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Dynamic crack propagation problems, including intersonic rupture, are simulated with two Hamiltonian based formulations of particle discretization scheme (PDS) FEM: the traditional displacement momentum form and the strain momentum form, for which consistent momentum conserving and symplectic integration schemes are derived. Numerical results are verified, and validated by comparing with photoelastic observations of a dynamic mode-I crack captured with a 1 Mfps camera. Both methods are successful in accurately reproducing the crack patterns observed in classical 2D and 3D dynamic rupture scenarios, as well as the near crack tip stress field during the propagation. The two methods are found to be numerically indifferentiable, although the displacement based method offers a significantly better computational performance. As a demonstrative application, we simulate the super-shear rupture in earthquakes, modeling the contact at the fault surface by a linear slip weakening friction law. The Burridge–Andrews mechanism naturally appears in the simulations, making the crack front jump from the sub-Rayleigh regime to the intersonic regime and propagate while producing shear Mach cones.

Snow slab avalanches, characterized by a distinct, broad fracture line, are released following anticrack propagation in highly porous weak snow layers buried below cohesive slabs. The anticrack mechanism is driven by the volumetric collapse of the weak layer, which leads to the closure of crack faces and to the onset of frictional contact. Here, on the basis of snow fracture experiments, full-scale avalanche measurements and numerical simulations, we report the existence of a transition from sub-Rayleigh anticrack to supershear crack propagation. This transition follows the Burridge–Andrews mechanism, in which a supershear daughter crack nucleates ahead of the main fracture front and eventually propagates faster than the shear wave speed. Furthermore, we show that the supershear propagation regime can exist even if the shear-to-normal stress ratio is lower than the static friction coefficient as a result of the loss of frictional resistance during collapse. This finding shows that snow slab avalanches have fundamental similarities with strike-slip earthquakes., Nature Physics, 18, ISSN:1745-2473, ISSN:1745-2481

SUMMARYField studies have characterized natural faults as rough, non-planar surfaces at all scales. Fault roughness induces local stress perturbations during slip, which dramatically affect rupture behaviour, resulting in slip heterogeneity. However, the relation between fault roughness and slip heterogeneity remains a key knowledge gap between current numerical and field studies. In this study, we analyse numerical simulations of earthquake rupture to determine how roughness influences final slip. Using a rupture catalogue containing thousands of dynamic rupture simulations on band-limited self-similar fractal fault profiles with varying roughness and background shear stress levels, we quantify how fault roughness affects the spectral characteristics of the resulting slip distribution. We find that slip distributions become increasingly more self-affine, that is, containing more short wavelength fluctuations as compared to the self-similar fault profiles, as roughness increases. We also find that, at very short wavelengths (

With the availability of new instrumentation for more complete ground motion measurements, as rotation or strain measurements using optical technology, novel application opportunities in seismology arise. Back azimuth information can be determined from combined measurements of rotations and translations at a single site. Such six degree-of-freedom (6-DoF) measurements are reasonably stable in delivering similar information compared to a small-scale array of three-component seismometers. Here we investigate whether a 6-DoF approach is applicable for imaging earthquake rupture propagation. While common approaches determining the timing and location of energy sources generating seismic waves rely on the information of P-waves, here we take S-waves into account. We analyze 2-D and 3-D synthetic cases of unilateral but complex rupture propagation. The back azimuths of directly arriving SH-waves in the 2-D case, and P-converted SV-waves and SH-waves in the 3-D case are tracked. For data analysis in terms of wave polarity we compare a cross-correlation approach using a grid-search optimization algorithm with a polarization analysis method using point measurements. We successfully recover rupture path and rupture velocity with only one station, under the assumption of an approximately known fault location. Using more than one station, rupture imaging in space and time is possible without a priori assumptions. We demonstrate robustness of the approach in resolving relatively small variations of rupture velocity, and rupture jumping across off set fault segments. We discuss the effects of rupture directivity, supershear rupture velocity, source-receiver geometry as well as potential and challenges for the method.

International audience; Earthquake rupture speed can affect ground shaking and therefore seismic hazard. Seismological observations show that large earthquakes span a continuum of rupture speeds, from slower than Rayleigh waves up to P-wave speed, and include speeds that are predicted to be unstable by two-dimensional theory. This discrepancy between observations and theory has not yet been reconciled by a quantitative model. Here we present numerical simulations that show that long ruptures with oblique slip (both strike-slip and dip-slip components) can propagate steadily at various speeds, including those previously suggested to be unstable. The obliqueness of slip and the ratio of fracture energy to static energy release rate primarily control the propagation speed of long ruptures. We find that the effects of these controls on rupture speed can be predicted by extending the three-dimensional theory of fracture mechanics to long ruptures with oblique slip. This model advances our ability to interpret supershear earthquakes, to constrain the energy ratio of faults based on observed rupture speed and rake angle, and to relate the potential rupture speed and size of future earthquakes to the observed slip deficit along faults.

How does fault slip follow an earthquake rupture front propagating faster than the local shear-wave velocity (i.e., at supershear speed)? How does a supershear rupture front pass through a geometrically complex fault system? Resolving the evolution of such complex earthquake ruptures is fundamental to our understanding of earthquake-source physics, but these events have not been well captured by conventional waveform inversions of observational data. We applied a new framework of finite-fault inversion to globally observed teleseismic waveforms and resolved both the spatiotemporal evolution of slip and the fault geometry of the 2018 Palu earthquake (moment magnitude 7.6) in Sulawesi, Indonesia. We show that supershear rupture propagation for this event was sustained by transient slip stagnation and advancement as the rupture front passed through the geometrically complex fault system. This peculiar inchworm-like slip evolution was caused by the rupture front encountering fault bends with favorable and unfavorable orientations for rupture propagation. Our analysis also identified the possible existence of a fault junction beneath Palu Bay connecting an unmapped primary fault in northern Sulawesi with the Palu-Koro fault in the south.

Many earthquakes propagate at sub‐Rayleigh speeds. Earthquakes propagating at supershear speeds, though less common, are by far more destructive. Hence, it is important to quantify the motion characteristics associated with both types of earthquake ruptures. Here we report on the spatiotemporal properties of dynamic ruptures measured in our laboratory experiments using the dynamic digital image correlation technique. Earthquakes are mimicked by the frictional rupture propagating along the interface of two Homalite plates. Digital images of the propagating ruptures are captured by an ultrahigh‐speed camera and processed with digital image correlation in order to produce sequences of evolving displacement and velocity maps. Our measurements reveal the full‐field structure of the velocity components, bridge the gap between previous spatially sparse velocimeter measurements available only at two to three locations, and enable us to quantify the attenuation patterns away from the interface.

