State-dependent Friction Law Research Articles

A physical explanation for an unusually long-duration slow slip event in the Nankai Trough

The Dense Oceanfloor Network System for Earthquakes and Tsunamis (DONET) and the Long Term Borehole Monitoring System (LTBMS), installed above the source region of the 1944 Tonankai earthquake, revealed that crustal deformation is driven by slow slip events (SSEs) in the shallower extension of megathrust earthquakes. However, there are unresolved questions about (A) the duration of the SSE in February 2012, which was longer than expected for SSEs with similar magnitudes, and (B) the relationship of the spatial distribution of fault slip between the SSEs in February and December 2012 under the condition of drilling disturbance. To clarify these questions, we re-analyzed the pore/seafloor pressure data associated with the SSEs. Our refined fault models show that the SSE in February had a significantly slower propagation speed and a longer duration than others, while the SSE in December was comparable to others. We interpret that the difference in duration and propagation speed is related to external and internal stress perturbations, respectively. Using the ocean modeling JCOPE (Japan Coastal Ocean Predictability Experiment), we identified that the decrease and subsequent increase in seafloor pressure due to the passage of the Kuroshio meander coincided with the latter part of the longer duration of the SSE in February and its termination, respectively. This suggests that the Kuroshio meander might affect the duration of SSEs. Our refined fault model also indicates that the amount of shear stress accumulation was small before the occurrence of the SSE in February, which triggered the slow propagation of aseismic slip based on a rate- and state-dependent friction law. These results imply that we need to consider the variety of SSEs from the viewpoint of stress perturbation due to not only interaction between fault segments but also external forces from oceanographic phenomena.

Analysis of Fluid-Injection-Induced Seismicity Using a Dynamic Sliding Model Incorporating the Rate- and State-Dependent Friction Law

Summary Earthquakes can be triggered by fluid injection into underground formations. Fluid injection can cause large changes in the underground volume that exert stresses on nearby preexisting faults, leading to seismic activity. Assuming an increase in underground development activities in the future, our understanding of the mechanism underlying induced seismicity must be improved, and methods must be developed to properly assess the risk of seismic events. The objective of this study is to develop a seismicity prediction model that calculates the magnitude and timing of triggered earthquakes or seismic events occurring during various subsurface fluid injection activities. We developed an injection-induced seismicity analysis model that predicts the dynamic earthquake nucleation caused by changes in stress and pore pressure that occur during various subsurface activities. The governing equations consisting of the dynamic motion of the poroelastic spring-slider system, rate and state friction laws and pore pressure diffusion equation were solved using the embedded semi-implicit Runge-Kutta (SIRK) method. The dynamic sliding model was also incorporated into the finite element method (FEM) model, considering the variations in the stresses and pore pressures in the formation. A field case study was also conducted to compare the model results with typical microseismicity responses observed from hydraulic fracturing treatments in shale fields. Contrary to the popular understanding derived from Amonton’s law, the dynamic friction model revealed that a large normal stress on the fault leads to rapid sliding. A larger normal stress accumulates a large amount of elastic energy until it slips owing to fluid injection, nucleating large seismic waves. The poroelastic spring-slider model estimated reasonable microseismic magnitudes for hydraulic fracturing treatment but overestimated the time required to trigger a microseismic event under field conditions. To improve the analysis results, the poroelastic spring-slider model was coupled with a linear elastic FEM that considered the complex interplay of stress changes from hydraulic fracturing and the associated pore pressure variation in the formation. Compared with the field data, the coupled simulation model estimated a reasonable timing for the induced microseismic events when the increasing pore pressure during hydraulic fracturing penetrated deep into the formation. These findings suggest the existence of permeable natural fractures in the formation, which intensify early frictional sliding during treatment. The seismicity prediction model presented in this study simulates the magnitude and timing of seismic nucleation, helping to manage and mitigate the environmental impacts of induced seismicity during various subsurface development activities, such as oil and gas extraction, hydraulic fracturing, geothermal, and carbon dioxide sequestration. Moreover, the case study results imply that the time series of seismic events predicted by the model can be used to understand the possible fracture geometry and extent of fluid invasion for field applications. Key Terms and Phrases induced seismicity, subsurface fluid injection, rate- and state-dependent friction law, embedded semi-implicit Runge-Kutta method, finite element analysis

