Modelling the Dynamic Relationship Between Mining Induced Seismic Activity and Production Rates, Depth and Size: A Mine-Wide Hierarchical Model

The dynamic properties of mining induced seismic activity with respect to production rate, depth and size are studied in seven orebodies in the same underground iron ore mine. The objective is to understand the relationship between the measured seismic activity and the: seismic decay time, planned production rate, production size and mining depth. This relationship is the first step to individually customise the production rate for each orebody in the mine, make short-term predictions of future seismicity given planned productions, and to find out in what way the available predictors affect the seismicity. The seismic response with respect to the dependent variables is parametrised and the estimated decay times for each orebody, which are of particular interest here, are compared. An autoregressive model is proposed to capture the dynamic relationship between the induced seismic activity, the current production rate and the past seismic activity. Bayesian estimation of the parameters is considered and parameter constraints are incorporated in the prior distributions. The models for all orebodies are tied together and modelled hierarchically to capture the underlying joint structure of the problem, where the mine-wide parameters are learnt together with the individual orebody parameters from the observed data. Comparisons between the parameters from the hierarchical model and independent models are given. Group-level regressions reveal dependencies on size and mining depth. Model validation with posterior predictive checking using several discrepancy measures could not detect any model deficiencies or flaws. Posterior predictive intervals are evaluated and inference of model parameters are presented.