Stick-slip Events Research Articles

Effects of inclination angle and confining pressure on triaxial unloading-induced slip behaviors of shale fractures

To explore the effects of fracture inclination angle θ and confining pressure σ3t on the slip behaviors and friction properties of fractures, the triaxial unloading-induced slip experiments were performed on the shale fractures. The results show that the σ3t controls the slip modes of fractures, while the θ affects the occurrence of the stick-slip events during the quasi-static slip stage. With the increase in σ3t, the main slip modes of fracture transform from the stable-slip to stick-slip, and eventually to the creep-slip. The increase in θ facilitated the occurrence of stick-slip events. As the θ increased from 30° to 50°, the number of stick-slip events increased from 0 to 3 and from 2 to 4 for σ3t = 10 MPa and 20 MPa, respectively. For σ3t = 40 MPa, no stick-slip event occurred in the slipping process. The θ and σ3t have great effects on interaction modes between asperities, which directly affected the friction properties of fractures. With increasing σ3t, the void spaces between the asperities were further compacted, resulting in the transition of asperity interaction from overriding mode to shear-off mode. The transition of asperity interaction model therefore brought about the weakening of friction coefficient at the activation point and the onset of dynamic slip stage. There is a competitive relationship between the θ and σ3t for the evolution of the friction properties of fractures. As the θ increase from 30° to 50°, for σ3t = 10 MPa, the mean sheared-off thickness decreased from 0.502 mm to 0.433 mm, while for σ3t = 40 MPa, the mean sheared-off thickness decreased from 0.505 mm to 0.319 mm. With the increment of θ, the anisotropy of joint roughness coefficient was weakened. We suggested that by adjusting the fracturing angle of hydro-fracturing, the earthquakes with large seismic moments may be effectively mitigated.

Towards the systematic reconnaissance of seismic signals from glaciers and ice sheets – Part 1: Event detection for cryoseismology

Abstract. Cryoseismology is a powerful toolset for progressing the understanding of the structure and dynamics of glaciers and ice sheets. It can enable the detection of hidden processes such as brittle fracture, basal sliding, transient hydrological processes, and calving. Addressing the challenge of detecting signals from many different processes, we present a novel approach for the semi-automated detection of events and event-like noise, which is well-suited for use as Part 1 of a workflow where unsupervised machine learning will be used as Part 2 (Latto et al., 2024) to facilitate the main reconnaissance of diverse detected event types. Implemented in the open-source and widely used ObsPy Python package, the multi-STA/LTA algorithm constructs a hybrid characteristic function from a set of short-term average (sta)–long-term average (lta) pairs (refer to Sect. 2 in the main text for an explanation of how uppercase and lowercase STA/sta and LTA/lta abbreviations are differentiated). We apply the algorithm to data from a seismic array deployed on the Whillans Ice Stream (WIS) in West Antarctica (austral summer 2010–2011) to form a “catch-all” catalogue of events and event-like noise. The new algorithm compares favorably with standard approaches, yielding a diversity of seismic events, including all previously identified stick-slip events (Pratt et al., 2014), teleseisms, and other noise-type signals. In terms of a catalogue overview, we investigate a partial association of seismicity with the tidal cycle and a slight association with ice temperature changes of the Antarctic summer. The new algorithm and workflow will assist in the comparison of different glacier environments using seismology, the identification of process change over time, and the targeting of possible subsequent high-resolution studies.

Towards the systematic reconnaissance of seismic signals from glaciers and ice sheets – Part 2: Unsupervised learning for source process characterization

Abstract. Given the high number and diversity of events in a typical cryoseismic dataset, in particular those recorded on ice sheet margins, it is desirable to use a semi-automated method of grouping similar events for reconnaissance and ongoing analysis. We present a workflow for employing semi-unsupervised cluster analysis to inform investigations of the processes occurring in glaciers and ice sheets. In this demonstration study, we make use of a seismic event catalogue previously compiled for the Whillans Ice Stream, for the 2010–2011 austral summer (outlined in Part 1, Latto et al., 2024). We address the challenges of seismic event analysis for a complex wave field by clustering similar seismic events into groups using characteristic temporal, spectral, and polarization attributes of seismic time series with the k-means++ algorithm. This provides the basis for a reconnaissance analysis of a seismic wave field that contains local events (from the ice stream) set in an ambient wave field that itself contains a diversity of signals (mostly from the Ross Ice Shelf). As one result, we find that two clusters include stick-slip events that diverge in terms of length and initiation locality (i.e., central sticky spot and/or the grounding line). We also identify a swarm of high-frequency signals on 16–17 January 2011 that are potentially associated with a surface melt event from the Ross Ice Shelf. Used together with the event detection presented in Part 1, the semi-automated workflow could readily be generalized to other locations and, as a possible benchmark procedure, could enable the monitoring of remote glaciers over time and comparisons between locations.

