A Percolation Model for Induced Seismicity: An Avalanche Burst Model for Classic b-Value Seismicity.

In the interest of being able to reproduce the kinds of fracture networks produced during hydraulic fracking, we use percolation models which, near criticality, seem to produce the kinds of networks consistent with those produced during fracking. To better approximate the natural fracture network present in the deep sediment during fracking, we apply a modified invasion percolation algorithm on a correlated lattice, coupled with an avalanche-based model for bursts to reproduce the characteristic b-value seismicity and spatial distribution of earthquakes resulting from fracking. We also analyze a number of the properties observed in the burst statistics of the model. One such property is the fractal dimension D­_f. Using a box counting method, we find that as the cluster size increases, the fractal dimension, D_f asymptotically approaches the value 1.9. We also analyze the shortest distance between sites of the clusters, and find that the scaling exponent is characterized by the D_min=1.21.

Next we examine the nature of the burst clusters produced. We find that if the burst threshold is far from the critical value, the bursts are numerous but small in magnitude. As the burst threshold approaches the critical value P=0.5, the bursts become scale invariant making increasingly larger bursts more common. We compare our results to data from earthquakes both in tectonic and volcanic regimes, and for regions of induced seismicity. We find that tectonic earthquakes are apparently characterized by near-critical behavior (P~0.5), whereas regions of induced and volcanic seismicity are characterized by occupation probabilities P<0.5.