Mining-Induced Seismicity Associated with Self-Similar Propagation of Sliding Zones

Mining operations near faults can induce sliding zones which grow further driven by the excess of the shear stress over friction at the loci of initiation. To model interaction between the sliding zones we assume, guided by the Guttenberg-Richter law, that the distribution of their sizes is self-similar and the self-similarity is maintained in the process of their growth. We show that the latter is only possible if the sliding zones are coplanar and that the exponent and the prefactor of the distribution function are uniquely determined. The addition of a new sliding zone does not change the distribution but rather increases the upper cut-off. This happens either by instantaneous growth of the added zone to the maximum size producing the strongest microseismic event or by initiating a cascade of intermediate crack growth producing a series of smaller events. The found energy distribution permits risk assessment based on the determination of the probability of hazardous events. The model parameters can be determined by observing statistical moments of the energy distribution combined with the determination of fault deformation from its influence on the approaching excavations by displacement monitoring.