Universality class for loopless invasion percolation models and a percolation avalanche burst model for hydraulic fracturing

Invasion percolation is a model that was originally proposed to describe growing networks of fractures. Here we describe a loopless algorithm on random lattices, coupled with an avalanche-based model for bursts. The model reproduces the characteristic $b$-value seismicity and spatial distribution of bursts consistent with earthquakes resulting from hydraulic fracturing (``fracking''). We test models for both site invasion percolation and bond invasion percolation. These have differences on the scale of site and bond lengths $l$. But since the networks are characterized by their large-scale behavior, $l\ensuremath{\ll}L$, we find small differences between scaling exponents. Though data may not differentiate between models, our results suggest that both models belong to different universality classes.