Transient postseismic slip and aftershock triggering: A case study of the 2008 MW7.9 Wenchuan Earthquake, China

In this study, we investigate how a stress variation generated by a fault that experiences transient postseismic slip (TPS) affects the rate of aftershocks. First, we show that the postseismic slip from Rubin-Ampuero model is a TPS that can occur on the main fault with a velocity-weakening frictional motion, that the resultant slip function is similar to the generalized Jeffreys-Lomnitz creep law, and that the TPS can be explained by a continuous creep process undergoing reloading. Second, we obtain an approximate solution based on the Helmstetter-Shaw seismicity model relating the rate of aftershocks to such TPS. For the Wenchuan sequence, we perform a numerical fitting of the cumulative number of aftershocks using the Modified Omori Law (MOL), the Dieterich model, and the specific TPS model. The fitting curves indicate that the data can be better explained by the TPS model with a B/A ratio of approximately 1.12, where A and B are the parameters in the rate- and state-dependent friction law respectively. Moreover, the p and c that appear in the MOL can be interpreted by the B/A and the critical slip distance, respectively. Because the B/A ratio in the current model is always larger than 1, the model could become a possible candidate to explain aftershock rate commonly decay as a power law with a p-value larger than 1. Finally, the influence of the background seismicity rate r on parameters is studied; the results show that except for the apparent aftershock duration, other parameters are insensitive to r.

Estimation of time-variable friction parameters using machine learning

SUMMARY The laboratory-derived rate- and state-dependent friction (RSF) law governs rock friction. Although a number of studies have investigated the RSF friction parameters, they are not fully understood yet within a physical framework. In this study, we estimated the variation of RSF parameters during stick-slip cycles, in order to have insights into the temporal variation of fault conditions during slipping, which may help understand the relation between the change in friction parameters and the generation of gouge particles. To get a more refined understanding of the evolution of RSF parameters, we estimated these parameters for each of the hundreds of stick-slip events that occurred on laboratory faults during an experiment. We used experiment data for which the gouge particles were removed from the laboratory faults at the beginning of each experiment; this procedure made possible to evaluate the influence of the gouge layer evolution on the variation of the RSF parameters. Since the amount of data was very large, we adopted a random forest (RF) machine learning approach for data analysis. The RF model was trained on simulated friction data and then applied to the experiment stick-slip event data to estimate the RSF parameters. To generate simulated friction data of stick-slip events, a one-degree-of-freedom spring-slider model governed by the RSF law was assumed. From plots of friction change as a function of displacement, some representative features were extracted to account for the RSF parameters and were used as input to the RF algorithm. Using the RF approach, we captured the variation of the RSF parameters a, $b - a$ and ${D}_{\mathrm{c}}\ $defined in the RSF law. The results show that during a first transient phase, the parameter a becomes smaller, while parameters $b - a$ and ${D}_{\mathrm{c}}$ become larger, as the gouge layer becomes thicker. The variation of the RSF parameters becomes less pronounced during the following steady-state phase. These results suggest that the variation of RSF friction parameters may be related to the evolution of the gouge layer.