An earthquake is an event of dynamic, unstable slip that releases elastic energy stored in the earth's crust. This abrupt energy release requires the weakening of the slipping fault that is manifested by a strength drop from a static level to a dynamic level. The fault weakening occurs in two general zones: The rupture-front at the earthquake tip, and the frictional zone in the wake of the propagating front. Here, we analyze the weakening processes of the rupture-front in experimental stick-slips, and compare these processes to the weakening in the frictional zone. Our experimental analysis focuses on high-speed monitoring (1 MHz) of the strain-fields associated with spontaneous, unstable ruptures propagating bilaterally from a nucleation site along a circular fault. The ruptures propagated at velocities ranging from slow (∼100 m/s) to supershear, and the fault weakening by the rupture-front, defined by WS = [strength drop/peak strength], is proportional to the rupture propagation velocity. WS ranged 0.08-0.58 during tiny slip-displacements of 3.7-43 microns, in agreement with similar weakening intensity in a few sets of dynamic rupture experiments. In contrast, frictional weakening, which is traditionally analyzed in constant-velocity experiments, requires slip-displacements in the range of 0.1-10 m to reach similar weakening intensity. Therefore, in terms of slip-displacements, rupture-front weakening is more efficient than frictional weakening by orders of magnitude. Further, we observed that a rupture-front transported its intense weakening from a nucleation site to the entire experimental fault, and we argue that the equivalent process can occur along natural faults. If the rupture of a tiny earthquake, e.g., M

International audience; The city of Istanbul is characterized by one of the highest levels of seismic risk in the Mediterranean region. An important source of such increased risk is the high probability of large earthquake occurrence during the coming years, which stands at about 65% likelihood owing to the existing seismic gap and the post-1999 earthquake stress transfer at the western portion of the North Anatolian fault zone.In this study, we simulated hybrid broadband time histories from selected earthquakes having magnitude M-w > 7.0 in the Sea of Marmara within 10-20 km of Istanbul, the most probable scenarios for simulated generation of the devastating 1509 event in this region. Physics-based rupture scenarios, which may be an indication of potential future events, are adopted to estimate the ground-motion characteristics and its variability in the region. Two simulation techniques are used to compute a realistic time series, considering generic rock site conditions. The first is a full 3D wave propagation method used for generating low-frequency seismograms, and the second is a stochastic finite-fault model approach based on dynamic corner-frequency high-frequency seismograms. Dynamic rupture is generated and computed using a boundary integral equation method, and the propagation in the medium is realized through a finite-difference approach. The results from the two simulation techniques are then merged by performing a weighted summation at intermediate frequencies to calculate a broadband synthetic time series.The simulated hybrid broadband ground motions are validated by comparing peak ground acceleration, peak ground velocity (PGV), and spectral accelerations (5% damping) at different periods with the ground-motion prediction equations in the region. Our simulations reveal strong rupture directivity and supershear rupture effects over a large spatial extent, which generate extremely high near-fault motions exceeding the 250 cm/s PGV along the entire length of the ruptured fault.

Recent studies in dynamic source modeling and kinematic source inversion show that earthquake rupture may contain greater complexity than we previously anticipated, including multiple slipping at a given point on a fault. Finite source inversion methods suffer from the nonuniqueness of solutions, and it may become more serious if we aim to resolve more complex rupture models. In this study, we perform synthetic inversion tests with dynamically generated complex rupture models, including both supershear rupture and slip reactivation, to understand the possibility of resolving complex rupture processes by inverting seismic waveform data. We adopt a linear source inversion method with multiple windows, allowing for slipping from the nucleation of rupture to the termination at all locations along a fault. We regularize the model space effectively in the Bayesian framework and perform multiple inversion tests by considering the effect of inaccurate Green’s functions and station distributions. We also perform a spectral stability analysis. Our results show that it may be possible to resolve both a supershear rupture front and reactivated secondary slipping using the linear inversion method if those complex features are well separated from the main rupture and produce a fair amount of seismic energy. It may be desirable to assume the full complexity of an earthquake rupture when we first develop finite source models after a major event occurs and then assume a simple rupture model for stability if the estimated models do not show a clear pattern of complex rupture processes.

The onset of frictional motion at the interface between two distinct bodies in contact is characterized by the propagation of dynamic rupture fronts. We combine friction experiments and numerical simulations to study the properties of these frictional rupture fronts. We extend previous analysis of slow and sub-Rayleigh rupture fronts and show that strain fields and the evolution of real contact area in the tip vicinity of supershear ruptures are well described by analytical fracture-mechanics solutions. Fracture-mechanics theory further allows us to determine long sought-after interface properties, such as local fracture energy and frictional peak strength. Both properties are observed to be roughly independent of rupture speed and mode of propagation. However, our study also reveals discrepancies between measurements and analytical solutions that appear as the rupture speed approaches the longitudinal wave speed. Further comparison with dynamic simulations illustrates that, in the supershear propagation regime, transient and geometrical (finite sample thickness) effects cause smaller near-tip strain amplitudes than expected from the fracture-mechanics theory. By showing good quantitative agreement between experiments, simulations and theory over the entire range of possible rupture speeds, we demonstrate that frictional rupture fronts are classic dynamic cracks despite residual friction., 20 pages including 11 figures

Since the early years of the linear elastic theory of fracture [linear elastic fracture mechanics (LEFM)], scientists have sought to understand and predict how fast cracks grow in a material or slip fronts propagate along faults. While shear cracks can travel faster than the shear wave speed, the Rayleigh wave speed is the limiting speed theoretically predicted for tensile failure. This work uncovers the existence of supershear episodes in the tensile (mode I) rupture of linearly elastic materials beyond the maximum allowable (sub-Rayleigh) speed predicted by the classical theory of dynamic fracture. While the admissible rupture speeds predicted by LEFM are verified for smooth crack fronts, we present numerically how a supershear burst can emerge from a discontinuity in crack front curvature. Using a spectral formulation of the three-dimensional elastodynamic equations coupled with a cohesive model of fracture, we study how these short-lived bursts create shock waves persisting far from the discontinuity site. This study provides insight on crack front instabilities present in the rapid tensile failure of brittle materials due to large distortions of the rupture front.

A large strike-slip earthquake occurred in the Caribbean Sea on 28 January 2020. We inverted teleseismic P-waveforms from the earthquake to construct a finite-fault model by a new method of inversi...

