Moment tensors and micromechanical models

Abstract

A numerical modelling approach that simulates cracking and failure in rock and the associated seismicity is presented and a technique is described for quantifying the seismic source mechanisms of the modelled events. The modelling approach represents rock as an assemblage of circular particles bonded together at points of contact. The connecting bonds can break under applied stress forming cracks and fractures in the modelled rock. If numerical damping is set to reproduce realistic levels of attenuation, then energy is released when the bonds break and seismic source information can be obtained as damage occurs. A technique is described by which moment tensors and moment magnitudes can be calculated for these simulated seismic events. The technique basically involves integrating around the source and summing the components of force change at the surrounding particle contacts to obtain the elements of the moment tensor matrix. The moment magnitude is then calculated from the eigenvalues of the moment tensor. The modelling approach is tested by simulating a well-controlled experiment in which a tunnel is excavated in highly stressed granite while microseismicity is recorded. The seismicity produced by the model is compared to the actual recorded seismicity underground. The model reproduces the spatial and temporal distribution of seismicity observed around the tunnel and also the magnitudes of the events. A direct comparison between the actual and simulated moment tensors is not performed due to the two-dimensional nature of the model, however, qualitative comparisons are presented and it is shown that the model produces intuitively realistic source mechanisms. The ability to obtain seismic source information from the models provides a unique means for model validation through comparison with actual recorded seismicity. Once it is established that the model is performing in a realistic manner, it can then be used to examine the micromechanics of cracking, failure and the associated seismicity and to help resolve the non-uniqueness of the geophysical interpretation. This is demonstrated by examining in detail the mechanics of one of the modelled seismic events by observation of the time dependence of the moment tensor and by direct examination of the particle motions at the simulated source.