Abstract. This study explores stress drops and earthquake sequences in the simplest pressure-sensitive elasto-plastic media using two-dimensional simulations, emphasizing the critical role of temporal and spatial resolution in accurately capturing stress evolution and strain localization during seismic cycles. Our analysis reveals that stress drops – triggered by plastic deformation once local stresses reach the yield criterion – resemble fault rupture mechanics, where accumulated strain energy is suddenly released, simulating earthquake-like behavior. Finer temporal and spatial discretization leads to sharper stress drops and lower minimum stress values, for simulations that have not converged yet. Displacement accumulates gradually during interseismic periods and intensifies during major stress drops, capturing key features of natural earthquake cycles. The histogram of stress drop amplitudes exhibits a non-Gaussian distribution. This “solid turbulence” behavior suggests that stress is redistributed across spatial and temporal scales, with implications for understanding the variability of stress drop magnitudes. Our results demonstrate that high-resolution elasto-plastic models can reproduce essential features of earthquake nucleation and stress drop behavior without relying on complex friction laws or velocity-dependent weakening mechanisms. These findings emphasize the necessity of incorporating plasticity into fault slip models to better understand the mechanisms of fault weakening and rupture. Furthermore, our work suggests that extending these models to three-dimensional fault systems and incorporating material heterogeneity and fluid interactions could offer deeper insights into seismic hazard assessment and earthquake mechanics.

Earthquake rupture velocity and stress drop interaction in the Campi Flegrei volcanic caldera

Abstract Earthquake stress drop (Δσ) may increase with depth and stress in the brittle lithosphere. However, the range of uncertainty in Δσ and the lack of constraints on absolute stress make it difficult to establish whether they are correlated. Here, we investigate Δσ dependence on depth and maximum shear stress ( τ max ) based on ~11 years of seismicity in the northeastern Japanese forearc following the 2011 Tohoku-Oki megathrust earthquake. We interpret Δσ estimates computed using both individual spectra and spectral-ratio methods and find that Δσ exhibits a clear depth dependence within the seismically active upper ~60 km of the forearc lithosphere ( ~ 0.8 MPa per 10 km). We further compare Δσ values with quantitative τ max estimates from finite-element models of force balance. We find that median Δσ values increase with τ max in the brittle forearc lithosphere and that earthquake stress release is proportional to τ max . The dependence of Δσ on τ max explains the apparent depth dependence of Δσ and suggests that average Δσ values provide a relative measure of the stress at failure. In the northeastern Japanese forearc, Δσ values remained roughly constant in the decade following the Tohoku-Oki earthquake, suggesting negligible changes in failure stress in the forearc since the mainshock.

Understanding the stress–strain behaviour of rocks is essential for ensuring the safe and stable operation of rock structures in engineering. The spring model is conceptually simple and can capture complete stress–strain curves, but the traditional form neglects the influence of confining pressure. In this study, an improved spring model is proposed that incorporates confining pressure effects through empirical relationships between model parameters and confining pressure. Implemented in MATLAB, the model successfully reproduces the stress–strain curves of red layer rocks under confining pressures of 1, 3 and 4 MPa, showing close agreement with experimental results in both the peak strength and post-peak behaviour. Parametric analysis reveals that the spring retention force factor primarily controls the post-peak stress drop, the diameter-to-height ratio influences the slope of the curve, and the mean maximum deformation determines the peak strength. Additionally, the model can simulate both Class I and Class II curves by adjusting the relative deformation capacities of the spring blocks, and it captures the transition from uniform to localized failure modes. These findings demonstrate that the improved spring model offers a simple yet effective tool for simulating rock mechanical behaviour under varying confining pressures.

