Rate-state Friction Research Articles

Effect of lateral stress on frictional properties of a fracture in sandstone

The injection of large volumes of natural gas into geological formations, as is required for underground gas storage, leads to alterations in the effective stress exerted on adjacent faults. This increases the potential for their reactivation and subsequent earthquake triggering. Most measurements of the frictional properties of rock fractures have been conducted under normal and shear stresses. However, faults in gas storage facilities exist within a true three-dimensional (3D) stress state. A double-direct shear experiment on rock fractures under both lateral and normal stresses was conducted using a true triaxial loading system. It was observed that the friction coefficient increases with increasing lateral stress, but decreases with increasing normal stress. The impact of lateral and normal stresses on the response is primarily mediated through their influence on the initial friction coefficient. This allows for an empirical modification of the rate-state friction model that considers the influence of lateral and normal stresses. The impact of lateral and normal stresses on observed friction coefficients is related to the propensity for the production of wear products on the fracture surfaces. Lateral stresses enhance the shear strength of rock (e.g. Mogi criterion). This reduces asperity breakage and the generation of wear products, and consequently augments the friction coefficient of the surface. Conversely, increased normal stresses inhibit dilatancy on the fracture surface, increasing the breakage of asperities and the concomitant production of wear products that promote rolling deformation. This ultimately reduces the friction coefficient.

Frictional and poromechanical properties of the Delaware Mountain Group: Insights into induced seismicity in the Delaware Basin

The Delaware Basin in West Texas and Southeast New Mexico has experienced a proliferation in seismic activity since 2016. The seismic activity is primarily due to subsurface injection of wastewater into shallow and deep reservoirs. However, the precise mechanisms connecting fluid injection to seismic activity are not well understood. To shed light on these processes, we measured rate-state friction and poromechanical properties of rocks sampled from the Delaware Mountain Group (DMG) at pressures and stresses representative of in-situ conditions. Experiments were conducted inside a pressure vessel and loaded at a true-triaxial stress state. The samples exhibit velocity-strengthening behavior and transition to velocity-neutral behavior with increasing slip. We also measure frictional healing and demonstrate that the healing rates are consistent with those measured from quartz-feldspathic-rich rocks. Experiments were conducted under a constant pore-pressure boundary condition where transient changes in pore-volume were compensated by modulating the fluid volume within the fault. Our data show that a step increase in sliding velocity leads to dilatancy and causes an influx of fluid into the fault. In contrast, a step decrease in sliding velocity causes the fault zone to compact and reduces fluid flow into the fault. Data show that changes in flow rate scale systematically with fault slip velocity. Broadly speaking, the frictional and poromechanical data indicate that shallow faults within the DMG should favor aseismic creep as opposed to unstable slip. Our data are consistent with elastic dislocation models of fault slip and InSAR data, indicating that faulting in the DMG is predominantly aseismic. The lack of velocity weakening behavior observed in our samples indicates that heterogenous frictional properties are needed to explain the co-existence of both aseismic and seismic slip in the DMG.

Influence of joint inclination on mechanical behaviors of shales during unloading-induced slip processes

