SUMMARY
In this paper, we propose a two-step procedure for the automated detection of micro-earthquakes, using single-station, three-component passive seismic data. The first step consists of the computation of an appropriate characteristic function, along with an energy-based thresholding scheme, in order to attain an initial discrimination of the seismic noise from the ‘useful’ information. The three-component data matrix is factorized via the singular value decomposition by means of a properly selected moving window and for each step of the windowing procedure a diagonal matrix containing the estimated singular values is formed. The ${L_2}$-norm of the singular values resulting from the above-mentioned windowing process defines the time series which serves as a characteristic function. The extraction of the seismic signals from the initial record is achieved by following a histogram-based thresholding scheme. The histogram of the characteristic function, which constitutes its empirical probability density function, is estimated and the optimum threshold value is chosen corresponds to the bin that separates the above-mentioned histogram in two different areas delineating the background noise and the outliers. Since detection algorithms often suffer from false alarms, which increase in extremely noisy environments, as a second stage, we propose a new ‘decision-making’ scenario to be applied on the extracted intervals, for the purpose of decreasing the probability of false alarms. In this context, we propose a methodology, based on comparing among autoregressive models estimated both on isolated seismic noise, in addition to the detections resulting from the first stage. The performance and efficiency of the proposed technique is supported by its application to a series of experiments that were based on both synthetic and real data sets. In particular, we investigate the effectiveness of the characteristic function, along with the thresholding scheme by subjecting them to noise robustness tests using synthetic seismic noise, with different statistical characteristics and at noise levels varying from 5 down to –5 dB. Results are compared with those obtained by the implementation of a three-component version of the well-known STA/LTA algorithm to the same data set. Moreover, the proposed technique and its potential to distinguish seismic noise from the useful information through the proposed decision making scheme is evaluated, by its application to real data sets, acquired by three-component short-period recorders that were installed for monitoring the microseismic activity in areas characterized by different noise attributes.
Bias Removal for Goldstein Filtering Power Using a Second Kind Statistical Coherence Estimator
