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We present a tutorial demonstration using a surrogate-model based uncertainty quantification (UQ) approach to study dynamic earthquake rupture on a rough fault surface. The UQ approach performs model calibration where we choose simulation points, fit and validate an approximate surrogate model or emulator, and then examine the input space to see which inputs can be ruled out from the data. Our approach relies on the mogp_emulator package to perform model calibration, and the FabSim3 component from the VECMA toolkit to streamline the workflow, enabling users to manage the workflow using the command line to curate reproducible simulations on local and remote resources. The tools in this tutorial provide an example template that allows domain researchers that are not necessarily experts in the underlying methods to apply them to complex problems. We illustrate the use of the package by applying the methods to dynamic earthquake rupture, which solves the elastic wave equation for the size of an earthquake and the resulting ground shaking based on the stress tensor in the Earth. We show through the tutorial results that the method is able to rule out large portions of the input parameter space, which could lead to new ways to constrain the stress tensor in the Earth based on earthquake observations. This article is part of the theme issue 'Reliability and reproducibility in computational science: implementing verification, validation and uncertainty quantification in silico'. [ABSTRACT FROM AUTHOR]

The process of earthquake appearance in its focus is analyzed on the basis of the oscillation theory. The earthquake focus consisting for simplicity of two blocks (granitic and basaltic) is studied mathematically and physically. The block sizes, density and Young's modulus of the rocks composing these blocks are considered to be known. We assume that the blocks are located on an edge of a regional tectonic fault. The tectonic plate or subplate, moving with a given speed u of shearing, is on the other edge of the fault. The mechanical interaction of the fault edges is due to the friction, which depends on the relative velocity V = u − dx/dt, where x is a coordinate of the concrete block. Physical-mathematical equations of block motion are solved using analytical methods. As a result, we find complete information about seismic vibrations in the focus and their characteristics. The evolutions of kinetic, potential and total energy as well as the function of dissipation in the focus and magnitude of the earthquake are calculated. The computations were carried out at different speeds of movement u. This allowed us to study the dependence of the earthquake magnitude on the velocity u of the main plate. The constructed original model of the earthquake focus unmasks the mechanism of seismic oscillations and their properties. [ABSTRACT FROM AUTHOR]

Seismicity in the Central Apennines is characterized by normal faulting with dip NE‐SW near 45°. If the stress at the hypocenter of the 2016 Norcia (Mw = 6.5) and 2009 L'Aquila (Mw = 6.3 on the Paganica fault) earthquakes originated only from stress transfer from previous historical events, the orientation of the principal stress axes would have been inconsistent with the observed tensional regime. The additional contribution of a regional stress is thus required, but Global Navigation Satellite System geodesy provides only stress rates. We empirically estimate a time multiplier for the regional stress rate, computed with a dense Global Navigation Satellite System network, such that the principal stress axes resulting from the sum of the stress transferred by previous events and the regional stress rate multiplied by the empirical temporal scale are consistent with normal faulting, both at the L'Aquila and Norcia hypocenters. Based on a Catalogue of 36 events of magnitude larger than 5.6, we estimate the total Coulomb stress at depths and along planes parallel to those of L'Aquila and Norcia. We provide evidence of an asymmetry of the Coulomb stress leading to a stress concentration near the hypocenter of the two events just prior of the 2009 and 2016 earthquakes. This stress anomaly disappeared after the two events. Similar stress patterns are observed for earlier events, which took place in 1461 at L'Aquila, 1703 on the Montereale plain, and in 1703 at Norcia/Valnerina. The 1997 sequence of Colfiorito exhibits a similar, anisotropic Coulomb stress pattern. Other areas with a similar stress anisotropy could be seismic gaps. Key Points: Elastic stress in Central Apennines slowly builds up and is occasionally released by earthquakes up to magnitude 7.2Stress buildup and release can be computed using GNSS velocity data and historical events in the past 700 yearsA stress reservoir located in the Gran Sasso mountain releases elastic energy on nearby faults along preferred directions of stress buildup [ABSTRACT FROM AUTHOR]