Avalanches and Extreme Value Statistics of a Mesoscale Moving Contact Line.

We report direct atomic force microscopy measurements of pinning-depinning dynamics of a circular moving contact line (CL) over the rough surface of a micron-sized vertical hanging glass fiber, which intersects a liquid-air interface. The measured capillary force acting on the CL exhibits sawtoothlike fluctuations, with a linear accumulation of force of slope k (stick) followed by a sharp release of force δf, which is proportional to the CL slip length. From a thorough analysis of a large volume of the stick-slip events, we find that the local maximal force F_{c} needed for CL depinning follows the extreme value statistics and the measured δf follows the avalanche dynamics with a power law distribution in good agreement with the Alessandro-Beatrice-Bertotti-Montorsi (ABBM) model. The experiment provides an accurate statistical description of the CL dynamics at mesoscale, which has important implications to a common class of problems involving stick-slip motion in a random defect or roughness landscape.

Experiment study on shear behavior and properties of granite fractures under real-time high-temperature conditions

Direct shear tests were conducted on granite fractures with similar joint roughness coefficients under real-time high temperatures (up to 400 °C) and constant normal stiffness conditions. In this study, the shearing process was monitored via acoustic emission, and fracture surface morphology was measured with three-dimensional laser scanning. With increasing temperature, peak and residual shear strengths, peak friction coefficient, and maximum normal dilation became higher. In contrast, peak normal displacement and peak shear displacement decreased. The apparent cohesion and internal friction angle exhibited opposite trends as temperature increased, primarily due to competition between thermal hardening and thermal cracking. The elastic strain energy of stick-slip events increased with temperature. From 100 °C to 400 °C, the degradation of fracture roughness and the volume of sheared-off asperities grew. Real-time temperature influences shear properties and is mainly attributed to physical and geometrical changes. Acoustic emission parameters, including count, energy, and hit, show segmented variation during fracture shearing. Based on parameter analyses of the average frequency and rise angle values, during the shearing process, the proportion of shear cracks at each stage varied with temperature. Shear failure was the predominant failure mode. Results from this study provide insight into the shear behavior of granite fractures under real-time high temperatures.

Global and local neuronal coding of tactile information in the barrel cortex.

During tactile sensation in rodents, the whisker movements across surfaces give rise to intricate whisker motions that encompass discrete and transient stick-slip events, effectively conveying valuable information regarding surface properties. These surface characteristics are transformed into cortical neuronal responses. This study examined the coding strategies underlying these transformations in rat whiskers. We found that changes in surface coarseness modified the number and magnitude of stick-slip events, which in turn both modulated properties of neuronal responses. Global changes in the number of stick-slip events primarily affected neuronal discharge rates and the degree of neuronal synchronization. In contrast, local changes in the magnitude of stick-slip events affected the transformation of these kinematic and kinetic characteristics into neuronal discharges. Most cortical neurons exhibited surface coarseness selectivity through global and local stick-slip event properties. However, this selectivity varied across coding strategies in the same neurons, given that each coding strategy reflected different aspects of changes in whisker-surface interactions. The degree of spatial similarity in surface coarseness preference in adjacently recorded neurons differed among these coding strategies. Adjacently recorded neurons exhibited the same surface coarseness preference in their firing rates but not through other coding strategies. Through these results, we were able to show that local stick-slip event properties contribute to texture discrimination, complementing and surpassing global coding in this context. These findings suggest that the representation of surface coarseness in the cortex may rely on concurrent coding strategies that integrate tactile information across different spatiotemporal scales.

How frictional slip evolves

Earthquake-like ruptures break the contacts that form the frictional interface separating contacting bodies and mediate the onset of frictional motion (stick-slip). The slip (motion) of the interface immediately resulting from the rupture that initiates each stick-slip event is generally much smaller than the total slip logged over the duration of the event. Slip after the onset of friction is generally attributed to continuous motion globally attributed to ‘dynamic friction’. Here we show, by means of direct measurements of real contact area and slip at the frictional interface, that sequences of myriad hitherto invisible, secondary ruptures are triggered immediately in the wake of each initial rupture. Each secondary rupture generates incremental slip that, when not resolved, may appear as steady sliding of the interface. Each slip increment is linked, via fracture mechanics, to corresponding variations of contact area and local strain. Only by accounting for the contributions of these secondary ruptures can the accumulated interface slip be described. These results have important ramifications both to our fundamental understanding of frictional motion as well as to the essential role of aftershocks within natural faults in generating earthquake-mediated slip.

