Seismic hazard estimation using databases with bimodal frequency-magnitude behaviour

Many underground mines experience seismic events associated with rock mass failure which can be of sufficient magnitude to pose a significant hazard to operations. Probabilistic seismic hazard assessments are typically performed assuming a Gutenberg-Richter distribution for the frequency-magnitude relation for which the parameters are obtained from a best fit to the data. This distribution assumes self-similar data above the magnitude of completeness but this is not always valid. The breakdown in self-similarity can occur when there are multiple superimposed seismic sources, or when there are artificial noise sources such as orepasses and underground crushers. This paper introduces an alternative parametric technique to decompose a bimodal frequency-magnitude relation into two sub-distributions. The composite distribution method assumes that two separate distributions are underlying the observed frequency-magnitude behaviour. This assumption was tested with respect to a single Gutenberg-Richter model to describe frequency-magnitude behaviour. The hypercube optimisation algorithm was used to solve the parameters of the two superimposed distributions while minimising the residual sum of squares for the fit compared to the observed data. The mXrap software was used to implement the method at multiple underground mines for specific volumes and for grid-based analysis. The results show that locally, the seismic hazard can be severely underestimated if a single Gutenberg-Richter model is assumed but this can be improved with the composite distribution method.