The Punchbowl Fault, California, USA, is an example of a simple fault zone that has a relatively narrow fault core with further slip localization to principal slip zones. We sampled the principal slip zone, fault core, and wall rocks and conducted hydrous pyrolysis experiments to analyze biomarker thermal maturity within the Punchbowl Fault. Using biomarker maturity as a proxy for temperature rise, we show that the existing principal slip zone experienced greater temperature rise than the surrounding fault core and wall rock, and therefore, we infer that earthquake slip localized along this layer. Furthermore, evidence of slight thermal maturity within the ultracataclasite suggests that the fault core is made up at least in part of reworked former principal slip zones. Using a wide range of possible layer thicknesses, we find that the maximum temperature range during a single earthquake could have varied from ~460 to 1,060 °C at 1‐m/s slip velocity. However, not all samples from within the principal slip zone show a temperature rise, indicating that layer thickness, slip, or shear stress varied during slip. Our temperature estimate also allows us to constrain the frictional energy dissipated during the earthquake to 2.2–25 MJ/m2. Our study demonstrates that localized slip structures can be directly linked to seismicity and that small changes in earthquake or fault parameters can lead to changes in temperature (and likely fault strength) at small scales. Plain Language Summary: Faults are complicated structures, and it would be useful to be able to map which parts of faults have slipped during earthquakes rather than at slower rates. It has been hypothesized that earthquakes occur along narrow structures within fault zones, but lab experiments at slower slip rates can also occur along narrow structures. Because faults heat up during earthquakes, we can look for geologic evidence of high temperatures within a fault to map where within the fault earthquake slip occurred. Here we map past earthquakes in the Punchbowl Fault, CA, USA, an ancient strand of the San Andreas Fault. We show that earthquakes occurred along small structures within the fault zone as had been previously hypothesized and that parts of the fault zone are made up of older, recycled small structures. Furthermore, we estimate how hot the fault might have gotten during an earthquake, which helps constrain the physics and chemistry of fault zone rocks during earthquake slip. Key Points: Biomarker thermal maturity reveals temperature rise along structures that hosted localized paleoseismic slip at the Punchbowl Fault, California, USATemperature ranged from 464 to 1,062 °C, depending on slipping zone thickness and assuming that the maturity signal is from a single eventTemperature rise is heterogeneous along strike, suggesting that fault strength could be highly variable during earthquakes [ABSTRACT FROM AUTHOR]

The maximum expected earthquake magnitude is an important parameter in seismic hazard and risk analysis because of its strong influence on ground motion. In the context of injection-induced seismicity, the processes that control how large an earthquake will grow may be influenced by operational factors under engineering control as well as natural tectonic factors. Determining the relative influence of these effects on maximum magnitude will impact the design and implementation of induced seismicity management strategies. In this work, we apply a numerical model that considers the coupled interactions of fluid flow in faulted porous media and quasidynamic elasticity to investigate the earthquake nucleation, rupture, and arrest processes for cases of induced seismicity. We find that under certain conditions, earthquake ruptures are confined to a pressurized region along the fault with a length-scale that is set by injection operations. However, earthquakes are sometimes able to propagate as sustained ruptures outside of the zone that experienced a pressure perturbation. We propose a faulting criterion that depends primarily on the state of stress and the earthquake stress drop to characterize the transition between pressure-constrained and runaway rupture behavior. [ABSTRACT FROM AUTHOR]

Abstract: Interseismic frictional healing is an essential process in the seismic cycle. Observations of both natural and laboratory earthquakes demonstrate that the magnitude of stress drop scales with the logarithm of recurrence time, which is a cornerstone of the rate and state friction (RSF) laws. However, the origin of this log linear behavior and short time “cutoff” for small recurrence intervals remains poorly understood. Here we use RSF laws to demonstrate that the back‐projected time of null‐healing intrinsically scales with the initial frictional state θi. We explore this behavior and its implications for (1) the short‐term cutoff time of frictional healing and (2) the connection between healing rates derived from stick‐slip sliding versus slide‐hold‐slide tests. We use a novel, continuous solution of RSF for a one‐dimensional spring‐slider system with inertia. The numerical solution continuously traces frictional state evolution (and healing) and shows that stick‐slip cutoff time also scales with frictional state at the conclusion of the dynamic slip process θi (=Dc/Vpeak). This numerical investigation on the origins of stick‐slip response is verified by comparing laboratory data for a range of peak slip velocities. Slower slip motions yield lesser magnitude of friction drop at a given time due to higher frictional state at the end of each slip event. Our results provide insight on the origin of log linear stick‐slip evolution and suggest an approach to estimating the critical slip distance on faults that exhibit gradual accelerations, such as for slow earthquakes. [ABSTRACT FROM AUTHOR]

Deformation of a saturated rock in the field and laboratory may occur in a broad range of conditions, ranging from undrained to drained. The poromechanical response is often anisotropic, and in a brittle rock, closely related to preexisting and stress-induced cracks. This can be modeled as a rock matrix embedded with an anisotropic system of cracks. Assuming microisotropy, expressions for three of the poroelastic coefficients of a transversely isotropic rock were derived in terms of the crack density tensor. Together with published results for the five effective elastic moduli, this provides a complete micromechanical description of the eight independent poroelastic coefficients of such a cracked rock. Relatively simple expressions were obtained for the Skempton pore pressure tensor, which allow one to infer the crack density tensor from undrained measurement in the laboratory, and also to infer the Biot-Willis effective stress coefficients. The model assumes a dilute concentration of noninteractive penny-shaped cracks, and it shows good agreement with experimental data for Berea sandstone, with crack density values up to 0.6. Whereas predictions on the storage coefficient and normal components of the elastic stiffness tensor also seem reasonable, significant discrepancy between model and measurement was observed regarding the off-diagonal and shear components of the stiffness. A plausible model had been proposed for development of very strong anisotropy in the undrained response of a fault zone, and the model here placed geometric constraints on the associated fracture system. [ABSTRACT FROM AUTHOR]

