Bizzarri, Andrea

Earthquake prediction, no matter what the timescale, has been and continues to be a contentious subject and it is indubitably a prominent challenge for modern seismology and earthquake physics. Indeed, few natural events can have the catastrophic consequences of earthquakes (earthquakes today accounts for about 60 % of natural fatalities). A physical description of earthquake represents an amenable approach to the prediction, but it suffers of some limitations, basically due to the notorious ignorance about the initial state of a given fault and about the physical law controlling its traction evolution. Independently on those intrinsic, epistemic limitations, the concept of the earthquake recurrence, based upon the idea of the cyclic (or characteristic) earthquake, has been often invoked to describe (and thus to predict) subsequent instability events on a seismogenic structure. In this paper, by using the simplest analog fault model, the one–degree–of–freedom mass–spring system, we quantitatively show that the concepts of the recurrence time and the earthquake cycle have limitations (even not meaningless). We will discuss in a compendious synopsis all the possible physical mechanisms which can dramatically affect the recurrence time. Our conclusions emphasize again that the competing mechanisms potentially occurring during faulting, even in the simplest and idealized condition of an isolated fault, can significantly complicate the regular cyclicity of earthquakes predicted by the analog fault system. These conclusions can contribute to the debate about the role of the physical modelling of earthquakes in the contest of seismic hazard assessment.

The introduction of the linear slip–weakening friction law permits the solution of the elasto–dynamic equation for a rupture which develops on a fault, by removing the singularity in the components of stress tensor, thereby ensuring a finite energy flux at the crack tip. With this governing model, largely used by seismologists, it is possible to simulate a single earthquake event but, in absence of remote tectonic loading, it requires the introduction of an artificial procedure to initiate the rupture, i.e, to reach the failure stress point. In this paper, by studying the dynamic rupture propagation and the solutions on the fault and on the free surface, we systematically compare three conceptually and algorithmically different nucleation strategies widely adopted in the literature: the imposition of an initially constant rupture speed, the introduction of a shear stress asperity, and the perturbation to the initial particle velocity field. Our results show that, contrarily to supershear ruptures which tend to “forget” their origins, subshear ruptures are quite sensitive to the adopted nucleation procedure, which can bias the runaway rupture. We confirm that that the most gradual transition from imposed nucleation and spontaneous propagation is obtained by initially forcing the rupture to expand at a properly chosen, constant speed (0.75 times the Rayleigh speed). We also numerically demonstrate that a valid alternative to this strategy is an appropriately smoothed, elliptical shear stress asperity. Moreover, we evaluate the optimal size of the nucleation patch where the procedure is applied; our simulations indicate that its size has to equal the critical distance of Day (1982) in case of supershear ruptures and to exceed it in case of subshear ruptures.

A rate- and state-dependent governing law with temperature-dependent constitutive parameters is considered on the basis of laboratory inferences. We model the whole seismic cycle of a homogeneous fault obeying to such a law by adopting a spring-slider dashpot fault analog model. We show that the variations of the parameter a (accounting for the so-called direct effect) with the temperature cause the system to enter, at high speeds, in a conditionally stable regime and also in a velocity strengthening regime. Although we do not observe the complete cessation of slip we can see a severe reduction of the degree of the instability of the fault. In particular, the peaks of the sliding velocity are reduced, as well as the developed temperature due to frictional sliding and the released stress during each instability event. Moreover, the recurrence times are reduced of a factor of two with respect to a reference configuration, where the canonical formulation of rate and state friction (with temporally constant parameters) is assumed. The obtained results can help the interpretation of high velocities laboratory experiments and further illuminate the importance of the temperature in the context of seismic hazard assessment.

The determination of the earthquake energy budget remains a challenging issue for Earth scientists, as understanding the partitioning of energy is a key towards the understanding the physics of earthquakes. Here we estimate the partition of the mechanical work density into heat and surface energy (energy required to create new fracture surface) during seismic slip on a location along a fault. Earthquake energy partitioning is determined from field and microstructural analyses of a fault segment decorated by pseudotachylyte (solidified friction-induced melt produced during seismic slip) exhumed from a depth of ~10 km—typical for earthquake hypocenters in the continental crust. Frictional heat per unit fault area estimated from the thickness of pseudotachylytes is ~27 MJ m−2. Surface energy, estimated from microcrack density inside clast (i.e., cracked grains) entrapped in the pseudotachylyte and in the fault wall rock, ranges between 0.10 and 0.85 MJ m−2. Our estimates for the studied fault segment suggest that ~97–99% of the energy was dissipated as heat during seismic slip. We conclude that at 10 km depth, less than 3% of the total mechanical work density is adsorbed as surface energy on the fault plane during earthquake rupture.

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.

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 explore the relationships between the fracture energy density (E_G) and the key parameters characterizing earthquake sources, such as the rupture velocity (v_r), the total fault slip (u_tot), and the dynamic stress drop (Dt_d). We perform several numerical experiments of three‐dimensional, spontaneous, fully dynamic ruptures developing on planar faults of finite width, obeying different governing laws and accounting for both homogeneous and heterogeneous friction. Our results indicate that E_G behaves differently, depending on the adopted governing law and mainly on the rupture mode (pulselike or cracklike, sub‐ or supershear regime). Subshear, homogeneous ruptures show a general agreement with the theoretical prediction of E_G *proportional to* (1 - (v_r/v_S)^2)^(1/2), but for ruptures that accelerate up to supershear speeds it is difficult to infer a clear dependence of fracture energy density on rupture speed, especially in heterogeneous configurations. We see that slip pulses noticeably agree with the theoretical prediction of E_G *proportional to* u_tot^2 , contrarily to cracklike solutions, both sub‐ and supershear and both homogeneous and heterogeneous, which is in agreement with seismological inferences, showing a scaling exponent roughly equal to 1. We also found that the proportionality between E_G and Dt_d^2, expected from theoretical predictions, is somehow verified only in the case of subshear, homogeneous ruptures with RD law. Our spontaneous rupture models confirm that the total fracture energy (the integral of EG over the whole fault surface) has a power law dependence on the seismic moment, with an exponent nearly equal to 1.13, in general agreement with kinematic inferences of previous studies. Overall, our results support the idea that E_G should not be regarded as an intrinsic material property.

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.

The time of occurrence of an earthquake is related to the state of the fault, tectonic loading, and possible triggering mechanisms, and it plays a prominent role in hazard assessment. In this paper we incorporate the effects of wear generation into a seismogenic model. We show that without wear the recurrence time of repeated earthquakes is constant through time and it is controlled by the initial conditions, tectonic loading and constitutive properties, including the presence of pore fluids. Our results indicate that considering the wear development into the fault model dramatically affects the temperature evolution of the fault, the stress release, the developed cosesimic slip and ultimately the duration of the seismic cycle. Moreover, we find that as long as the slipping zone thickness increases, the recurrence time continuously decreases through time. This further complicates the predictability of a subsequent earthquake, even in the simple case of an isolated fault.