# Online Analysis of Seismic Signals

## Abstract

Seismic signals can be modeled as non-stationary time series. Methods for analyzing non-stationary time series that have been recently developed are proposed in Adak [1], West, et al. [25] and Ombao, et al. [12]. These methods require that the entire series be observed completely prior to analyses. In some situations, it is desirable to commence analysis even while the time series is being recorded. In this paper, we develop a statistical method for analyzing seismic signals while it is being recorded or observed. The basic idea is to model the seismic signal as a piecewise stationary autoregressive process. When a block of time series becomes available, an AR model is fit, the AR parameters estimated and the Bayesian Information criterion (BIC) value is computed. Adjacent blocks are combined to form one big block if the BIC for the combined block is less than the sum of the BIC for each of the split adjacent blocks. Otherwise, adjacent blocks are kept as separate. In the event that adjacent blocks are combined as a Single block, we interpret the observations at those two blocks as likely to have been generated by one AR process. When the adjacent blocks are separate, the observations at the two blocks were likely to have been generated by different AR processes. In this Situation, the method has detected a change in the spectral and distributional parameters of the time series.

Simulation results suggest that the proposed method is able to detect changes in the time series as they occur. Moreover, the proposed method tends to report changes only when they actually occur. The methodology will be useful for seismologists who need to monitor vigilantly changes in seismic activities. Our procedure is inspired by Takanaini [23] which uses the Akaike Information Criterion (AIC). We report simulation results that compare the online BIC method with the Takanami method and discuss the advantages and disadvantages of the two online methods. Finally, we apply the online BIC method to a seismic waves dataset.

## Key words

Non-stationary time series Autoregressive models Akaike information criterion Bayesian information criterion Time-frequency analysis Seismic signals.## Preview

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