The Japan Trench Fast Drilling Project (JFAST) endeavored to establish the stress state on the shallow subduction megathrust that slipped during the M9 Tohoku earthquake. Borehole breakout data from the drill hole can constrain both the orientation and magnitude of the principal stresses. Here we reanalyze those data to refine our understanding of the stress state on the fault. In particular, we (1) improve the identification of breakouts, (2) consider a fuller range of stress states consistent with the data, and (3) incorporate new and more robust laboratory constraints on rock strength. The original conclusion that the region is in a normal faulting regime after the earthquake is strengthened by the new analysis. The combined analysis suggests that the earthquake released sufficient elastic strain energy to reset the local stress field. [ABSTRACT FROM AUTHOR]

Earthquakes are the result of slip along faults and are due to the decrease of rock frictional strength (dynamic weakening) with increasing slip and slip rate. Friction experiments simulating the abrupt accelerations (>>10 m/s2), slip rates (∼1 m/s), and normal stresses (>>10 MPa) expected at the passage of the earthquake rupture along the front of fault patches, measured large fault dynamic weakening for slip rates larger than a critical velocity of 0.01-0.1 m/s. The dynamic weakening corresponds to a decrease of the friction coefficient (defined as the ratio of shear stress vs. normal stress) up to 40%-50% after few millimetres of slip (flash weakening), almost independently of rock type. The microstructural evolution of the sliding interfaces with slip may yield hints on the microphysical processes responsible for flash weakening. At the microscopic scale, the frictional strength results from the interaction of micro- to nano-scale surface irregularities (asperities) which deform during fault sliding. During flash weakening, the visco-plastic and brittle work on the asperities results in abrupt frictional heating (flash heating) and grain size reduction associated with mechano-chemical reactions (e.g., decarbonation in CO2-bearing minerals such as calcite and dolomite; dehydration in water-bearing minerals such as clays, serpentine, etc.) and phase transitions (e.g., flash melting in silicate-bearing rocks). However, flash weakening is also associated with grain size reduction down to the nanoscale. Using focused ion beam scanning and transmission electron microscopy, we studied the micro-physical mechanisms associated with flash heating and nanograin formation in carbonate-bearing fault rocks. Experiments were conducted on pre-cut Carrara marble (99.9% calcite) cylinders using a rotary shear apparatus at conditions relevant to seismic rupture propagation. Flash heating and weakening in calcite-bearing rocks is associated with a shock-like stress release due to the migration of fast-moving dislocations and the conversion of their kinetic energy into heat. From a review of the current natural and experimental observations we speculate that this mechanism tested for calcite-bearing rocks, is a general mechanism operating during flash weakening (e.g., also precursory to flash melting in the case of silicate-bearing rocks) for all fault rock types undergoing fast slip acceleration due to the passage of the seismic rupture front. [ABSTRACT FROM AUTHOR]

Chlorite is a common, but understudied phyllosilicate mineral along continental and subduction zone faults. To understand the potential role of chlorite in different modes of fault slip, we measure the constitutive frictional properties of chlorite at low rates of deformation and shallow hydrothermal conditions by shearing powdered samples of water-saturated chlorite in the triaxial saw-cut configuration. Experiments were conducted at 25 to 130 °C, 130 MPa confining pressure, pore pressures from 10 MPa to 120 MPa, slip rates from 0.001 to 10 μm/s, and shear displacements up to 7.5 mm. The frictional strength of chlorite increases with increasing temperature from 25 to 130 °C (μ = 0.4 to 0.46), accompanied by an increased abundance of Riedel shears. Chlorite also transitions from rate-strengthening behavior at fast slip rates (0.1 to 10 μm/s) to rate-weakening or rate-neutral behavior at lower slip rates (0.001 to 0.01 μm/s), consistent with one hypothesis for the cause of slow slip. This transition in frictional behavior reflects different microphysical processes controlling the direct and evolution effects of friction. At low deformation rates, the magnitude and temperature sensitivity of the direct effect (a) are consistent with subcritical fracture. In contrast, the evolution effect (b) is insensitive to temperature and increases systematically with decreasing strain rate. We propose the increase in b and resulting rate-weakening behavior of chlorite with decreasing slip rate is controlled by time-dependent properties of adsorbed water to mineral surfaces. • Chamosite, the Fe2+ endmember of chlorite, is frictionally stronger (μ = 0.4–0.5) than Mg-rich chlorites previously studied. • Chlorite rate-weakens at slow slip rates which may be controlled by time-dependent properties of water films. • Chlorite strengthens with increasing temperature under shallow hydrothermal conditions. [ABSTRACT FROM AUTHOR]

