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We study the October 30th 2016 Norcia earthquake (MW 6.5) to retrieve the rupture history by jointly inverting seismograms and coseismic GPS displacements obtained by dense local networks. The adopted fault geometry consists of a main normal fault striking N155°and dipping 47° belonging to the Mt. Vettore-Mt. Bove fault system (VBFS) and a secondary fault plane striking N210° and dipping 36° to the NW. The coseismic rupture initiated on the VBFS and propagated with similar rupture velocity on both fault planes. Up-dip from the nucleation point, two main slip patches have been imaged on these fault segments, both characterized by similar peak-slip values (~3 m) and rupture times (~3 s). After the breakage of the two main slip patches, coseismic rupture further propagated southeastward along the VBFS, rupturing again the same fault portion that slipped during the August 24th earthquake. The retrieved coseismic slip distribution is consistent with the observed surface breakages and the deformation pattern inferred from InSAR measurements. Our results show that three different fault systems were activated during the October 30th earthquake. The composite rupture model inferred in this study provides evidences that also a deep portion of the NNE-trending section of the Olevano-Antrodoco-Sibillini (OAS) thrust broke co-seismically, implying the kinematic inversion of a thrust ramp. The obtained rupture history indicates that, in this sector of the Apennines, compressional structures inherited from past tectonics can alternatively segment boundaries of NW-trending active normal faults or break co-seismically during moderate-to-large magnitude earthquakes.

ThedeterminationoftheearthquakeenergybudgetremainsachallengingissueforEarthscientists,asunderstandingthepartitioningofenergyisa keytowardsthe understandingthe physicsofearthquakes. Here weestimatethe partitionofthe mechanical workdensity intoheatandsurfaceenergy (energyrequiredtocreatenewfracturesurface)duringseismicsliponalocationalongafault.Earthquakeenergypartitioningisdeterminedfromfield 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. © 2008 Elsevier B.V. All rights reserved.

Several independent indicators imply a high probability of a great ( M > 8) earthquake rupture of the subduction megathrust under the Mentawai Islands of West Sumatra. The human consequences of such an event depend crucially on its tsunamigenic potential, which in turn depends on unpredictable details of slip distribution on the megathrust and how resulting seafloor movements and the propagating tsunami waves interact with bathymetry. Here we address the forward problem by modelling about 1000 possible complex earthquake ruptures and calculating the seafloor displacements and tsunami wave height distributions that would result from the most likely 100 or so, as judged by reference to paleogeodetic data. Additionally we carry out a systematic study of the importance of the location of maximum slip with respect to the morphology of the fore-arc complex. Our results indicate a generally smaller regional tsunami hazard than was realised in Aceh during the December 2004 event, though more than 20% of simulations result in tsunami wave heights of more than 5 m for the southern Sumatran cities of Padang and Bengkulu. The extreme events in these simulations produce results which are consistent with recent deterministic studies. The study confirms the sensitivity of predicted wave heights to the distribution of slip even for events with similar moment and reproduces Plafker's rule of thumb. Additionally we show that the maximum wave height observed at a single location scales with the magnitude though data for all magnitudes exhibit extreme variability. Finally, we show that for any coastal location in the near field of the earthquake, despite the complexity of the earthquake rupture simulations and the large range of magnitudes modelled, the timing of inundation is constant to first order and the maximum height of the modelled waves is directly proportional to the vertical coseismic displacement experienced at that point. These results may assist in developing tsunami preparedness strategies around the Indian Ocean and in particular along the coasts of western Sumatra.

We study the effect of time-variable normal stress perturbations on a creeping fault which satisfies a velocity-weakening rate- and state-dependent friction law and is slipping at constant speed. We use the spring-block model and include the effect of inertia. To account for the variable normal stress, we use the description introduced by Linker and Dieterich [1992], which links normal stress fluctuations to changes of the state variable. We consider periodic perturbations of the normal stress in time (as caused, for instance, by tides) and compare the behavior for two commonly used friction laws (the “slip” and the “ageing” laws). Their mechanical response is shown to be significantly different for normal stress fluctuations. It could be used to probe these two laws during laboratory friction experiments. We show that there is a resonance phenomenon, involving strong amplification of the shear and velocity response of the interface, when the spring stiffness is modestly above its critical value (or when, at a given stiffness, the normal stress is modestly below its critical value). We show that such an amplification is also observed when periodic fluctuations of the shear loading are considered, making the resonance phenomenon a general feature of the response of a near-critical creeping surface to periodic fluctuations of the external loading. Analytical solutions are based on a linear expansion for low amplitude of normal or shear stress variations and are in very good agreement with numerical solutions. A method to find the evolution of friction in the case of an arbitrary perturbation of the normal stress is also presented. The results show that a creeping fault may be destabilized and enter a stick-slip regime owing to small normal stress oscillations. This may also account for a mechanism for the generation of “creep bursts.” However, these phenomena require very specific parameter ranges to excite the resonance, which may not be met very generally in nature. This study illustrates the importance of the normal stress fluctuations on stable sliding and suggests further friction laboratory experiments.