The surrounding rock between two ultra-closely spaced roadways, under biaxial compression (BC) condition, exhibits high failure propensity and consequently poses serious threats to the coal mining operations. The counter-pulled rockbolt (hereinafter referred as “bolt”) is widely employed to improve the stability of this kind of surrounding rock. However, the strength, deformation, macro- and micro-failure behaviors of bolted surrounding rock under BC condition are insufficiently understood. Therefore, these performances of the bolted samples (BSs) are investigated by using biaxial compressive experiments and acoustic emission (AE) technology. The research results indicate that the bolt diameter has an obvious capacity in improving the peak and residual strength of BSs, the bolt pretension force can significantly enhance the peak strength of BSs, yet has a minimal impact on the residual strength. Three types of axial stress-axial strain curves were categorized: post-peak instantaneous stress drop type, post-peak multi-step stress drop type and post-peak stress delay drop type. A new reinforcement effect, termed as the all-directional reinforcement effect of the bolt was observed. Insights into the influence of bolts on the elastic modulus and lateral displacement of the samples under BC condition were obtained, and two mechanisms for the reinforcement effect of bolt on the lateral displacement of samples were revealed. When the lateral pressure σ2 is 8.89 MPa, the effect of the bolt on the failure pattern of BSs is not obvious. Nevertheless, the fracture angle increases with the increase of bolt diameter and pretension force. The micro-failure crack types were classified based on AE parameters of AF–RA and it was found that the micro-failure of the BSs was dominated by shear cracks. The micro-failure process of the BSs underwent three stages, with most micro-failures occurring in Stage II. A new approach capable of computing the peak strength or the equivalent cohesion (c*) and equivalent internal friction angle (φ*) of sample reinforced by pretension bolt is proposed and used to calculate c* and φ* of the BSs under BC condition.

Conventional studies suggest that faults in the shallow subsurface resist earthquake nucleation, because their frictional strength increases as slip accelerates (i.e., velocity-strengthening friction). Contrary to this widely held notion, such nominally stable faults frequently host earthquakes induced by human activities. Here, we resolve this contradiction using numerical models that simulate both geological and earthquake timescales using rate-and-state friction. Faults could develop significant interface strength, expressed as increase in static frictions by around 0.25, due to "healing" over thousands to millions of years. This strength gain can be released to nucleate earthquakes, also on velocity-strengthening faults. These earthquakes exhibit efficient frictional weakening similar to those natural earthquakes on velocity-weakening faults but follow revised nucleation stages and length scales. Seismic hazard for subsequent earthquakes is reduced and vastly different. Velocity-strengthening faults can no longer host earthquakes, because subsequent slip on human lifetimes is stable. Velocity-weakening fault segments may still nucleate earthquakes, but with sharply reduced stress drops. Neighboring ruptured velocity-strengthening segments impede rupture propagation and hence reduce anticipated future earthquake magnitudes. Both the increased hazard for the first induced earthquake and less hazardous subsequent events need to be properly assessed and communicated to maintain public confidence for using the subsurface for the energy transition.

The 18 March 2020 M 5.6 Magna, Utah earthquake near Salt Lake City was recorded by more than 160 strong motion/broadband stations. The ground motions compare favorably with the NGA-West2 ground motion models (GMMs) using estimates of V S30 but there are numerous exceptions. The purpose of this study was to evaluate the site effects at 26 seismic stations located in the Salt Lake Valley. We evaluated the data from the mainshock and seven largest aftershocks ( M 3.9 to 4.6) and performed a one-dimensional (1D) random vibration theory equivalent-linear site response analysis (SRA). We compared our predicted site amplification with the recorded ground motions to evaluate which features in the data could be predicted using a 1D approach. We first updated the 2008 Utah Geological Survey shallow shear-wave velocity (V S ) database. Shallow V S profiles were assigned to each seismic station and extended to the source depth of 7 km using the Wasatch Front Community Velocity Model. Next an inversion was performed to evaluate stress drops, kappa, and Q(f) using recordings from 109 earthquakes ( M 2.9 to 5.6). The resulting parameters were then used in the SRA for four Salt Lake Valley site categories to compute linear amplification factors (AFs). These factors were then compared with the AFs (response spectra) implied by the NGA-West2 GMMs for the 26 seismic stations. Horizontal-to-vertical spectral ratios were also calculated from the recorded data and compared with the AFs (Fourier amplitude spectra) from the SRA to evaluate the consistency of the predicted site resonant frequencies. Our predicted AFs for the mainshock generally agree with the NGA-West2 AFs except for the softest unit where we predict more soil nonlinearity and higher long-period amplification. Our results also show an underprediction at short periods and close-in distances which may be due to a source effect, for example, radiation pattern and/or rupture directivity.

