1 Purpose
The classification of seismic signals of volcanic origin is an important task in monitoring active volcanoes. The number and size of certain types of seismic events usually increase before periods of volcanic crisis and can be used to quantify the volcanic activity.
We are using a system based upon a combination of different methods. To enable a first robust event detection in the continuous data stream different modules are implemented in the real time system Earthworm. Among those software modules are classical trigger algorithm like STA/LTA and cross-correlation master event matching which is also used to detect different classes of signals. Furthermore an additional module is implemented in the real time system to compute continuous activity parameters. Here the real time seismic amplitude measurement (RSAM) [1].
For the HMM-based classification module valuable short time features are extracted fom the continuous data stream. The Hidden Markov Model Toolkit (HTK) which is mainly intended for speech recognition is used for building-up a classifier for volcanic events from an individual data example. By using this 'Learning-while-recording' approach thus allowing to be independent from previously marked training sets and allowing for the fast build-up of a volcanic signal classification scheme as early as events have been identified.
- Fig. 1: Sketch of a HMM generating a seismogram with three states. The observed feature vector ot1 is generated from the observation probability b1(ot1). The model stays in the first state with the transition probability a11 or changes in the next state with the transition probability a12.
- Fig 2: The overall output distribution of the unlabeled data stream is modelled by mixtures of Gaussians. The mean value of each Gaussian is indicated by a diamond. The event model is obtained by tracking the features extracted from the reference waveform in the feature-space. The Gaussians passed are indicated by non-white diamonds.
- Fig 3: The background model is created as a parallel connection of all mixture component extracted from the overall output distribution.
1.1 Theoretical background
The classification process works in two steps: First of all a valuable set of wave field parameters for characterizing different source types of seismic sources is extracted in a sliding window from an unknown continuous data stream. Among those features are polarization, spectral as well as time-domain attributes. The second step is the classification: based on the features extracted before, the object is associated with one category.
For the classification task we use context dependent hidden Markov models [Fig. 1] which represent a stochastic description observations and hence are able to handle the great variabilities of volcano-seismic signal characteristics. If there is a model Λ and a sequence of observations O it is possible to calculate the probability that the sequence O has been generated by the model Λ.
A detailed description of hidden Markov models and its application can be found in Ohrnberger [2] and Beyreuther et al. [3].
The training procedure can be described as follows: First, we extract a valuable set of wave field parameters in a sliding window fashion from an unlabeled. In the following these parameters are used to extract a fixed number of clusters in the feature space. Each cluster corresponds to a mixture component of the overall output distribution which is modeled by Gaussian mixture densities densities [Fig. 2].
An HMM for the background is created as a parallel connection of M states, one for each of the Gaussians extracted before [Fig. 3]. In the following the sequence of features extracted from the reference waveform is modelled by tracking the features in the feature space [Fig. 2]. Thus the number of states as well as a first estimate of observation and transition probabilities is obtained. The output distribution for each state corresponds to the mean and the covariance of the associated cluster [Fig. 4]. The duration of each state (self transition aii) is estimated from the number of successive time steps the feature is associated to that specific cluster.
1.2 Literature
[1] Endo, E.T. and T. Murray, 1991. Real-time Seismic Amplitude Measurement (RSAM): a volcano monitoring and prediction tool. Bull. of Volcanol., 53(7), 533-545.
[2] Ohrnberger M., 2001. Continous Automatic Classification of Seismic Signals of Volcanic origin at Mt. Merapi, Java, Indonesia. PhD thesis, Institut für Geowissenschaften, Universität Postdam.
[3] Beyreuther, M., Carniel, R. and J. Wassermann, 2008. Continuous Hidden Markov Models: Application to automatic earthquake detection and classification at Las Canadas caldera, Tenerife. J. Volcanol. Geotherm. Res., 176, 513-518.