We study the stress transferred by the June 27, 1988, M = 5.3 and August 8, 1989, M = 5.4 Lake Elsman earthquakes, the largest events to strike within 15 km of the future Loma Prieta rupture zone during 74 years before the 1989 M = 6.9 Loma Prieta earthquake. We find that the first Lake Elsman event brought the rupture plane of the second event 0.3–1.6 bars (0.03–0.16 MPa) closer to Coulomb failure but that the Lake Elsman events did not bring the future Loma Prieta hypocentral zone closer to failure. Instead, the Lake Elsman earthquakes are calculated to have reduced the normal stress on (or “undamped”) the Loma Prieta rupture surface by 0.5–1.0 bar (0.05–0.10 MPa) at the site where the greatest slip subsequently occurred in the Loma Prieta earthquake. This association between the sites of peak unclamping and slip suggests that the Lake Elsman events did indeed influence the Loma Prieta rupture process. Unclamping the fault would have locally lowered the resistance to sliding. Such an effect could have been enhanced if the lowered normal stress permitted fluid infusion into the undamped part of the fault. Although less well recorded, the ML = 5.0 1964 and ML = 5.3 1967 Corralitos events struck within 10 km of the southwest end of the future Loma Prieta rupture. No similar relationship between the normal stress change and subsequent Loma Prieta slip is observed, although the high-slip patch southwest of the Loma Prieta epicenter corresponds roughly to the site of calculated Coulomb stress increase for a low coefficient of friction. The Lake Elsman-Loma Prieta result is similar to that for the 1987 M = 6.2 Elmore Ranch and M = 6.7 Superstition Hills earthquakes, suggesting that foreshocks might influence the distribution of mainshock slip rather than the site of mainshock nucleation.

[1] We perform a retrospective forecast experiment on the 1992 Landers sequence comparing the predictive power of commonly used model frameworks for short-term earthquake forecasting. We compare a modified short-term earthquake probability (STEP) model, six realizations of the epidemic-type aftershock sequence (ETAS) model, and four models that combine Coulomb stress changes calculations and rate-and-state theory to generate seismicity rates (CRS models). We perform the experiment under the premise of a controlled environment with predefined conditions for the testing region and data for all modelers. We evaluate the forecasts with likelihood tests to analyze spatial consistency and the total amount of forecasted events versus observed data. We find that (1) 9 of the 11 models perform superior compared to a simple reference model, (2) ETAS models forecast the spatial evolution of seismicity best and perform best in the entire test suite, (3) the modified STEP model matches best the total number of events, (4) CRS models can only compete with empirical statistical models by introducing stochasticity in these models considering uncertainties in the finite-fault source model, and (5) resolving Coulomb stress changes on 3-D optimally oriented planes is more adequate for forecasting purposes than using the specified receiver fault concept. We conclude that statistical models perform generally better than the tested physics-based models and parameter value updates using the occurrence of aftershocks generally improve the predictive power in particular for the purely statistical models in space and time.

[1] We use the Dieterich (1994) physics-based approach to simulate the spatiotemporal evolution of seismicity caused by stress changes applied to an infinite population of nucleating patches modeled through a rate- and state-dependent friction law. According to this model, seismicity rate changes depend on the amplitude of stress perturbation, the physical constitutive properties of faults (represented by the parameter Aσ), the stressing rate, and the background seismicity rate of the study area. In order to apply this model in a predictive manner, we need to understand the impact of physical model parameters and the correlations between them. First, we discuss different definitions of the reference seismicity rate and show their impact on the computed rate of earthquake production for the 1992 Landers earthquake sequence as a case study. Furthermore, we demonstrate that all model parameters are strongly correlated for physical and statistical reasons. We discuss this correlation, emphasizing that the estimations of the background seismicity rate, stressing rate, and Aσ are strongly correlated to reproduce the observed aftershock productivity. Our analytically derived relation demonstrates the impact of these model parameters on the Omori-like aftershock decay: the c value and the productivity of the Omori law, implying a p value smaller than or equal to 1. Finally, we discuss an optimal strategy to constrain model parameters for near-real-time forecasts.