To investigate the effect of joint inclination on the mechanical behaviors of unloading-induced slip processes, shale samples with different joint inclinations (θ) were tested under constant axial stress and graded unloading of confining pressure to induce slip. The results show that the slip tests resulted in scratches and damage of the rock matrix, thus increasing joint roughness coefficient (JRC) of saw-cut surface samples by values of 4.69, 2.75 and 2.67 for θ = 30°, 40° and 50°, respectively. With the unloading of confining pressure, the samples experienced creep slip, quasi-static slip, and dynamic slip, respectively. The velocity at creep slip, quasi-static slip and dynamic slip decreased with the increase in θ. The average velocities of quasi-static slip are 2.9 × 10−2 mm/s, 1.1 × 10−2 mm/s and 2.1 × 10−3 mm/s for θ = 30°, 40° and 50°, respectively. As the slip progresses, the micro-convexities on the joint are sheared off, resulting in a deterioration of the interlocking effect, which causes the occurrence time of quasi-static slip to advance in an unloading stage and the duration to increase. The friction coefficient (μ) decreased by 2.22%, which changes from 0.45 to 0.44 for the sample with θ = 30°, indicating that the friction strength was slightly weakened during the unloading-induced slip. As θ increases, the friction strength of the sample was enhanced. The μ increased by 19.23% from 0.52 to 0.62 and increased by 28.81% from 0.59 to 0.76 for the sample with θ=40° and 50°, respectively. Based on the experimental results, the unloading-induced slip behaviors were fitted with the rate and state friction law. However, the mechanical behavior of the sample has changed from “shear slip” to “slip failure” as the joint inclination increase, which resulted in the dynamic slip of the sample with θ = 40° and 50° being opposite to the rate weakening described in the rate state friction law.

A Source Model for Earthquakes near the Nucleation Dimension

ABSTRACT Earthquake self-similarity is a controversial topic, both observationally and theoretically. Theory predicts a finite nucleation dimension, implying a break of self-similarity below a certain magnitude. Although observations of non-self-similar earthquake behavior have been reported, their interpretation is challenging due to trade-offs between source and path effects and assumptions on the underlying source model. Here, I introduce a source model for earthquake nucleation and quantify the resulting scaling relations between source properties (far-field pulse duration, seismic moment, stress drop). I derive an equation of motion based on fracture mechanics for a circular rupture obeying rate–state friction and a simpler model with constant stress drop and fracture energy. The latter provides a good approximation to the rate–state model and leads to analytical expressions for far-field displacement pulses and spectra. The onset of ground motion is characterized by exponential growth with characteristic timescale t0=R0/vf, with R0 the nucleation dimension and vf a limit rupture velocity. Therefore, normalized displacements have a constant duration, proportional to the nucleation length rather than the source dimension. For ray paths normal to the fault, the exponential growth results in a Boatwright spectrum with n = 1, γ=2 and corner frequency ωc=1/t0. For other orientations, the spectrum has an additional sinc(·) term with a corner frequency related to the travel-time delay across the asperity. Seismic moments scale as M0∼R(R−R0)R0, in which R is the size of asperity, becoming vanishingly small as R→R0. Therefore, stress drops estimated from M0 and fc are smaller than the nominal stress drop, and they increase with magnitude up to a constant value, consistent with several seismological studies. The constant earthquake duration is also in agreement with reported microseismicity: for 0<Mw<2 events studied by Lin et al. (2016) in Taiwan, the observed durations imply a nucleation length between 45 and 80 m.

3-D Simulations of earthquakes rupture jumps: 1. Homogeneous pre-stress conditions

SUMMARYObservational and modelling studies indicate that earthquake ruptures can jump between fault sections as large as ∼3 and ∼5 km for compressional and extensional offsets, respectively. Here, we compare characteristics of the rupture jump process on parallel but offset fault sections from traditional 3-D dynamic rupture simulations governed by slip weakening friction using the finite element code, FaultMod, to those from quasi-dynamic simulations governed by rate- and state-dependent friction (rate-state friction) using the code RSQSim. These simulations use spatially uniform initial stresses. For a variety of measures the rupture renucleation position on the offset fault, the rate-state friction and slip weakening friction models produce very similar results. The principal difference is the additional occurrence of delayed rupture jumps that arise from the time- and stress-dependent nucleation that is characteristic of rate-state friction. For immediate rupture jumps, models with slip weakening friction span greater offsets than those with rate-state friction. However the jump distances are nearly identical when delayed rupture jumps are included in the comparisons. We propose that delayed rupture jumps are the likely mechanism for adjacent large-earthquake pairs and clusters. Based on the similarity of renucleation positions with both dynamic and quasi-dynamic models, we conclude that the renucleation positions for rupture initiation on the receiver fault (separated by less than ∼3 km from the source fault) are primarily controlled by static stress changes induced by slip on the initiating fault. However, in light of the slightly greater maximum jump distances (>3 km) seen with the dynamic slip weakening friction model, dynamic stress changes from seismic waves play an increasingly important role as offset distances increase.

