Simulating Induced Earthquakes in Complex Fault Systems
Authors: Im Kyungjae , Avouac Jean-Philippe , Kim Taeho , Li Linxuan 
Published: August 2024

Much progress has recently been made in the development of stress-based models for forecasting induced earthquakes. Models based on a point-source representation of earthquake nucleation can already be used to estimate seismicity rates. Forecasting magnitudes with stress-based models remains a challenge that requires taking fault finite size and network geometry into account. Quake-DFN, an open-source earthquake simulator, was developed to address this challenge. It allows simulating sequences of earthquakes in a 3-D Discrete Fault Network governed by rate and state friction, a phenomenological law established based on laboratory observations. Our simulation method aligns with the widely used quasi-dynamic earthquake simulators, but it also has the unique capability to simulate realistic discrete fault geometry and inertial overshoot effect. Quake-DFN was benchmarked against three publicly available simulation results: (1) the rupture of a planar fault with uniform prestress, (2) the propagation of a rupture across a stepover separating two parallel planar faults, and (3) a branch fault system with a secondary fault splaying from a main fault. Next, we explored the factors that determine the magnitudes of injection-induced earthquakes for various fault geometries and loading mechanisms. Firstly, we investigated a single planar fault system. Depending on the initial state, the simulations demonstrate both self-arrested ruptures with a log-linear evolution of maximum magnitude with injection volume and runaway ruptures where the entire fault ruptured early stage. We showed that these behaviors can be theoretically explained with fracture mechanics. Using the same geometry, we additionally conduct simulations with frictional heterogeneity and find that simple heterogeneity patterns can result in a Gutenberg-Richter-like magnitude distribution, making the earthquake sequence more realistic and potentially allowing us to investigate the origin of the magnitude distribution. We then test a slightly more complex fault system – a uniformly distributed discrete faults. In this system, weakly interacting small faults are distributed with different initial states corresponding to Dietrich's model (1994), a widely used earthquake model in induced earthquake studies. We find some inherent assumptions in the Dieterich model (e.g., all faults are critically stressed) may lead to a biased interpretation of induced earthquakes. Lastly, we conducted simulations with varied initial states using a fault network and stress field similar to the one that was activated during the 2011 Prague, Oklahoma, earthquake sequence. The simulations produce realistic earthquake sequences, and a few simulations successfully reproduce the foreshock-mainshock pattern observed in the actual earthquake sequence. We note that Quake-DFN can easily be coupled (one-way) with existing geomechanical models and, hence, can further accommodate inhomogeneous permeability structures. Quake-DFN uses laboratory-measured friction parameters and further allows exploring the uncertainty of laboratory measurements by simulating a wide range of parameter space due to its low computational cost. These examples show that Quake-DFN is a useful tool to forecast a large variety of earthquake sequences and, most importantly, magnitudes induced by a fluid injection near a known fault system.