[1] We discuss the impact of uncertainties in computed coseismic stress perturbations on the seismicity rate changes forecasted through a rate- and state-dependent frictional model. We aim to understand how the variability of Coulomb stress changes affects the correlation between predicted and observed changes in the rate of earthquake production. We use the aftershock activity following the 1992 M7.3 Landers (California) earthquake as a case study. To accomplish these tasks, we first analyze the variability of stress changes resulting from the use of different published slip distributions. We find that the standard deviation of the uncertainty is of the same size as the absolute stress change and that their ratio, the coefficient of variation (CV), is approximately constant in space. This uncertainty has a strong impact on the forecasted aftershock activity if a rate-and-state frictional model is considered. We use the early aftershocks to invert for friction parameters and the coefficient of variation by means of the maximum likelihood method. We show that, when the uncertainties are properly taken into account, the inversion yields stable results, which fit the spatiotemporal aftershock sequence. The analysis of the 1992 Landers sequence demonstrates that accounting for realistic uncertainties in stress changes strongly improves the correlation between modeled and observed seismicity rate changes. For this sequence, we measure a friction parameter Asn � 0.017 MPa and a coefficient of stress variation CV = 0.95.

[1] We model the spatial and temporal pattern of seismicity during a sequence of moderate-magnitude normal faulting earthquakes, which struck in 1997 the Umbria-Marche sector of Northern Apennines (Italy), by applying the Dieterich (1994) rate- and state-dependent constitutive approach. The goal is to investigate the rate of earthquake production caused by repeated coseismic stress changes computed through a 3-D elastic dislocation model in a homogeneous half-space. The reference seismicity rate is assumed time independent, and it is estimated by smoothing the seismicity that occurred in the previous decade without declustering. We propose an analytical relation for deriving the stressing rate directly from the reference seismicity rate. This allows us to perform a tuning of the constitutive parameter Aσ (where A accounts for the direct effect of friction in the rate- and state-dependent model and σ is the effective normal stress) into the Dieterich model through a maximum likelihood method, which yields for this seismic sequence a best fitting value equal to 0.04 MPa. Our computations show that, although seven out of eight main shocks are located in areas of increased rate of earthquake production, numerous aftershocks are located in seismicity shadows. Our simulations point out that the adopted value of Aσ strongly affects the pattern of both seismicity shadow and areas of enhanced rate of earthquake production. We conclude that solely accounting for static stress changes caused by the main shocks of this seismic sequence is not sufficient to forecast the complex spatial and temporal evolution of seismicity.

[1] In the paper ‘‘Earthquake fracture energy inferred from kinematic rupture models on extended faults’’ by E. Tinti, P. Spudich and M. Cocco (Journal of Geophysical Research, 110, B12303, doi:10.1029/2005JB003644, 2005), all values of work density (Wb and We) and total work (Eb) should be corrected by multiplication by a factor 2, because of a systematic error in the calculational subroutine. This correction applies to all the average and point estimates to make them consistent with equation (1). We include here a corrected Table 2. We regret to point out that the breakdown work shown in Figures 7, 8, 9, 10, and 11 must be multiplied by a factor of 2. Because this change is systematic, it does not modify the inferred scaling relationships with seismic moment and slip. JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, B07301, doi:10.1029/2008JB005829, 2008

We attempt to reconcile current understanding of the earthquake energy balance with recent estimates of fracture energy from seismological investigations and surface energy from geological observations. The complex structure of real fault zones suggests that earthquakes in such fault structures are dominated by scale-dependent processes. We present a model for an inelastic fault zone of finite thickness embedded in an elastic crust represented at a macroscopic scale by a mathematical plane of zero thickness. The constitutive properties of the fault zone are governed by physical processes controlling gouge and damage evolution at meso- and micro-scale. However, in order to model and interpret seismological observations, we represent dynamic fault weakening at the macroscopic scale in terms of traction evolution as a function of slip and other internal variables defining a phenomenological friction or contact law on the virtual mathematical plane. This contact law is designed to capture the main features of dynamic fault weakening during earthquake rupture. In this study we assume that total shear traction is friction and corresponds to shear resistance of the whole fault zone. We show that seismological observations, depending on finite and limited wavelength and frequency bandwidth, can only provide an estimate of breakdown stress drop and breakdown work (a more general definition of seismological fracture energy) representing a lower bound of the total intrinsic power of dissipation on the fault zone. We emphasize that geological estimates of surface energy can be compared with seismological estimates of breakdown work only if they are representative of the same macroscopic scale. In this case, it emerges that, contrary to surface energy, seismological breakdown work represents a non-negligible contribution to the earthquake energy budget.