Transient gravity changes are expected to occur at all distances during an earthquake rupture, even before the arrival of seismic waves. Here we report on the search of such a prompt gravity signal in data recorded by a superconducting gravimeter and broadband seismometers during the 2011 Mw 9.0 Tohoku-Oki earthquake. During the earthquake rupture, a signal exceeding the background noise is observed with a statistical significance higher than 99% and an amplitude of a fraction of μGal, consistent in sign and order of magnitude with theoretical predictions from a first-order model. While prompt gravity signal detection with state-of-the-art gravimeters and seismometers is challenged by background seismic noise, its robust detection with gravity gradiometers under development could open new directions in earthquake seismology, and overcome fundamental limitations of current earthquake early-warning systems imposed by the propagation speed of seismic waves., Earthquakes have been theorised to produce gravity signals that may arrive before seismic waves, but until now they had not been detected. Montagner et al. have detected prompt gravity signals from the 2011 Tohoku-Oki earthquake thus allowing an early warning of earthquakes before seismic wave arrival.

High frequency energy radiation of large earthquakes is a key to evaluating shaking damage and is an important source characteristic for understanding rupture dynamics. We developed a new inversion method, Image Deconvolution Back-Projection (IDBP) to retrieve high frequency energy radiation of seismic sources by linear inversion of observed images from a back-projection approach. The observed back-projection image for multiple sources is considered as a convolution of the image of the true radiated energy and the array response for a point source. The array response that spreads energy both in space and time is evaluated by using data of a smaller reference earthquake that can be assumed to be a point source. The synthetic test of the method shows that the spatial and temporal resolution of the source is much better than that for the conventional back-projection method. We applied this new method to the 2001 M w 7.8 Kunlun earthquake using data recorded by Hi-net in Japan. The new method resolves a sharp image of the high frequency energy radiation with a significant portion of supershear rupture.

The most general frictional motion in nature involves bimaterial interfaces, when contacting bodies possess different elastic properties. Frictional motion occurs when the contacts composing the interface separating these bodies detach via propagating rupture fronts. Coupling between slip and normal stress variations is unique to bimaterial interfaces. Here we use high speed simultaneous measurements of slip velocities, real contact area and stresses to explicitly reveal this bimaterial coupling and its role in determining different classes of rupture modes and their structures. We directly observe slip-pulses, highly localized slip accompanied by large local reduction of the normal stress near the rupture tip. These pulses propagate in the direction of motion of the softer material at a selected (maximal) velocity and continuously evolve while propagating. In the opposite direction bimaterial coupling favors crack-like ‘supershear' fronts. The robustness of these structures shows the importance of bimaterial coupling to frictional motion and modes of frictional dissipation., Friction commonly involves different material types (bimaterials) at their sliding interface. Here, in laboratory experiments Shlomai and Fineberg reveal effects uniquely due to biomaterial coupling, with slip-pulses and crack-like supershear fronts dominating opposing propagation directions.

The potential for strong ground shaking in large earthquakes partly depends on how fast the earthquake rupture propagates. It is observed that strike-slip earthquakes usually propagate at speeds slower than the Rayleigh wave speed (v_R) but occasionally jump to speeds faster than the S wave speed (v_s), or supershear speeds. Supershear earthquakes can be more catastrophic and cause unusually large ground motions at long distances. Here we use both fully dynamic rupture simulations and high-resolution seismic observations to show that supershear earthquakes can be induced by damaged fault zones, the low-velocity layers of damaged rocks that typically exist around major faults and serve as waveguides for high-frequency energy. In contrast to supershear ruptures in homogeneous media, supershear ruptures in damaged fault zones can occur under relatively low fault stress and propagate stably at speeds within the range usually considered as unstable.

This paper focuses on a blast-induced Mach cone followed by trailing Rayleigh waves during blast stress waves chasing a running crack in an epoxy plate, using the photoelasticity method and high-speed photography. A Mach cone and trailing Rayleigh waves were visualized and interpreted based on isochromatic fringes, agreeing well with theoretical wave paths. The Mach cone was the coalescence of shear wavelets generated by P waves on crack surfaces, which was verified by the half-cone angle, equal to arcsin (CS/CP). Effects of the Mach cone and trailing Rayleigh waves on the running crack were evaluated by measuring crack velocity and dynamic stress intensity factors (SIFs) of the crack tip. It was found that the Mach cone decreased both crack velocity and SIFs, while trailing Rayleigh waves had the opposite effect. Finally, because of similarities, the findings in our experiments were discussed with those in the supershear rupture. In particular, effects of the Mach cone and trailing Rayleigh waves on the running crack were consistent with particle motion near the fault in the supershear rupture.

The rupture fronts that mediate the onset of frictional sliding may propagate at speeds below the Rayleigh wave speed or may surpass the shear wave speed and approach the longitudinal wave speed. While the conditions for the transition from sub-Rayleigh to supershear propagation have been studied extensively, little is known about what dictates supershear rupture speeds and how the interplay between the stresses that drive propagation and interface properties that resist motion affects them. By combining laboratory experiments and numerical simulations that reflect natural earthquakes, we find that supershear rupture propagation speeds can be predicted and described by a fracture mechanics–based equation of motion. This equation of motion quantitatively predicts rupture speeds, with the velocity selection dictated by the interface properties and stress. Our results reveal a critical rupture length, analogous to Griffith’s length for sub-Rayleigh cracks, below which supershear propagation is impossible. Above this critical length, supershear ruptures can exist, once excited, even for extremely low preexisting stress levels. These results significantly improve our fundamental understanding of what governs the speed of supershear earthquakes, with direct and important implications for interpreting their unique supershear seismic radiation patterns., Science Advances, 4 (7), ISSN:2375-2548

The dynamic rupture process and near-source ground motion of the 1999 Mw 7.1 Duzce Earthquake are simulated. The fault rupture is governed by the slip-weakening friction model coupled to a three-dimensional viscoelastic wave equation. The problem is solved numerically by a 3-D dynamic rupture code that uses a generalized finite difference method. Initial parameterization of stress drop (Delta tau) and strength excess (S-e) for dynamic rupture calculations is obtained from the slip velocity distribution of a kinematic waveform inversion (KI) model by solving the elastodynamic equation with the kinematic slip as a boundary condition. Using the kinematic slip distribution and observed ground motion as constraints, a trial and error procedure was followed to define the stress parameterization. Preferred model describes the source in terms of stress with three asperities (located, respectively, at the deep, middle and shallow) and strong barriers between asperities. S-e is as high as 19 Mpa at barriers between the three asperities and Delta tau is maximum about 40 Mpa at the deepest asperity. This heterogeneity in stress distribution produces abrupt jumps in rupture velocity, exhibiting locally apparent rupture speed exceeding the P wave velocity at the borders between barriers and asperities, due to sharp changes of fault strength and stress drop at those areas. Overall, consistent with other studies, the rupture propagation is dominated by supershear speed toward the eastern asperities and at shallow surface. Simulated surface rupture at the eastern fault is consistent with other studies; nevertheless, the western shallower parts did not rupture during the simulation, suggesting that those regions may have already broken during the 1999 Kocaeli event, which occurred three months earlier. Ground motion simulation catches the major characteristics of the observed waveforms. Distribution of simulated peak ground velocity (PGV) in low frequency (0.1-0.5 Hz.) inside the study area reveals the propagation pattern on the field, with PGV reaching to 1.2 and 2.2 m/s in the NS and EW components, respectively.

