Bizzarri, Andrea

The single-body mass-spring analog model has been largely used to simulate the recurrence of earthquakes on faults described by rate- and state-dependent rheology. In this paper, the fault was assumed to be governed by the classical slip-weakening (SW) law in which the frictional resistance linearly decreases as the developed slip increases. First, a closed-form fully analytical solution to the 1D elastodynamic problem was derived, expressing the time evolution of the slip and its time derivative. Second, a suitable mechanism for the recovery of stress during the interseismic stage of the rupture was proposed, and this stress recovery was shown quantitatively to make possible the simulation of repeated instabilities with the SW law. Moreover, the theoretical predictions were shown to be compatible with the numerical solutions obtained by adopting a rate and state constitutive model. The analytical solution developed here is, by definition, dynamically consistent and nonsingular. Moreover, the slip velocity function within the coseismic time window found here can be easily incorporated into slip inversion algorithms.

We study how heterogeneous rupture propagation affects the coherence of shear– and Rayleigh–Mach wave fronts radiated by supershear earthquakes. We address this question using numerical simulations of ruptures on a planar, vertical strike–slip fault embedded in a three–dimensional, homogeneous, linear elastic half–space. Ruptures propagate spontaneously in accordance with a linear slip–weakening friction law through both homogeneous and heterogeneous initial shear stress fields. In the 3–D homogeneous case, rupture fronts are curved due to interactions with the free surface and the finite fault width; however, this curvature does not greatly diminish the coherence of Mach fronts relative to cases in which the rupture front is constrained to be straight, as studied by Dunham and Bhat (2008). Introducing heterogeneity in the initial shear stress distribution causes ruptures to propagate at speeds that locally fluctuate above and below the shear–wave speed. Calculations of the Fourier amplitude spectra (FAS) of ground velocity time histories corroborate the kinematic results of Bizzarri and Spudich (2008): 1) The ground motion of a supershear rupture is richer in high frequency with respect to a subshear one. 2) When a Mach pulse is present, its high frequency content overwhelms that arising from stress heterogeneity. Present numerical experiments indicate that a Mach pulse causes approximately an –1.7 high frequency falloff in the FAS of ground displacement. Moreover, within the context of the employed representation of heterogeneities and over the range of parameter space that is accessible with current computational resources, our simulations suggest that while heterogeneities reduce peak ground velocity and diminish the coherence of the Mach fronts, ground motion at stations experiencing Mach pulses should be richer in high frequencies compared to stations without Mach pulses. In contrast to the foregoing theoretical results, we find no average elevation of 5%–damped absolute response spectral accelerations (SA) in the period band 0.05–0.4 s observed at stations that presumably experienced Mach pulses during the 1979 Imperial Valley, 1999 Kocaeli, and 2002 Denali Fault earthquakes compared to SA observed at non–Mach pulse stations in the same earthquakes. A 20% amplification of short period SA is seen only at a few of the Imperial Valley stations closest to the fault. This lack of elevated SA suggests that either Mach pulses in real earthquakes are even more incoherent that in our simulations, or that Mach pulses are vulnerable to attenuation through nonlinear soil response. In any case, this result might imply that current engineering models of high frequency earthquake ground motions do not need to be modified by more than 20% close to the fault to account for Mach pulses, provided that the existing data are adequately representative of ground motions from supershear earthquakes.

Though mode II shear fractures (primarily strike–slip earthquakes) can not only exceed the shear wave speed of the medium, but can even reach the compressional wave speed, steady–state calculations showed that speeds between the Rayleigh and shear wave speeds were not possible, thus defining a forbidden zone. For more than 30 years it was believed that this result in which the rupture jumps over the forbidden zone, also holds for 3–D ruptures, in which mode II and mode III (mainly dip–slip faulting) are mixed. Using unprecedentedly fine spatial and temporal grids, we show that even in the simple configuration of homogeneous fault properties and linear slip–weakening friction law, a realistic 3–D rupture which starts from rest and accelerates to some higher velocity, actually does pass smoothly through this forbidden zone, but very fast. The energy flux from the rupture tip is always positive, even within the so-called forbidden zone, contrary to the 2–D case. Finally, our results show that the width of the cohesive zone initially decreases, then increases as the rupture exceeds the shear wave speed and finally again decreases as the rupture accelerates to a speed of ~ 90% of the compressional wave speed.

We investigate the dynamic traction evolution during the spontaneous propagation of a 3-D earthquake rupture governed by slip-weakening or rate- and state-dependent constitutive laws and accounting for thermal pressurization effects. The analytical solutions as well as temperature and pore pressure evolutions are discussed in the companion paper by Bizzarri and Cocco. Our numerical experiments reveal that frictional heating and thermal pressurization modify traction evolution. The breakdown stress drop, the characteristic slip-weakening distance, and the fracture energy depend on the slipping zone thickness (2w) and hydraulic diffusivity (w). Thermally activated pore pressure changes caused by frictional heating yield temporal variations of the effective normal stress acting on the fault plane. In the framework of rate- and state-dependent friction, these thermal perturbations modify both the effective normal stress and the friction coefficient. Breakdown stress drop, slip-weakening distance, and specific fracture energy (J/m2) increase for decreasing values of hydraulic diffusivity and slipping zone thickness. We propose scaling relations to evaluate the effect of w and w on these physical parameters. We have also investigated the effects of choosing different evolution laws for the state variable. We have performed simulations accounting for the porosity evolution during the breakdown time. Our results point out that thermal pressurization modifies the shape of the slip-weakening curves. For particular configurations, the traction versus slip curves display a gradual and continuous weakening for increasing slip: in these cases, the definitions of a minimum residual stress and the slip-weakening distance become meaningless.