Tidal Modulation of Ice Streams: Effect of Periodic Sliding Velocity on Ice Friction and Healing

Basal slip along glaciers and ice streams can be significantly modified by external time-dependent forcing, although it is not clear why some systems are more sensitive to tidal stresses. We have conducted a series of laboratory experiments to explore the effect of time varying load point velocity on ice-on-rock friction. Varying the load point velocity induces shear stress forcing, making this an analogous simulation of aspects of ice stream tidal modulation. Ambient pressure, double-direct shear experiments were conducted in a cryogenic servo-controlled biaxial deformation apparatus at temperatures between −2°C and −16°C. In addition to a background, median velocity (1 and 10 μm/s), a sinusoidal velocity was applied to the central sliding sample over a range of periods and amplitudes. Normal stress was held constant over each run (0.1, 0.5 or 1 MPa) and the shear stress was measured. Over the range of parameters studied, the full spectrum of slip behavior from creeping to slow-slip to stick-slip was observed, similar to the diversity of sliding styles observed in Antarctic and Greenland ice streams. Under conditions in which the amplitude of oscillation is equal to the median velocity, significant healing occurs as velocity approaches zero, causing a high-amplitude change in friction. The amplitude of the event increases with increasing period (i.e. hold time). At high normal stress, velocity oscillations force an otherwise stable system to behave unstably, with consistently-timed events during every cycle. Rate-state friction parameters determined from velocity steps show that the ice-rock interface is velocity strengthening. A companion paper describes a method of analyzing the oscillatory data directly. Forward modeling of a sinusoidally-driven slider block, using rate-and-state dependent friction formulation and experimentally derived parameters, successfully predicts the experimental output in all but a few cases.

Propagation of a precursory detachment front along a seismogenic plate interface in a rate–state friction model of earthquake cycles

SUMMARYA numerical simulation of earthquake cycles at the subduction zone of a plate interface was conducted, using a rate- and state-dependent friction law, to examine aseismic sliding processes propagating into a locked plate interface. In the model, a reverse fault is assumed in a 2-D uniform elastic half-space, and relative plate motion is imposed with a constant velocity. Simulated earthquakes occur repeatedly at a shallower seismogenic plate interface with a velocity-weakening frictional property, while stable sliding occurs in the deeper part, in which a velocity-strengthening frictional property is assumed. During interseismic periods, deep stable sliding causes shear stress to concentrate at the deeper edge of the locked plate interface, and a partial drop in stress occurs, resulting in plate detachment. The resulting detachment front propagates upwards along the seismogenic plate interface until an earthquake occurs, causing aseismic sliding with a sliding velocity significantly lower than the imposed relative plate velocity. The propagation velocity of the detachment front is almost constant in each case, and it is proportional to the relative plate velocity and inversely proportional to the effective normal stress. Episodic events of increased slip velocity occur in the latter half of an interseismic period when the characteristic slip distance is small. Updip propagation of episodic slip is arrested by a low stress barrier, and episodic slips backpropagate downdip. During the final few years of the simulation cycle, the average sliding velocity is approximately inversely proportional to the time to occurrence for a large interplate earthquake.