[1] We present a two-stage nonlinear technique to invert strong motions records and geodetic data to retrieve the rupture history of an earthquake on a finite fault. To account for the actual rupture complexity, the fault parameters are spatially variable peak slip velocity, slip direction, rupture time and risetime. The unknown parameters are given at the nodes of the subfaults, whereas the parameters within a subfault are allowed to vary through a bilinear interpolation of the nodal values. The forward modeling is performed with a discrete wave number technique, whose Green's functions include the complete response of the vertically varying Earth structure. During the first stage, an algorithm based on the heat-bath simulated annealing generates an ensemble of models that efficiently sample the good data-fitting regions of parameter space. In the second stage (appraisal), the algorithm performs a statistical analysis of the model ensemble and computes a weighted mean model and its standard deviation. This technique, rather than simply looking at the best model, extracts the most stable features of the earthquake rupture that are consistent with the data and gives an estimate of the variability of each model parameter. We present some synthetic tests to show the effectiveness of the method and its robustness to uncertainty of the adopted crustal model. Finally, we apply this inverse technique to the well recorded 2000 western Tottori, Japan, earthquake (Mw 6.6); we confirm that the rupture process is characterized by large slip (3-4 m) at very shallow depths but, differently from previous studies, we imaged a new slip patch (2-2.5 m) located deeper, between 14 and 18 km depth.

[1] We present seismological evidence for the existence of an actively slipping low-angle normal fault (15° dip) located in the northern Apennines of Italy. During a temporary seismic experiment, we recorded ∼2000 earthquakes with ML ≥ 3.1. The microseismicity defines a 500 to 1000 m thick fault zone that crosscuts the upper crust from 4 km down to 16 km depth. The fault coincides with the geometry and location of the Alto Tiberina Fault (ATF) as derived from geological observations and interpretation of depth-converted seismic reflection profiles. In the ATF hanging wall the seismicity distribution highlights minor synthetic and antithetic normal faults (4–5 km long) that sole into the detachment. The ATF-related seismicity shows a nearly constant rate of earthquake production, ∼3 events per day (ML ≤ 2.3), and a higher b value (1.06) with respect to the fault hanging wall (0.85) which is characterized by a higher rate of seismicity. In the ATF zone we also observe the presence of clusters of earthquakes occurring with relatively short time delays and rupturing the same fault patch. To explain movements on the ATF, oriented at high angles (∼75°) to the maximum vertical principal stress, we suggest an interpretative model in which crustal extension along the fault is mostly accommodated by aseismic slip in velocity strengthening areas while microearthquakes occur in velocity weakening patches. We propose that these short-lived frictional instabilities are triggered by fluid overpressures related to the buildup of CO2-rich fluids as documented by boreholes in the footwall of the ATF.

[1] We investigate the role of frictional heating and thermal pressurization on earthquake ruptures by modeling the spontaneous propagation of a three-dimensional (3-D) crack on a planar fault governed by assigned constitutive laws and allowing the evolution of effective normal stress. We use both slip-weakening and rate- and state-dependent constitutive laws; in this latter case we employ the Linker and Dieterich evolution law for the state variable, and we couple the temporal variations of friction coefficient with those of effective normal stress. In the companion paper we investigate the effects of thermal pressurization on the dynamic traction evolution. We solve the 1-D heat conduction equation coupled with Darcy's law for fluid flow in porous media. We obtain a relation that couples pore fluid pressure to the temperature evolution on the fault plane. We analytically solve the thermal pressurization problem by considering an appropriate heat source for a fault of finite thickness. Our modeling results show that thermal pressurization reduces the temperature increase caused by frictional heating. However, the effect of the slipping zone thickness on temperature changes is stronger than that of thermal pressurization, at least for a constant porosity model. Pore pressure and effective normal stress evolution affect the dynamic propagation of the earthquake rupture producing a shorter breakdown time and larger breakdown stress drop and rupture velocity. The evolution of the state variable in the framework of rate- and state-dependent friction laws is very different when thermal pressurization is active. In this case the evolution of the friction coefficient differs substantially from that inferred from a slip-weakening law. This implies that the traction evolution and the dynamic parameters are strongly affected by thermal pressurization.

[1] 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 (ω). 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 ω 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.

[1] We have attempted to provide a careful examination of a class of approaches for estimating the conditional probability of failure of a single large earthquake, particularly approaches that account for static stress perturbations to tectonic loading as in the approaches of Stein et al. (1997) and Hardebeck (2004). We have developed a general framework based on a simple, generalized rate change formulation and applied it to these two approaches to show how they relate to one another. We also have attempted to show the connection between models of seismicity rate changes applied to (1) populations of independent faults as in background and aftershock seismicity and (2) changes in estimates of the conditional probability of failure of a single fault. In the first application, the notion of failure rate corresponds to successive failures of different members of a population of faults. The latter application requires specification of some probability distribution (density function or PDF) that describes some population of potential recurrence times. This PDF may reflect our imperfect knowledge of when past earthquakes have occurred on a fault (epistemic uncertainty), the true natural variability in failure times, or some combination of both. We suggest two end-member conceptual single-fault models that may explain natural variability in recurrence times and suggest how they might be distinguished observationally. When viewed deterministically, these single-fault patch models differ significantly in their physical attributes, and when faults are immature, they differ in their responses to stress perturbations. Estimates of conditional failure probabilities effectively integrate over a range of possible deterministic fault models, usually with ranges that correspond to mature faults. Thus conditional failure probability estimates usually should not differ significantly for these models.