Mapping full-field displacement and strain changes on the Earth's surface following an earthquake is of paramount importance to enhance our understanding of earthquake mechanics. Currently, aerial and satellite images taken pre- and post-earthquake can be processed with sub-pixel correlation algorithms to infer the co-seismic ground deformations (e.g., [, ]). However, the interpretation of this data is not straightforward due to the inherent complexity of natural faults and deformation fields. To gain understanding into rupture mechanics and to help interpret complex rupture features occurring in nature, we develop a laboratory earthquake setup capable of reproducing displacement and strain maps similar to those obtained in the field, while maintaining enough simplicity so that clear conclusions can be drawn. Earthquakes are mimicked in the laboratory by dynamic rupture propagating along an inclined frictional interface formed by two Homalite plates under compression (e.g., []). In our study, the interface is partially glued, in order to confine the rupture before it reaches the ends of the specimen. The specimens are painted with a speckle pattern to provide the surface with characteristic features for image matching. Images of the specimens are taken before and after dynamic rupture with a 4 Megapixels resolution CCD camera. The digital images are analyzed with two software packages for sub-pixel correlation: VIC-2D (Correlated Solutions Inc.) and COSI-Corr []. Both VIC-2D and COSI-Corr are able to characterize the full-field static displacement of the experimentally produced dynamic shear ruptures. The correlation analysis performed with either software clearly shows (i) the relative displacement (slip) along the frictional interface, (ii) the rupture arrest on the glued boundaries, and (iii) the presence of wing cracks. The obtained displacement measurements are converted to strains, using non-local de-noising techniques; stresses are obtained by introducing Homalite's constitutive properties. This study is a first step towards using the digital image correlation method in combination with high-speed photography to capture the highly transient phenomena involved in dynamic rupture. [ABSTRACT FROM AUTHOR]

Earthquakes are the result of slip along faults and are due to the decrease of rock frictional strength (dynamic weakening) with increasing slip and slip rate. Friction experiments simulating the abrupt accelerations (>>10 m/s2), slip rates (~1 m/s), and normal stresses (>>10 MPa) expected at the passage of the earthquake rupture along the front of fault patches, measured large fault dynamic weakening for slip rates larger than a critical velocity of 0.01–0.1 m/s. The dynamic weakening corresponds to a decrease of the friction coefficient (defined as the ratio of shear stress vs. normal stress) up to 40%–50% after few millimetres of slip (flash weakening), almost independently of rock type. The microstructural evolution of the sliding interfaces with slip may yield hints on the microphysical processes responsible for flash weakening. At the microscopic scale, the frictional strength results from the interaction of micro- to nano-scale surface irregularities (asperities) which deform during fault sliding. During flash weakening, the visco-plastic and brittle work on the asperities results in abrupt frictional heating (flash heating) and grain size reduction associated with mechano-chemical reactions (e.g., decarbonation in CO2-bearing minerals such as calcite and dolomite; dehydration in water-bearing minerals such as clays, serpentine, etc.) and phase transitions (e.g., flash melting in silicate-bearing rocks). However, flash weakening is also associated with grain size reduction down to the nanoscale. Using focused ion beam scanning and transmission electron microscopy, we studied the micro-physical mechanisms associated with flash heating and nanograin formation in carbonate-bearing fault rocks. Experiments were conducted on pre-cut Carrara marble (99.9% calcite) cylinders using a rotary shear apparatus at conditions relevant to seismic rupture propagation. Flash heating and weakening in calcite-bearing rocks is associated with a shock-like stress release due to the migration of fast-moving dislocations and the conversion of their kinetic energy into heat. From a review of the current natural and experimental observations we speculate that this mechanism tested for calcite-bearing rocks, is a general mechanism operating during flash weakening (e.g., also precursory to flash melting in the case of silicate-bearing rocks) for all fault rock types undergoing fast slip acceleration due to the passage of the seismic rupture front.

Seismological observations show that many destructive earthquakes nucleate within, or propagate through, thick sequences of carbonates and evaporites. For example, along the Apennines range (Italy) carbonate and evaporite sequences are present at hypocentral depths for recent major earthquakes (5.0

Abstract: To investigate the physical processes operating in active fault zones, we conduct analogue laboratory experiments where we track the morphological and mechanical evolution of an interface during slip. Our laboratory friction experiments consist of a halite (NaCl) slider held under constant normal load that is dragged across a coarse sandpaper substrate. This set-up is a surrogate for a fault surface, where brittle and plastic deformation mechanisms operate simultaneously during sliding. Surface morphology evolution, frictional resistance and infra-red emission are recorded with cumulative slip. After experiments, we characterize the roughness developed on slid surfaces, to nanometer resolution, using white light interferometry. We directly observe the formation of deformation features, such as slip parallel linear striations, as well as deformation products or gouge. The striations are often associated with marginal ridges of positive relief suggesting sideways transport of gouge products in the plane of the slip surface in a snow-plough-like fashion. Deeper striations are commonly bounded by triangular brittle fractures that fragment the salt surface and efficiently generate a breccia or gouge. Experiments with an abundance of gouge at the sliding interface have reduced shear resistance compared to bare surfaces and we show that friction is reduced with cumulative slip as gouge accumulates from initially bare surfaces. The relative importance of these deformation mechanisms may influence gouge production rate, fault surface roughness evolution, as well as mechanical behavior. Finally, our experimental results are linked to Nature by comparing the experimental surfaces to an actual fault surface, whose striated morphology has been characterized to centimeter resolution using a laser scanner. It is observed that both the stress field and the energy dissipation are heterogeneous at all scales during the maturation of the interface with cumulative slip. Importantly, we show that the formation of striations on fault planes by mechanical abrasion involves transport of gouge products in the fault plane not only along the slip direction, but also perpendicular to it. [Copyright &y& Elsevier]