Physical conditions and frictional properties in the source region of a slow-slip event

Recent geodetic studies have shown that slow-slip events can occur on subduction faults, including their shallow (<15 km depth) parts where tsunamis are also generated. Although observations of such events are now widespread, the physical conditions promoting shallow slow-slip events remain poorly understood. Here we use full waveform inversion of controlled-source seismic data from the central Hikurangi (New Zealand) subduction margin to constrain the physical conditions in a region hosting slow slip. We find that the subduction fault is characterized by compliant, overpressured and mechanically weak material. We identify sharp lateral variations in pore pressure, which reflect focused fluid flow along thrust faults and have a fundamental influence on the distribution of mechanical properties and frictional stability along the subduction fault. We then use high-resolution data-derived mechanical properties to underpin rate–state friction models of slow slip. These models show that shallow subduction fault rocks must be nearly velocity neutral to generate shallow frictional slow slip. Our results have implications for understanding fault-loading processes and slow transient fault slip along megathrust faults. A shallow slow-slip source region has laterally variable elastic properties and pore pressure, and near-velocity-neutral frictional properties, according to seismic imaging of part of the Hikurangi subduction margin and data-constrained modelling.

Cascadia megathrust earthquake rupture model constrained by geodetic fault locking.

Paleo-earthquakes along the Cascadia subduction zone inferred from offshore sediments and Japan coastal tsunami deposits approximated to M9+ and ruptured the entire margin. However, due to the lack of modern megathrust earthquake records and general quiescence of subduction fault seismicity, the potential megathrust rupture scenario and influence of downdip limit of the seismogenic zone are still obscure. In this study, we present a numerical simulation of Cascadia subduction zone earthquake sequences in the laboratory-derived rate-and-state friction framework to investigate the potential influence of the geodetic fault locking on the megathrust sequences. We consider the rate-state friction stability parameter constrained by geodetic fault locking models derived from decadal GPS records, tidal gauge and levelling-derived uplift rate data along the Cascadia margin. We incorporate historical coseismic subsidence inferred from coastal marine sediments to validate our coseismic rupture scenarios. Earthquake rupture pattern is strongly controlled by the downdip width of the seismogenic, velocity-weakening zone and by the earthquake nucleation zone size. In our model, along-strike heterogeneous characteristic slip distance is required to generate margin-wide ruptures that result in reasonable agreement between the synthetic and observed coastal subsidence for the AD 1700 Cascadia Mw∼9.0 megathrust rupture. Our results suggest the geodetically inferred fault locking model can provide a useful constraint on earthquake rupture scenarios in subduction zones. This article is part of the theme issue 'Fracture dynamics of solid materials: from particles to the globe'.

“Bristle-State” Friction: Modeling Slip Initiation and Transient Frictional Evolution From High-Velocity Earthquake Rupture Experiments

Lamont-Doherty Fellowship in Earth and Environmental Sciences National Science Foundation (NSF) 1615203 National Research Center for Integrated Natural Disaster Management ANID/FONDAP/15110017 Andean Geothermal Center of Excellence, CEGA 15090013

Effects of Barriers on Fault Rupture Process and Strong Ground Motion Based on Various Friction Laws

A barrier may induce a supershear rupture on a fault. This paper focuses on two questions: One is whether the existence of a barrier accelerates the propagation speed of a whole fault rupture, and the other is what are the effects of friction laws and strength of a barrier on the rupture propagation process. For these purposes, classical slip-weakening, rate-state, and modified slip-weakening friction laws are employed to simulate the effect of a barrier on the fault rupture process. The simulation results showed that the rupture speed of the fault obviously decreases when the rupture front propagates to the barriers, and the rupture speed obviously increases when the rupture front leaves barriers. It was also found that a barrier on a fault may induce a supershear rupture via the rate-state friction law. The simulation results also showed that with the increase of barrier strength, the rupture speed near barriers fluctuates more and more; when the barrier strength exceeds a certain level, a supershear rupture area appears on the fault; with the increase of barrier strength, the propagation distance of the rupture at supershear wave velocity correspondingly increases. In addition, with the increase of barrier strength, the overall rupture duration of the fault slightly increases. This indicates that a barrier cannot shorten the total duration of a fault rupture. Though a barrier will lead to a supershear rupture, it just regulates the distribution of the rupture speed on the fault surface. Moreover, with the increase of barrier strength, the peak ground acceleration caused by rupture through the barrier also increases, indicating that the existence of a barrier may lead to the intensification of seismic hazards.