Large variability of earthquake stress drops and scaled energy has been commonly reported in the literature, but it is difficult to assess how much of this variability is caused by underlying physical source processes rather than simply observational uncertainties. Here we examine a variety of dynamically realistic rupture scenarios for circular and elliptical faults and investigate to what extent the variability in seismically estimated stress drops and scaled energy comes from differences in source geometry, rupture directivity, and rupture speeds. We numerically simulate earthquake source scenarios using a cohesive-zone model with the small-scale yielding limit, where the solution approaches a singular crack model with spontaneous healing of slip. Compared to symmetrical circular source models, asymmetrical models result in larger variability of estimated corner frequencies and scaled energy over the focal sphere. The general behavior of the spherical averages of corner frequencies and scaled energy in the subshear regime extends to the supershear regime, although shear Mach waves generated by the propagation of supershear rupture lead to much higher corner frequency and scaled energy estimates locally. Our results suggest that at least a factor of 2 difference in the spherical average of corner frequencies is expected in observational studies simply from variability in source characteristics almost independent of the actual stress drops, translating into a factor of 8 difference in estimated stress drops. Furthermore, radiation efficiency estimates derived from observed seismic spectra should not be directly interpreted as describing rupture properties unless there are independent constraints on rupture speed and geometry.

Friction plays a key role in how ruptures unzip faults in the Earth’s crust and release waves that cause destructive shaking. Yet dynamic friction evolution is one of the biggest uncertainties in earthquake science. Here we report on novel measurements of evolving local friction during spontaneously developing mini-earthquakes in the laboratory, enabled by our ultrahigh speed full-field imaging technique. The technique captures the evolution of displacements, velocities and stresses of dynamic ruptures, whose rupture speed range from sub-Rayleigh to supershear. The observed friction has complex evolution, featuring initial velocity strengthening followed by substantial velocity weakening. Our measurements are consistent with rate-and-state friction formulations supplemented with flash heating but not with widely used slip-weakening friction laws. This study develops a new approach for measuring local evolution of dynamic friction and has important implications for understanding earthquake hazard since laws governing frictional resistance of faults are vital ingredients in physically-based predictive models of the earthquake source., The role of friction is key to understanding how faults may rupture and generate earthquakes. Here, the authors capture the local evolution of dynamic friction in laboratory experiments via a new approach using a high-speed imaging technique, which may be used to understand the frictional resistance of faults.

Earthquake finite‐source inversions provide us with a window into earthquake dynamics and physics. Unfortunately, rise time, an important source parameter that describes the local slip duration, is still quite poorly resolved. This may be at least partly due to sparsity of currently available seismic networks, which have average sensor spacing of a few tens of kilometers at best. However, next generation observation systems could increase the density of sensing by orders of magnitude. Here, we explore whether such dense networks would improve the resolution of the rise time in idealized scenarios. We consider steady‐state pulselike ruptures with spatially uniform slip, rise time, and rupture speed and either Haskell or Yoffe slip‐rate function on a vertical strike‐slip fault. Synthetic data for various network spacings are generated by forward wave propagation simulations, and then source inversions are carried out using that data. The inversions use a nonparametric linear inversion method that does not impose any restrictions on rupture complexity, rupture velocity, or rise time. We show that rupture velocity is an important factor in determining the rise‐time resolution. For sub‐Rayleigh rupture speeds, there is a characteristic length related to the decay of the wavefield away from the fault that depends on rupture speed and rise time such that only networks with smaller station spacings can adequately resolve the rise time. For supershear ruptures, the wavefield contains homogeneous S waves the decay of which is much slower, and an adequate resolution of the rise time can be achieved for all station spacings considered in this study (up to few tens of kilometers). Finally, we find that even if dense measurements come at the expense of large noise (e.g., 1 cm/s noise for space‐based optical systems), the conclusions on the performance of dense networks still hold.

We investigate numerically the passage of spontaneous, dynamic in-plane shear ruptures from initiation to their final rupture speed, using very fine grids. By carrying out more than 120 simulations, we identify two different mechanisms controlling supershear transition. For relatively weaker faults, the rupture speed always passes smoothly and continuously through the range of speeds between the Rayleigh and shear wave speeds (the formerly considered forbidden zone of rupture speeds). This, however, occurs in a very short time, before the ruptures reach the compressional wave speed. The very short time spent in this range of speeds may explain why a jump over these speeds was seen in some earlier numerical and experimental studies and confirms that this speed range is an unstable range, as predicted analytically for steady state, singular cracks. On the other hand, for relatively stronger faults, we find that a daughter rupture is initiated by the main (mother) rupture, ahead of it. The mother rupture continues to propagate at sub-Rayleigh speed and eventually merges with the daughter rupture, whose speed jumps over the Rayleigh to shear wave speed range. We find that this daughter rupture is essentially a “pseudorupture,” in that the two sides of the fault are already separated, but the rupture has negligible slip and slip velocity. After the mother rupture merges with it, the slip, the slip velocity, and the rupture speed become dominated by those of the mother rupture. The results are independent of grid sizes and of methods used to nucleate the initial rupture.

It is well known that fault step overs can under some circumstances allow through-going rupture and under other circumstances cause rupture to terminate. However, the effects of different friction law formulations on jumping rupture have not been extensively explored. In this study we use the 2-D dynamic finite element method to investigate how different frictional parameterizations affect the ability of rupture to jump a step over, in both extensional and compressional settings. We compare linear slip-weakening friction and three forms of rate- and state-dependent friction: the aging law, slip law, and slip law with strong rate weakening. We have found that for friction parameterizations with the same effective slip-weakening distance, the functional forms of such friction laws can have a significant effect on maximum jump distance. With friction laws scaled to have equivalent fracture energies, we find that the functional forms of such friction laws have a second-order effect on jumping rupture. Finally, with our specific parameterizations we find that delays in rupture across the step over systems can lead to a previously unseen mode of supershear transition once the rupture renucleates on the secondary fault segment, even if the initial stress field precludes such a transition. Studies using multiple friction laws in complex geometries such as fault step overs can lead to better understanding of the dependence of rupture properties on the type of friction law utilized in models and statistical analysis.