We analyze the structure of the Archaean Pretorius fault in TauTona mine, South Africa, as well as the rupture-zone that recently reactivated it. The analysis is part of the Natural Earthquake Laboratory in South African Mines (NELSAM) project that utilizes the access to 3.6 km depth provided by the mining operations. The Pretorius fault is a 10 km long, oblique-strike-slip fault with displacement of up to 200 m that crosscuts fine to very coarse grain quartzitic rocks in TauTona mine. We identify here three structural zones within the fault-zone: (1) an outer damage zone, 100 m wide, of brittle deformation manifested by multiple, widely spaced fractures and faults with slip up to 3 m; (2) an inner damage zone, 25-30 m wide, with high density of anastomosing conjugate sets of fault segments and fractures, many of which carry cataclasite zones; and (3) a dominant segment, with a cataclasite zone up to 50 cm thick that accommodated most of the Archaean slip of the Pretorius fault, and is regarded as the 'principal slip zone' (PSZ). This fault-zone structure indicates that during its Archaean activity, the Pretorius fault entered the mature fault stage in which many slip events were localized along a single, PSZ. The mining operations continuously induce earthquakes, including the 2004, M2.2 event that rejuvenated the Pretorius fault in the NELSAM project area. Our analysis of the M2.2 rupture-zone shows that (1) slip occurred exclusively along four, pre-existing large, quasi-planer segments of the ancient fault-zone; (2) the slipping segments contain brittle cataclasite zones up to 0.5 m thick; (3) these segments are not parallel to each other; (4) gouge zones, 1-5 mm thick, composed of white 'rock-flour' formed almost exclusively along the cataclasite-host rock contacts of the slipping segments; (5) locally, new, fresh fractures branched from the slipping segments and propagated in mixed shear-tensile mode; (6) the maximum observed shear displacement is 25 mm in oblique-normal slip. The mechanical analysis of this rupture-zone is presented in Part II (H eesakkers et al., Earthquake Rupture at Focal Depth, Part II: Mechanics of the 2004 M2.2 Earthquake Along the Pretorius Fault, TauTona mine, South Africa , this volume). [ABSTRACT FROM AUTHOR]

Abstract: During fluid injection experiments at the geothermal site of Soultz-sous-Forêts (France), more than 114,000 induced seismic events with magnitudes between −2.0 and +2.9 were detected by a local downhole monitoring network. Of these, 35,039 events are sufficiently constrained to be located. Hypocenters align along a sub-vertical, planar structure with the apparent width being dominated by data scattering indicating that seismic activity predominantly occurs along a (pre-existing) larger scale fault structure. For this scenario, we present a numerical model to simulate hydraulic overpressures and induced seismicity during hydraulic injection. The numerical model is based on the physical processes of fluid pressure and stress diffusion with triggering of the induced seismicity being controlled by Coulomb friction. Even in its simplest form of a fault zone without any structural heterogeneity, the numerical model reproduces typical observations at Soultz-sous-Forêts, such as number and magnitude of induced events, hypocenter locations (including the Kaiser effect), occurrence of post-injection seismicity, and the largest magnitude event occurring several days after shut-in. [Copyright &y& Elsevier]

Abstract: Earthquakes are sensitive to the along-strike segmentation of the faults they break, especially in their initiation, propagation and arrest. We examine that segmentation and search whether it shows any specific properties. We focus on the largest-scale fault segmentation which controls the largest earthquakes. It is well established that major segments within faults markedly shape their surface cumulative slip-length profiles; segments appear as large slip bumps separated by narrow, pronounced slip troughs (inter-segments). We use that property to examine the distribution (location, number, length) of the major segments in 927 active normal faults in Afar (East Africa) of various lengths (0.3–65km), cumulative slips (1–1300m), slip rates (0.5–5mm/yr), and ages (104–106 yr). This is the largest fault population ever analyzed. To identify the major bumps in the slip profiles and determine their number, location and length, we analyze the profiles using both the classical Fourier transform and a space–frequency representation of the profiles, the S-transform, which is well adapted for characterizing local spectral properties. Our work reveals the following results: irrespective of their length, 70% of the slip profiles have a triangular envelope shape, in conflict with the elastic crack concept. Irrespective of their length, the majority of the faults (at least 50–70%) have a limited number of major segments, between 2 and 5 and more commonly equal to 3–5. The largest-scale segmentation of the faults is thus self-similar and likely to be controlled by the fault mechanics. The slip deficits at the major inter-segment slip troughs tend to smooth as the faults accumulate more slip resulting in increased connection of the major segments. The faults having accumulated more slip therefore generally appear as un-segmented (10–30%). Our observations therefore show that, whatever the fault on which they initiate, large earthquakes face the same number of major segments to potentially break. The number of segments that they eventually break seems to depend on the slip history (structural maturity) of the fault. [Copyright &y& Elsevier]