ABSTRACT Existing ground-motion models (GMMs) for Türkiye have primarily relied on ergodic or partially nonergodic frameworks, which are limited in capturing systematic ground-motion characteristics and the trade-off between aleatory and epistemic uncertainties. This study uses a comprehensive Turkish database of over 35,000 shallow crustal ground-motion recordings spanning 1983–2023 to develop a fully nonergodic GMM that accounts for systematic source, site, and path effects. The backbone of the nonergodic model is a regionalized ergodic GMM developed as part of this study, which incorporates an event-specific attenuation term. The nonergodic systematic effects are modeled using Gaussian processes (GPs) based on the residuals of the ergodic backbone GMM. GP parameters are constrained through a variogram-based approach, which is shown to provide advantages compared to a direct GP fitting. Path effects are evaluated using cell-specific attenuation and spatially correlated GPs, accounting for variations in the quality factor and velocity structure. The evaluated source, site, and path terms exhibit different spatial patterns and correlation lengths across spectral periods. Potential factors influencing the patterns are discussed. In particular, we find that the correlation lengths of kappa and the site term at short periods are comparable, suggesting dominating kappa effects at short periods. In addition, we observe parallels between the estimated path effects and available quality factor maps for Türkiye. The spatial distribution of short-period source effects and regional stress drop in western Türkiye also share similarities. The developed nonergodic model reduces aleatory variability by 35%–50% depending on the spectral period. This reduction, once considered in the context of epistemic uncertainties, is key for seismic hazard quantification and performance-based earthquake engineering applications in Türkiye.

ABSTRACT Distributed acoustic sensing (DAS) systems offer a cost-effective way to create large-scale strainmeter arrays for seismological applications using fiber-optic cables. DAS-based strain measurements are known to be influenced by various factors, bringing into question their general reliability for accurate earthquake characterization. A 15-km-long DAS deployment in northern California was operational within 3 days of the 2022 Mw 6.4 Ferndale earthquake and ran continuously throughout the aftershock sequence. We utilize these aftershock data to validate DAS-based strain measurements in two ways. We first test the accuracy of DAS-based magnitude estimates from peak dynamic strains by comparing them with magnitude and attenuation scaling relations derived independently from traditional borehole strainmeter (BSM) data. We demonstrate that DAS-based magnitudes are comparable to BSM-based magnitudes when corrections for variations in site response along the fiber-optic cable are properly made. Magnitude errors are spatially correlated, potentially because of factors such as finite-fault effects (e.g., stress drop) or more complex, unmodeled path attenuation or because of wave propagation effects in heterogeneous media. We then apply more advanced source characterization methodology to the DAS data using a time-domain empirical Green’s function (EGF) deconvolution approach to measure details of the moment rate history. The EGF approach using DAS data depends on careful treatment of distorting factors such as anthropogenic sources of noise and optical phase wrapping but successfully isolates source spectra for moderate-magnitude earthquakes: source spectral ratios obtained from DAS data, broadband seismometer data, and BSM data in the same region show consistent results, revealing differences in directivity and spectral shape among earthquakes. Although further research is needed to refine source-time-function estimation techniques for DAS data, particularly for larger magnitude events, these case studies demonstrate the clear potential of DAS for earthquake source characterization.

Abstract Stress‐driven afterslip is often suggested to explain the complementary spatial pattern between coseismic and postseismic slip. However, the quantitative relationship between the mainshock and the subsequent afterslip is rarely examined. We propose a model of coseismic and postseismic slip distributions in which the coseismic faulting supplies enough energy to drive the afterslip of intraplate earthquakes. Applying this method to the 2016 Central Tottori earthquake shows that our model can reproduce the horizontal postseismic displacement near the source region and highlights the quantitative relationship to its mainshock in terms of stress drop and energy changes. Data driven models do not always yield reasonable mechanical properties; therefore, both kinematic and mechanical constraints should be considered to achieve reliable deformation models during the earthquake cycle.

Granular materials under loading exhibit intermittent avalanches of varying sizes prior to full yielding, a hallmark of natural failure phenomena such as landslides and earthquakes. While continuum models for postyield plastic flow are well established, a unified framework connecting preyield avalanche dynamics to bulk rheology remains lacking. Here, we introduce a birefringent double-shear experiment that enables sustained probing of avalanche statistics and quasistatic flow behavior near the yielding transition. We find that the avalanche regime exhibits rate-weakening behavior, while the plastic regime is rate-independent, resulting in dual rheology under identical local shear rates and indicating hysteresis and mechanical instability. Within a stress-activated framework, we identify the mean normalized stress drop, a measure for mesoscale avalanche size, as a key field variable that bridges the two regimes. Incorporating this variable, we formulate a unified constitutive model that captures the entire yielding transition. These findings establish mesoscale avalanche evolution as a central mechanism underlying granular yielding rheology.

