Stress Perturbations Research Articles

Quake-DFN: A Software for Simulating Sequences of Induced Earthquakes in a Discrete Fault Network

ABSTRACT We present an earthquake simulator, Quake-DFN, which allows simulating sequences of earthquakes in a 3D discrete fault network governed by rate and state friction. The simulator is quasi-dynamic, with inertial effects being approximated by radiation damping and a lumped mass. The lumped mass term allows for accounting for inertial overshoot and, in addition, makes the computation more effective. Quake-DFN is compared against three publicly available simulation results: (1) the rupture of a planar fault with uniform prestress (SEAS BP5-QD), (2) the propagation of a rupture across a stepover separating two parallel planar faults (RSQSim and FaultMod), and (3) a branch fault system with a secondary fault splaying from a main fault (FaultMod). Examples of injection-induced earthquake simulations are shown for three different fault geometries: (1) a planar fault with a wide range of initial stresses, (2) a branching fault system with varying fault angles and principal stress orientations, and (3) a fault network similar to the one that was activated during the 2011 Prague, Oklahoma, earthquake sequence. The simulations produce realistic earthquake sequences. The time and magnitude of the induced earthquakes observed in these simulations depend on the difference between the initial friction and the residual friction μi−μf, the value of which quantifies the potential for runaway ruptures (ruptures that can extend beyond the zone of stress perturbation due to the injection). The discrete fault simulations show that our simulator correctly accounts for the effect of fault geometry and regional stress tensor orientation and shape. These examples show that Quake-DFN can be used to simulate earthquake sequences and, most importantly, magnitudes, possibly induced or triggered by a fluid injection near a known fault system.

Intrusive mechanism of the 2018 Sierra Negra Galápagos eruption, constrained by 4D tomographic images

Understanding the mechanisms of magma intrusion underpins our ability to interpret geophysical monitoring signals at volcanoes and thus issue reliable forecasts of future activity. The basaltic caldera volcanoes of the western Galápagos Islands, Ecuador, exhibit exceptionally high rates of deformation driven by shallow magma accumulation and migration. However, the nature and evolution of magma storage at these volcanoes is poorly constrained by earthquake hypocentre locations or geodetic inversions. Here we show that transient variations in seismic velocity before, during, and after the 2018 eruption of the Sierra Negra volcano track the accumulation of magma in a shallow sill complex and the emplacement of a lateral flank intrusion. A four-dimensional tomographic technique applied to the P-wave arrivals of local earthquakes provides high spatiotemporal resolution of changes in the physical properties of the shallow volcanic system. In the month before the eruption, the expansion of a low-velocity zone above the sub-caldera sill complex coincides with caldera uplift and near-surface fracturing, driven by persistent shallow magma accumulation. A new low-velocity anomaly appeared progressively in the western flank of the volcano in the days after the onset of the eruption, coinciding with the opening of a curved sill that supplied magma to secondary eruptive fissures. The anomaly disappeared as the curved sill deflated after the initial opening, despite it remaining the conduit for magma from the caldera complex to the flank fissures. Low velocities across the shallow caldera after the end of the eruption likely result from rapid inflation due to recharge with fresh magma from depth. These results indicate a previously unknown complexity to the magmatic plumbing system at Sierra Negra and suggest velocity changes resulting from an interplay of thermal and stress perturbations.

Modulating effect of the divergent and rotational wind induced by mesoscale sea surface temperature perturbations in the Kuroshio Extension

AbstractMesoscale wind stress perturbations induced by sea surface temperature (SST) perturbations have a feedback effect on the ocean by influencing air–sea heat and momentum fluxes. Unlike the thermal feedback mechanism, which is well understood, the momentum feedback still needs to be studied, especially the respective roles of divergent and rotational wind components. In this study, momentum feedback was examined using an ocean model and an empirical equation, which solved wind stress field perturbations from their divergence and curl estimated from time‐evolving downwind and crosswind SST gradients. Through several numerical experiments, it was found that both the divergent and rotational wind can induce positive and negative temperature changes at varying regions and depths. This modulating effect is weak, with a maximum SST change of about 0.4°C on average, but it can reach the deep ocean beyond 1000 m.

4D Electrical Resistivity Imaging of Stress Perturbations Induced During High‐Pressure Shear Stimulation Tests

AbstractFluid flow through fractured media is typically governed by the distribution of fracture apertures, which are in turn governed by stress. Consequently, understanding subsurface stress is critical for understanding and predicting subsurface fluid flow. Although laboratory‐scale studies have established a sensitive relationship between effective stress and bulk electrical conductivity in crystalline rock, that relationship has not been extensively leveraged to monitor stress evolution at the field scale using electrical or electromagnetic geophysical monitoring approaches. In this paper we demonstrate the use time‐lapse 3‐dimensional (4D) electrical resistivity tomography to image perturbations in the stress field generated by pressurized borehole packers deployed during shear‐stimulation attempts in a 1.25 km deep metamorphic crystalline rock formation.