The question about physically admissible velocity of dynamic crack growth is of significance to safety engineering as well as to earthquake dynamics. Recent researches including numerical simulations, experimental observations and the analysis of strong earthquakes have shown a possibility of propagation of shear cracks in supershear regime, namely at velocities comparable with dilatational wave speed. The present paper is devoted to the theoretical (numerical) study of some fundamental aspects of this problem. It is shown that development of a sub Raleigh shear crack is connected with a vortex traveling ahead of the crack tip at a shear wave velocity. The stress concentration area ahead of the crack tip revealed by different authors (Burridge, Andrews, Geubelle, Rosakis and others) is connected with this vortex. Acceleration of a shear crack towards the longitudinal wave velocity is concerned with formation of a daughter crack by the mechanism of shearing (the daughter crack is formed in the center of vortex). Analysis of sub Raleigh to intersonic transition has shown that development of shear cracks is self-similar and depends on dimensionless parameters.

The paper is devoted to theoretical study of the longitudinal shear (mode II) crack unstable growth dynamics in brittle materials. We considered two main regimes of the dynamic propagation of the crack (sub-Rayleigh and supershear) and their implementation conditions. The research was carried out by computer simulation with the Movable Cellular Automaton method, using the generalized kinetic fracture model, which takes into account the finite duration of local fracture (fracture incubation time). It is shown that the fracture incubation time is a key parameter, which determines the transition conditions of the shear crack growth process from the sub-Rayleigh regime to supershear.

This study is devoted to the experimental investigation of the interaction of a propagating rupture with one or several mechanical heterogeneities. We developed a friction laboratory experiment where a soft elastic solid slides past a rigid flat plate. The system is coupled to an original medical imaging technique, ultrasound speckle interferometry, that allows observing the rupture dynamics as well as the emitted elastic shear wavefield into the solid body. We compare the dynamics of propagating rupture for a homogeneous flat interface and for three cases of heterogeneous sliding surfaces: (1) an interface with a single point-like barrier made of a small rock pebble, (2) an interface with a single linear barrier that joins the edges of the faults in a direction perpendicular to slip, and (3) an interface with multiple barriers disposed on half of its surface area, creating a heterogeneous zone. We obtain experimental observations of dynamic effects that have been predicted by numerical dynamic rupture simulations and provide experimental observations of the following phenomena: a barrier can stop or delay the rupture propagation; a linear single barrier can change the rupture velocity, increasing or decreasing it; we observe transition from subshear to supershear propagation due to the linear barrier; a large heterogeneous area slows down the rupture propagation. We observe a strong variability of the rupture dynamics occurring for identical frictional conditions, which we impute to heterogeneity of the stress field due to both the loading conditions and memory of the stress field due to previous rupture events.

One approach to investigate earthquake source processes is to produce kinematic source models from inversion of seismic records and geodetic data. The setup of the inversion requires a variety of assumptions and constraints to restrict the range of possible models. Here, we evaluate to what extent physically plausible earth- quake scenarios are reliably restituted in spite of these restrictions. We study which characteristics of ruptures, such as rupture velocity, slip distribution, stress drop, rise time, and slip function, can be reliably determined from the inversion of near-field seismic and geodetic data. Using spontaneous dynamic rupture simulations, we gen- erate five earthquake scenarios, each of which has different characteristics of the source process. Then we conduct a blind test by modeling the synthetic near-source data using a standard inversion scheme that optimizes the fit to the observations while searching for solutions with minimum roughness. The inversion procedure assumes a rupture front propagating away from the hypocenter with variable rupture velocity and a simple cosine slip-time function. Our results show that, overall, slip distribution and stress drop are reasonably well determined even for input models with relatively complex histories (such as a subshear rupture transitioning to supershear speeds). Depth-averaged rupture velocities are also reasonably well resolved although their estimate progressively deteriorates away from the hypocenter. The local rise time and slip function are not well resolved, but there is some sensitivity to the rupture pulse width, which can be used to differentiate between pulse-like and crack-like ruptures. Our test for understanding the inaccuracies in Green's functions shows that random 3D perturbations of 5% standard deviation do not lead to significant degradation of the estimation of earthquake source parameters. As remedies to the current limitations, we propose smoothing slip function parameters and using more complicated inversion schemes only if data necessitates them. Online Material: Figures showing snapshots of forward and inverse modeling of rupture, L curves, slip models, and waveform fits.

Seismic behaviors of long-span connected structures under multi-dimensional and earthquake excitation while considering wave passage effect are investigated through both numerical simulation and a shaking table test on a scaled model. It is found that seismic responses will be increased significantly if multi-dimensional earthquake excitation is considered; and wave-passage effect has diverse influence on different elements. Also special attentions should be paid to those elements near connections between the main tower and the corridor which inertial forces may change a lot when subjected to Traveling wave excitation with different apparent velocities. Moreover, the vertical acceleration responses of the corridor can be increased significantly due to wave passage effect. Therefore, it is necessary for aseismic design of long-span connected structure to take into account multi-dimensional earthquake components and multi-support earthquake excitations with different apparent velocities.

Large dynamic stresses near earthquake rupture fronts may induce an inelastic response of the surrounding materials, leading to increased energy absorption that may affect dynamic rupture. We systematically investigate the effects of off-fault plastic energy dissipation in 2-D in-plane dynamic rupture simulations under velocity-and-state-dependent friction with severe weakening at high slip velocity. We find that plasticity does not alter the nature of the transitions between different rupture styles (decaying versus growing, pulse-like versus crack-like, and subshear versus supershear ruptures) but increases their required background stress and nucleation size. We systematically quantify the effect of amplitude and orientation of background shear stresses on the asymptotic properties of self-similar pulse-like ruptures: peak slip rate, rupture speed, healing front speed, slip gradient, and the relative contribution of plastic strain to seismic moment. Peak slip velocity and rupture speed remain bounded. From fracture mechanics arguments, we derive a nonlinear relation between their limiting values, appropriate also for crack-like and supershear ruptures. At low background stress, plasticity turns self-similar pulses into steady state pulses, for which plastic strain contributes significantly to the seismic moment. We find that the closeness to failure of the background stress state is an adequate predictor of rupture speed for relatively slow events. Our proposed relations between state of stress and earthquake source properties in the presence of off-fault plasticity may contribute to the improved interpretation of earthquake observations and to pseudodynamic source modeling for ground motion prediction.