[1] In this introduction, we review much of the recent work related to stress transfer, earthquake triggering, and time-dependent seismic hazard in order to provide context for the special section on these subjects. Considerable advances have been made in the past decade, and we focus on our understanding of stress transfer at various temporal and spatial scales, review recent studies of the role of fluids in earthquake triggering, describe evidence for the connection between volcanism and earthquake triggering, examine observational evidence for triggering at all scales, and finally discuss the link between earthquake triggering and time-dependent seismic hazard. We conclude by speculating on future areas of research in the next decade.

[1] We study models of seismicity rate changes caused by the application of a static stress perturbation to a population of faults and discuss our results with respect to the model proposed by Dieterich (1994). These models assume a distribution of nucleation sites (e.g., faults) obeying rate-state frictional relations that fail at constant rate under tectonic loading alone, and predicts a positive static stress step at time t0 will cause an immediate increased seismicity rate that decays according to Omori's law. We show one way in which the Dieterich model may be constructed from simple general ideas, illustrated using numerically computed synthetic seismicity and mathematical formulation. We show that seismicity rate changes predicted by these models (1) depend on the particular relationship between the clock-advanced failure and fault maturity, (2) are largest for the faults closest to failure at t0, (3) depend strongly on which state evolution law faults obey, and (4) are insensitive to some types of population heterogeneity. We also find that if individual faults fail repeatedly and populations are finite, at timescales much longer than typical aftershock durations, quiescence follows a seismicity rate increase regardless of the specific frictional relations. For the examined models the quiescence duration is comparable to the ratio of stress change to stressing rate Δτ/, which occurs after a time comparable to the average recurrence interval of the individual faults in the population and repeats in the absence of any new load perturbations; this simple model may partly explain observations of repeated clustering of earthquakes.

[1] We estimate fracture energy on extended faults for several recent earthquakes by retrieving dynamic traction evolution at each point on the fault plane from slip history imaged by inverting ground motion waveforms. We define the breakdown work (Wb) as the excess of work over some minimum traction level achieved during slip. Wb is equivalent to "seismological" fracture energy (G) in previous investigations. Our numerical approach uses slip velocity as a boundary condition on the fault. We employ a three-dimensional finite difference algorithm to compute the dynamic traction evolution in the time domain during the earthquake rupture. We estimate Wb by calculating the scalar product between dynamic traction and slip velocity vectors. This approach does not require specifying a constitutive law and assuming dynamic traction to be collinear with slip velocity. If these vectors are not collinear, the inferred breakdown work depends on the initial traction level. We show that breakdown work depends on the square of slip. The spatial distribution of breakdown work in a single earthquake is strongly correlated with the slip distribution. Breakdown work density and its integral over the fault, breakdown energy, scale with seismic moment according to a power law (with exponent 0.59 and 1.18, respectively). Our estimates of breakdown work range between 4 × 105 and 2 × 107 J/m2 for earthquakes having moment magnitudes between 5.6 and 7.2. We also compare our inferred values with geologic surface energies. This comparison might suggest that breakdown work for large earthquakes goes primarily into heat production.

We investigate fault interaction through elastic stress transfer among a sequence of moderate-magnitude main shocks (5 < Mw < 6) which ruptured distinct normal fault segments during a seismic sequence in the Umbria-Marche region (central Apennines). We also model the spatial pattern of aftershocks and thier faulting mechanisms through Coulomb stress changes. We compute stress perturbations caused by earthquake dislocations in a homogeneous half-space. Our modeling result show that seven out of eight main shocks of the sequence occur in areas of enhanced Coulomb stress, implying that elastic stress transfer may have promoted the occurence of these moderate-magnitude events. Our Modelling results show that stress changes caused by normal faulting events reactivated and inverted the slip of a secondary N-S trending strike-slip fault inherited from compressional tectonics in its shallowest part (1-3 km). Of the 1517 available afterschocks, 82% are located in areas of positive stress changes for optimally oriented planes (OOPs) for Coulomb failure. However, only 45% of the 322 available fault plane solutions computed from polarity data is consistent with corresponding focal mechanisms associated with the OOPs. The comparison does not improve if we compute the optimally oriented planes for Coulomb failure by fixing the strike orientation of OOPs using information derived from structural geology. Our interpretation of these modeling results is that elastic stress transfer alone cannot jointly explain the aftershock spatial distribution and their focal mechanisms. Copyright 2005 by the American Geophysical Union.