Recent seismicity rate forecast for North East India: An approach based on rate state friction law

In this study, we have investigated the association of stress-field disparities through earthquake production rate in both spatially and temporally for Northeast region of India. Here, we have implemented the rate and state dependent friction law for forecasting the seismicity rate over MW ≥ 5.0 earthquake events during the period 2013–2015. The most valuable input model parameter of forecasting seismicity rate is Coulomb stresses changes (ΔCFF), which promote the seismicity rate. The ΔCFF distributions that exhibit significant stress increase in the close proximity of the mainshock sources are found to be diminished with the inverse of the distance from the fault rupture plane. Basically, background seismicity depends on the Coulomb stress changes. These Coulomb stress changes amplify the background seismicity, so a little change in stress can produce very low or high seismicity rate in areas of high ambient seismicity. In several zones the high seismicity rate is revealed by the dominancy of the low b-value. The observed background seismicity rate lies between the ranges of 0–4.0. The significant b-value is achieved in the range of 0.57–1.54 along with average value of 0.93. We have taken the value of constant consecutive parameters (i.e. Aσ = 0.05 MPa) and constant effective friction coefficient of μ'=0.4 for all the faults. However, in the forecast model we have obtained the stress perturbations and heterogeneous b-value to infer the reliable result in comparison to reference forecast model for the period of 1963–2012. In this study, we have also adopted the RELM experiment in CSEP testing Centre to verify the consistency of the result related to forecast for the duration of 2013–2015. The statistical test provided the satisfactory result for this study region.

Modeling earthquake sequences along the Manila subduction zone: Effects of three-dimensional fault geometry

To assess the potential of catastrophic megathrust earthquakes (MW > 8) along the Manila Trench, the eastern boundary of the South China Sea, we incorporate a 3D non-planar fault geometry in the framework of rate-state friction to simulate earthquake rupture sequences along the fault segment between 15°N-19°N of northern Luzon. Our simulation results demonstrate that the first-order fault geometry heterogeneity, the transitional-segment (possibly related to the subducting Scarborough seamount chain) connecting the steeper south segment and the flatter north segment, controls earthquake rupture behaviors. The strong along-strike curvature at the transitional-segment typically leads to partial ruptures of MW~8.3 and MW~7.8 along the southern and northern segments respectively. The entire fault occasionally ruptures in MW~8.8 events when the cumulative stress in the transitional-segment is sufficiently high to overcome the geometrical inhibition. Fault shear stress evolution, represented by the S-ratio, is clearly modulated by the width of seismogenic zone (W). At a constant plate convergence rate, a larger W indicates on average lower interseismic stress loading rate and longer rupture recurrence period, and could slow down or sometimes stop ruptures that initiated from a narrower portion. Moreover, the modeled interseismic slip rate before whole-fault rupture events is comparable with the coupling state that was inferred from the interplate seismicity distribution, suggesting the Manila trench could potentially rupture in a M8+ earthquake.

Full Assessment of Micromachine Friction Within the Rate-State Framework: Theory and Validation

Model parameters are extracted from the experimental results in a companion paper (Shroff and de Boer in Tribol Lett 63(3):31, 2016) according to rate-state friction theory. Perturbation theory and state-space modeling are used to compare predictions for the stick–slip to steady sliding bifurcation line with experimental results using these extracted parameters. The line is well predicted in k/N b − v p space. The average behavior of the stick–slip oscillations is in good agreement with the state-space simulations. We estimate the memory length d c using a state-space model and find that it lies between the monoplane chain length and the average asperity diameter. This work indicates that rate-state theory extends from the µm scale to the nm scale in the few contacts situation.