Seismic surface waves from large, distant earthquakes commonly trigger smaller earthquakes. However, delay times of hours to days between the surface waves and the triggered earthquakes weaken the causal connection. Furthermore, when there is no delay, the triggered earthquakes are typically too small or too obscured to obtain reliable source mechanisms. We present observations of instantaneous triggering of a strike-slip earthquake in central Alaska. Shear strain from the optimally aligned teleseismic Love wave induced a 24s exponential foreshock signal leading to the triggered earthquake. This nucleation phase, and the alignment of the triggered earthquake source mechanism with the teleseismic stress field, reveal the behavior of an existing fault under well-calibrated strain conditions. The Alaska earthquake provides the first observation of combined nucleation and triggering, and it suggests that transient stresses during nucleation may influence the subsequent earthquake rupture. Laboratory and theoretical studies of nucleation and triggering may help discriminate between different interpretations for the Alaska earthquake.

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. © 2012 Elsevier B.V.

During earthquakes , the rupture front propagates along faults at approximately 40–90 % of the shear or Rayleigh wave velocity, with slip rate often concentrated in a narrow region behind the front. Past studies have considered this phenomenon using a steady-state pulse-like rupture model and a slip-weakening friction law ; however, the results included a trade-off between rupture velocity and the scale of the pulse, which prevents the rupture velocity from being uniquely determined. In this study, we explore this issue and develop a model to determine rupture velocity by considering a friction law based on a numerical simulation of a past study for a slipping plane with its microscopic structure. We combine two models from past studies to construct a relationship between rupture velocity and some tectonophysical/geological parameters.

We study rapidly accelerating rupture fronts at the onset of frictional motion by performing high-temporal-resolution measurements of both the real contact area and the strain fields surrounding the propagating rupture tip. We observe large-amplitude and localized shear stress peaks that precede rupture fronts and propagate at the shear-wave speed. These localized stress waves, which retain a well-defined form, are initiated during the rapid rupture acceleration phase. They transport considerable energy and are capable of nucleating a secondary supershear rupture. The amplitude of these localized waves roughly scales with the dynamic stress drop and does not decrease as long as the rupture front driving it continues to propagate. Only upon rupture arrest does decay initiate, although the stress wave both continues to propagate and retains its characteristic form. These experimental results are qualitatively described by a self-similar model: a simplified analytical solution of a suddenly expanding shear crack. Quantitative agreement with experiment is provided by realistic finite-element simulations that demonstrate that the radiated stress waves are strongly focused in the direction of the rupture front propagation and describe both their amplitude growth and spatial scaling. Our results demonstrate the extensive applicability of brittle fracture theory to fundamental understanding of friction. Implications for earthquake dynamics are discussed.

The Mw7.9 Wenchuan earthquake of 12 May 2008 and Mw7.8 Kunlun Mountain earthquake of 14 November 2001 have equivalent energy magnitudes. However, the characteristics of the fault rupture processes and the geographical positions of these two great earthquakes are very different, and the damage and the public attention of the Kunlun Mountain earthquake are far less than the Wenchuan earthquake. The seismic wave energy information generated by great earthquakes is very rich. High-frequency energy of a big quake decays quickly within short time in a small scope, while low-frequency energy especially very low-frequency energy decays slowly, and can spread many laps around the Earth before consumed. We employ the spectral element method incorporated with large-scale parallel computing technology to investigate the characteristics of seismic wave propagation excited by the two great earthquakes. The transverse isotropic PREM (Preliminary Reference Earth Model) model is employed as a prototype for the numerical global Earth model. The Crust2.0 and S20RTS models are taken into consideration. These wave propagation processes are simulated by solving three-dimensional elastic wave governing equations. The visualization of the numerical results displays the profile with three components of the seismic wave propagation. Our calculation displays the thrusting and strike-slip of the source rupture processes of the Wenchuan earthquake and the left-lateral strike-slip of the source rupture process of the Kunlun Mountain earthquake, respectively. Comparison of low-frequency energy information of synthetic seismograms excited by the two earthquakes shows that the energy at low-frequency oscillation modes is broadly equivalent, but the energy of the Kunlun Mountain earthquake is slightly smaller than that of the Wenchuan event. The results also demonstrate that the frequency components are almost the same at low-frequency displacement amplitude spectra recorded at different stations between the two great earthquakes, but the energy is obviously different. These can further reveal that the characteristics of Earth's oscillation triggered by large earthquakes with different source ruptures are different, and the characteristics of Earth's oscillations recorded by different stations are also different.

Reliable ground‐motion prediction for future earthquakes depends on the ability to simulate realistic earthquake source models. Though dynamic rupture calculations have recently become more popular, they are still computationally demanding. An alternative is to invoke the framework of pseudodynamic (PD) source characterizations that use simple relationships between kinematic and dynamic source parameters to build physically self‐consistent kinematic models. Based on the PD approach of Guatteri et al. (2004), we propose new relationships for PD models for moderate‐to‐large strike‐slip earthquakes that include local supershear rupture speed due to stress heterogeneities. We conduct dynamic rupture simulations using stochastic initial stress distributions to generate a suite of source models in the magnitude M w 6–8. This set of models shows that local supershear rupture speed prevails for all earthquake sizes, and that the local rise‐time distribution is not controlled by the overall fault geometry, but rather by local stress changes on the faults. Based on these findings, we derive a new set of relations for the proposed PD source characterization that accounts for earthquake size, buried and surface ruptures, and includes local rise‐time variations and supershear rupture speed. By applying the proposed PD source characterization to several well‐recorded past earthquakes, we verify that significant improvements in fitting synthetic ground motion to observed ones is achieved when comparing our new approach with the model of Guatteri et al. (2004). The proposed PD methodology can be implemented into ground‐motion simulation tools for more physically reliable prediction of shaking in future earthquakes.

In this paper we consider a wide catalog of synthetic earthquakes, numerically modeled as spontaneous, fully dynamic, 3-D ruptures on extended faults, governed by different friction laws, including slip-dependent and rate- and state-dependent equations. We analyze the spatial correlations between the peak of fault slip velocity (vpeak) and the rupture speed (vr) at which the earthquake spreads over the fault. We found that vpeak positively correlates with vr and that the increase of vpeak is roughly quadratic. We found that near the transition between sub- and supershear regimes vpeak significantly diminishes and then starts to increase again with the square of vr . This holds for all the governing models we consider and for both homogeneous and heterogeneous configurations. Moreover, we found that, on average, vpeak increases with the magnitude of the event (vpeak ~ M00.18). Our results can be incorporated as constraints in the inverse modeling of faults.