Thermal efficiency of stick slip events along experimental analog faults

Most of the elastic energy released by earthquakes is believed to convert into heat; however, the reported experimental thermal efficiencies, defined as the ratio of frictional heat to elastic energy, are largely scattering, i.e., 50% or 90%. In this study, we conducted double direct shear experiments using halite powders as fault gouge under normal stresses of 10, 20, 30, 40, and 50 MPa to investigate the thermal efficiency of stick slip events. The results revealed two types of temperature changes during stick slip, resulting from stress drop and frictional heating. The temperature change caused by stress drop reduced thermal efficiency by 10%–20%. The scaling relationships between the friction heat, displacement and normal stress were also determined, which bridge the gap between the previous experimental conditions with only low and high normal stresses. The thermal efficiency was 50%–85%, and the specific value was inversely proportional to the fraction of stress drop. The thermal efficiencies was not a constant value and was closely related to the coseismic stress variation. The findings of this study suggest that the widely assumed 90% earthquake heat fraction is a consequence of specific stress change conditions.

Investigation of field scenarios using a 4n degrees of freedom transient torque and drag model

A coupled drill string dynamics model presents an opportunity to understand, replicate and potentially control the vibrations occurring along a drill string in a deep well. This paper describes a 4n degrees of freedom (4nDOF) model of the axial, torsional and lateral dynamics, consisting of coupled wave equations and lumped elements, which include modeling of the contact between the drill string and wellbore with a stiff string assumption. The model accounts for the bit-rock interaction, structural damping, and hydraulic forces acting on the lumped elements. The 4nDOF model is compared with three field scenarios from a drilling operation in the North Sea: a three-stage top drive start-up procedure, a drilling sequence starting from off-bottom conditions, and a backreaming operation at low rotational speed. The selected cases include instances of stick–slip and higher modes of torsional vibrations, which persist despite the use of a surface vibration mitigation system. High-frequency data recorded by a downhole measurement sub placed near the drill bit are used to verify the simulated downhole rotational speed and triaxial accelerations. The model is useful for analyzing torsional stick–slip events, which are replicated with a similar period and amplitude as in the downhole measurements. Furthermore, the model accurately reproduces the transition between first and second mode torsional oscillations upon the activation of a tuned top drive vibration mitigation system. The model can also be used to analyze lateral deformations and whirling of the drill string at various depths. The field case simulations show that the lateral dynamics can undergo significant changes at certain points in the drill string during torsional stick–slip and higher-mode torsional oscillations. The proposed model can be used to run simulations in close to real-time on a standard personal workstation, thus making it a valuable tool for devising and testing new drill string vibration mitigation solutions.

Nucleation Mechanism and Rupture Dynamics of Laboratory Earthquakes at Different Loading Rates

The loading rate of tectonic stress is not constant during long-term geotectonic activity and significantly affects the earthquake nucleation and fault rupture process. However, the mechanism underlying the loading rate effect is still unclear. In this study, we conducted a series of experiments to explore the effect of the loading rate on earthquake nucleation and stick–slip characteristics. Through lab experiments, faults were biaxially loaded at varying rates to produce a series of earthquakes (stick–slip events). Both shear strain and fault displacement were monitored during these events. The findings indicate a substantial effect of the loading rate on the recurrence interval and the shear stress drop of these stick–slip events, with the recurrence interval inversely proportional to the loading rate. The peak friction of the fault also decreases with the increasing loading rate. Notably, prior to the dynamic rupture of earthquakes, there exists a stable nucleation phase where slip occurs in a quasi-static manner. The critical nucleation length, or the distance required before the dynamic rupture, diminishes with both the loading rate and normal stress. A theoretical model is introduced to rationalize these observations. However, the rupture velocity of these lab-simulated earthquakes showed no significant correlation with the loading rate. Overall, this study enhanced our comprehension of earthquake nucleation and rupture dynamics in diverse tectonic settings.

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.

