Characteristics of Earthquake Cycles: A Cross-Dimensional Comparison of 0D to 3D Numerical Models

High-resolution computer simulations of earthquake sequences in three or even two dimensions pose great demands on time and energy, making lower-cost simplifications a competitive alternative. We systematically study the advantages and limitations of simplifications that eliminate spatial dimensions in quasi-dynamic earthquake sequence models, from 3D models with a 2D fault plane down to 0D or 1D models with a 0D fault point. We demonstrate that, when 2D or 3D models produce quasi-periodic characteristic earthquakes, their behavior is qualitatively similar to lower-dimension models. Certain coseismic characteristics like stress drop and fracture energy are largely controlled by frictional parameters and are thus largely comparable. However, other observations are quantitatively clearly affected by dimension reduction. We find corresponding increases in recurrence interval, coseismic slip, peak slip velocity, and rupture speed. These changes are to a large extent explained by the elimination of velocity-strengthening patches that transmit tectonic loading onto the velocity-weakening fault patch, thereby reducing the interseismic stress rate and enhancing the slip deficit. This explanation is supported by a concise theoretical framework, which explains some of these findings quantitatively and effectively estimates recurrence interval and slip. Through accounting for an equivalent stressing rate at the nucleation size h* into 2D and 3D models, 0D or 1D models can also effectively simulate these earthquake cycle parameters. Given the computational efficiency of lower-dimensional models that run more than a million times faster, this paper aims to provide qualitative and quantitative guidance on economical model design and interpretation of modeling studies.

Two end-member earthquake preparations illuminated by foreshock activity on a meter-scale laboratory fault

The preparation process of natural earthquakes is still difficult to quantify and remains a subject of debate even with modern observational techniques. Here, we show that foreshock activity can shed light on understanding the earthquake preparation process based on results of meter-scale rock friction experiments. Experiments were conducted under two different fault surface conditions before each run: less heterogeneous fault without pre-existing gouge and more heterogeneous fault with pre-existing gouge. The results show that fewer foreshocks occurred along the less heterogeneous fault and were driven by preslip; in contrast, more foreshocks with a lower b value occurred along the more heterogeneous fault and showed features of cascade-up. We suggest that the fault surface condition and the stress redistribution caused by the ongoing fault slip mode control the earthquake preparation process, including the behavior of foreshock activity. Our findings imply that foreshock activity can be a key indicator for probing the fault conditions at present and in the future, and therefore useful for assessing earthquake hazard.

Nucleation of Stick-Slip Instability Within a Large-Scale Experimental Fault: Effects of Stress Heterogeneities Due to Loading and Gouge Layer Compaction

Geodetic observations and large-scale laboratory experiments show that seismic instability is preceded by slow slip within a finite nucleation zone. In laboratory experiments rupture nucleation is studied mostly using bare (rock) interfaces, whereas upper crustal faults are typically filled with gouge. To investigate effects of gouge on rupture nucleation, we performed a biaxial shearing experiment on a 350 mm long saw-cut fault filled with gypsum gouge, at room temperature and a minimum horizontal stress σ 2 = 0.3-5 MPa. The gouge layer was sandwiched between polymethylmethacrylate (PMMA) plates For reference also a fault without gouge was deformed. Strain gauges and Digital Image Correlation were used to monitor the deformation field along the fault zone margins. Stick-slip behavior occurred on both the gouge-filled fault and the PMMA fault. Nucleation of instability on the PMMA fault persistently occurred from one location 2/3 to 3/4 along the fault adjacent to a slow slip zone at the fault end, but nucleation on the gouge-filled fault was more variable, nucleating at the ends and/or at approximately 2/3 along the fault, with precursory slip occurring over a large fraction of the fault. Nucleation correlated to regions of high average fault stress ratio τ/σ n , which was more variable for the gouge-filled fault due to small length scale variations in normal stress caused by heterogeneous gouge compaction. Rupture velocities and slip rates were lower for the gouge-filled fault than for the bare PMMA fault. Stick-slip persisted when σ 2 was lowered and the nucleation zone length increased, expanding from the center to the sample ends before transitioning into instability.