see Abstract Volume

We analyze the coseismic stress redistribution during the seismic sequence of June 17 2000 in South Iceland in which a mainshock (MS 6.6) was followed by three quite large events within few tens of seconds (8, 26 and 30 s respectively) at a distance up to about 90 km. We use this observational case to investigate the possibility of fault interaction by purely transient coseismic stress changes and in particular nearly instantaneous triggering. We compute the stress changes as functions of time in a stratified elastic half space by means of the discrete wavenumber and reflectivity method (Cotton and Coutant, 1997). We evaluate the dynamic stress caused by the mainshock at the three hypocenters of the subsequent events. Our results show that the onset of the last two events is slightly delayed with respect to the arrival time of the second positive peak of Coulomb Failure Function variation, while the first event stroked after the first positive peak. We also analysed the response of a rate- and state-dependent springslider model of fault perturbed by the shear stress and the normal stress variations that we computed as generated by the June 17 2000 mainshock at the three hypocenters. Assuming an initial sliding velocity comparable with tectonic velocity of the region, for the last two events, we obtained failure times close to the observed origin times, provided that the value of the initial effective normal stress is low enough, whereas the 8 s event requires closer to failure initial conditions to be reproduced. The 8 s event might already be close to failure at the time of the mainshock, due to its vicinity to the main event and the subsequent June 21 (MS 6.6) mainshock. Therefore the first aftershock does not provide us a clear evidence of dynamic triggering.

We present a model of seismogenesis on an extended 3-D fault, subject to the external perturbations of coseismic stress changes due to an earthquake occurring on another fault (the causative fault). As an application, we consider the spatio-temporal stress redistribution produced on the Hvalhn´ukur fault by the MS 6.6 2000 June 17 mainshock in the South Iceland Seismic Zone (SISZ). The latter is located nearly 64 kmfrom the causative fault and failed 26 s after the main shock with an estimated magnitudeMw = 5.25 ± 0.25, providing an example of instantaneous dynamic triggering. The stress perturbations are computed by means of a discrete wavenumber and reflectivity code. The response of the perturbed fault is then analysed solving the truly 3-D, fully dynamic (or spontaneous) problem accounting for crustal stratification. In a previous study, the response of the Hvalhn´ukur fault was analysed by using a spring–slider fault model (SS fault model), comparing the estimated perturbed failure time with the observed origin time. In addition to the perturbed failure time, this model can provide numerical estimates of many other dynamic features of the triggered event, which can be compared with available observations—the rupture history of the whole fault plane, its final extent and the seismic moment of the induced event.We show the key differences existing between a mass–spring model and this extended fault model; in particular, we show the essential role of the load exerted by the neighbouring slipping points of the fault. By considering both rate- and state-dependent laws and non-linear slip-dependent law, we show how the dynamics of the 26 s fault strongly depend on the assumed constitutive law and initial stress conditions. In the case of rate- and state-dependent friction laws, assuming an initial effective normal stress distribution that is suitable for the SISZ and consistent with previously stated conditions of instantaneous dynamic triggering of the Hvalhn´ukur fault, we obtain results in general agreement with observations.

We present a physical model that describes the behavior of spontaneous earthquake ruptures dynamically propagating on a fault zone and that accounts for the presence of frictional melt produced by the sliding surfaces. First, we analytically derive the solution for the temperature evolution inside the melt layer, which generalizes previous approximations. Then we incorporate such a solution into a numerical code for the solution of the elastodynamic problem. When a melt layer is formed, the linear slip‐weakening law (initially governing the fault and relying on the Coulomb friction) is no longer valid. Therefore we introduce on the fault a linearly viscous rheology, with a temperature‐dependent dynamic viscosity. We explore through numerical simulations the resulting behavior of the traction evolution in the cohesive zone before and after the transition from Coulomb friction and viscous rheology. The predictions of our model are in general agreement with the data from exhumed faults.We also find that the fault, after undergoing the breakdown stress drop controlled by the slip‐weakening constitutive equation, experiences a second traction drop controlled by the exponential weakening of fault resistance due to the viscous rheology. This further drop enhances the instability of the fault, increasing the rupture speeds, the peaks in fault slip velocity, and the fracture energy density.

We investigate the effects of non-uniform distribution of constitutive parameters on the dynamic propagation of an earthquake rupture. We use a 2D finite difference numerical method and we assume that the dynamic rupture propagation is governed by a rate- and state-dependent constitutive law. We first discuss the results of several numerical experiments performed with different values of the constitutive parameters a (to account for the direct effect of friction), b (controlling the friction evolution) and L (the characteristic length-scale parameter) to simulate the dynamic rupture propagation on homogeneous faults. Spontaneous dynamic ruptures can be simulated on velocity weakening (a < b) fault patches: our results point out the dependence of the traction and slip velocity evolution on the adopted constitutive parameters. We therefore model the dynamic rupture propagation on heterogeneous faults. We use in this study the characterization of different frictional regimes proposed by Boatwright and Cocco (1996) based on different values of the constitutive parameters a, b and L. Our numerical simulations show that the heterogeneities of the L parameter affect the dynamic rupture propagation, control the peak slip velocity and weakly modify the dynamic stress drop and the rupture velocity. Moreover, a barrier can be simulated through a large contrast of L parameter. The heterogeneity of a and b parameters affects the dynamic rupture propagation in a more complex way. A velocity strengthening area (a > b) can arrest a dynamic rupture, but can be driven to an instability if suddenly loaded by the dynamic rupture front. Our simulations provide a picture of the complex interactions between fault patches having different frictional properties and illustrate how the traction and slip velocity evolutions are modified during the propagation on heterogeneous faults. These results involve interesting implications for slip duration and fracture energy.