Statistical laws of stick-slip friction at mesoscale

Friction between two rough solid surfaces often involves local stick-slip events occurring at different locations of the contact interface. If the apparent contact area is large, multiple local slips may take place simultaneously and the total frictional force is a sum of the pinning forces imposed by many asperities on the interface. Here, we report a systematic study of stick-slip friction over a mesoscale contact area using a hanging-beam lateral atomic-force-microscope, which is capable of resolving frictional force fluctuations generated by individual slip events and measuring their statistical properties at the single-slip resolution. The measured probability density functions (PDFs) of the slip length δxs, the maximal force Fc needed to trigger the local slips, and the local force gradient {k}^{{prime} } of the asperity-induced pinning force field provide a comprehensive statistical description of stick-slip friction that is often associated with the avalanche dynamics at a critical state. In particular, the measured PDF of δxs obeys a power law distribution and the power-law exponent is explained by a new theoretical model for the under-damped spring-block motion under a Brownian-correlated pinning force field. This model provides a long-sought physical mechanism for the avalanche dynamics in stick-slip friction at mesoscale.

Numerical study of hydraulic characteristics of shale fractures during unloading-induced slipping: Effects of inclination angle and unloading rate

This study investigates the roles of inclination angle of fracture (θ) and unloading rate of confining pressure (Ur) on the hydraulic characteristics of shale fractures during the unloading-induced slipping process. A series of fluid flow simulations in the directions both parallel (x-directional) and perpendicular (y-directional) to the shear direction at different shear displacements (ds) were performed. The results show that the channeling effect is more pronounced in the y-direction than that in the x-direction. As ds increases, the fluid flow becomes less anisotropic, and the ratio of permeability in the y-direction (Ky) to that in the x-direction (Kx) gradually decreases first and then remains almost constant. Both Kx and Ky greatly increase with increasing in θ. The Ur significantly affects the permeability when ds increases to a certain value (i.e., 0.8 mm in this study). The efficiency of permeability enhancement represented by ΔK/Δds is evaluated. The mean ΔK/Δds during the slipping process for samples with θ = 50° is 4.73 times and 5.25 times larger than that for samples with θ = 30° in the x-direction and y-direction, respectively. With increasing Ur, the mean ΔK/Δds slightly increases first and then decreases. The occurrence of stick–slip events may control the ΔK/Δds.

A new approach for real-time prediction of stick–slip vibrations enhancement using model agnostic and supervised machine learning: a case study of Norwegian continental shelf

Efficient and safe drilling operations require real-time identification and mitigation of downhole vibrations like stick-slip, which can significantly diminish performance, reliability, and efficiency. This pioneering research introduces a robust machine learning approach combining model-agnostic regression techniques with Bayesian Optimized Extra Trees (BO_ET) to accurately predict stick-slip events in real-time using downhole sensor data. The model is rigorously tested and validated on a substantial offshore dataset comprising over 78,000 data points from a Norwegian continental shelf (NCS) oil field. The key input features encompassing real-time downhole and surface drilling parameters are carefully selected, including critical variables such as collar rotational speed, shock risks, annular pressure, torque, mud flow rate, drill string vibration severity, and other relevant measurements. These parameters offer significant insights into the occurrence of harmful stick-slip vibrations. Among several sophisticated machine learning models, the Extra Trees (ET) algorithm demonstrates superior performance with the lowest errors of 5.5056 revolutions per minute (r/min) Mean Absolute Error (MAE) and 9.9672 r/min Root Mean Square Error (RMSE) on out-of-sample test data. Further hyperparameter tuning of the ET algorithm via Bayesian Optimization dramatically reduces errors down to 0.002156 MAE and 0.024495 RMSE, underscoring the significant innovation and advantages of the proposed approach. By seamlessly incorporating real-time downhole sensor data and drill string mechanics, the model enables reliable identification of stick-slip events as they occur downhole. This grants opportunities to optimize critical drilling parameters including revolutions per minute (RPM), weight-on-bit (WOB), mud flow rates, and more to effectively mitigate stick-slip severity and improve the rate of penetration (ROP). Integrating the approach into automatic driller systems on offshore rigs offers immense benefits for drilling operations through substantially increased efficiency, fewer premature failures, lower costs, and significantly improved productivity and safety. Overall, this research strongly emphasizes the immense transformative potential of advanced data analytics and machine learning in enabling more efficient, economical, and sustainable drilling practices. The proposed model demonstrates clear superiority over existing methods and establishes a robust and reliable platform for real-time stick-slip prediction and mitigation, maximizing drilling performance.Graphical abstract

Origin of steady state stress fluctuations in a shear-thinning worm-like micellar system