Tertiary creep behavior for various rate- and state-dependent friction laws

Forecasting the acceleration of slow landslides to the point of catastrophic failure is crucial. It follows the Voight power-law model with the power exponent α, which is typically close to 2 but can be significantly smaller. Understanding the underlying mechanisms may improve landslide warnings. A previous study applied a rate- and state-dependent friction (RSF) law in the form of the aging law to the creep behavior of an underlying shear zone of landslides, and showed an α value of 2. The aging law is one of the conventional forms of RSF law, and we extended the analysis to other representative laws: the slip law, Perrin-Rice-Zheng (PRZ) law, composite law, and Nagata law. We showed that the acceleration is expressed in terms of the slip rate using the state-evolution equation. As the slip rate increases, α decays to 2, regardless of the frictional parameters, following a power law for the aging and Nagata laws and logarithmically for the slip and the composite laws. For the PRZ law, the asymptotic value of α is between 2 and 3 and depends on frictional parameters. In typical RSF laws, the logarithm of the slip rate is proportional to the friction coefficient or normalized shear stress f minus frictional strength Θ. The logarithmic direct effect and a linear increase with slip in f−Θ independent of the slip rate, which is a characteristic of aging and Nagata laws under constant stress conditions, leads to α=2. By contrast, a purely time-dependent increase in f−Θ would lead to α=1. If these two effects coexist, α increases from 1 to 2 with acceleration. In laboratory experiments of investigation of RSF law, constant-load creep tests in the tertiary-creep stage have been rarely conducted, but they could provide new insights on the form of the state-evolution equation and deserve future study.

Seismic magnitude calculation based on rate- and state-dependent friction law

Seismic magnitude calculation based on rate- and state-dependent friction law

Recurrence intervals for M > 7 Miyagi-ken-Oki earthquakes during an M ~ 9 earthquake cycle

The 2011 Tohoku-Oki great earthquake increased the difficulty of evaluating the long-term probability of seismic activity along the Japan Trench because of the unknown impact of the unprecedentedly large slip. In this study, the long-term activity of “Miyagi-ken-Oki earthquakes”, an M > 7 earthquake sequence off Miyagi Prefecture, located at the edge of the source area of the Tohoku-Oki earthquake was simulated. We conducted numerical simulations of earthquake generation cycles based on the rate- and state-dependent friction law representing the stress accumulation and release process on the plate interface. We also validated the results based on analyses of observational data, including time intervals and afterslip distributions for the previous Miyagi-ken-Oki earthquakes. The simulation results were then compared with repeating-earthquake-derived interplate slip observations over 30 years. The results showed that the spatial and temporal characteristics of aseismic slips on the plate interface near the M > 7 Miyagi-ken-Oki source were qualitatively reproduced. The time interval between the M ~ 9 earthquake and the first M > 7 earthquake is shorter than the average recurrence interval of M > 7 earthquakes during the latter stage of each M ~ 9 earthquake cycle. In contrast, the interval between the first and the second M > 7 earthquakes is the longest in each M ~ 9 earthquake cycle. The time intervals of the M > 7 earthquakes fluctuated in the early stage compared to those in the latter stage of the M ~ 9 earthquake cycle. These characteristics were associated with the extent of the locked and afterslip areas in and around the source. Hence, monitoring the spatio-temporal distribution of the slip rate in and around the source area during the preparation process of earthquakes occurring in the downdip area off Miyagi Prefecture is very important to assess whether the next M > 7 earthquake is approaching. Furthermore, earthquake cycle simulations combined with earthquake and slow slip monitoring can provide meaningful insights for long-term assessments of great interplate earthquakes.

Numerical Simulation of Episodic Aseismic Slip Events as Incomplete Nucleation of Seismic Slip Due to Heterogeneous Stress Distribution

ABSTRACT Shear stress concentration at the deeper edge of a locked fault affects detachment of the fault, such as upward propagation of aseismic sliding, episodic aseismic slip events, and partial seismic rupture. Numerical simulations of earthquake cycles on a strike-slip fault were conducted using a rate- and state-dependent friction law to investigate the occurrence conditions of episodic aseismic slip events within a fault having uniform velocity-weakening friction. When the velocity-weakening zone is much wider than the critical nucleation zone size, a rupture that seismically or aseismically breaks a part of the velocity-weakening zone occurs during the interseismic period between large earthquakes. The partial seismic rupture results in a small earthquake, and the partial slow rupture results in an episodic aseismic slip event. The seismic or aseismic rupture is arrested in a low-shear-stress area, which is caused by the preceding large earthquake. The episodic aseismic slip events may be regarded as incomplete nucleation of an earthquake, because the rupture is arrested before acceleration to seismic slip, and this process may explain episodic aseismic slip events at seismogenic depths. The width of the area of preseismic sliding immediately before a simulated large earthquake is similar to that of episodic aseismic slip.

