Evolving magnitude-frequency distributions during the Guy-Greenbrier (2010-11) induced earthquake sequence: Insights into the physical mechanisms of b-value shifts and large-magnitude curvature

Abstract:

In 2010-11, a sequence of earthquakes occurred on an unmapped basement fault near Guy, Arkansas. The events are likely to have been triggered by a nine month period of wastewater disposal during which 4.5x10⁵ m² of water was injected at two nearby wells. Magnitude-frequency distributions (MFD) for the induced sequence show two interesting properties: (i) a low Gutenberg-Richter (GR) b-value of ~0.8 during injection, increasing to 1.0 post-injection (ii) and downward curvature of the MFD at the upper magnitude limit. We use a coupled model of injection-triggering and earthquake rupture to show how the evolving MFD can be understood in terms of an effective stress increase on the fault, which arises from overpressuring and strength reduction.

Reservoir simulation is used to model injection into a horizontally extensive aquifer that overlies an impermeable basement containing a single permeable fault. Earthquake triggering occurs when the static strength, reduced by the modeled pressure increase, satisfies a Mohr-Coulomb criterion. Pressure evolution is also incorporated in a model of fault rupture, which is based on an expanding bilateral crack approximation to quasidynamic rupture propagation and static/dynamic friction evolution. An earthquake sequence is constructed as an ensemble of triggered ruptures for many realizations of a heterogeneous fractal stress distribution.

During injection, there is a steady rise in fluid pressure on the fault. In addition to its role in triggering earthquakes, rising pressure affects the rupture process by reducing the dynamic strength relative to fault shear stress; this is equivalent to tectonic stress increase in natural seismicity. As mean stress increases, larger events are more frequent and this is reflected in a lower b-value. The largest events, however, occur late in the loading cycle at very high stress; their absence in the early stages of injection manifests as downward curvature in the MFD at large magnitudes.