An earthquake is commonly described as a stick-slip frictional instability occurring along preexisting crustal faults. The seismic cycle of earthquake recurrence is characterized by long periods of quasi-static evolution, which precede sudden slip events accompanied by elastic wave radiation: the earthquake. This succession of processes over two well-distinguished time-scales recalls the behavior of nonlinear relaxation oscillations. We explore this connection by studying, in the framework of rate-and-state friction, the sliding of two identical slabs of elastic solid driven in opposite directions with a constant relative velocity. Our first innovation is to establish that the motion of a spring-block system is an asymptotic mechanical analogue of the frictional sliding of a single interface from which elastic waves radiate. Due to wave reflection at the boundaries, the equivalent mass of the block M = k(h/cs)2/12 is not independent of the equivalent spring stiffness k, where h/2 denotes the slab thickness and cs is the shear wave speed. Considering a non-monotonic friction law, we show that the relaxation oscillation regime is reached when the characteristic time-scale of frictionless oscillations is much greater than the characteristic time of frictional memory effects: (M/k)1/2 >> L/V*. We combine a composite approximation of the stick-slip cycle and numerical studies to show that the interfacial relaxation oscillations result from the subtle interplay of the non-monotonic properties of the friction law driving the long stress build-up of the quasi-static phase, and the inertial control of the fast slip phase originating from the wave propagation. We discuss the geophysical consequences for earthquake mechanics, and connections between the rate-and-state and Coulomb models of friction. [ABSTRACT FROM AUTHOR]

Abstract: Strain localization has important implications for the mechanical strength and stability of evolving fault zones. Structural fabrics interpreted as strain localization textures are common in natural and laboratory faults, however, the dynamic microscale processes controlling localization (and delocalization) are difficult to observe directly. Discrete numerical models of faulting allow a degree of dynamic visualization at the grain scale not easily afforded in nature. When combined with laboratory validation experiments and field observations, they become a powerful tool for investigating the dynamics of fault zone evolution. We present a method that implements realistic gouge evolution in 3D simulations of granular shear. The particle based model includes breakable bonds between individual particles allowing fracture of aggregate grains that are composed of many bonded particles. During faulting simulations, particle motions and interactions as well as the mechanical behavior of the entire system are continuously monitored. We show that a model fault gouge initially characterized by mono-disperse spherical aggregate grains gradually evolves, with accumulated strain, to a wide size distribution. The comminution process yields a highly heterogeneous textural signature that is qualitatively comparable to natural and laboratory produced fault gouges. Mechanical behavior is comparable to a first order with relevant laboratory data. Simulations also reveal a strong correlation between regions of enhanced grain size reduction and localized strain. Thus in addition to producing realistic fault gouge textures, the model offers the possibility to explore direct links between strain partitioning and structural development in fault zones. This could permit investigation of subtle interactions between high and low strain regions that may trigger localization–delocalization events and therefore control macroscopic frictional stability and hence the seismic potential of evolving fault zones. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: Active faults often contain distinct accumulations of granular wear material. During shear, this granular material accommodates stress and strain in a heterogeneous manner that may influence fault stability. We present new work to visualize the nature of contact force distributions during 3D granular shear. Our 3D discrete numerical models consist of granular layers subjected to normal loading and direct shear, where gouge particles are simulated by individual spheres interacting at points of contact according to simple laws. During shear, we observe the transient microscopic processes and resulting macroscopic mechanical behavior that emerge from interactions of thousands of particles. We track particle translations and contact forces to determine the nature of internal stress accommodation with accumulated slip for different initial configurations. We view model outputs using novel 3D visualization techniques. Our results highlight the prevalence of transient directed contact force networks that preferentially transmit enhanced stresses across our granular layers. We demonstrate that particle size distribution (psd) controls the nature of the force networks. Models having a narrow (i.e. relatively uniform) psd exhibit discrete pipe-like force clusters with a dominant and focussed orientation oblique to but in the plane of shear. Wider psd models (e.g. power law size distributions D =2.6) also show a directed contact force network oblique to shear but enjoy a wider range of orientations and show more out-of-plane linkages perpendicular to shear. Macroscopic friction level, is insensitive to these distinct force network morphologies, however, force network evolution appears to be linked to fluctuations in macroscopic friction. Our results are consistent with predictions, based on recent laboratory observations, that force network morphologies are sensitive to grain characteristics such as particle size distribution of a sheared granular layer. Our numerical approach offers the potential to investigate correlations between contact force geometry, evolution and resulting macroscopic friction, thus allowing us to explore ideas that heterogeneous force distributions in gouge material may exert an important control on fault stability and hence the seismic potential of active faults. [Copyright &y& Elsevier]

