Slip-weakening Friction Law Research Articles

Dynamic Rupture Models of the 2016 ML 5.8 Gyeongju, South Korea, Earthquake, Constrained by a Kinematic Rupture Model and Seismic Waveform Data

ABSTRACT The ML 5.8 earthquake that jolted Gyeongju in southeastern Korea in 2016 was the country’s largest inland event since instrumental seismic monitoring began in 1978. We developed dynamic rupture models of the Gyeongju event constrained by near-source ground-motion data using full 3D spontaneous dynamic rupture modeling with the slip-weakening friction law. Based on our results, we propose two simple dynamic rupture models with constant strength excess (SE) and slip-weakening distance (Dc) that produce near-source ground-motion waveforms compatible with recorded ones in the low-frequency band. Both dynamic models exhibit relatively large stress-drop values, consistent with previous estimates constrained by source spectrum analyses. The fracture energy estimates were also larger than those predicted by a scaling relationship with the seismic moment. The dynamic features constrained in this study by spontaneous rupture modeling and waveform comparison may help understand the source and ground-motion characteristics of future large events in southeastern Korea and thus the seismic hazard of the region.

Time-domain Green’s function in poroelastic mediums and its application to 3-D spontaneous rupture simulation

SUMMARY Plenty of studies have suggested that pore fluid may play an important role in earthquake rupture processes. Establishing numerical models can provide great insight into how pore fluid may affect earthquake rupture processes. However, numerical simulation of 3-D spontaneous ruptures in poroelastic mediums is still a challenging task. In this paper, it is found that a closed-form time-domain Green’s function of Biot’s poroelastodynamic model can be constructed when the source frequency and source-field distance are within a certain range. The time-domain Green’s function is validated by being transformed into the frequency domain and comparing with the frequency-domain Green’s functions obtained by former papers. Poroelastic wave propagation phase diagrams for various two-phase poroelastic mediums are then plotted to show the applicable range of frequency and source-field distance for the new time-domain Green’s function. It is shown that the applicable range not only include the frequency and spatial range of concern in seismology but also overlap that in acoustics. Based on the time-domain Green’s function, the boundary integral equations (BIEs) for modelling dynamic ruptures in elastic mediums are extended to fluid-saturated mediums. In the meantime, a functional relationship between the effective stress tensor and the total stress tensor in fluid-saturated mediums is also obtained, which allows us to directly obtain the effective stress by BIEs. The spontaneous rupture processes controlled by the slip-weakening friction law on faults in elastic mediums and in fluid-saturated mediums are compared. It is found that under the same conditions, fluid-saturated rocks are more prone to supershear rupture than dry rocks. This result suggests that pore fluid may promote the excitation of supershear rupture. The poroelastic wave propagation phase diagrams also suggest that simulating a coseismic phase in the real scale requires a certain sample length in laboratories. They also suggest that an undrained governing equation is suitable for seismic wave propagation simulation in poroelastic media.

Influences of across-strike heterogeneous viscosity on the earthquake cycle in a three-dimensional strike-slip fault model

Geodetic observations have shown that there exist large differences in the viscosity of the deep lithosphere across many large strike-slip faults. Heterogeneity in lithospheric viscosity structure can influence the efficiency of stress transfer and thus may have a significant effect on the earthquake cycle. Until now, how the lateral viscosity variation across strike-slip faults affects the earthquake cycles is still not well understood. Here, we investigate the effects of across-strike viscosity variation on long-term earthquake behaviors with a three-dimensional strike-slip fault model. Our model is a quasi-static model which is controlled by the slip-weakening friction law and power-law rheology. By comparing with the reference case, we find that low viscosity on one side of the fault results in a smaller rupture area but with a higher Coulomb stress drop on the ruptured fault region. In addition, low viscosity also leads to a small Coulomb stress accumulation rate. These combined effects increase the earthquake recurrence interval by approximately 10% and the earthquake moments by about 30% when the low viscosity is related to a geothermal gradient of 30 ​K/km. In addition, across-strike viscosity variation causes asymmetric interseismic ground surface deformation rate. As the viscosity contrast increases, the difference in the interseismic ground surface deformation rate between the two sides of the fault gradually increases, although the asymmetric feature is not pronounced. This asymmetry of interseismic ground deformation rate across a strike-slip fault is supposed to result in asymmetric coseismic deformation if the long-term plate motion velocity is invariant. As a result, this kind of asymmetry of interseismic deformation may influence the evaluation of potential earthquake hazards along large strike-slip faults with lateral viscosity contrast.