[1] We model the coseismic and postseismic stress changes and the surface deformation caused by earthquake dislocations through a three-dimensional (3-D) finite element numerical procedure applied to the 1992 Landers and the 1999 Hector Mine earthquakes. Our goal is to investigate the stress interaction between these complex nonplanar fault systems. The modeling strategy proposed in this study allows the calculation of elastic deformation and Coulomb stress changes either by imposing the slip distribution as a boundary condition along assigned faults or by retrieving the slip pattern on preexisting faults imposing the regional stress field. We study how different initial stress conditions (including the depth dependence of isotropic components of the regional stress), different values of Coulomb friction coefficient, and the 1-D rigidity layering can affect the slip pattern on assumed faults and the resulting Coulomb stress changes. We propose here an original approach to simultaneously model slip distribution, surface deformation, and stress perturbations consistently with the rheological parameters of the lithosphere and its state of stress.

[1] We study a seismic swarm that occurred in 1989–1990 at the Alban Hills volcano and interpret the seismicity pattern in terms of Coulomb stress changes caused by magma intrusion in a local volcanic source and the extensional tectonic stress field. We first image the three-dimensional (3-D) structure of the volcano through a tomographic inversion of P waves and S-P arrival times recorded by a temporary local network. A high Vp and Vp/Vs body exists beneath the area of most recent volcanic activity, which we interpret as a solidified magma body delimiting the position of the volcanic source. We have relocated 661 events (M ≤ 4.0) using this 3-D velocity model and we have computed 64 fault plane solutions. Elevation changes, measured between 1951 and 1994 along a 33-km-long line crossing the western part of the volcano, reveal an uplift of 0.3 m. We model these data to constrain the position and geometry of the volcanic source. We compute the vertical deformation in a homogeneous half-space, testing different volcanic sources (spherical magma chamber, sill and dike). We model the Coulomb stress changes caused by the local volcanic source and the regional tectonic stress field. The inflation of magma generates an increase of Coulomb stress larger than 0.5 MPa in the area where the seismicity is located. More than 85% of fault plane solutions are consistent with the stress perturbations induced by the volcanic source. We conclude that microearthquakes at the Alban Hills are promoted by elastic stress changes caused by volcanic unrest episodes.

[1] In this study we aim to understand the effect of static and dynamic stress changes in promoting earthquake failures on secondary faults. Toward this goal we solve the equation of motion of a spring-slider dynamic system including inertia and using rate- and state-dependent constitutive laws. We separately investigate the dynamic response of this fault analog system to a sudden stress change represented either as a stress step or as a stress pulse, which are used to model permanent (static) and transient (dynamic) stress perturbations. The induced earthquake failure does not occur immediately at the application of the coseismic stress change, but it is delayed in time: we define this time interval as the triggering delay. For a given stress perturbation, we analyze the dependence of triggering delays on different system conditions and constitutive parameters. Our results clearly show that the effects of static and dynamic stress changes are quite different. While a static stress change is able to advance as well as to delay an induced instability depending on its sign, a dynamic stress pulse is only able to promote a nearly instantaneous failure, provided its amplitude is positive and large enough with respect to the direct effect of friction. In other words, dynamic stress changes can only cause nearly instantaneous failures, without any relevant triggering delay. These results should be considered in interpreting the seismicity rate changes caused by large earthquakes at least as long as seismic events are interpreted as sliding instabilities obeying rate- and state-dependent friction laws.

We investigate the spatiotemporal evolution of dynamic stress outside a rupturing extended fault. The dynamic stress variations caused by a coseismic rupture in a half space are computed by using the discrete wavenumber and reflectivity methods. After a transient phase, the stress time history evolves to the final static stress value. We compare the static stress changes resulting from this model with those computed from a static dislocation model. We have applied this method to study the interactions between the first two normal faults which ruptured during the 1980 (MS 6.9) Irpinia earthquake. These two subevents are separated in time by nearly 20 s, while the third (and last) subevent occurred 40 s after the rupture onset. We compute the dynamic stress changes caused by the rupture of the first subevent. Our modeling results show that the dynamic stress peak on the second subevent fault plane is reached between 7 s and 8 s after the rupture initiation on the main fault. On the average the static stress level on the second subevent (20 s) fault plane is reached nearly after 14 s. The dynamic rupture did not jump from a rupturing segment to the adjacent one immediately, but the triggering of the 20 s subevent is delayed by roughly 10 s with respect to the instant of occurrence of the dynamic stress peak induced by the 0 s event. The dynamic stress pulse propagates along the strike direction of the second subevent fault plane at an average velocity of nearly 3.4 km/s. The delayed triggering of the second subevent can be interpreted in terms of the frictional properties of the faults. In particular, rate- and state-dependent frictional law can explain a delayed instability after a sudden change in stress. Using the estimated values of the subevent triggering delay and the shear stress change, we attempt to constrain the parameter Aσ on the 20 s fault. The values here inferred agree well with those resulting from previous studies.

