Critical Slip-weakening Distance Research Articles

Effects of fault roughness on estimating critical slip-weakening distance from fault slip history: A laboratory study

Earthquakes are the dynamic rupture of faults governed by fault weakening processes. Critical slip-weakening distance (Dc) is a crucial source parameter of earthquakes, and the determination of Dc is of great concern to semiologists. However, determining Dc for natural earthquakes is challenging due to the trade-off in inversed source models. To solve this problem, Fukuyama and his coworkers proposed a simple method (denoted as the F&M method) to estimate Dc directly from slip-velocity functions. According to the F&M method, the fault slip at the peak slip velocity (Dc') can be used as an approximation of Dc. However, the feasibility of this method has not been completely resolved. Here, we performed laboratory earthquake rupture experiments to examine the validity of the F&M method. Experiments were conducted on faults with different roughness and stress level. We studied the effect of fault roughness on the validity of the F&M method. Our results show that the increase in fault roughness could complicate the fault weakening process, producing repeated weakening and strengthening phase, which leads to a prominent deviation between Dc' and Dc. Furthermore, we also observed a correlation between the critical slip-weakening distance Dc and the final fault slip D. Such correlation implies the scale-dependent nature of Dc, which is consistent with seismic observations in the field.

Inferring Critical Slip-Weakening Distance from Near-Fault Accelerogram of the 2014 Mw 6.2 Ludian Earthquake

Abstract To better assess potential earthquake hazards requires a better understanding of fault friction and rupture dynamics. Critical slip-weakening distance (Dc) as one of the key friction parameters, however, is hard to determine on natural faults. For strike-slip earthquakes, we may directly estimate the Dc from Dc″—the double near-fault ground displacement at the time of the peak velocity (Fukuyama and Mikumo, 2007). Yet near-fault observations are very few, and, thus, there were only limited earthquakes with such Dc″ estimation. In 2014, an Mw 6.2 strike-slip event—the Ludian earthquake—occurred in southwest China. The strong-motion station (LLT) that is ∼0.45 km from the fault recorded the earthquake and enabled us to estimate Dc″ from the accelerograms. We inspect the polarity of the accelerometers and compare the integrated velocities with waveforms of nearby broadband stations. We also analyze the particle motion at the LLT station and retrieve the earthquake initiation at the intersection of the conjugated faults. We then apply the baseline correction to the seismograms, recover the ground velocities and displacements, and obtain the value of Dc″=0.1 m at the station. The recovered final displacements are compared with the predicted ground displacements of a finite-fault model. The discrepancy of fault-parallel displacements might imply limited underestimation of Dc″, and the estimated upper limit is 0.3 m. Comparison between the Dc″ and final slip on the fault patch follows the scaling of previous larger earthquakes. Analysis of the near-fault accelerometer data enhances our understanding on the earthquake source of the Ludian earthquake. This case extends the lower magnitude boundary of the Dc″ values obtained from natural faults and opens a window into the friction property in the seismically active region.

Spatiotemporal Evolution of Microseismicity Seismic Source Properties at the Irpinia Near-Fault Observatory, Southern Italy

ABSTRACTWe estimate the source parameters of small-magnitude earthquakes that occurred during 2008–2020 in the Irpinia faults area (southern Italy). We apply a spectral decomposition approach to isolate the source contribution from propagation and site effects for ∼3000 earthquakes in the local magnitude range between ML 0 and 4.2. We develop our analyses in three steps. First, we fit the Brune (1970) model to the nonparametric source spectra to estimate corner frequency and seismic moment, and we map the spatial distribution of stress drop across the Irpinia area. We found stress drops in the range 0.4–8.1 MPa, with earthquakes deeper than 7 km characterized by higher average stress drop (i.e., 3.2 MPa). Second, assuming a simple stress-release model (Kanamori and Heaton, 2000), we derive fracture energy and critical slip-weakening distance. The spatial variability of stress drop and fracture energy allows us to image the present stress conditions of fault segments activated during the 23 November 1980 Ms 6.9 earthquake. The variability of the source parameters shows clear patterns of the fault mechanical properties, suggesting that the Irpinia fault system can be divided into three main sectors, with the northern and southern ones showing different properties from the central one. Our results agree with previous studies indicating the presence of fluids with different composition in the different sectors of the Irpinia fault system. In the third step, we compare the time evolution of source parameters with a time series of geodetic displacement recorded near the fault system. Temporal trends in the correlation between geodetic displacement and different source parameters indicate that the poroelastic deformation perturbation generated by the karst aquifer recharge is modulating not only the occurrence rate of microseismicity (D’Agostino et al., 2018) but may lead to rupture asperities with different sizes and characteristics.