Rupture-induced dynamic pore pressure effect on rupture

The ordinary elasticity model is often used in dynamic rupture earthquake simulation without incorporating the poroelasticity effect in rocks. In consideration that rocks are porous and saturated, we carry out a two-dimensional simulation of spontaneous rupture in a poroelastic medium with a finite difference time domain scheme. In particular, the influence of the rupture-induced pore pressure on the rupture process is investigated. The fault plane is idealized as an impermeable layer of negligible thickness, and the rupture is assumed to be governed by the slip-weakening friction law. Results show that an impermeable fault plane leads to a rupture-induced pore pressure change, which promotes or hinders the rupture process by altering effective normal compressive stress (normal compressive stress minus pore pressure). It is remarkable that super-shear rupturing will occur when the porosity of the rock around the fault increases to some extent. The comparison with the permeable fault model suggests that the permeability of the fault and the porosity of rocks around the fault significantly influence the dynamic rupture process.

Antiplane spectral boundary integral equation method for an interface between a layer and a half-plane

A numerical scheme is proposed for simulating dynamic antiplane fracture at an interface between a layer and a half-plane. The scheme is a spectral boundary integral equation method which relates the shear stress and the displacement discontinuity at the interface in the spectral domain. In previous studies, numerical schemes have been developed for fracture problems in unbounded solids. This is the first work where a spectral boundary integral equation method has been developed for a system one of whose constituents is a finite solid, namely, a layer. The spectral scheme involves performing time convolution of the spectral amplitude of the shear stress at the interface of the layer and half-space. Numerically, conversion between the spectral domain and spatial domain is done by the Fast Fourier Transform. The numerical scheme is validated through comparison with known solutions of model problems. Use of the numerical method is illustrated by simulating 2D antiplane slip rupture propagation wherein the spectral boundary integral equation is coupled with a slip-weakening friction law. We illustrate the role of initial stress distribution on the modes of rupture propagation at the interface, which can be crack-like or pulse-like. The effect of the layer thickness on the critical nucleation size for dynamic rupture propagation is also studied numerically.

Dynamic Modeling of the 2020 Mw 6.0 Jiashi Earthquake: Constrained by Geodetic and Seismic Observations

AbstractThe 2020 Mw 6.0 Jiashi earthquake is the largest event recorded in the Jiashi region in the last 17 yr. Here we try to explore the primary characteristics of this event by using dynamic rupture modeling, and later compare our results with the Interferometric Synthetic Aperture Radar (InSAR) data and near-source ground-motion observations. To focus on the geometric effects of the seismogenic fault, we conduct spontaneous rupture simulations in a homogenous material by using a linear slip-weakening friction law. Our results show that the synthetic data fits well with the observations, including the InSAR data and strong ground-motion waveforms. Significantly, the low dip angle segments at both ends of the rupture area along the dip-slip direction have behaved as “stress barriers,” which stop the rupture propagation. In other words, the rupture could be arrested by the near-horizontal segments rather than being prevented by the steeper ramp proposed by the previous studies. Thus, our physics-based dynamic modeling shows how the fault geometry controls the 2020 Mw 6.0 Jiashi earthquake rupture. Our work contributes to understand the complex nature of the low dip angle listric-reverse fault.

Spectral formulation of the boundary integral equation method for antiplane problems

A spectral formulation of the boundary integral equation method for antiplane problems is presented. The boundary integral equation method relates the slip and the shear stress at an interface between two half-planes. It involves evaluating a space-time convolution of the shear stress or the slip at the interface. In the spectral formulation, the convolution with respect to the spatial coordinate is performed in the spectral domain. This leads to greater numerical efficiency. Prior work on the spectral formulation of the boundary integral equation method has performed the elastodynamic convolution of the slip at the interface. In the present work, the convolution is performed of the shear stress at the interface. The spectral formulation is developed both for an interface between identical solids and for a bi-material interface. It is validated by numerically calculating the response of the interface to harmonic and to impulsive disturbances and comparing with known analytical solutions. To illustrate use of the method, dynamic slip rupture propagation with a slip-weakening friction law is simulated.