During the past 1000 years, eruptions of Vesuvius have often been accompanied by large earthquakes in the Apennines 50-60 km to the northeast. Statistical investigations had shown that earthquakes often preceded eruptions, typically by less than a decade, but did not provide a physical explanation for the correlation. Here, we explore elastic stress interaction between earthquakes and eruptions under the hypothesis that small stress changes can promote events when the Apennine normal faults and the Vesuvius magma body are close to failure. We show that earthquakes can promote eruptions by compressing the magma body at depth and opening suitably oriented near-surface conduits. Voiding the magma body in turns brings these same normal faults closer to Coulomb failure, promoting earthquakes. Such a coupling is strongest if the magma reservoir is a dike oriented normal to the regional extension axis, parallel to the Apennines, and the near-surface conduits and fissures are oriented normal to the Apennines. This preferred orientation suggests that the eruptions issuing from such fissures should be most closely linked in time to Apennine earthquakes. Large Apennine earthquakes since 1400 are calculated to have transferred more stress to Vesuvius than all but the largest eruptions have transferred to Apennine faults, which may explain why earthquakes more commonly lead than follow eruptions. A two-way coupling may thus link earthquakes and Vesuvius eruptions along a 100-km-long set of faults. We test the statistical significance of the earthquake-eruption correlation in the two-way coupling zone, and find a correlation significant at the 95% confidence level.

The horizontal components of 45 strong motion accelerograms recorded in Friuli, Italy, from May to September 1976, have been analyzed in order to estimate the stress drop of eight thrust faulting earthquakes. Two different stress parameters, the Brune stress drop Δσ and the apparent stress σa, have been considered. The Friuli main shock has a strong stress drop (Δσ ≈ 800 bars), while the aftershocks have stress drops which range from 250 to 400 bars. Five accelerograms written by the Montenegro, Yugoslavia, earthquake of April 1979 have also been analyzed. This thrust faulting earthquake had a stress drop of Δσ ≈ 900 bars. The stress drops of these thrust faulting earthquakes are compared to the stress drops determined by Rovelli et al. (1988a) for nine normal faulting earthquakes which occurred in the Apennines region from 1979 to 1984. The radiated energies and apparent stresses have also been calculated for the set of Apennine earthquakes. The thrust faulting earthquakes in the Alpine-Dynaride region exhibit higher values for both the Brune and the apparent stress than the normal faulting earthquakes in the Apennines region. Excluding the Friuli and Montenegro main shocks, the Brune stress drops of the thrust faults are approximately 3 times those of the normal faults, while the apparent stresses are twice as large. This difference is statistically significant at a confidence level of 95%. The same difference also emerges from the scaling of the peak ground motions recorded in these two regions, suggesting an enhanced severity of the seismic input in the Alpine-Dynaride environment compared with the Apennines.

We study coseismic and postseismic stress fields caused by a normal faulting earthquake in a self-gravitating, stratified, viscoelastic spherical Earth over distances from a few to hundreds of kilometers. We investigate the contribution of postseismic relaxation on the induced Coulomb stress for extensional tectonic settings accounting for the effects of the Earth stratification. We use a numerical code based on the spherical self-gravitating Earth model developed by Piersanti et al. [1995, 1997]. We study how postseismic relaxation can modify the state of stress at the base of the seismogenic layer where large earthquakes are believed to nucleate. We compare our results with those obtained by means of a three-dimensional dislocation model in an elastic half-space, which does not account for the time-dependent postseismic stress transfer. The viscoelastic relaxation process modifies the coseismic stress changes during time periods from several decades to centuries. The postseismic stress is generally greater than the coseismic stress change. Postseismic relaxation increases the Coulomb stress near the causative faults and tends to reduce the stress shadow areas. The temporal evolution of Coulomb stress reveals that in addition to the viscosity value, the thickness of the elastic layer controls the time at which the relaxation process is completed. A larger thickness of the elastic layer yields a faster relaxation in the first few decades after the seismic event but smaller postseismic stress amplitudes at longer timescales. One of the most significant results of this study is the extreme sensitivity of the timescales of the viscoelastic relaxation to small changes in the thickness and depth of the shallowest viscoelastic layer as well as in variation of the viscosity. Such a result suggests that the interpretation of the time evolution of the postseismic signals only in terms of viscosity values could lead to misleading conclusions.