Dynamic Rupture Study of Near-Field Velocity Pulses during the 2016 Kumamoto Earthquake, Japan

ABSTRACT Simulating the ground motions of future earthquakes requires a proper understanding and modeling of source, path, and site effects. Ground motions recorded during recent earthquakes very close to their ruptured faults provide new evidence of the importance of source effects and suggest that physics-based rupture modeling is critical to account for them. Here, we develop dynamic rupture models to simulate the near-fault ground motions generated by the 2016 Kumamoto, Japan, earthquake (Mw 7.0) at Nishihara village, which feature a large-amplitude velocity pulse. Comparison of mainshock and foreshock waveforms suggests that the source of the velocity pulse is on the Futagawa fault segment located very close to the site. Our dynamic models use the spectral element method and are built upon a previous kinematic description of the event via a so-called “characterized source model,” with three strong-motion generation areas (SMGAs) on the assumed fault plane. We first develop a reference model that reproduces the main features of the rupture process in agreement with previous results of kinematic source inversion. We then examine the sensitivity of the simulated near-fault ground motions to the frictional parameters (critical slip-weakening distance and stress drop) in the shallow part of the fault and to the geometrical properties of the shallow SMGA. Even assuming drastically different frictional properties in the shallow part of the fault, the amplitude of the simulated ground motions was affected little. On the other hand, changes of geometrical properties of the shallow SMGA generated large differences in simulated ground motions. The results indicate that geometrical features of the shallow SMGA played a more important role in generating near-fault ground motions with velocity pulses as observed at Nishihara village during the 2016 Kumamoto earthquake.

Application of a parameter-shifted grey wolf optimizer for earthquake dynamic rupture inversion

Global optimization is an essential approach to any inversion problem. Recently, the grey wolf optimizer (GWO) has been proposed to optimize the global minimum, which has been quickly used in a variety of inversion problems. In this study, we proposed a parameter-shifted grey wolf optimizer (psGWO) based on the conventional GWO algorithm to obtain the global minimum. Compared with GWO, the novel psGWO can effectively search targets toward objects without being trapped within the local minimum of the zero value. We confirmed the effectiveness of the new method in searching for uniform and random objectives by using mathematical functions released by the Congress on Evolutionary Computation. The psGWO algorithm was validated using up to 10,000 parameters to demonstrate its robustness in a large-scale optimization problem. We successfully applied psGWO in two-dimensional (2D) synthetic earthquake dynamic rupture inversion to obtain the frictional coefficients of the fault and critical slip-weakening distance using a homogeneous model. Furthermore, this algorithm was applied in inversions with heterogeneous distributions of dynamic rupture parameters. This implementation can be efficiently applied in 3D cases and even in actual earthquake inversion and would deepen the understanding of the physics of natural earthquakes in the future.

Effects of seismogenic width and low-velocity zones on estimating slip-weakening distance from near-fault ground deformation

