Towards Reconciling Magnitude-Invariant Stress Drops with Dynamic Weakening

The energy budget of earthquakes is a question of significant fundamental and practical interest. Using rate-and-state fault models that produce earthquake sequences, we focus on exploring the breakdown energy portion G of this budget and its relation to stress drop in events over a range of magnitudes. We focus on understanding which models can reproduce the observation that breakdown energy increases with increasing magnitude, but stress drop appears to be magnitude-invariant.

We begin with simulations with pure rate-and-state friction and study how breakdown energy changes with characteristic slip distance L of rate-and-state friction, a parameter often selected based on numerical tractability. We explore values of L ranging two orders of magnitude and calculate breakdown energy G for events with various amounts of slip. The values of G in our simulations are similar to those of natural earthquakes. However, we find nearly-constant values of G across a range of slips for a given L, as well as decreasing G with smaller values of L, as expected based on prior studies. Hence simulations with laboratory-like values of L (0.01-0.1 mm), necessary for producing microseismicity, would result in breakdown energies too small for large events, compared with observations.

We then proceed to a model utilizing dynamic weakening due to thermal pressurization of pore fluid within the fault core. Co-seismic weakening through mechanisms such as thermal pressurization can explain the trend of increasing breakdown energy with magnitude as shown by Rice (JGR, 2006) in a simplified slip model. Our goal is to explore this result in fully dynamic simulations that produce a series of seismic events of different sizes, and investigate whether it can be reconciled with the magnitude-invariant stress drop. We find that our sequences are able to capture the trend of increasing breakdown energy with increasing magnitude while also displaying roughly magnitude-invariant stress drops for a range of the smaller magnitude events. Our current work is directed towards studying the stress drops for the largest, model-spanning events, which can be smaller, larger, or similar depending on the model assumptions.