We simulate the propagation of earthquake waves in the continental margin of Antarctica using the elastic wave modeling algorithm, which is modified to be suitable for acoustic-elastic coupled media and earthquake source. To simulate the various types of earthquake source, the staggered-grid finite-difference method, which is composed of velocity-stress formulae, can be more appropriate to use than the conventional, displacement-based, finite-difference method. We simulate the elastic wave propagation generated by earthquakes combining 3D staggered-grid finite-difference algorithm composed of displacement-velocity-stress formulae with double couple mechanisms for earthquake source. Through numerical tests for left-lateral strike-slip fault, normal fault and reverse fault, we could confirm that the first arrival of P waves at the surface is in a good agreement with the theoretically-predicted results based on the focal mechanism of an earthquake. Numerical results for a model made after the subduction zone in the continental margin of Antarctica showed that earthquake waves, generated by the reverse fault and propagating through the continental crust, the oceanic crust and the ocean, are accurately described.

This paper describes a technique for determining the potential energy of deformed material around a future earthquake rupture, with this energy being stored during the precursory period. The basic parameters are the following: rupture length on the Earth’s surface after the earthquake has occurred L, rupture depth h, and the relative block movement along the rupture strike line \(\bar u\). We compared the results for 44 large earthquakes with those derived by determining seismic wave energy from earthquake magnitude.

Mikumo et al. (2003) showed that it is possible to estimate the breakdown slip (Dc) as the slip at the time of the peak slip rate for rupture propagation with subshear speeds. Cruz-Atienza et al. (2009) later attempted to extend this method to extract information about Dc as the displacement at the time of the peak particle velocity from seismic strong-motion records. However, a reasonably accurate estimate of Dc was only possible in a narrow zone adjacent to the fault (typically on the order of hundreds of meters) due to the fast decay with distance from the fault of the seismic energy related to the stress breakdown process. When the rupture propagates with supershear-speeds, on the other hand, this energy is carried much farther away from the fault by Mach waves, in particular Rayleigh Mach waves when rupture reaches the Earth's surface (Dunham and Bhat, 2008). Here, we present a new approach to estimate Dc from strong-motion records containing Mach waves. First, we show that the method by Mikumo et al. is valid for supershear rupture propagation. This method is then used to estimate Dc via an asymptotic approximation of the slip and slip-rate time histories from the Mach waves. Using spontaneous rupture simulations we demonstrate that, for a visco-elastic half-space model, Dc can be estimated within an error of 40% from Mach waves that have propagated a distance of at least 3 km from the fault. The method is applied to estimate Dc for the 2002 Mw7.9 Denali, Alaska, earthquake (∼ 1.5 m) and for the 1999 Mw7.6 Izmit, Turkey, earthquake (∼ 1.7 m).

An idealized rupture, propagating smoothly near a terminal rupture velocity, radiates energy that is focused into a beam. For rupture velocity less than the S-wave speed, radiated energy is concentrated in a beam of intense fault-normal velocity near the projection of the rupture trace. Although confined to a narrow range of azimuths, this beam diverges and attenuates. For rupture velocity greater than the S-wave speed, radiated energy is concentrated in Mach waves forming a pair of beams propagating obliquely away from the fault. These beams do not attenuate until diffraction becomes effective at large distance. Events with supershear and sub-Rayleigh rupture velocity are compared in 2D plane-strain calculations with equal stress drop, fracture energy, and rupture length; only static friction is changed to determine the rupture velocity. Peak velocity in the sub-Rayleigh case near the termination of rupture is larger than peak velocity in the Mach wave in the supershear case. The occurrence of supershear rupture propagation reduces the most intense peak ground velocity near the fault, but it increases peak velocity within a beam at greater distances.

The introduction of the linear slip-weakening friction law permits the solution of the elastodynamic equation for a rupture that 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 the 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 article, by studying the dynamic rupture propagation and the solutions on the fault and on the free surface, I 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. My results show that, contrary 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. I confirm 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). I also numerically demonstrate that a valid alternative to this strategy is an appropriately smoothed, elliptical shear stress asperity. Moreover, I evaluate the optimal size of the nucleation patch where the procedure is applied; the simulations indicate that its size has to equal the critical distance of Day (1982) in the case of supershear ruptures and to exceed it in the case of subshear ruptures.

Destructive large earthquakes occur as dynamic frictional ruptures along pre-existing interfaces (or faults) in the Earth’s crust. One of the important issues in earthquake dynamics is the local duration of relative displacement or slip. Seismic inversions show that earthquakes may propagate as self-healing pulse-like ruptures, with local slip duration being much shorter than the overall rupture duration. Yet many classical models produce crack-like ruptures, with local slip durations comparable to the overall rupture duration. We study rupture modes in an experimental set up designed to mimic a fault prestressed both in compression and in shear. Our experiments demonstrate systematic variation from crack-like to pulse-like rupture modes as nondimensional shear prestress is decreased. The results of our experiments are consistent with theories of ruptures on interfaces with velocity-weakening friction. To consider the possibility that slip-weakening friction can also result in such rupture mode transition in the presence of the dynamic nucleation procedure employed by the experimental setup, we conduct numerical simulations with linear slip-weakening friction. In the simulations, we use the parameter regimes that were shown in previous studies to reproduce supershear transition distances obtained in the same experimental setup. We find that simulations with linear slip-weakening friction are unable to reproduce pulse-like ruptures, even in the presence of the dynamic initiation procedure. Our experimental results and simulations imply that velocity-weakening friction plays an important role in dynamic behavior of shear ruptures and needs to be included in earthquake models.

The 2008 Wenchuan earthquake occurred in an active earthquake zone, i.e., Longmenshan tectonic zone. Seismic waves triggered by this earthquake can be used to explore the characteristics of the fault rupture process and the hierarchical structure of the Earth’s interior. We employ spectral element method incorporated with large-scale parallel computing technology, to investigate the characteristics of seismic wave propagation excited by Wenchuan earthquake. We calculate synthetic seismograms with one-point source model and three-point source model respectively. The AK135 model is employed as a prototype of our numerical global Earth model. The Earth’s ellipticity, Earth’s medium attenuation, and topography data are taken into consideration. These wave propagation processes are simulated by solving three-dimensional elastic wave governing equations. Three-dimensional visualization of our numerical results displays the profile of the seismic wave propagation. The three-point source, which is proposed from the latest investigations through field observation and reverse estimation, can better demonstrate the spatial and temporal characteristics of the source rupture process than the one-point source. We take comparison of synthetic seismograms with observational data recorded at 16 observatory stations. Primary results show that the synthetic seismograms calculated from three-point source agree well with the observations. This can further reveal that the source rupture process of Wenchuan earthquake is a multi-rupture process, which is composed by at least three or more stages of rupture processes.