SUMMARYFault weakening process controls earthquake rupture propagation and is of great significance to impact the final earthquake size and seismic hazard. Critical slip-weakening distance (${D_c}$) is one of the key parameters, which however is of difficult endeavours to be determined on natural faults, mainly due to its strong trade-off with the fault strength drop. An estimation method of ${D_c}$ proposed by Fukuyama et al. provides a simple and direct reference of ${D_c}$ on real faults from the near-fault ground displacement at the peak of ground velocity (${D_c}^{\prime\prime}$). However, multiple factors may affect the observed near-fault ground velocity and thus need to be considered when estimating ${D_c}.$ In this work we conduct 3-D finite element numerical simulations to examine the effects of finite seismogenic width and near-fault low velocity zones (LVZs) on the results of ${D_c}^{\prime\prime}$. In uniform models with constant prescribed ${D_c}$, the derived ${D_c}^{\prime\prime}$ values increase with seismogenic width. Furthermore, the scaling between ${D_c}^{\prime\prime}$ and final slip in models with a constant ${D_c}$ indicates that the scale-dependent feature of ${D_c}^{\prime\prime}$ might not be related to variation in friction properties. With a near-fault LVZ, ${D_c}^{\prime\prime}$ values show significant magnification. The width of the LVZ plays a more important role in enlarging ${D_c}$ estimation compared to the depth of the LVZ. Complex wavefields and multiple wiggles introduced by the LVZ could lead to delay pick and then cause large deviation. The value of ${D_c}$ on the fault may be overestimated through ${D_c}^{\prime\prime}$ from limited stations only.

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.

Dynamic Modelling of Induced Seismicity by Using Seismic Efficiency Constraints and a New Scaling Law for Slip-Weakening Distance

In the numerical simulation of induced seismicity, much attention is generally paid to the calibration of the frictional resistance of the causative fault to obtain a seismic moment consistent with that of the actual event, whereas sufficient investigation is not made in the estimation of the slip-weakening distance Dc as well as in the calibration of seismically radiated energy. The present study addresses this problem by numerically and analytically investigating the relation between Dc and seismic source parameters. First, this study performs the dynamic simulation of an induced seismic event caused by a decrease in the effective normal stress. The analysis demonstrated that seismic efficiency η can be used to improve the accuracy of estimating the critical slip-weakening distance and the coefficient of kinetic friction µd whilst considering not only seismic moment but also radiated energy in the calibration. This gave insight into the development of the new calibration method for induced seismicity that considers energy-related seismic source parameters. Furthermore, a new scaling law of the slip-weakening distance was derived from the theoretical expression of seismic efficiency η, considering seismic moment Mo and scaled energy $$ \hat{e} $$. The proposed scaling law can yield the relation between Dc and Mo, which is shown to be similar to that obtained from a previous study, but additionally considers the relation between seismically radiated energy and Dc. The dependency of Dc on seismically radiated energy implied from the proposed scaling law has been verified from the dynamic analyses where η = 0.06 was used to place a constraint on Dc for seismic events with different magnitudes. The developed numerical simulation methodology of induced seismicity as well as the scaling law considering the energy indices significantly contributes to improving the accuracy of back-analysis, thus leading to a more accurate estimation of the mechanical properties of faults and/or shear zones in seismically active regions of deep underground mines or reservoirs composed of discontinuous hard rock masses.

A brief discussion on the relationship between apparent stress and slip-weakening law based on the energy partition criteria

According to the representation theorem of seismic energy radiation, we know that, at any point on the fault, the instantaneous seismic radiation energy, ES, the seismic moment M0, and the apparent stress σa=µES /M0 (µ is the shear modulus on the fault plane) should be positive values at any time during an earthquake faulting. However, we have noticed that, in recent source parameter inversion scheme for deriving the critical slip-weakening distance, the apparent stress used as a constraint condition on the fault plane could be less than zero or negative value, and the negative part was considered as dissipation energy and incorporated to the fracture energy. Although the mathematical formula in such case has no influence to the final resolution, however, the earthquake dynamic source process violates obviously the basic physical law, which could results in the overestimating of radiated seismic energy. In this study, we have proposed an alternative way to take account of the apparent stress expression based on the earthquake energy partition principle, and at the same time, we have also suggested that an additional constraint regarding to the radiation energy conservation on the fault could be added into the source parameter inversion in order to estimate the critical slip-weakening distance Dc.

Dynamic rupture process of the 1999 Chi-Chi, Taiwan, earthquake

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

Meshing scheme in the computation of spontaneous fault rupture process

The choice of spatial grid size has been being a crucial issue in all kinds of numerical algorithms. By using BIEM (Boundary Integral Equation Method) to calculate the rupture process of a planar fault embedded in an isotropic and homogeneous full space with simple discretization scheme, this paper focuses on what grid size should be applied to control the error as well as maintaining the computing efficiency for different parameter combinations of (Dc, Te), where Dc is the critical slip-weakening distance and Te is the initial stress on the fault plane. We have preliminarily found the way of properly choosing the spatial grid size, which is of great significance in the computation of seismic source rupture process with BIEM.