Assessing the role of selected constraints in Bayesian dynamic source inversion: application to the 2017Mw 6.3 Lesvos earthquake

SUMMARYA dynamic finite-fault source inversion for stress and frictional parameters of the Mw 6.3 2017 Lesvos earthquake is carried out. The main shock occurred on June 12, offshore the southeastern coast of the Greek island of Lesvos in the north Aegean Sea. It caused 1 fatality, 15 injuries, and extensive damage to the southern part of the island. Dynamic rupture evolution is modelled on an elliptic patch, using the linear slip-weakening friction law. The inversion is posed as a Bayesian problem and the Parallel Tempering Markov Chain Monte Carlo algorithm is used to obtain posterior probability distributions by updating the prior distribution with progressively more constraints. To calculate the first posterior distribution, only the constraint that the model should expand beyond the nucleation patch is used. Then, we add the constraint that the model should reach a moment magnitude similar to that obtained from our centroid moment tensor inversion. For the final posterior distribution, 15 acceleration records from Greek and Turkish strong motion networks at near regional distances (≈ 30–150 km) in the frequency range of 0.05–0.15 Hz are used. The three posterior distributions are compared to understand how much each constraint contributes to resolving different quantities. The most probable values and uncertainties of individual parameters are also calculated, along with their mutual trade-offs. The features best determined by seismograms in the final posterior distribution include the position of the nucleation region, the mean direction of rupture (towards WNW), the mean rupture speed (with 68 per cent of the distribution lying between 1.4 and 2.6 km s–1), radiated energy (12–65 TJ), radiation efficiency (0.09–0.38) and the mean stress drop (2.2–6.5 MPa).

Love Wave or Slip Wave?

Abstract Conventional models of the structure of the Earth, such as the Preliminary Reference Earth Model (PREM), assume a bonded interface between the crust and the upper mantle. The bonded contact model is consistent with the observation of Love waves during an earthquake. However, anomalies in the Love wave dispersion have been reported in the literature. When slip occurs at the crust-mantle interface, another kind of an interfacial wave, called the slip wave can exist. It is shown that the dispersion relation of the slip wave, with a slip weakening friction law, appears to be in agreement with the observations at seismic frequencies. This suggests that slip could occur at the crust-mantle interface.

Sensitivity of the Seismic Moment Released During Fluid Injection to Fault Hydromechanical Properties and Background Stress

Fluid pressure perturbations in subsurface rocks affect the fault stability and can induce both seismicity and aseismic slip. Nonetheless, observations show that the partitioning between aseismic and seismic fault slip during fluid injection may strongly vary among reservoirs. The processes and the main fault properties controlling this partitioning are poorly constrained. Here we examine, through 3D hydromechanical modeling, the influence of fault physical properties on the seismic and aseismic response of a permeable fault governed by a slip-weakening friction law. We perform a series of high-rate, short-duration injection simulations to evaluate the influence of five fault parameters, namely the initial permeability, the dilation angle, the friction drop, the critical slip distance, and the initial proximity of stress to failure. For sake of comparison between tests, all the simulations are stopped for a fixed rupture distance relative to the injection point. We find that while the fault hydraulic behavior is mainly affected by the change in initial permeability and the dilation angle, the mechanical and seismic response of the fault strongly depends on the friction drop and the initial proximity of stress to failure. Additionally, both parameters, and to a lesser extent the initial fault permeability and the critical slip distance, impact the spatiotemporal evolution of seismic events and the partitioning between seismic and aseismic moment. Moreover, this study shows that a modification of such parameters does not lead to a usual seismic moment-injected fluid volume relationship, and provides insights into why the fault hydromechanical properties and background stress should be carefully taken into account to better anticipate the seismic moment from the injected fluid volume.

Exploring Physical Links between Fluid Injection and Nearby Earthquakes: The 2012 Mw 4.8 Timpson, Texas, Case Study

ABSTRACTIn this work, we integrate a fluid-flow model of 3D deformable porous media with a dynamic rupture model of earthquakes in 3D heterogeneous geologic medium. The method allows us to go beyond fault failure potential analyses and to examine how big an earthquake can be if part of a fault reaches failure due to fluid injection. We apply the method to the 17 May 2012 Mw 4.8 Timpson, Texas, earthquake as a case study. The simulated perturbations of pore pressure and stress from wastewater injection at the time of the mainshock are high enough (several MPa) to trigger an earthquake. Dynamic rupture modeling could reproduce the major observations from the Mw 4.8 event, including its size, focal mechanism, and aftershock sequence, and thus building a more convincing physical link between fluid injection and the Mw 4.8 earthquake. Furthermore, parameter space studies of dynamic rupture modeling allow us to place some constraints on fault frictional properties and background stresses. For the Timpson case, we find that a dynamic friction coefficient of ∼0.3, a value of ∼0.1 m for the critical slip distance in the slip-weakening friction law, and uniform effective normal stress are associated with the Timpson earthquake fault. By reproducing main features of the aftershock sequence of the mainshock, we also demonstrate that the method has potential to become a predictive tool for fluid injection design in the future.

