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.

Rupture, waves and earthquakes

Normally, an earthquake is considered as a phenomenon of wave energy radiation by rupture (fracture) of solid Earth. However, the physics of dynamic process around seismic sources, which may play a crucial role in the occurrence of earthquakes and generation of strong waves, has not been fully understood yet. Instead, much of former investigation in seismology evaluated earthquake characteristics in terms of kinematics that does not directly treat such dynamic aspects and usually excludes the influence of high-frequency wave components over 1 Hz. There are countless valuable research outcomes obtained through this kinematics-based approach, but "extraordinary" phenomena that are difficult to be explained by this conventional description have been found, for instance, on the occasion of the 1995 Hyogo-ken Nanbu, Japan, earthquake, and more detailed study on rupture and wave dynamics, namely, possible mechanical characteristics of (1) rupture development around seismic sources, (2) earthquake-induced structural failures and (3) wave interaction that connects rupture (1) and failures (2), would be indispensable.

Observation of long supershear rupture during the magnitude 8.1 Kunlunshan earthquake

The 2001 Kunlunshan earthquake was an extraordinary event that produced a 400-km-long surface rupture. Regional broadband recordings of this event provide an opportunity to accurately observe the speed at which a fault ruptures during an earthquake, which has important implications for seismic risk and for understanding earthquake physics. We determined that rupture propagated on the 400-km-long fault at an average speed of 3.7 to 3.9 km/s, which exceeds the shear velocity of the brittle part of the crust. Rupture started at sub-Rayleigh wave velocity and became supershear, probably approaching 5 km/s, after about 100 km of propagation.

Seismic Evidence for an Earthquake Nucleation Phase

Near-source observations show that earthquakes initiate with a distinctive seismic nucleation phase that is characterized by a low rate of moment release relative to the rest of the event. This phase was observed for the 30 earthquakes having moment magnitudes 2.6 to 8.1, and the size and duration of this phase scale with the eventual size of the earthquake. During the nucleation phase, moment release was irregular and appears to have been confined to a limited region of the fault. It was characteristically followed by quadratic growth in the moment rate as rupture began to propagate away from the nucleation zone. These observations suggest that the nucleation process exerts a strong influence on the size of the eventual earthquake.