HR: 0830h
AN: NG41C-0076    [PDF]
TI: Regularized Deterministic Annealing Hidden Markov Models for Identificationand Analysis of Seismic and Aseismic events.
AU: * Granat, R A
EM: granat@aig.jpl.nasa.gov
AF: Jet Propulsion Laboratory, 4800 Oak Grove Dr., Pasadena, CA 91109 United States
AU: Clayton, R
EM: clay@gps.caltech.edu
AF: California Institute of Technology, 1200 California Blvd., Pasadena, CA 91125 United States
AU: Kedar, S
EM: sharon@cobra.jpl.nasa.gov
AF: Jet Propulsion Laboratory, 4800 Oak Grove Dr., Pasadena, CA 91109 United States
AU: Kaneko, Y
EM: ykaneko@gps.caltech.edu
AF: California Institute of Technology, 1200 California Blvd., Pasadena, CA 91125 United States
AB: We employ a robust hidden Markov model (HMM) based technique to perform statistical pattern analysis of suspected seismic and aseismic events in the poorly explored period band of minutes to hours. The technique allows us to classify known events and provides a statistical basis for finding and cataloging similar events represented elsewhere in the observations. In this work, we focus on data collected by the Southern California TriNet system. The hidden Markov model (HMM) approach assumes that the observed data has been generated by an unobservable dynamical statistical process. The process is of a particular form such that each observation is coincident with the system being in a particular discrete state. The dynamics are the model are constructed so that the next state is directly dependent only on the current state -- it is a first order Markov process. The model is completely described by a set of parameters: the initial state probabilities, the first order Markov chain state-to-state transition probabilities, and the probability distribution of observable outputs associated with each state. Application of the model to data involves optimizing these model parameters with respect to some function of the observations, typically the likelihood of the observations given the model. Our work focused on the fact that this objective function has a number of local maxima that is exponential in the model size (the number of states). This means that not only is it very difficult to discover the global maximum, but also that results can vary widely between applications of the model. For some domains which employ HMMs for such purposes, such as speech processing, sufficient a priori information about the system is available to avoid this problem. However, for seismic data in general such a priori information is not available. Our approach involves analytical location of sub-optimal local maxima; once the locations of these maxima have been found, then we can employ a modified optimization procedure based on the application of statistical priors. These priors induce a regularized learning strategy that is designed to avoid the located sub-optimal points in the parameter space. The end result is a robust technique for estimating the optimal parameters of an HMM and thereby the statistical properties of the data. We compare this method to the method of deterministic annealing as applied to hidden Markov models, and discuss a combined algorithm that employs both techniques simultaneously to the advantage of each. We present preliminary results of the technique as applied to the TriNet data set, with particular emphasis on location and recognition of seismic and aseismic signals with a period of minutes to hours.
DE: 3210 Modeling
DE: 7230 Seismicity and seismotectonics
DE: 7294 Instruments and techniques
SC: Nonlinear Geophysics [NG]
MN: 2003 Fall Meeting