Non-deterministic dynamics of mining-induced ground oscillations

Abstract

Recordings of ground acceleration induced by M2 seismic event triggered by deep mining are analyzed, in order to confirm the stochastic nature of the process. Three components of ground acceleration were examined: north-south, east-west and vertical. Surrogate data testing was conducted by testing the three hypotheses: the observed data are independent random numbers drawn from some fixed but unknown distribution, the recordings originate from a stationary linear stochastic process with Gaussian inputs and the recordings originated from a stationary Gaussian linear process that has been distorted by a monotonic, instantaneous, time-independent nonlinear function. Results of surrogate data testing indicate that ground acceleration triggered by deep mining belongs to a group of nonlinear systems and stochastic processes with Gaussian distribution of stochastic part. Analysis was conducted by embedding the recorded time series, for each direction, into appropriate embedding space using mutual information method (embedding delay) and false nearest neighbour technique (embedding dimension). Mutual information method resulted in the values of embedding delay of τ = 29, τ = 18 and τ = 12, for each direction, while the false nearest neighbour method indicated that the percentage of false nearest neighbour increases with the increase of embedding dimension, confirming the absence of determinism in the recorded ground acceleration time series. Recorded series were further examined by invoking stationarity and deterministic test, including the calculation of maximal Lyapunov exponent. Deterministic factor κ < 1, relatively large cross-prediction error and a low value of maximal Lyapunov exponent confirm the stochasticity of the mining-induced ground acceleration. This is the first time that recordings of mining-induced seismic events are examined using the nonlinear time series analysis. Moreover, results obtained for the first time emphasize the need of stochastic approach in modelling the mining-induced ground oscillations.