Crack to pulse transition and magnitude statistics during earthquake cycles on a self-similar rough fault

Abstract

Faults in nature demonstrate fluctuations from planarity at most length scales that are relevant for earthquake dynamics. These fluctuations may influence all stages of the seismic cycle; earthquake nucleation, propagation, arrest, and inter-seismic behavior. Here I show quasi-dynamic plane-strain simulations of earthquake cycles on a self-similar and finite 10 km long rough fault with amplitude-to-wavelength ratio α = 0.01. The minimum roughness wavelength, λ min , and nucleation length scales are well resolved and much smaller than the fault length. Stress relaxation and fault loading is implemented using a variation of the backslip approach, which allows for efficient simulations of multiple cycles without stresses becoming unrealistically large. I explore varying λ min for the same stochastically generated realization of a rough fractal fault. Decreasing λ min causes the minimum and maximum earthquakes sizes to decrease. Thus the fault seismicity is characterized by smaller and more numerous earthquakes, on the other hand, increasing the λ min results in fewer and larger events. However, in all cases, the inferred b-value is constant and the same as for a reference no-roughness simulation (α = 0). I identify a new mechanism for generating pulse-like ruptures. Seismic events are initially crack-like, but at a critical length scale, they continue to propagate as pulses, locking in an approximately fixed amount of slip. I investigate this transition using simple arguments and derive a characteristic pulse length, L c = λ min /(4π 4 α 2) and slip distance, δ c based on roughness drag. I hypothesize that the ratio λ min /α 2 can be roughly estimated from kinematic rupture models. Furthermore, I suggest that when the fault size is much larger than L c , then most space-time characteristics of slip differ between a rough fault and a corresponding planar fault.

Precursory Slow Slip and Foreshocks on Rough Faults

“…A similar transition from few large ruptures to many smaller ones was found by Heimisson (2020) when increasing k max ; since the amplitude of normal stress perturbations grows with k max (Equation 10), this is consistent with our findings. Similarly, we expect that increasing fault roughness would have the same effect, since Δ σ rms increases with the product of roughness and accrued slip.…”

“…Perhaps the most ubiquitous and best characterized source of heterogeneity is geometrical roughness: faults are fractal surfaces (Brodsky et al., 2016; Candela et al., 2009, 2012; Power & Tullis, 1991; Power et al., 1987, 1988; Sagy et al., 2007). Numerical and theoretical studies have shown that fault roughness has a first‐order effect on rupture nucleation (Tal et al., 2018), as well as propagation and arrest (Dunham et al., 2011; Fang & Dunham, 2013; Heimisson, 2020; Ozawa et al., 2019).…”

Mainshock and Aftershock Sequence Simulation in Geometrically Complex Fault Zones

“…Slip on a rough fault produces an additional shear resistance, which is expressed as where δ is slip and H is the Hurst exponent. Roughness drag enhances pulse‐like ruptures and deviation from the classical elliptic crack (Dieterich & Smith, 2009; Heimisson, 2020), which reduces the stress concentration at the fault tips.…”

“…The pulse‐like ruptures only occur and the effect of roughness drag is only important if the rupture length is larger than λ min /(4 π 4 α 2 ) (Heimisson, 2020). Otherwise, the classical elliptic crack is realized and the stress concentration around the tips is strong.…”

Long-term magnetic anomalies and their possible relationship to the latest greater Chilean earthquakes in the context of the seismo-electromagnetic theory

“…Recently, Tarduno et al (2015) argued that SAMA is being created by a topography structure in the CMB beneath southern Africa. Not only is SAMA linked with global magnetic features such as a geomagnetic dipole moment (e.g., Heirtzler, 2002;Gubbins et al, 2006), it also corresponds to the closer area between the Earth's surface and radiation belt. This proximity allows more charged particles and more disturbances in the magnetic field near the Chilean margin (e.g., Kivelson and Russell, 1995).…”