A new micromechanical damage model for quasi-brittle geomaterials with non-associated and state-dependent friction law

In this paper, we shall present a new micromechanical damage model for capturing the mechanical behaviors of quasi-brittle geomaterials under a wide range of compressive stress. Two essential coupled non-linear mechanisms are taken into account: plastic deformation related to frictional sliding along the microcrack surfaces, and microscopic damage induced by the initiation and propagation of microcracks. Within the framework of thermodynamics and Mori–Tanaka homogenization scheme, free energy and thermodynamic forces, including the local stress applied on the microcracks and damage driving force are deduced. The main novelty of this work lies in presenting a new physically based non-associated and state-dependent friction law to capture the plastic distortion, in which the friction coefficient is no longer a constant but a state-dependent variable varying with the surface asperities of microcracks. The relationship between the friction coefficient and mean local stress, as well as microscopic damage is subtly defined. Intriguingly, a macroscopic strength criterion is derived as an inherent part of the proposed model without rotation of the principal stress. Moreover, semi-analytical stress–strain–damage relationships of the proposed model can be derived under conventional triaxial compression. These up-scaling analyses provide a powerful tool for parameter calibration. For application, the semi-implicit return mapping algorithm with plasticity-damage decoupling correction procedure (SRM-PDDC) is adopted for numerical implementation. To demonstrate the performance of the micromechanical model, we compare the model predictions with experimental data of quasi-brittle rocks in literature as well as the results obtained by Zhu et al. (2016). Finally, the applicable condition of the SRM-PDDC algorithm is discussed in detail.

Modelling seismicity pattern of reservoir-induced earthquakes including poroelastic stressing and nucleation effects

SUMMARY Abnormal seismic activities near reservoirs usually show a strong spatiotemporal correlation with the water filling history. Reservoir-induced seismicity is thought to be related to crustal pore pressure and stress changes caused by water impounded behind the dams. Though the Coulomb-type stress analysis helps illuminate areas that would be under risk following reservoir impoundment, it lacks the ability to explain the temporal characteristics of reservoir-induced seismicity. We present a numerical investigation of the seismicity rate evolution of reservoir-induced earthquakes. Our modelling employs a fully coupled 2-D poroelastic model to calculate the pore pressure and stress changes caused by water impoundment and incorporates the rate- and state-dependent friction law to investigate the seismicity rate. We demonstrate that shallow earthquakes are mainly caused by pore pressure increase, while poroelastic stress transfer takes the dominant role at depth. Whether a fault would be brought close to failure depends on its geometrical properties and its relative location to the reservoir. The temporal evolution of reservoir-induced earthquakes is primarily controlled by tectonic environment instead of the diffusion of pore pressure.

Dynamic earthquake sequence simulation with an SBIEM accounting for interseismic poroelastic rebound

Afterslip inside a coseismic slip patch is rarely observed, though some previous studies suggest that it is driven by poroelastic rebound (PER). These studies assume constant frictional strength, whereas time-dependent strengthening (healing) of a fault is expected from laboratory experiments, which provide a basis for a rate- and state-dependent friction law (RSF). In this study, quasistatic poroelasticity (PE) was implemented in a dynamic earthquake sequence simulation using a spectral boundary integral equation method, and the effect of PER on the behavior of a fault governed by RSF was examined. Spatio-temporal convolution for PE would significantly affect the resolution of the numerical simulation affordable. This problem has been resolved by numerical approximation of the time dependency of Green’s function of PE in the wavenumber domain, definition of memory variables, and reformulation of the temporal convolution into ordinary differential equations of them. In the novel method, the additional numerical costs due to PE are negligible. A planar fault with a rate-weakening patch embedded in the rate-strengthening region was simulated. Because it is the healing of the fault that competes against PER, both the aging law and slip law were examined, which have different characteristics in the evolution of the fault strength. The simulation results indicate that PER causes postseismic loading to the patch, but the healing efficiently suppresses afterslip not only for the aging law, but also for the slip law. When cases with different friction laws are compared, the healing is more significant for the aging law, which has log-t strengthening at a limit of Vto 0. However, the effect of PER on the slip rate is minor for the slip law. The slip law yields additional healing if the fault is accelerated by loading owing to PER. The simulation results are consistent with the absence of afterslip within the coseismic slip patches in the observations.Graphical

