The Dynamics of Elongated Earthquake Ruptures

Abstract

The largest earthquakes propagate laterally after saturating the fault's seismogenic width and reach large length‐to‐width ratios L/W. Smaller earthquakes can also develop elongated ruptures due to confinement by heterogeneities of initial stresses or material properties. The energetics of such elongated ruptures is radically different from that of conventional circular crack models: they feature width‐limited rather than length‐dependent energy release rate. However, a synoptic understanding of their dynamics is still missing. Here we combine computational and analytical modeling of long ruptures in three dimension (3D) and 2.5D (width‐averaged) to develop a theoretical relation between the evolution of rupture speed and the along‐strike distribution of fault stress, fracture energy, and rupture width. We find that the evolution of elongated ruptures in our simulations is well described by the following rupture‐tip‐equation‐of‐motion: Gc=G0()1−v̇rWvs2γAαsP where Gc is the fracture energy, G0 is the steady state energy release rate, vs is the S wave speed, vr is the rupture speed, v̇r=dvr/italicdt is the rupture acceleration, and γ/AαsP is a known function of rupture speed. The steady energy release rate is limited by rupture width as G0 = γ∆τ2W/μ, where γ is a geometric factor, ∆τ is the stress drop (spatially smoothed over a length scale smaller than W), and μ is the shear modulus. If Gc is a constant and exactly balanced by G0, the rupture can in principle propagate steadily at any speed. If Gc increases with rupture speed, steady ruptures have a well‐defined speed and are stable. When Gc ≠ G0, the rupture acquires an inertial effect: the rupture‐tip‐equation‐of‐motion depends explicitly on rupture acceleration. This inertial effect does not exist in the classical theory of dynamic rupture in 2‐D unbounded media and in unbounded faults in 3D, but emerges in 2‐D bounded media or, as shown here, as a consequence of the finite rupture width in 3D. These findings highlight the essential role of the seismogenic width on rupture dynamics. Based on the rupture‐tip‐equation‐of‐motion we define the rupture potential, a function that determines the size of next earthquake, and we propose a conceptual model that helps rationalize one type of “supercycles” observed on segmented faults. More generally, the theory developed here can yield relations between earthquake source properties (final magnitude, moment rate function, radiated energy) and the heterogeneities of stress and strength along the fault, which can then be used to extract statistical information on fault heterogeneity from source time functions of past earthquakes or as physics‐based constraints on finite‐fault source inversion and on seismic hazard assessment.

Dilatancy Toughening of Shear Cracks and Implications for Slow Rupture Propagation

“…Their spatial extent ranges from 50 to 100 km, and they are associated to stress drops ranging from 2 to 100 kPa (Michel et al, 2019;Schmidt & Gao, 2010). The stress intensity factor at the tip of such ruptures can be approximated by Hawthorne and Rubin (2013); Weng and Ampuero (2019…”

Does a Damaged‐Fault Zone Mitigate the Near‐Field Impact of Supershear Earthquakes?—Application to the 2018 7.5 Palu, Indonesia, Earthquake

“…We model a dynamic rupture on a vertical strike‐slip fault with finite seismogenic width . For the sake of computational efficiency, we adopt a reduced‐dimensionality (2.5‐D) model, which has been shown to be a successful approximation of 3‐D rupture models on elongated faults (Weng & Ampuero, ). The 2.5‐D approach is derived by isolating a single vertical Fourier mode to account for the constrained depth profile of slip.…”

“…However, previous studies modeling supershear rupture in a LVFZ were based on 2‐D models that ignored the finiteness of the seismogenic depth, while the Palu earthquake rupture has a high length‐to‐width ratio (150‐km length vs. a typical seismogenic depth of 15–20 km for strike‐slip earthquakes). Recent theory and simulations show that the seismogenic width controls the evolution of rupture speed in elongated faults (Weng & Ampuero, ). Thus, the first question we address, in section , is: Can the presence of a LVFZ lead to a steady‐state supershear rupture running at the damaged‐rock wave speed in a long rupture with finite seismogenic width?…”

The State of Pore Fluid Pressure and 3‐D Megathrust Earthquake Dynamics

“…Each pulse consists of multiple rupture fronts, which are caused by reflected waves and head waves generated at structural interfaces and the complex free surface (Huang et al, 2014). We note that pulse-like rupture is here not caused by self-healing due to the dynamics of fault strength (Gabriel et al, 2012), but due to geometric constraints (Weng & Ampuero, 2019). Figure 5 compares slip, PSR, Δτ s , and Vr on the megathrust at the end of the earthquakes in Scenarios 3-6.…”