Observed meltwater-induced flexure and fracture at a doline on George VI Ice Shelf, Antarctica

Abstract Global Navigation Satellite System (GNSS) observations and ground-based timelapse photography obtained over the record-high 2019/2020 melt season are combined to characterise the flexure and fracture behaviour of a previously formed doline on George VI Ice Shelf, Antarctica. The GNSS timeseries shows a downward vertical displacement of the doline centre with respect to the doline rim of ~60 cm in response to loading from a central meltwater lake. The GNSS data also show a tens-of-days episode of rapid-onset, exponentially decaying horizontal displacement, where the horizontal distance between the doline rim and its centre increases by ~70 cm. We interpret this event as the initiation and/or widening of a fracture, aided by stress perturbations associated with meltwater loading in the doline basin. Viscous flexure modelling indicates that the meltwater loading generates tensile surface stresses exceeding 75 kPa. This, together with our timelapse photos of circular fractures around the doline, suggests the first such documentation of meltwater-loading-induced ‘ring fracture’ formation on an ice shelf, equivalent to the fracture type proposed as part of the chain-reaction lake drainage process involved in the 2002 breakup of the Larsen B Ice Shelf.

Shale fault reactivation during hydraulic fracturing in the Sichuan Basin: Evidence from shear experiments and stress perturbation calculations

Induced seismicity triggered during hydraulic fracturing for shale gas exploitation in the Sichuan Basin has aroused wide public concern with these earthquakes closely correlated with the reactivation of faults within the reservoir. The target shale reservoirs in the Sichuan Bain are currently located in the Longmaxi formation. To explore instability on these faults, we conducted shear experiments on simulated fault gouges under hydrothermal conditions to assess frictional stability and also evaluated the stress perturbations resulting from multistage hydraulic fracturing. Experimental results show that the frictional instability on these faults is primarily controlled by both mineral composition and the applied temperatures. With a decrease in the contents of phyllosilicate minerals or an increase in applied temperatures, the shale faults exhibit a transition from velocity-strengthening to velocity-weakening behaviour, indicating the potential for unstable fault slip. The stress perturbations resulting from multistage hydraulic fracturing were calculated from a dislocation model of the fluid-driven fracture. These results show that the stress changes resulting from multistage hydraulic fracturing are sufficient to reactivate adjacent unstable faults in the shale reservoir and trigger the seismicity. Our experimental and modelling results highlight the importance of shale composition, temperature, and stress perturbations on shale fault stability. These results have significant implications for understanding the shale fault instability and the potential triggering of induced seismicity during hydraulic fracturing in the Sichuan Basin.

Elastic Stress Coupling Between Supraglacial Lakes

AbstractSupraglacial lakes have been observed to drain within hours of each other, leading to the hypothesis that stress transmission following one drainage may be sufficient to induce hydro‐fracture‐driven drainages of other nearby lakes. However, available observations characterizing drainage‐induced stress perturbations have been insufficient to evaluate this hypothesis. Here, we use ice‐sheet surface‐displacement observations from a dense global positioning system array deployed in the Greenland Ice Sheet ablation zone to investigate elastic stress transmission between three neighboring supraglacial lake basins. We find that drainage of a central lake can place neighboring basins in either tensional or compressional stress relative to their hydro‐fracture scarp orientations, either promoting or inhibiting hydro‐fracture initiation beneath those lakes. For two lakes located within our array that drain close in time, we identify tensional surface stresses caused by ice‐sheet uplift due to basal‐cavity opening as the physical explanation for these lakes' temporally clustered hydro‐fracture‐driven drainages and frequent triggering behavior. However, lake‐drainage‐induced stresses in the up‐flowline direction remain low beyond the margins of the drained lakes. This short stress‐coupling length scale is consistent with idealized lake‐drainage scenarios for a range of lake volumes and ice‐sheet thicknesses. Thus, on elastic timescales, our observations and idealized‐model results support a stress‐transmission hypothesis for inducing hydro‐fracture‐driven drainage of lakes located within the region of basal cavity opening produced by the initial drainage, but refute this hypothesis for distal lakes.