Stability of steady frictional sliding at an interface between two elastic layers

Instabilities in dynamic antiplane frictional sliding on a planar interface between two elastic layers with dissimilar elastic properties are studied. At the interface, a rate- and state-dependent friction law with a positive instantaneous dependency on slip velocity and velocity weakening behaviour in the steady state is assumed to be in effect. The linearized response of the sliding of the two elastic layers to a Fourier mode perturbation along the interface is studied. A key aspect of the problem is that interfacial waves exist for the problem in both freely slipping and bonded contact. The growth rate of slip instabilities and their phase velocities are obtained numerically. The stability of both rapid and slow slip is analyzed. The results show that one mechanism for instabilities is the destabilization due to friction of interfacial waves in freely slipping contact and in bonded contact. The effect of layer thickness on the stability results is also studied.

Sensitivity of a simple earthquake nucleation model to small parameter perturbation: Conditions for the occurrence of deterministic chaos

A new mechanism that may account for the onset of chaotic dynamics of earthquake faults is proposed and analyzed. The concept is to build on the Burridge-Knopoff model, which integrates the spring-block setup with the Dieterich-Ruina's rate- and state-dependent friction law to interpolate for the key aspects of earthquake episodes, including the seismic nucleation, fracture propagation and arrest, as well as the rupture healing. Results obtained indicate that deterministic chaos occur in case frictional parameters exhibit small oscillations about their equilibrium values. Based on the construction of appropriate phase portraits, power spectra and the Lyapunov exponents it could be concluded that a single time-dependent parameter is sufficient for the chaotic behavior to emerge, while the fully developed chaos is found when two perturbed parameters are brought into play.

Subduction earthquake sequences in a non-linear visco-elasto-plastic megathrust

SUMMARYWe present a 2-D thermomechanical computational framework for simulating earthquake sequences in a non-linear visco-elasto-plastic compressible medium. The method is developed for a plane-strain problem and incorporates an invariant formulation of the classical rate- and state-dependent friction law and an adaptive time-stepping, which allows the time step to vary by many orders of magnitude during a simulation. Long-term tectonic convergence is imposed by displacing a boundary at a constant rate, whereas temperature-dependent viscosity is solved using a rapidly converging Newton–Raphson scheme. The 2-D volume is discretized using finite differences on a fully staggered grid and marker-in-cell techniques. An adaptive free-surface approximation is used to modulate the air viscosity with the time step, which allows stresses to vanish on the free surface during the propagation of fast slipping events. We present a set of increasingly complex models in which we investigate how inertia, radiation damping, thermally activated non-linear rheology and off-megathrust splay-fault events affect sequences of seismic and aseismic slip on a simplified subduction megathrust. The new method provides a unique computational framework to analyse earthquake sequences and to connect forearc deformation with the dynamic properties of the megathrust, thus providing a physical link between observations spanning from slow interseismic strain accumulation to localized coseismic slip of individual earthquakes and post-seismic viscoelastic relaxation.