Near-Source Released Energy in Relation to Fracture Energy on Earthquake Faults

The near-source energy released on a fault is estimated through the strain energy change and the fracture energy from the results of kinematic waveform inversion and dynamic modeling for two different types of earthquakes: a shallow crustal earthquake, the 2000 Tottori, Japan ( M w 6.6) earthquake, and an in-slab event, the 1999 Oaxaca, Mexico ( M w 7.5) earthquake. The procedure incorporates the spatial distribution of slip, critical slip-weakening distance, stress drop, and strength excess. The results show that the near-source energy density estimated over major asperities on the fault is nearly the same for the two earthquakes, while the fracture energy on the in-slab fault is appreciably larger than that for the crustal fault, suggesting higher strength in the in-slab fault zone. The near-source released energy on major asperities is significantly larger than the fracture energy in the two earthquakes.

Estimation of the Critical Slip-Weakening Distance: Theoretical Background

It has been shown that a trade-off exists between estimates of the break- down strength drop and the critical slip-weakening distance (e.g., Guatteri and Spu- dich, 2000). For this reason, only the fracture energy, proportional to these two parameters, may be estimated from waveform modeling. However, Mikumo et al. (2003) proposed a new technique to estimate the slip-weakening distance of earth- quakes, separate from the fracture energy. For this method to be valid, the peak slip- velocity time must be close to the stress breakdown time. Here we explain the theo- retical background of this assumption and clarify the limitations of this technique using numerical simulations based on the boundary integral equation method. The theoretical analysis using the boundary integral equation and some numerical tests indicates that a rather smooth rupture process and relatively sharp change in stress at the stress breakdown time in the slip-weakening curve ensure the validity of the method.

Stress-Breakdown Time and Slip-Weakening Distance Inferred from Slip-Velocity Functions on Earthquake Faults

We estimate the critical slip-weakening distance on earthquake faults by using a new approach, which is independent of the estimate of fracture energy or radiated seismic energy. The approach is to find a physically based relation between the breakdown time of shear stress Tb, the time of peak slip-velocity Tpv, and the slip-weakening distance Dc, from the time histories of shear stress, slip, and slip velocity at each point on the fault, which can be obtained from dynamic rupture calculations using a simple slip-weakening friction law. Numerical calculations are carried out for a dynamic shear crack propagating either spontaneously or at a fixed rupture velocity on a vertical fault located in a 3D half-space and a more realistic horizontally layered structure, with finite-difference schemes. The results show that Tpv is well correlated with Tb for faults even with a heterogeneous stress-drop dis- tribution, except at locations near strong barriers and the fault edges. We also inves- tigate this relation for different types of slip-weakening behavior. We have applied the method to two recent, strike-slip earthquakes in western Japan, the 2000 Tottori and the 1995 Kobe events. We integrated the slip-velocity functions on the vertical fault obtained from kinematic waveform inversion of strong- motion and teleseismic records from the arrival time of rupture Tr to the time of the peak-slip velocity Tpv, and we then corrected the slip obtained at Tpv for the errors expected from the dynamic calculations. It was found that the slip-weakening dis- tance D c estimated in the frequency window between 0.05 and 0.5 Hz ranges between 40 and 90 cm on the two earthquake faults. However, if we consider the limited frequency resolution of the observed waveforms, probable time errors in the slip- velocity functions obtained from kinematic inversion, and the uncertainty of the slip- weakening behavior, the above estimates may be those located between the minimum resolvable limit and the upper bound of their real values. The estimated Dc values do not necessarily seem to indicate larger values in the shallower part and smaller values in the deeper part of the fault, but rather a spatially heterogeneous distribution that appears to be dependent on the local maximum slip. This possible dependence might be interpreted by the frictional properties of the fault such as the degree of roughness or the thickness of gouge layers, in addition to stress heterogeneities.