Analysis and modelling of mining induced seismicity
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Earthquakes and other seismic events are known to have catastrophic effects on people and property. These large-scale events are almost always preceded by smallerscale seismic events called precursors, such as tremors or other vibrations. The use of precursor data to predict the realization of seismic hazards has been a long-standing technical problem in different disciplines. For example, blasting or other mining activities have the potential to induce the collapse of rock surfaces, or the occurrence of other dangerous seismic events in large volumes of rock. In this study, seismic data (T4) obtained from a mining concern in South Africa were considered using a nonlinear time series approach. In particular, the method of surrogate analysis was used to characterize the deterministic structure in the data, prior to fitting a predictive model. The seismic data set (T4) is a set of seismic events for a small volume of rock in a mine observed over a period of 12 days. The surrogate data were generated to have structure similar to that of T4 according to some basic seismic laws. In particular, the surrogate data sets were generated to have the same autocorrelation structure and amplitude distributions of the underlying data set T4. The surrogate data derived from T4 allow for the assessment of some basic hypotheses regarding both types of data sets. The structure in both types of data (i.e. the relationship between the past behavior and the future realization of components) was investigated by means of three test statistics, each of which provided partial information on the structure in the data. The first is the average mutual information between the reconstructed past and futures states of T4. The second is a correlation dimension estimate, Dc which gives an indication of the deterministic structure (predictability) of the reconstructed states of T4. The final statistic is the correlation coefficients which gives an indication of the predictability of the future behavior of T4 based on the past states of T4. The past states of T4 was reconstructed by reducing the dimension of a delay coordinate embedding of the components of T4. The map from past states to future realization of T4 values was estimated using Long Short-Term Recurrent Memory (LSTM) neural networks. The application of LSTM Recurrent Neural Networks on point processes has not been reported before in literature. Comparison of the stochastic surrogate data with the measured structure in the T4 data set showed that the structure in T4 differed significantly from that of the surrogate data sets. However, the relationship between the past states and the future realization of components for both T4 and surrogate data did not appear to be deterministic. The application of LSTM in the modeling of T4 shows that the approach could model point processes at least as well or even better than previously reported applications on time series data.
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