Earthquake dynamics constrained from laboratory experiments: new insights from granular materials

The traction evolution is a fundamental ingredient to model the dynamics of an earthquake rupture which ultimately controls, during the coseismic phase, the energy release, the stress redistribution and the consequent excitation of seismic waves. In the present paper we explore the use of the friction behavior derived from laboratory shear experiments performed on granular materials at low normal stress. We find that the rheological properties emerging from these laboratory experiments can not be described in terms of preexisting governing models already presented in literature; our results indicate that neither rate–and state–dependent friction laws nor nonlinear slip–dependent models, commonly adopted for modeling earthquake ruptures, are able to capture all the features of the experimental data. Then, by exploiting a novel numerical approach, we directly incorporate the laboratory data into a code to simulate the fully dynamic propagation of a 3–D slip failure. We demonstrate that the rheology of the granular material, imposed as fault boundary condition, is dynamically consistent. Indeed, it is able to reproduce the basic features of a crustal earthquake, spontaneously accelerating up to some terminal rupture speed, both sub– and supershear.

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.

Time to seismic failure induced by repeating SSEs in a single-degree-of-freedom spring-slider model

SUMMARYSome large earthquakes may have been triggered by large slow slip events (SSEs). This paper studies the time it takes from the most recent SSE to seismic failure in a situation where earthquakes are influenced by periodic SSEs, unlike in earlier studies that investigated the impact of a single SSE imposed at an arbitrary timing during a seismic cycle. A single-degree-of-freedom (SDOF) spring-slider model obeying a rate- and state-dependent friction (RSF) law is used to study the time to failure. The results are compared with those in Ohtani et al., which simulates megathrust earthquakes triggered by large, spontaneous SSEs along the deeper extension of a seismogenic zone in a 2-D elastic medium. Suppose a model fault under steady-rate tectonic loading is also impacted by stress steps induced by periodic SSEs. In the absence of SSEs, there is only a unique value of the characteristic slip distance L of RSF for a given seismic return period T. In the presence of SSEs, by contrast, synchronization occurs, and there exists a finite range of L values that corresponds to the same T. The timing (phase difference) of earthquakes relative to the SSEs varies continuously with L within that range. This study focuses on the case where T is triple the SSE return period, TSSE, (T = 3TSSE) to allow comparison with Ohtani et al. For each value of L in that range, disturbance tests that assign random values to T0, the timing of the third SSE within the seismic cycle, are conducted to obtain a probability distribution for tf, the time from that SSE to seismic failure. The distribution is converted into P(t; L), the cumulative probability that seismic failure occurs within time t of the SSE. The P(t; L) is averaged over the different L values to produce $\bar{P}$(t), which takes account of variability in the strength excess on the seismic fault at the time of the SSE, a parameter that is generally unknown. These numerical disturbance tests are conducted for three different values of an SSE size parameter. It is found that the larger the SSEs, the more intensely seismic failure is concentrated within short time intervals following an SSE. For the largest SSE, whereby a single SSE accounts for 3/10 of the total stress accumulated during a seismic cycle, there is a 50 per cent probability that seismic failure occurs within 132 d. These results contrast with those of Ohtani et al., in which tf was found to be concentrated more intensely within even shorter time intervals following an SSE (80 per cent probability that seismic failure occurs within 2.78 d of the SSE). It is suggested the timing of SSE-triggered seismic failure is concentrated more strongly on a fault embedded in a continuum because of a factor that cannot be taken into account by an SDOF model—a spatial structure of stress concentration that is already there on the fault even before the triggering event, the SSE.

Earthquake triggering model based on normal-stress-dependent Nagata law: application to the 2016 Mie offshore earthquake

We propose a normal-stress-dependent Nagata law. Nagata et al. (J Geophys Res 117:B02314, 2012) revised the rate- and state-dependent friction law by introducing the shear stress dependence. We further extended the Nagata law by incorporating the normal stress dependence obtained by Linker and Dieterich (J Geophys Res 97:4923–4940, 1992). We performed numerical simulations of earthquake triggering by assuming the extended Nagata law. In the case of repeated earthquakes, we applied dynamic Coulomb failure function (CFF) perturbation due to normal or shear stress changes. CFF perturbation increased the slip velocity after the cessation of perturbation, relative to that of the repeated events without triggering. This leads to dynamic earthquake triggering for certain perturbation amplitudes with time to instability of 0 to several tens of days. In addition, triggering potential of the static CFF jump (ΔCFFs) was investigated. Static stress perturbation has a higher triggering potential than dynamic stress perturbation for the same magnitude of CFF. The equivalent ΔCFFeq is evaluated for dynamic perturbation that results in a triggering potential approximately the same as in the case of static stress perturbation if ΔCFFs = ΔCFFeq. We calculated ΔCFFeq on the interface of the Philippine Sea plate for the Mie offshore earthquake, which occurred around the Nankai Trough on April 1, 2016, using OpenSWPC. The results shows that ΔCFFeq is large around the trough, where slow slip events followed the Mie earthquake, suggesting that a large ΔCFFeq may have triggered slow slip events.

