HR: 1330h
AN: S52F-0178    [PDF]
TI: A Hidden Markov Approach to Modeling Interevent Earthquake Times
AU: * Chambers, D
EM: daniel.chambers@bc.edu
AF: Department of Mathematics, Boston College, Chestnut Hill, MA 02467 United States
AU: Ebel, J E
EM: ebel@bc.edu
AF: Weston Observatory, Department of Geology and Geophysics Boston College, Weston, MA 02493 United States
AU: Kafka, A L
EM: kafka@bc.edu
AF: Weston Observatory, Department of Geology and Geophysics Boston College, Weston, MA 02493 United States
AU: Baglivo, J
EM: jenny.baglivo@bc.edu
AF: Department of Mathematics, Boston College, Chestnut Hill, MA 02467 United States
AB: A hidden Markov process, in which the interevent time distribution is a mixture of exponential distributions with different rates, is explored as a model for seismicity that does not follow a Poisson process. In a general hidden Markov model, one assumes that a system can be in any of a finite number k of states and there is a random variable of interest whose distribution depends on the state in which the system resides. The system moves probabilistically among the states according to a Markov chain; that is, given the history of visited states up to the present, the conditional probability that the next state is a specified one depends only on the present state. Thus the transition probabilities are specified by a k by k stochastic matrix. Furthermore, it is assumed that the actual states are unobserved (hidden) and that only the values of the random variable are seen. From these values, one wishes to estimate the sequence of states, the transition probability matrix, and any parameters used in the state-specific distributions. The hidden Markov process was applied to a data set of 110 interevent times for earthquakes in New England from 1975 to 2000. Using the Baum-Welch method (Baum et al., Ann. Math. Statist. 41, 164-171), we estimate the transition probabilities, find the most likely sequence of states, and estimate the k means of the exponential distributions. Using k=2 states, we found the data were fit well by a mixture of two exponential distributions, with means of approximately 5 days and 95 days. The steady state model indicates that after approximately one fourth of the earthquakes, the waiting time until the next event had the first exponential distribution and three fourths of the time it had the second. Three and four state models were also fit to the data; the data were inconsistent with a three state model but were well fit by a four state model.
DE: 7223 Seismic hazard assessment and prediction
DE: 7230 Seismicity and seismotectonics
DE: 7299 General or miscellaneous
SC: Seismology [S]
MN: 2003 Fall Meeting