INFLUENCE OF VISCOSITY ON THE THERMAL ENERGY PRODUCED IN SEISMIC FAULT: ONE-DIMENSIONAL MODELING

This study is focused on thermal energy due to slip-weakening friction, but also on the temperature distribution. In this paper, we considered a one-body spring-slider model in the presence of slip-weakening friction and viscosity. We examine the effect of slip-weakening friction law and viscosity on thermal energy. We established the expression of thermal energy produced by slip-weakening friction in the case that we considered a simplified linearly slip-weakening friction law. Numerical simulation with Euler method are made for determining the thermal energy in the case of three others slip-weakening friction law, i.e., the thermal-pressurization (TP) friction law, the softening-hardening (SH) friction law and a simple slip-weakening (SW) friction law. The effect of the viscosity strongly modifies the results of the evolution of the temperature and the thermal energy. We establish that the TP friction law is better to evaluate the thermal energy in seismic fault. We solve the 1-D heat conduction equation by numerical simulation. We showed that, contrary to others frictions forces the slip-weakening friction law better illustrate the accumulation of thermal energy produced in seismic fault and temperature distribution.

Effects of Initial Stress Field and Critical Slip-Weakening Distance on Rupture Selectivity of 3D Buried Branched Faults

ABSTRACTUsing the boundary integral equation method with the slip-weakening friction law, we investigate the effects of the initial stress field and the critical slip-weakening distance on the rupture selectivity on the 3D buried branched faults. The numerical results show that after reaching the bifurcation line between the main fault and the branched faults, rupture continues to propagate on one or both bifurcation planes (BPs), with rupture on one plane more favorable than the other. The initial stress distribution plays a decisive role in the selection of the favorable BP (FBP), and there is a critical status of stress distribution, around which rupture propagates on both planes, whereas the FBP switches between the two. For a given fault geometry, the critical status of initial stress, which is described by a ratio Fp between normal stresses, is related to the critical slip-weakening distance Dc.

Application of PDS–FEM to simulate dynamic crack propagation and supershear rupture

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

Dynamic models of earthquake rupture along branch faults of the eastern San Gorgonio Pass region in California using complex fault structure

AbstractGeologic data suggest that the Coachella Valley segment of the southern San Andreas fault (southern California, USA) is past its average recurrence time period. At its northern edge, this right-lateral fault segment branches into the Mission Creek and Banning strands of the San Andreas fault. Depending on how rupture propagates through this region, there is the possibility of a throughgoing rupture that could lead to the channeling of damaging seismic energy into the Los Angeles Basin. The fault structures and potential rupture scenarios on these two strands differ significantly, which highlights the need to determine which strand provides a more likely rupture path and the circumstances that control this rupture path. In this study, we examine the effect of different assumptions about fault geometry and initial stress pattern on the dynamic rupture process to test multiple rupture scenarios and thus investigate the most likely path(s) of a rupture that starts on the Coachella Valley segment. We consider three types of fault geometry based on the Southern California Earthquake Center Community Fault Model, and we create a three-dimensional finite-element mesh for each of them. These three meshes are then incorporated into the finite-element method code FaultMod to compute a physical model for the rupture dynamics. We use a slip-weakening friction law, and consider different assumptions of background stress, such as constant tractions and regional stress regimes with different orientations. Both the constant and regional stress distributions show that rupture from the Coachella Valley segment is more likely to branch to the Mission Creek than to the Banning fault strand. The fault connectivity at this branch system seems to have a significant impact on the likelihood of a throughgoing rupture, with potentially significant impacts for ground motion and seismic hazard both locally and in the greater Los Angeles metropolitan area.

Effect of the time-weakening friction law during the nucleation process

Based on dynamic rupture simulations on a planar fault in a homogeneous half-space, we investigated the nucleation processes using the time-weakening friction law. Both the characteristic time and the rupture speed in the nucleation asperity play an important role in determining rupture behaviors on a fault plane following the time-weakening friction law, with which rupture starts from a single point in the nucleation asperity and propagates at a given speed toward the boundary of the nucleation area. Rupture with a small characteristic time or a large rupture speed in the nucleation asperity propagates earlier from the hypocenter. Rupture following the slip-weakening friction law requires a smaller radius of nucleation patch to have similar rupture front contours of the time-weakening friction law. Even if the rupture velocity in the nucleation patch of the time-weakening friction law increases to infinity, the peak slip rate in the nucleation asperity is smaller than that of the slip-weakening law. The peak ground velocity distributions of ruptures following the two friction laws are also compared.