A parallel code to calculate rate-state seismicity evolution induced by time dependent, heterogeneous Coulomb stress changes

The estimation of space and time-dependent earthquake probabilities, including aftershock sequences, has received increased attention in recent years, and Operational Earthquake Forecasting systems are currently being implemented in various countries. Physics based earthquake forecasting models compute time dependent earthquake rates based on Coulomb stress changes, coupled with seismicity evolution laws derived from rate-state friction. While early implementations of such models typically performed poorly compared to statistical models, recent studies indicate that significant performance improvements can be achieved by considering the spatial heterogeneity of the stress field and secondary sources of stress. However, the major drawback of these methods is a rapid increase in computational costs. Here we present a code to calculate seismicity induced by time dependent stress changes. An important feature of the code is the possibility to include aleatoric uncertainties due to the existence of multiple receiver faults and to the finite grid size, as well as epistemic uncertainties due to the choice of input slip model. To compensate for the growth in computational requirements, we have parallelized the code for shared memory systems (using OpenMP) and distributed memory systems (using MPI). Performance tests indicate that these parallelization strategies lead to a significant speedup for problems with different degrees of complexity, ranging from those which can be solved on standard multicore desktop computers, to those requiring a small cluster, to a large simulation that can be run using up to 1500 cores.

Rate-state friction in microelectromechanical systems interfaces: Experiment and theory

A microscale, multi-asperity frictional test platform has been designed that allows for wide variation of normal load, spring constant, and puller step frequency. Two different monolayer coatings have been applied to the surfaces—tridecafluorotris(dimethylamino)silane (FOTAS, CF3(CF2)5(CH2)2 Si(N(CH3)2)3) and octadecyltrichlorosilane (OTS, CH3(CH2)17SiCl3). Static friction aging was observed for both coatings. Simulating the platform using a modified rate-state model with discrete actuator steps results in good agreement with experiments over a wide control parameter subspace using system parameters extracted from experiments. Experimental and modeling results indicate that (1) contacts strengthen with rest time, exponentially approaching a maximum value and rejuvenating after inertial events, and (2) velocity strengthening is needed to explain the shorter than expected length of slips after the friction block transitions from a stick state. We suggest that aging occurs because tail groups in the monolayer coatings reconfigure readily upon initial contact with an opposing countersurface. The reconfiguration is limited by the constraint that head groups are covalently bound to the substrate.

Software for Efficient Static Dislocation-Traction Calculations in Fault Simulators

Research Article| October 01, 2014 Software for Efficient Static Dislocation–Traction Calculations in Fault Simulators Andrew M. Bradley Andrew M. Bradley Department of Geophysics, Stanford University, 397 Panama Mall, 3rd Floor, Stanford, California 94305 U.S.A.ambrad@cs.stanford.edu Search for other works by this author on: GSW Google Scholar Seismological Research Letters (2014) 85 (6): 1358–1365. https://doi.org/10.1785/0220140092 Article history first online: 14 Jul 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation Andrew M. Bradley; Software for Efficient Static Dislocation–Traction Calculations in Fault Simulators. Seismological Research Letters 2014;; 85 (6): 1358–1365. doi: https://doi.org/10.1785/0220140092 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietySeismological Research Letters Search Advanced Search Quasistatic or quasidynamic rate–state friction (QRSF) simulators are used to study the mechanics of faults (e.g., Shibazaki and Shimamoto, 2007). The displacement discontinuity method (DDM; Crouch and Starfield, 1983) meshes the fault or faults into N elements and constructs a matrix of Green’s functions (GFs) relating slip to stress. The simulator evolves strength and slip in time. Usually, the most expensive part of a simulation time step is the matrix–vector product (MVP) of the slip distribution with the DDM matrix; the straightforward implementation performs O(N2) operations. A simulator performs thousands to millions of MVPs... You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Seismic versus aseismic slip: Probing mechanical properties of the northeast Japan subduction zone