[1] We model the traction evolution and shear stress degradation near the tip of a propagating dynamic rupture by solving the elastodynamic equation for a 2-D in-plane fault obeying rate- and state-dependent friction laws and adopting a finite difference numerical method. Modeling results clearly show that our dynamic solution implies a slip dependence of fault friction, as previously observed either in laboratory experiments or in theoretical models. However, the resulting equivalent slip-weakening distance (d0eq) is different from the length scale parameter (L) characteristic of the rate and state formulation. We demonstrate that the state variable evolution controls the slip acceleration and the absorbed fracture energy. The adopted constitutive parameters a, b, and L affect the traction dependence on slip. We present the results of several numerical simulations, performed after a careful control of the available resolution of the cohesive zone, to unravel the dependence of the equivalent slip-weakening distance on the constitutive parameters. We also propose analytical relations to interpret our numerical results, which point out that the traction evolution within the cohesive zone cannot be prescribed a priori in the framework of rate-and-state constitutive laws. In particular, the yield stress and the kinetic friction level depend on particular slip velocity values characteristic of specific stages of the breakdown process. Finally, we discuss how the adopted evolution law affects the slip-weakening curve by comparing the simulations performed with a slip and a slowness law. The former yields smaller equivalent slip-weakening distances than the latter.

We consider how variations in fault frictional properties affect the phenomenology of earthquake faulting. In particular, we propose that lateral variations in fault friction produce the marked heterogeneity of slip observed in large earthquakes. We model these variations using a rate- and state-dependent friction law, where we differentiate velocity-weakening behavior into two fields: the strong seismic field is very velocity weakening and the weak seismic field is slightly velocity weakening. Similarly, we differentiate velocity-strengthening behavior into two fields: the compliant field is slightly velocity strengthening and the viscous field is very velocity strengthening. The strong seismic field comprises the seismic slip concentrations, or asperities. The two “intermediate” fields, weak seismic and compliant, have frictional velocity dependences that are close to velocity neutral: these fields modulate both the tectonic loading and the dynamic rupture process. During the interseismic period, the weak seismic and compliant regions slip aseismically, while the strong seismic regions remain locked, evolving into stress concentrations that fail only in main shocks. The weak seismic areas exhibit most of the interseismic activity and aftershocks but can also creep seismically. This “mixed” frictional behavior can be obtained from a sufficiently heterogeneous distribution of the critical slip distance. The model also provides a mechanism for rupture arrest: dynamic rupture fronts decelerate as they penetrate into unloaded complaint or weak seismic areas, producing broad areas of accelerated afterslip. Aftershocks occur on both the weak seismic and compliant areas around a fault, but most of the stress is diffused through aseismic slip. Rapid afterslip on these peripheral areas can also produce aftershocks within the main shock rupture area by reloading weak fault areas that slipped in the main shock and then healed. We test this frictional model by comparing the seismicity and the coseismic slip for the 1966 Parkfield, 1979 Coyote Lake, and 1984 Morgan Hill earthquakes. The interevent seismicity and aftershocks appear to occur on fault areas outside the regions of significant slip: these regions are interpreted as either weak seismic or compliant, depending on whether or not they manifest interevent seismicity.

[1] Pore pressure changes are rigorously included in Coulomb stress calculations for fault interaction studies. These are considered changes under undrained conditions for analyzing very short term postseismic response. The assumption that pore pressure is proportional to fault-normal stress leads to the widely used concept of an effective friction coefficient. We provide an exact expression for undrained fault zone pore pressure changes to evaluate the validity of that concept. A narrow fault zone is considered whose poroelastic parameters are different from those in the surrounding medium, which is assumed to be elastically isotropic. We use conditions for mechanical equilibrium of stress and geometric compatibility of strain to express the effective normal stress change within the fault as a weighted linear combination of mean stress and fault-normal stress changes in the surroundings. Pore pressure changes are determined by fault-normal stress changes when the shear modulus within the fault zone is significantly smaller than in the surroundings but by mean stress changes when the elastic mismatch is small. We also consider an anisotropic fault zone, introducing a Skempton tensor for pore pressure changes. If the anisotropy is extreme, such that fluid pressurization under constant stress would cause expansion only in the fault-normal direction, then the effective friction coefficient concept applies exactly. We finally consider moderately longer timescales than those for undrained response. A sufficiently permeable fault may come to local pressure equilibrium with its surroundings even while that surrounding region may still be undrained, leading to pore pressure change determined by mean stress changes in those surroundings.