Abstract: Inherent to black-coal mining in New South Wales (Australia) since 1801, the discharge of ground water may have triggered the M5.6 Newcastle earthquake in 1989. 4-dimensional geomechanical model simulations reveal that widespread water removal and coal as deep as a 500 m depth resulted in an unload of the Earth''s crust. This unload caused a destabilization process of the pre-existing Newcastle fault in the interior of the crust beneath the Newcastle coal field. In tandem, an increase in shear stress and a decrease in normal stress may have reactivated this reverse fault. Over the course of the last fifty years, elevated levels of lithostatic stress alterations have accelerated. In 1991, based on the modeling of the crust''s elastostatic response to the unload, there has been the minimal critical shear stress changes of 0.01 Mega Pascal (0.1 bar) that reached the Newcastle fault at a depth where the 1989 mainshock nucleated. Hence, it can be anticipated that other faults might also be critically stressed in that region for a couple of reasons. First, the size of the area (volume) that is affected by the induced stress changes is larger than the ruptured area of the Newcastle fault. Second, the seismic moment magnitude of the 1989 M5.6 Newcastle earthquake is associated with only a fraction of mass removal (1 of 55), following McGarr''s mass-moment relationship. Lastly, these findings confirm ongoing seismicity in the Newcastle region since the beginning of the 19th century after a dormant period of 10,000 years of no seismicity. [Copyright &y& Elsevier]

Abstract: We revisit the April 1979 Montenegro earthquake sequence to invert for finite-fault slip models for the mainshock of 15 April 1979 (Mw 7.1) and of the strongest aftershock of 24 May 1979 (Mw 6.2) using P, SH and SV waveforms, retrieved from IRIS data center. We also used body waveform modelling inversion to confirm the focal mechanism of the mainshock as a pure thrust mechanism and rule out the existence of considerable strike slip component in the motion. The mainshock occurred along a shallow (depth 7 km), low angle (14°) thrust fault, parallel to the coastline and dipping to the NE. Our preferred slip distribution model for the mainshock indicates that rupture initiated from SE and propagated towards NW, with a speed of 2.0 km/s. Moment was released in a main slip patch, confined in an area of L ∼50 km× W ∼23 km. The maximum slip (∼2.7 m) occurred ∼30 km to the NW of the hypocenter (location of rupture initiation). The average slip is 49 cm and the total moment release over the fault is 4.38e19 Nm. The slip model adequately fits the distribution of the Mw ≥4.3 aftershocks, as most of them are located in the regions of the fault plane that did not slip during the mainshock. The 24 May 1979 (Mw 6.2) strongest aftershock occurred ∼40 km NW of the mainshock. Our preferred slip model for this event showed a characteristic two-lobe pattern, where each lobe is ∼7.5×7.5 km2. Rupture initiated in the NW lobe, where the slip obtained its maximum value of 45 cm, very close to the hypocenter, and propagated towards the south-eastern lobe where it reached another maximum value — for this lobe — of 30 cm, approximately 10 km away from the hypocenter. To indirectly validate our slip models we produced synthetic PGV maps (Shake maps) and we compared our predictions with observations of ground shaking from strong motion records. All comparisons were made for rock soil conditions and in general our slip models adequately fit the observations especially at the closest stations where the shaking was considerably stronger. Through the search of the parameter space for our inversions we obtained an optimum location for the mainshock at 42.04°N and 19.21° E and we also observed that better fit to the observations was obtained when the fault was modeled as a blind thrust fault. [Copyright &y& Elsevier]

SUMMARY A model of a ductile fault zone is incorporated into a forward 3-D earthquake model to better constrain fault-zone hydraulics. The conceptual framework of the model fault zone was chosen such that two distinct parts are recognized. The fault core, characterized by a relatively low permeability, is composed of a coseismic fault surface embedded in a visco-elastic volume that can creep and compact. The fault core is surrounded by, and mostly sealed from, a high permeability damaged zone. The model fault properties correspond explicitly to those of the coseismic fault core. Porosity and pore pressure evolve to account for the viscous compaction of the fault core, while stresses evolve in response to the applied tectonic loading and to shear creep of the fault itself. A small diffusive leakage is allowed in and out of the fault zone. Coseismically, porosity is created to account for frictional dilatancy. We show in the case of a 3-D fault model with no in-plane flow and constant fluid compressibility, pore pressures do not drop to hydrostatic levels after a seismic rupture, leading to an overpressured weak fault. Since pore pressure plays a key role in the fault behaviour, we investigate coseismic hydraulic property changes. In the full 3-D model, pore pressures vary instantaneously by the poroelastic effect during the propagation of the rupture. Once the stress state stabilizes, pore pressures are incrementally redistributed in the failed patch. We show that the significant effect of pressure-dependent fluid compressibility in the no in-plane flow case becomes a secondary effect when the other spatial dimensions are considered because in-plane flow with a near-lithostatically pressured neighbourhood equilibrates at a pressure much higher than hydrostatic levels, forming persistent high-pressure fluid compartments. If the observed faults are not all overpressured and weak, other mechanisms, not included in this model, must be at work in nature, which need to be investigated. Significant leakage perpendicular to the fault strike (in the case of a young fault), or cracks hydraulically linking the fault core to the damaged zone (for a mature fault) are probable mechanisms for keeping the faults strong and might play a significant role in modulating fault pore pressures. Therefore, fault-normal hydraulic properties of fault zones should be a future focus of field and numerical experiments. [ABSTRACT FROM AUTHOR]