Fault slip may involve slow aseismic creep and fast seismic rupture, radiating seismic waves manifested as earthquakes. These two complementary behaviors accommodate the long-term plate convergence of major subduction zones and are attributed to fault frictional properties. It is conventionally assumed that zones capable of seismic rupture on the subduction megathrust are confined to between about 10 to 50 km depth; however, the actual spatiotemporal distribution of fault mechanical parameters remains elusive for most subduction zones. The 2011 Tohoku Mw 9.0 earthquake ruptured with >50 m slip up to the trench, thus challenging this conventional assumption, and provides a unique opportunity to probe the mechanical properties of the Japan subduction zone. Drawing on the inferred distribution of coseismic and postseismic slip, it has recently been suggested that portions of the megathrust are capable of switching between seismic and aseismic behavior. Kinematic models of the coseismic rupture and 15-month postseismic afterslip of this event suggest that the coseismic rupture triggered widespread frictional afterslip with equivalent moment magnitude of 8.17–8.53, in addition to viscoelastic relaxation in the underlying mantle. The identified linear relation between modeled afterslip, slip inferred from repeating earthquakes on the plate interface, and the cumulative number of aftershocks within 15 km distance of the subduction thrust suggests that most aftershocks are a direct result of afterslip. We constrain heterogeneous rate-state friction parameters of the subduction thrust from the computed coseismic stress changes and afterslip response. Our results indicate a variable pattern along dip and strike, characterizing areas down-dip and south of the main rupture zone as having velocity-strengthening properties. In agreement with seismic tomographic models of plate boundary elastic properties and geologic evidence for previous M>8.5 megathrust earthquakes on this section of the plate boundary, we suggest that the obtained pattern of the frictional properties is characteristic of subducted material and thus persistent in time and space.

Aftershock sequence simulations using synthetic earthquakes and rate-state seismicity formulation

We use an efficient earthquake simulator that incorporates rate-state constitutive properties and uses boundary element method to discretize the fault surfaces, to generate the synthetic earthquakes in the fault system. Rate-and-state seismicity equation is subsequently employed to calculate the seismicity rate in a region of interest using the Coulomb stress transfer from the main shocks in the fault system. The Coulomb stress transfer is obtained by resolving the induced stresses due to the fault patch slips onto the optimal-oriented fault planes. The example results show that immediately after a main shock the aftershocks are concentrated in the vicinity of the rupture area due to positive stress transfers and then disperse away into the surrounding region toward the background rate distribution. The number of aftershocks near the rupture region is found to decay with time as Omori aftershock decay law predicts. The example results demonstrate that the rate-and-state fault system earthquake simulator and the seismicity equations based on the rate-state friction nucleation of earthquake are well posited to characterize the aftershock distribution in regional assessments of earthquake probabilities.

The Uses of Dynamic Earthquake Triggering

Dynamic triggering of earthquakes by seismic waves is a robustly observed phenomenon with well-documented examples from over 30 major earthquakes. We are now in a position to use dynamic triggering as a natural experiment to probe the reaction of faults to the known stresses from seismic waves. We show here that dynamic triggering can be used to investigate the distribution of stresses required for failure on faults. In some regions, faults appear to be uniformly distributed over their loading cycles with equal numbers at all possible stresses from failure. Regions under tectonic extension, at the interface between locked and creeping faults, or subject to anthropogenic forcing are most prone to triggered failure. Predictions of future seismicity rates based on seismic wave amplitudes are theoretically possible and may provide similar results to purely stochastic prediction schemes. The underlying mechanisms of dynamic triggering are still unknown. The prolonged triggered sequences require a multistage process such as shear failure from rate-state friction coupled to aseismic creep or continued triggering through a secondary cascade. Permeability enhancement leading to drainage or pore pressure redistribution on faults is an alternative possibility.