Understanding the mechanisms of injection-induced fault slip is critical for managing subsurface energy technologies. This study experimentally investigates the influences of the intermediate principal stress (σy), minimum principal stress (σx), and injection pressure (P) on fault slip initiation stress and velocity. Experiments were conducted on pre-faulted granite specimens (100 mm cubes) using a true triaxial apparatus, simulating in situ stress conditions. The results reveal a two-stage slip process: an initial stable stage dominated by elastic energy accumulation, followed by a slip stage characterized by rapid energy release and stick–slip oscillations. We found that slip initiation stress increases linearly with both σy and σx, but decreases linearly with increasing P. A higher σy delays slip initiation but can lead to larger stress drops and higher slip velocities upon failure. Conversely, fluid injection weakens the fault by reducing effective normal stress, exhibiting a dual effect: it lowers the stress required for slip and enhances the instantaneous slip velocity after initiation. Our findings provide quantitative, mechanistic insights into fault slip behavior, serving as a critical benchmark for numerical simulations and contributing to improved assessment and mitigation of injection-induced seismicity across various engineering applications.

Stress drop behavior of the earthquakes associated with the September 19, 2021, La Palma volcanic eruption in Cumbre Vieja, Canary Islands (Spain)

Statistical damage constitutive of oil shale considering post-peak stress drop: taking the Seven Member of Yanchang Formation in Ordos Basin as an example

Abstract Understanding the interplay of various energy sinks during seismic fault slip is essential for advancing earthquake physics and improving hazard assessment. However, quantifying the energy consumed by major dissipative processes remains a challenge. In this study, we investigate energy partitioning during laboratory earthquakes (“lab‐quakes”) by performing general shear stick‐slip experiments on synthetic granitic cataclasites at elevated confining pressure. Using ultrasound, microstructural, and novel magnetism‐based thermal analyses, we independently quantified the energy allocated to seismic radiation, new surfaces, and heat dissipation. These estimates showed good agreement with far‐field measurements of mechanical work during the lab‐quake. Our findings revealed that under the experimental conditions the majority of the released energy (68%–98%) is dissipated as heat, while seismic radiation accounts for 1%–8%, and the creation of new surfaces consumes <1%–32%. Microstructural observations indicate pre‐failure deformation, which includes comminution and development of the principal slip zone, significantly influences energy partitioning. This effect is further evident in the measured shear stress drops, where events with higher stress drops proportionally emitted more energy as seismic waves. This study is the first to constrain the full energy budget of lab‐quakes from an observational standpoint, providing critical insights into the dynamics of fault rupture and energy dissipation processes.

We estimate the stress drop ∆σ for 551 earthquakes from the 2019 Ridgecrest sequence in Southern California using a spectral decomposition. To assess the impact of propagation model assumptions, we apply a 2D cell-based approach that accounts for lateral attenuation variations and compare results with previous models using distance and depth-dependent attenuation. The 95% confidence interval for azimuthal-dependent attenuation over an 80 km radius is 0.290 at 2 Hz and 0.473 at 14 Hz (log10 units). While the 2D model reveals significant azimuthal variations, the overall ∆σ distribution remains similar to that from a simple distance-dependent model, at least for the analyzed data set. High ∆σ is observed near the M7.1 and M6.4 events, while lower values appear at shallower depths, especially toward the Coso region and near the left-lateral fault junction of the M6.4 sequence. All models consistently identify a high-∆σ region at 4-8 km depth between stations CLC and WRC2, north of the M7.1 hypocenter, where the main fault bends. While spatial comparisons reveal more localized differences, the most pronounced impact arises when the attenuation model incorporates depth dependence.

Both the 2023 Mw 7.8 Pazarcık earthquake (strike-slip fault) in Turkey, and the 2008 Mw 7.9 Wenchuan earthquake (reverse-slip fault) in China occurred on the Eurasian seismic belt, with comparable moment magnitudes. This study investigates the ground-motion characteristics of both earthquakes, using ground motion intensity measures (IMs), including peak ground accelerations (PGA), peak ground velocities (PGV), pseudospectral accelerations (PSAs) at T = 0.2–5.0 s, 5–95% significant duration, Arias intensity (Ia) and Newmark displacement. The Pazarcık earthquake shows negative between-event residuals (δBe) at T < 0.2 s and positive δBe at T > 0.2 s, indicating source effects in BSSA14 model over- and under- prediction respectively. The Wenchuan earthquake, however, displays uniformly positive δBe (all T), revealing source effects underprediction. Larger δBe values were observed at long/intermediate period (T > 0.2 s) for Pazarcık earthquake, but smaller at short period (T < 0.2 s), compared with Wenchuan event. Such period-dependent differences of ground motions between the two events may be attributable to fault types and Fault slip distribution at depth. Within the structure natural frequency range (0.5–1.5 Hz) of the primary buildings in both earthquakes affected area, more recordings for Pazarcık earthquake exceeded PGA and PGV thresholds from Chinese intensity scale IX, implying that its ground motion has greater impact on structures damage. The Wenchuan earthquake exhibits larger Arias intensity and greater deviations from predicted models compared to the Pazarcık event, reflecting its ground motion richer high-frequency content. These differences in Arias intensity may be attributable to different fault types and stress drop (Δσ) between the two earthquakes. At similar distances, Wenchuan earthquake exhibits longer 5–95% significant duration than Pazarcık’s. The result may be attributed to their different fault styles, rupture directivity, and rupture mechanisms. Both earthquakes produced Newmark displacements values exceeding 2 cm at multiple sites, indicating significant landslide hazards in their respective affected regions.

