JOURNAL OF THE BALKAN GEOPHYSICAL SOCIETY, Vol. 2, No 3, August 1999, p. 75-83, 3 figs.
A discrete Markov model for earthquake occurrences
in Southern Alaska and Aleutian Islands
Theodoros M. Tsapanos and Alexandra A. Papadopoulou
Aristotle University of Thessaloniki,Geophysical Laboratory, 54006 Thessaloniki, Greece. E-mail: tsapanos@ geo.auth.gr
Aristotle University of Thessaloniki, Department of Mathematics, Operations Research Section, 54006 Thessaloniki, Greece.
( Received 21 January 1999; accepted 15 August 1999 )
Abstract: A large number of stochastic models are currently available for the earthquake occurrence. The Markov model is applied to data from the area of southern Alaska (peninsula of Alaska and Shumagin islands) and the Aleutian Islands in order to investigate for great earthquake occurrence in space and time. The model defines a process in which successive state occupancies are governed by the transition probabilities of the Markov process. Each element pij , of the transition probability matrix represents the probability that the state is j at the time t+1, given that the state was i at the time t, and the probability can be written as: pij=Prob[Xt+1=j | Xt=i]. The area of southern Alaska and Aleutian Islands is divided in three seismic zones that are defined as states in the present study. Thus the earthquakes, which migrate from zone to zone, i.e. from state to state, carry with them the number of the zone in which they occurred. In this way we can examine the genesis of the earthquakes in the investigated area in a quantitative way, through the transition probabilities of the defined process. A pattern for an east-west migration, in space and in time, of large (M>7.0) earthquakes is found. A two-state Markov model is applied in the three zones, which suggests periods of activity and quiescence. The application of this model makes it possible to establish whether in a specific time period a state is in an active or an inactive period and this is useful for seismic hazard analysis.
Key Words: Markov Model, Transition Probability, East-west Pattern, Alaska and Aleutian Islands.