Large, irregular stress fluctuations under a constant applied shear rate are observed during the flow of dilute worm-like micellar solutions even at low Reynolds numbers. Statistical properties of such fluctuations showing signatures of chaos and elastic turbulence have been studied extensively. Although the mechanisms like boundary slippage, dynamics of shear band interface, time-dependent secondary flows, and inertio-elastic effects are conceived as the possible factors for such striking flow properties, their contributions in different non-linear flow regimes remain poorly understood. Here, we study the Taylor–Couette flow of a well-characterized aqueous worm-like micellar system formed by 2 wt. % cetyltrimethylammonium tosylate and 100 mM sodium chloride (2 wt. % CTAT + 100 mM NaCl). For a fixed applied shear-rate just beyond the onset of shear-thinning, high-speed optical imaging in the flow-gradient plane reveals spatiotemporally varying velocity gradients in the system. In this regime, the magnitude of stress fluctuations remains insignificant. However, the fluctuation becomes substantial beyond a critical shear rate deep inside the non-linear regime of the flow curve when significant free-surface undulations, sustained stick-slip, and elastic recoil events are observed. Imaging in the flow-vorticity and the gradient-vorticity plane indicates that such dynamics are primarily driven by the elasticity-induced turbulent flows in the system. Furthermore, in this regime, we find that the characteristic persistent time of stress fluctuations matches well with the time scales of the stick-slip events, as well as the micellar breaking time, indicating a possible connection between the striking stress dynamics and the micellar kinetics.

Deterministic and stochastic chaos characterize laboratory earthquakes

We analyze frictional motion for a laboratory fault as it passes through the stability transition from stable sliding to unstable motion. We study frictional stick-slip events, which are the lab equivalent of earthquakes, via dynamical system tools in order to retrieve information on the underlying dynamics and to assess whether there are dynamical changes associated with the transition from stable to unstable motion. We find that the seismic cycle exhibits characteristics of a low-dimensional system with average dimension similar to that of natural slow earthquakes (<5). We also investigate local properties of the attractor and find maximum instantaneous dimension ≳10, indicating that some regions of the phase space require a high number of degrees of freedom (dofs). Our analysis does not preclude deterministic chaos, but the lab seismic cycle is best explained by a random attractor based on rate- and state-dependent friction whose dynamics is stochastically perturbed. We find that minimal variations of 0.05% of the shear and normal stresses applied to the experimental fault influence the large-scale dynamics and the recurrence time of labquakes. While complicated motion including period doubling is observed near the stability transition, even in the fully unstable regime we do not observe truly periodic behavior. Friction's nonlinear nature amplifies small scale perturbations, reducing the predictability of the otherwise periodic macroscopic dynamics. As applied to tectonic faults, our results imply that even small stress field fluctuations (≲150 kPa) can induce coefficient of variations in earthquake repeat time of a few percent. Moreover, these perturbations can drive an otherwise fast-slipping fault, close to the critical stability condition, into a mixed behavior involving slow and fast ruptures.

Precursory predictors of the onset of stick-slip frictional instability

Defining precursory phenomena that forewarn the onset of stick slip events remains an elusive but central goal in earthquake and other failure forecasting. We present a method to define the timing of instability by separately decoupling velocity and inertial effects in a spring-slider system. System state is defined in phase-space by velocity and inertia that in turn control critical stiffness and define the onset of instability while sliding velocity V = VLk/(k + dF/du) remains finite. A general energy analysis defines velocity and inertial effects (coefficients) that act against each other to promote/suppress instability by respectively increasing/decreasing critical stiffness. Repetitive stick-slip experiments define features of stick-slip cycles and identify a precursory trend in accelerating slip that precedes the onset of unstable sliding. We represent this precursory acceleration (dV/dt) immediately preceding instability by a general power-law relation dV/dt = AVα that reduces to V = B(ci + ti-t)-β. This represents the “true” timing of the onset of stick slip, ti relative to that “projected” from the linearization of the precursory data, tf, with tf=ci + ti. ci represents the small offset between the “predicted” and “true” timing of the onset of stick slip resulting from velocity and inertial effects and may be considered as the error in prediction. This error is one-order of magnitude smaller (∼3 ms) than the lead-time that forewarns of the event (∼40 ms) in our experiments and thus is useful as a predictor. Three independent methods using power-law, linear and criticality relationships confirm the fidelity of the timing of the slip instability transition evident in the stick slip data. This theoretical treatment suggests that the underlying physical meaning of the parameter c in the modified Omori law R∼(c + tM-t)-q is the time of the main shock in advance of the timing of the singularity predicted for an ideal response.