Parametrizing Physics-Based Earthquake Simulations

Utilizing earthquake source parameter scaling relations, we formulate an extensible slip weakening friction law for quasi-static earthquake simulations. This algorithm is based on the method used to generate fault strengths for a recent earthquake simulator comparison study of the California fault system. Here we focus on the application of this algorithm in the Virtual Quake earthquake simulator. As a case study we probe the effects of the friction law’s parameters on simulated earthquake rates for the UCERF3 California fault model, and present the resulting conditional probabilities for California earthquake scenarios. The new friction model significantly extends the moment magnitude range over which simulated earthquake rates match observed rates in California, as well as substantially improving the agreement between simulated and observed scaling relations for mean slip and total rupture area.

Slip of a one-body dynamical spring-slider model in the presence of slip-weakening friction and viscosity

<span style="font-family: 新細明體;">This study is focused on analytic study at small displacements and numerical simulations of slip of a one-body dynamical slider-slider model in the presence of slip-weakening friction and viscosity. Analytic results with numerical computations show that the displacement of the slider is controlled by the decreasing rate, [gamma], of friction force with slip and viscosity, [eta], of fault-zone material. The natural period of the system with slip-weakening friction and viscosity is longer than that of the system without the two factors. There is a solution regime for <span style="font-family: 新細明體;">[eta]</span> and <span style="font-family: 新細明體;">[gamma]</span> to make the slider slip steadily without strong attenuation. The viscous effect is stronger than the frictional effect. Meanwhile, a change of <span style="font-family: 新細明體;">[eta]</span> results in a larger effect on the slip of the slider than a change of <span style="font-family: 新細明體;">[gamma]</span>. Numerical simulations are made for a one-body dynamical slider-slider model in the presence of three slip-weakening friction laws, i.e., the thermal-pressurization (TP) friction law, the softening-hardening (SH) friction law, and a simple slip-weakening (SW) friction law, and viscosity. Results show that slip-weakening friction and viscosity remarkably affect slip of the slider. The TP and SW friction laws cause very similar results. The results caused by the SH friction law are quite different from those by the other two. For the cases in study, the fixed points are not an attractor.</span>

A numerical study on dynamic shear rupture along frictional faults

The Wenchuan earthquake (Sichuan province, China, 2008) was caused by the dynamic rupture of Longmen Mountain fault. Such catastrophic disaster had led to a huge damage of life as well as major economic loss. The Longmen Mountain fault consisted of three faults with complex geometries, which gathered together as a main fault underground. The dynamic shear ruptures along the faults including bends and branches are frequently observed during earthquakes. In this study, the finite element method (FEM) is adopted to simulate the dynamic ruptures along both straight and branched faults, which are considered as frictional interfaces. A slip-weakening friction law is used to describe the interface behavior along faults. For the straight fault, the effects of pre-stress state and nucleation parameters on the dynamic shear rupture process are investigated; for the branched faults, the effects of pre-stress state and fault geometry on the rupture path selection are presented. The results are used to explain the rupture mechanism of Longmen Mountain fault during the earthquake.

Calculation of the local rupture speed of dynamically propagating earthquakes

The velocity at which a propagating earthquake advances on the fault surface is of pivotal importance in the contest of the source dynamics and in the modeling of the ground motions generation. In this paper the problem of the determination of the rupture speed (<em>v_<sub>r</sub></em>) is considered. The comparison of different numerical schemes to compute <em>v<sub>r</sub></em> from the rupture time (<em>t_<sub>r</sub></em>) shows that, in general, central finite differences schemes are more accurate than forward or backward schemes, regardless the order of accuracy. Overall, the most efficient and accurate algorithm is the five–points stencil method at the second–order of accuracy. It is also shown how the determination of <em>t_<sub>r</sub></em> can affect <em>v<sub>_r </sub></em>; numerical results indicate that if the fault slip velocity threshold (<em>v_<sub>l</sub></em>) used to define <em>t_<sub>r</sub></em> is too high (<em>v<sub>_l</sub></em> ≥ 0.1 m/s) the details of the rupture are missed, for instance the rupture tip bifurcation occurring for 2–D supershear rupture. On the other hand, for <em>v_<sub>l</sub></em> ≤ 0.01 m/s the results appear to be stable and independent on the choice of <em>v_<sub>l </sub></em>. Finally, it is demonstrated that in the special case of the linear slip–weakening friction law the definitions of <em>t_<sub>r</sub></em> from the threshold criterion on the fault slip velocity and from the achievement of the maximum yield stress are practically equivalent.