Modeling Induced Seismicity as Invasion Percolation on a Correlated Lattice.

Abstract:

We introduce a loopless site invasion percolation model(LSIP) using fractional Brownian statistics to describe the long range correlations between sites in porous media.Though induced seismicity seems to be well described as a critical phenomena, in percolation models with independent, random site strengths, criticality is described by a single set of scaling exponents. We show how multiple cluster scaling power laws can result by changing the generalized Hurst parameter controlling site correlations. This allows us to account for variations in the observed Gutenber-Richter b-values observed from induced seismicity. Further, in previous correlated invasion percolation studies, fractal behavior was found in only a subset of the range of Hurst exponent, H. Because of our loopless condition keeping clusters from becoming compact(D_f →2), we find fractal behavior persists for the entire range of Hurst exponent.