A Discrete Elements Study of the Frictional Behavior of Fault Gouges.

A series of discrete elements simulations is presented for the study of fault gouges' frictional response. The gouge is considered to have previously undergone ultra-cataclastic flow and long-time consolidation loading. We explore the effect of different particle characteristics such as size, polydispersity, and also shearing velocities on gouge's response under the conditions met in the seismogenic zone. Monte-Carlo analyses suggest that the local stick-slip events disappear when averaging over a large number of numerical samples. Moreover, the apparent material frictional response remains almost unaffected by the spatial randomness of particles' position and by the particle's size distribution. On the contrary, the mean particle size controls the formation and thickness of the observed shear bands, which appear after the peak friction is met. Furthermore, the apparent friction evolution fits well to an exponential decay law with slip, which involves a particle size dependent critical slip distance. For the studied conditions and depth, the shearing velocity is found to play a secondary role on the apparent frictional response of the gouge, which highlights the importance of analyses involving multiphysics for studying the rheology of fault gouges. Besides improving the understanding of the underlying physics of the problem, the above findings are also useful for deriving pertinent constitutive models in the case of modeling with continuum theories.

Deep learning for laboratory earthquake prediction and autoregressive forecasting of fault zone stress

Earthquake forecasting and prediction have long and in some cases sordid histories but recent work has rekindled interest based on advances in early warning, hazard assessment for induced seismicity and successful prediction of laboratory earthquakes. In the lab, frictional stick-slip events provide an analog for earthquakes and the seismic cycle. Labquakes are also ideal targets for machine learning (ML) because they can be produced in long sequences under controlled conditions. Indeed, recent works show that ML can predict several aspects of labquakes using fault zone acoustic emissions (AE). Here, we extend these works with: 1) deep learning (DL) methods for labquake prediction, 2) by introducing an autoregressive (AR) forecasting DL method to predict fault zone shear stress, and 3) by expanding the range of lab fault zones studied. The AR methods allow forecasting stress at future times via iterative predictions using previous measurements. Our DL methods outperform existing ML models and can predict based on limited training. We also explore forecasts beyond a single seismic cycle for aperiodic failure. We describe significant improvements to existing methods of labquake prediction and demonstrate: 1) that DL models based on Long-Short Term Memory and Convolution Neural Networks predict labquakes under conditions including pre-seismic creep, aperiodic events and alternating slow/fast events and 2) that fault zone stress can be predicted with fidelity, confirming that acoustic energy is a fingerprint of fault zone stress. Our DL methods predict time to start of failure (TTsF) and time to the end of Failure (TTeF) for labquakes. Interestingly, TTeF is successfully predicted in all seismic cycles, while the TTsF prediction varies with the amount of preseismic fault creep. We report AR methods to forecast the evolution of fault stress using three sequence modelling frameworks: LSTM, Temporal Convolution Network and Transformer Network. AR forecasting is distinct from existing predictive models, which predict only a target variable at a specific time. The results for forecasting beyond a single seismic cycle are limited but encouraging. Our ML/DL models outperform the state-of-the-art and our autoregressive model represents a novel framework that could enhance current methods of earthquake forecasting.

Onset mechanism of granular avalanches in inclining layers using a continuum model

• Critical conditions for the onset of macro scale avalanches are presented. • Onset of macro scale avalanches occur in the small area in granular layers. • Stresses and packing fractions reach the maxima at the onset of avalanches. • Both of dilatancy and densification occur at the same time in granular layers. • Aggregates of stick-slip like events are formed in the longitudinal direction. What is the onset mechanism of macro scale avalanches? How do macro scale avalanches happen in the granular layers in an inclining box? The answers to these questions are the main part of our article aims. Using 3-dimensional simulation method we show the stresses, the stress ratios and the packing fractions in the processes where the onset of macro scale avalanches takes place. Based on our results the critical conditions of the onset of avalanches are presented. The onset mechanism of granular avalanches is elucidated. The onset of macro scale avalanches occurs in the small area, about 2% of the whole area, in the inclining granular layers. These are the conditions for the onset of macro scale avalanches that the shear and normal stresses and the packing fraction reach the maximum values at the same inclining angle. Then the stress ratio should be larger than the static frictional coefficient of materials. Aggregates of stick-slip like event are formed in the longitudinal direction. The number of aggregates decreases and the physical quantities in the aggregates rapidly increase with increasing inclining angle in the small area in which the onset of macro scale avalanche occurs.