Physical and chemical fluid–rock interactions are implicated in controlling earthquake nucleation and recurrence. In particular, interseismic compaction, sealing and healing of fractured fault rocks can lead to strength recovery and stabilisation of fault zones. In contrast, these same processes can also assist increases in pore fluid pressures and consequent destabilisation of faults. Here, we present high-temperature, hydrothermal experiments designed to assess the evolution of strength of fault zones in previously intact rock, and also characterise the associated changes to porosity and permeability. Cores of Fontainebleau sandstone were initially loaded to failure in a high-pressure gas–medium apparatus. The failed specimens were then hydrothermally reacted at 927°C for variable duration under isostatic conditions, and subsequently re-fractured to determine the ‘interseismic’ strength recovery. In the most extreme case, hydrothermally induced gouge compaction, cementation and crack healing resulted in 75% strength recovery after reaction for 6 h. Isostatic hydrothermal treatment also resulted in dramatic reduction in porosity and permeability. Strength of the fault zone following hydrothermal reaction appears to be closely correlated to porosity, consistent with previous studies on brittle failure of porous aggregates. The experimental results show how hydrothermal reactions in fault zones may lead to two competing, time-dependent effects; fault strengthening due to increased cohesion in the fault zone and fault weakening arising from elevated pore pressures within a well cemented, low-permeability gouge layer. [Copyright &y& Elsevier]

Earthquake mechanics may be determined by the geometry of a fault system. Slip on a fractal branching fault surface can explain: 1) regeneration of stress irregularities in an earthquake; 2) the concentration of stress drop in an earthquake into asperities; 3) starting and stopping of earthquake slip at fault junctions, and 4) self-similar scaling of earthquakes. Slip at fault junctions provides a natural realization of barrier and asperity models without appealing to variations of fault strength. Fault systems are observed to have a branching fractal structure, and slip may occur at many fault junctions in an earthquake. Consider the mechanics of slip at one fault junction. In order to avoid a stress singularity of order 1/r, an intersection of faults must be a triple junction and the Burgers vectors on the three fault segments at the junction must sum to zero. In other words, to lowest order the deformation consists of rigid block displacement, which ensures that the local stress due to the dislocations is zero. The elastic dislocation solution, however, ignores the fact that the configuration of the blocks changes at the scale of the displacement. A volume change occurs at the junction; either a void opens or intense local deformation is required to avoid material overlap. The volume change is proportional to the product of the slip increment and the total slip since the formation of the junction. Energy absorbed at the junction, equal to confining pressure times the volume change, is not large enongh to prevent slip at a new junction. The ratio of energy absorbed at a new junction to elastic energy released in an earthquake is no larger than P/µ where P is confining pressure and µ is the shear modulus. At a depth of 10 km this dimensionless ratio has th value P/µ= 0.01. As slip accumulates at a fault junction in a number of earthquakes, the fault segments are displaced such that they no longer meet at a single point. For this reason the volume increment for a given slip increment becomes larger. A juction with past accumulated slip ??0 is a strong barrier to earthquakes with maximum slip um < 2 (P/µ) u0 = u0/50. As slip continues to occur elsewhere in the fault system, a stress concentration will grow at the old junction. A fresh fracture may occur in the stress concentration, establishing a new triple junction, and allowing continuity of slip in the fault system. The fresh fracture could provide the instability needed to explain earthquakes. Perhaps a small fraction (on the order of P/µ) of the surface that slips in any earthquake is fresh fracture. Stress drop occurs only on this small fraction of the rupture surface, the asperities. Strain change in the asperities is on the order of P/µ. Therefore this model predicts average strais change in an earthquake to be on the order of (P/µ)2 = 0.0001, as is observed.

An active fault zone is home to a plethora of complex structural and geometric features that are expected to affect earthquake rupture nucleation, propagation, and arrest, as well as interseismic deformation. Simulations of these complexities have been largely done using continuum plasticity or scalar damage theories. In this paper, we use a highly efficient novel hybrid finite element-spectral boundary integral equation scheme to investigate the dynamics of fault zones with small scale pre-existing branches as a first step towards explicit representation of anisotropic damage features in fault zones. The hybrid computational scheme enables exact near-field truncation of the elastodynamic field allowing us to use high resolution finite element discretization in a narrow region surrounding the fault zone that encompasses the small scale branches while remaining computationally efficient. Our results suggest that the small scale branches may influence the rupture in ways that may not be realizable in homogenized continuum models. Specifically, we show that these short secondary branches significantly affect the post event stress state on the main fault leading to strong heterogeneities in both normal and shear stresses and also contribute to the enhanced generation of high frequency radiation. The secondary branches also affect off-fault plastic strain distribution and suggest that co-seismic inelasticity is sensitive to pre-existing damage features. We discuss our results in the larger context of the need for modeling earthquake ruptures with high resolution fault zone physics. • The secondary faults increase total energy dissipation. • The secondary faults lead to heterogeneous stress field on the main fault. • The secondary faults promote high frequency generation. • The secondary faults promote normal undulation on the main fault. [ABSTRACT FROM AUTHOR]