Laboratory study on the effects of fault waviness on granodiorite stick-slip instabilities

SUMMARY The effects of fault waviness on the fault slip modes are unclear. Laboratory study on the effects of the centimetre-scale fault contact distribution, which is mainly controlled by the fault waviness, on granodiorite stick-slip instabilities may help to unveil some aspects of the problem. The fast and slow stick-slip motions were separately generated in two granodiorite samples of the same roughness but different fault contact distributions in the centimetre scale in the laboratory. The experimental results show the following: (1) the fault with the small contact area and heterogeneous contact distribution generates fast stick-slip instabilities, while the fault with the large contact area and homogeneous contact distribution produces slow stick-slip events; (2) the nucleation processes of the fast stick-slip events are characterized by abrupt changes once the nucleation zones expand to the critical nucleation length that is observed to be shorter than the fault length, while the slow stick-slip events appear as a gradual evolution of the nucleation zones leading to total fault sliding. These indicate that, unlike the micron-scale fault contact distribution controlled by roughness, which depends mainly on the grain size of the abrasives used for lapping the fault surface, the centimetre-scale fault contact distribution, which depends mainly on the waviness of the fault surface profile, also plays an important role in the fault slip modes. In addition, the effects of the fault waviness on the fault friction properties are preliminarily analysed based on the rate- and state-dependent friction law.

Fully dynamic earthquake sequence simulation of a fault in a viscoelastic medium using a spectral boundary integral equation method: does interseismic stress relaxation promote aseismic transients?

Along subduction interfaces or some major faults, a seismogenic layer in the upper crust is underlain by a zone of slow-slip events (SSEs) and tremors, and seismicity disappears at greater depths. The transition between seismogenic and aseismic behavior may be caused by changes in the frictional properties of the fault or changes in viscoelastic properties of the surrounding medium. Although aseismic transients have been numerically generated in previous studies by changing the frictional properties and compared to SSEs, the effect of viscoelasticity on the transition remains to be studied. In this study, we implemented interseismic viscoelastic stress relaxation in a simulation code for two-dimensional antiplane fully dynamic earthquake sequences in a uniform elastic material based on a spectral boundary integral equation method. In the implementation, we developed a suitable algorithm in which the viscoelastic relaxation is calculated by evolution of an “effective slip,” which gives viscoelastic stress change on the fault if convolved with a static Green’s function. We conducted parametric studies for a fault with a rate-weakening patch on two parameters: viscoelastic relaxation time t_{c} and characteristic length of the state evolution in the rate- and state-dependent friction law L. The behavior of the simulated fault can be classified into four classes, earthquakes (EQ), aseismic transients (AT), stable sliding (SS), and stuck (ST), in which the central part of the rate-weakening patch has a diminishingly small slip rate and is permanently locked. A phase diagram of the fault behavior shows that there are two different types of seismogenic–aseismic transition. As L increases, an EQ patch changes to an AT patch before becoming an SS patch, as has been reported in previous studies in an elastic limit. The boundary between AT and SS can be explained via linear stability analysis of a system composed of a spring, a dashpot, and sliders. As t_{c} decreases, the recurrence interval of the earthquakes diverges, and an EQ patch changes to an ST patch unless L is within a narrow range. Therefore, the transition associated with SSEs and tremors is dominated by changes in frictional properties rather than changes in viscoelastic properties.