Abstract Elastocaloric cooling (eCC) is the most promising alternative to conventional refrigeration, leveraging the reversible martensitic transformations in nickel titanium (NiTi) shape memory alloys (SMAs) to achieve substantial adiabatic temperature changes. This study investigates the feasibility of commercially available NiTi sheets for such applications. Samples processed via electrical discharge machining (EDM), laser machining, and diamond smoothing were characterized using scanning electron microscopy (SEM), optical microscope (OM), differential scanning calorimetry (DSC), IR thermography (IR-TG), digital image correlation (DIC), and acoustic emission (AE). The sheets exhibited superelastic behavior with a critical transformation stress of ~ 400 MPa and an adiabatic temperature change of ± 20 K. However, rapid functional degradation occurred in the initial loading cycles, marked by a 50 MPa drop in transformation stress, 0.5% irreversible strain, and a temperature change reduction to ± 2 K after the first five cycles. SEM analysis after 150 cycles confirmed martensitic microstructure formation, correlating with AE signals indicative of dislocation activity and an increasing amount of retained martensite. These results highlight the microstructural challenges and issues when envisioning the use of NiTi sheets under tensile loading for elastocaloric (eC) applications. They motivate a discussion of how future studies should explore compressive loading configurations, addressing challenges such as buckling and localized martensitic phase transformation, to better exploit the potential of NiTi sheets in eC regenerators.

We use remote sensing observations to document surface deformation caused by the 2025 Mw7.7 Mandalay earthquake. This event is a unique case of an extremely long (~510 km) and sustained supershear rupture probably favored by the rather smooth and continuous geometry of this section of the structurally mature Sagaing Fault. The seismic rupture involved the locked portion of the fault over its entire depth extent (0 to 13 km) with a remarkably uniform slip distribution that averages 3.3 m, and an average stress drop of 4.7 MPa. No shallow-slip deficit is observed. The rupture extent challenges usual scaling laws relating earthquake magnitude, fault length, and slip. The fault ruptured along a known seismic gap that last ruptured in 1839 and tailed off into sections that ruptured during large earthquakes in 1930 and 1946. The amplitude and spatial distribution of fault slip in the 2025 event conform only approximatively to the slip-predictable model and the segmentation inferred from the fault geometry and past ruptures. Plausible sequences of earthquakes with variable magnitude, segmentation, and return periods, including events similar to the 2025 earthquake are produced in quasidynamic simulations using a simplified but nonplanar fault geometry. Based on this simulation, Mw>7.5 events return irregularly with an interevent time of ~141 y on average and a SD of ~40 y. The simulation is consistent with the historical seismicity and with the maximum magnitude ~Mw7.9 and return period (~250 y) derived from moment conservation. Data assimilation into such simulations could provide a way for time-dependent hazard assessment in the future.

We investigated the rupture dynamics of the 2025 Mw 7.7 Mandalay, Myanmar earthquake, using a video recording of surface rupture, strong motion recordings, waveform simulation, and satellite imagery. Our assessment, based on the S-wave observation in the video and rupture arrival time at a seismic station 246 km south of the hypocenter, suggests that rupture decelerated to subshear speeds (~3 km/s) from initial supershear propagation (~6 km/s) before reaching the camera location. This deceleration is also supported by comparison between the fault-normal acceleration patterns seen in the video and that simulated by kinematic rupture modeling. Additionally, satellite imagery indicated a local minimum in slip (2-3 m) approximately 40-60 km south of the epicenter, suggesting a region of reduced stress drop that likely caused the temporary deceleration. Beyond this point, the rupture appears to have re-established supershear propagation.