In this study, we preliminarily investigated the dynamic rupture process of the 1999 Chi-Chi, Taiwan, earthquake by using an extended boundary integral equation method, in which the effect of ground surface can be exactly included. Parameters for numerical modeling were carefully assigned based on previous studies. Numerical results indicated that, although many simplifications are assumed, such as the fault plane is planar and all heterogeneities are neglected, distribution of slip is still consistent roughly with the results of kinematic inversion, implying that for earthquakes in which ruptures run up directly to the ground surface, the dynamic processes are controlled by geometry of the fault to a great extent. By taking the common feature inferred by various kinematic inversion studies as a restriction, we found that the critical slip-weakening distance Dc should locate in a narrow region [60 cm, 70 cm], and supershear rupture might occur during this earthquake, if the initial shear stress before the mainshock is close to the local shear strength.

SUMMARY Taiwan Chelungpu-fault Drilling Project (TCDP) was initiated to understand the physical mechanisms involved in the large displacements of the 1999 Taiwan Chi-Chi earthquake. Continuous measurements of cores (including laboratory work) and a suite of geophysical downhole logs, including P- and S-wave sonic velocity, gamma ray, electrical resistivity, density, temperature, electrical borehole images and dipole-shear sonic imager, were acquired in Hole-A over the depth of 500–2003 m. Integrated studies of cores and logs facilitate qualitative and quantitative comparison of subsurface structures and physical properties of rocks. A total of 10 subunits were divided on the basis of geophysical characteristics. Generally, formation velocity and temperature increase with depth as a result of the overburden and thermal gradient, respectively. Gamma ray, resistivity, formation density, shear velocity anisotropy and density-derived porosity are primarily dependent on the lithology. Zones with changes of percentage of shear wave anisotropy and the fast shear polarization azimuth deduced from Dipole Shear-Imager (DSI) are associated with the appearance of fractures, steep bedding and shear zones. The fast shear wave azimuth is in good agreement with overall dip of the bedding (approximately 30° towards SE) and maximum horizontal compressional direction, particularly in the Kueichulin Formation showing strong shear wave velocity anisotropy. Bedding-parallel fractures are prevalent within cores, whereas minor sets of high-angle, NNW–SSE trending with N- and S-dipping fractures are sporadically distributed. The fault zone at depth 1111 m (FZA1111) is the Chi-Chi earthquake slip zone and could be a fluid conduit after the earthquake. The drastic change in fast shear wave polarization direction across the underlying, non-active Sanyi thrust at depth 1710 m reflects changes in stratigraphy, physical properties and structural geometry.

We study properties of dynamic ruptures and the partition of energy between radiation and dissipative mechanisms using two-dimensional in-plane calculations with the finite element method. The model consists of two identical isotropic elastic media separated by an interface governed by rate- and state-dependent friction. Rupture is initiated by gradually overstressing a localized nucleation zone. Different values of parameters controlling the velocity dependence of friction, the strength excess parameter and the length of the nucleation zone, lead to the following four rupture modes: supershear crack-like rupture, subshear crack-like rupture, subshear single pulse and supershear train of pulses. High initial shear stress and weak velocity dependence of friction favor crack-like ruptures, while the opposite conditions favor the pulse mode. The rupture mode can switch from a subshear single pulse to a supershear train of pulses when the width of the nucleation zone increases. The elastic strain energy released over the same propagation distance by the different rupture modes has the following order: supershear crack, subshear crack, supershear train of pulses and subshear single pulse. The same order applies also to the ratio of kinetic energy (radiation) to total change of elastic energy for the different rupture modes. Decreasing the dynamic coefficient of friction increases the fraction of stored energy that is converted to kinetic energy. General considerations and observations suggest that the subshear pulse and supershear crack are, respectively, the most and least common modes of earthquake ruptures.

Understanding sub-Rayleigh-to-intersonic transition of mode II cracks is a fundamental problem in fracture mechanics with important practical implications for earthquake dynamics and seismic radiation. In the Burridge–Andrews mechanism, an intersonic daughter crack nucleates, for sufficiently high prestress, at the shear stress peak traveling with the shear wave speed in front of the main crack. We find that sub-Rayleigh-to-intersonic transition and sustained intersonic propagation occurs in a number of other models that subject developing cracks to intersonic loading fields. We consider a spontaneously expanding sub-Rayleigh crack (or main crack) which advances, along a planar interface with linear slip-weakening friction, towards a place of favorable heterogeneity, such as a preexisting subcritical crack or a small patch of higher prestress (similar behavior is expected for a small patch of lower static strength). For a range of model parameters, a secondary dynamic crack nucleates at the heterogeneity and acquires intersonic speeds due to the intersonic stress field propagating in front of the main crack. Transition to intersonic speeds occurs directly at the tip of the secondary crack, with the tip accelerating rapidly to values numerically equal to the Rayleigh wave speed and then abruptly jumping to an intersonic speed. Models with favorable heterogeneity achieve intersonic transition and propagation for much lower prestress levels than the ones implied by the Burridge–Andrews mechanism and have transition distances that depend on the position of heterogeneity. We investigate the dependence of intersonic transition and subsequent crack propagation on model parameters and discuss implications for earthquake dynamics.

Physical limits on possible maximum ground motion at Yucca Mountain, Nevada, the designated site of a high-level radioactive waste repository, are set by the shear stress available in the seismogenic depth of the crust and by limits on stress change that can propagate through the medium. We find in dynamic deterministic 2D calculations that maximum possible horizontal peak ground velocity (PGV) at the underground repository site is 3.6 m/sec, which is smaller than the mean PGV predicted by the probabilistic seismic hazard analysis (PSHA) at annual exceedance probabilities less than 10 -6 per year. The physical limit on vertical PGV, 5.7 m/sec, arises from supershear rupture and is larger than that from the PSHA down to 10 -8 per year. In addition to these physical limits, we also calculate the maximum ground motion subject to the constraint of known fault slip at the surface, as inferred from paleoseismic studies. Using a published probabilistic fault displacement hazard curve, these calculations provide a probabilistic hazard curve for horizontal PGV that is lower than that from the PSHA. In all cases the maximum ground motion at the repository site is found by maximizing constructive interference of signals from the rupture front, for physically realizable rupture velocity, from all parts of the fault. Vertical PGV is maximized for ruptures propagating near the P -wave speed, and horizontal PGV is maximized for ruptures propagating near the Rayleigh-wave speed. Yielding in shear with a Mohr–Coulomb yield condition reduces ground motion only a modest amount in events with supershear rupture velocity, because ground motion consists primarily of P waves in that case. The possibility of compaction of the porous unsaturated tuffs at the higher ground-motion levels is another attenuating mechanism that needs to be investigated.