakes then the number of earthquakes for the given interval of time will be r times the number occupying each state for all except the last. The numbers agree surprisingly well for such a simple model. The model is not sophisticated enough to explain a peak in the earthquake distribution.

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