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 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:G_c=G_0 (1-(v ̇_r W)/(v_s^2 ) 1/(〖Aα〗_s^P ))where G_c is the fracture energy, G_0 the steady-state energy release rate, v_s the S wave speed, v_r the rupture speed, v ̇_r=dv_r/dt the rupture acceleration, α_s=√(1-(v_r/v_s )^2 ), A = π and P = 3 for rupture acceleration and A = 1.2π and P = 2.6 for rupture deceleration. The steady energy release rate is limited by rupture width as G_0=〖∆τ〗^2 W/πμ, where ∆τ is the stress drop (spatially smoothed over a length scale smaller than W) and μ the shear modulus. If G_c is a constant and exactly balanced by G_0, the rupture can in principle propagate steadily at any speed. If G_c increases with rupture speed, steady ruptures have a well-defined speed and are stable. When G_c≠G_0, 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 2D unbounded media and unbounded fault in 3D, but emerges in 2D 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 “super-cycles” 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.

Characteristics of earthquake ruptures and dynamic off-fault deformation on propagating faults

“…Firstly, the counterclockwise bending behavior of RT2 corresponds to the one of a wing crack (tension fracture) in laboratory experiments (illustrated in Fig. 1d; e.g., Cooke, 1997;Willemse and Pollard, 1998). Secondly, we record a significant amount of opening for RT2, which varies in the range of 50 %-100 % compared to the shear component of RT2.…”

“…Secondly, we record a significant amount of opening for RT2, which varies in the range of 50 %-100 % compared to the shear component of RT2. This is another similarity to a classical tension fracture, which is typically an opening-mode crack (Willemse and Pollard, 1998). Nonetheless, the dominant shear component alludes to a transition or an approximation to a wing crack rather than the development of a classical wing crack.…”

“…Nonetheless, the dominant shear component alludes to a transition or an approximation to a wing crack rather than the development of a classical wing crack. Such classical wing cracks are typically found in laboratory experiments and as subsidiary cracks in nature (e.g., Lee et al, 2016;Birren and Reber, 2019;Mutlu and Pollard, 2008;Willemse and Pollard, 1998). In the following we briefly attempt to link our model observations with the theory of wing cracks and normal and reverse faults in nature.…”

Does a damaged fault zone mitigate the near-field landslide risk during supershear earthquakes?—Application to the 2018 magnitude 7.5 Palu earthquake.

“…However, previous studies modeling supershear rupture in a LVFZ were based on 2D 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, 2019).…”

“…On the other hand, waves trapped by a LVFZ can amplify ground motion (Spudich & Olsen, 2001;Ben-Zion et al, 2003;Peng et al, 2003;Huang et al, 2014;Kurzon et al, 2014 els on elongated faults (Weng & Ampuero, 2019). The fault bisects a LVFZ with uniform properties, embedded in an unbounded, homogeneous host rock medium ( Figure 1a).…”