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

J Martinsson,W Törnman

doi:10.1007/s00024-019-02378-y

Abstract

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.

Highlights

To individually customise the mining operations with respect to the seismic impact in a certain orebody, it is important to understand how mining operations and mining conditions affect the measured seismic activity in the volume
The inference is based on Markov Chain Monte Carlo (MCMC) methods (Gelman et al 2004; Kruschke 2014; Chen et al 2000) providing realistic estimates of credible intervals of parameter values (Martinsson 2012) compared to, e.g., approximations based on derivatives
We found no evidence that would indicate model deficiencies based on posterior predictive checks on standard discrepancy measures, and the actual observations are typical of the replicated observations generated using the model

Summary

Introduction

To individually customise the mining operations with respect to the seismic impact in a certain orebody, it is important to understand how mining operations and mining conditions affect the measured seismic activity in the volume Even though this effect is different for each orebody in the mine considered here (LKAB’s iron-ore mine in Malmberget, northern Sweden) the orebodies are still related. They share the geological features present in the region (Bergman et al 2001; Debras 2010), but they are subjected to the same mining method (sublevel caving) and fairly similar mining conditions (Wettainen and Martinsson 2014). The model parameters and corresponding predictors for each orebody are embedded in the likelihood function in the same way as with non-hierarchical models, while hyperparameters and corresponding group-level predictors are embedded in the prior distributions

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Discussion

Conclusion