Numerical modeling of a confined falling liquid film sheared by a gas flow in a plate heat exchanger of an NH3/H20 absorption chiller

In recent years, the demand for cooling has seen a substantial increase, primarily due to rising summertime temperatures. Conventional mechanical compression air conditioners have played a predominant role in fulfilling this demand, albeit at the cost of significant electricity consumption. In response, absorption chillers have emerged as an eco-friendly alternative, powered by sustainable heat sources like solar energy or industrial waste heat. The present work is conducted within the framework of developing compact absorption chillers incorporating plate heat exchangers. It builds upon prior research by improving an existing numerical model for falling film plate heat exchangers within an NH3/H2O absorption chiller. This former numerical model evaluates the coupled heat and mass transfer between the liquid film and the vapor flow while excluding hydrodynamic interactions at the liquid-vapor interface. The current investigation aims to address compactness and cost-efficiency limitations in absorption chillers. The consequences of operation within confined spaces were numerically evaluated. An innovative analytical model was developed to quantify the influence of the interactions at the liquid-vapor interface. Shear stress and interfacial perturbations were considered compared to the classical Nusselt model, enabling the evaluation of the changes in the average film thickness and the flooding phenomenon. This analytical model was then added to the previously developed heat and mass transfer model. The numerical model was applied to both the desorber and absorber units. The results show that increased confinement has minimal effects on the transfer coefficients. Additionally, an approach is suggested for estimating flooding in confined spaces and the results are compared with various correlations available in the literature.

PAGER-scFGA: unveiling cell functions and molecular mechanisms in cell trajectories through single-cell functional genomics analysis.

Background: Understanding how cells and tissues respond to stress factors and perturbations during disease processes is crucial for developing effective prevention, diagnosis, and treatment strategies. Single-cell RNA sequencing (scRNA-seq) enables high-resolution identification of cells and exploration of cell heterogeneity, shedding light on cell differentiation/maturation and functional differences. Recent advancements in multimodal sequencing technologies have focused on improving access to cell-specific subgroups for functional genomics analysis. To facilitate the functional annotation of cell groups and characterization of molecular mechanisms underlying cell trajectories, we introduce the Pathways, Annotated Gene Lists, and Gene Signatures Electronic Repository for Single-Cell Functional Genomics Analysis (PAGER-scFGA). Results: We have developed PAGER-scFGA, which integrates cell functional annotations and gene-set enrichment analysis into popular single-cell analysis pipelines such as Scanpy. Using differentially expressed genes (DEGs) from pairwise cell clusters, PAGER-scFGA infers cell functions through the enrichment of potential cell-marker genesets. Moreover, PAGER-scFGA provides pathways, annotated gene lists, and gene signatures (PAGs) enriched in specific cell subsets with tissue compositions and continuous transitions along cell trajectories. Additionally, PAGER-scFGA enables the construction of a gene subcellular map based on DEGs and allows examination of the gene functional compartments (GFCs) underlying cell maturation/differentiation. In a real-world case study of mouse natural killer (mNK) cells, PAGER-scFGA revealed two major stages of natural killer (NK) cells and three trajectories from the precursor stage to NK T-like mature stage within blood, spleen, and bone marrow tissues. As the trajectories progress to later stages, the DEGs exhibit greater divergence and variability. However, the DEGs in different trajectories still interact within a network during NK cell maturation. Notably, PAGER-scFGA unveiled cell cytotoxicity, exocytosis, and the response to interleukin (IL) signaling pathways and associated network models during the progression from precursor NK cells to mature NK cells. Conclusion: PAGER-scFGA enables in-depth exploration of functional insights and presents a comprehensive knowledge map of gene networks and GFCs, which can be utilized for future studies and hypothesis generation. It is expected to become an indispensable tool for inferring cell functions and detecting molecular mechanisms within cell trajectories in single-cell studies. The web app (accessible at https://au-singlecell.streamlit.app/) is publicly available.

Combinatorial impact of physico-chemical parameters and wastewater responses on freshwater fish (Rita rita) of river Ganga

This work wass designed to analyze the possibility of heavy metals inducing oxidative stress and biochemical perturbations effect on fresh water fish and their impact directly or indirectly on the human race. Due to continuous drainage of municipal waste, tanneries, and pesticides in Ganga River, lifeline of millions of people is heavily affected. The physico-chemical qualities of Ganga River were analyzed in quarterly basis during year 2018 to 2021, by taking the freshwater sample of different locations in Kanpur. While collecting the sample water the average temperature 27.6°, DO value of selected locations were fairly poor with an average of DO 6.67 mg L-1 and BOD ranged from 11.93 to 20.79 mg L-1. On the other hand the BOD ranged from 11.93 to 20.79 mg L-1 which is far more than WHO standards. Additionally, levels of antioxidants in enzymatic and non-enzymatic tissues serve as proxies for fish exposure to oxidant pollutants. Higher physico-chemical responses indicate contaminants and heavy metals may be playing an important role that have to be considered. The heavy metals are affecting the antioxidant defense system particularly seen in liver and kidney of fish and this affect on kidney and liver functioning as the concentrations of heavy metals rises. The relation between enzymatic activity and the metabolite showing negatively correlation that is noted highly significant to this study (r = -0.87, t = 10.14, p* ≤0.05).

Fracture behavior of sandstone with partial filling flaw under mixed-mode loading: Three-point bending tests and discrete element method (DEM) numerical approach

The fracture behavior of natural fracture in the geological reservoir subjected to filling property, affects the crack initiation and propagation under stress perturbation. Partial filling flaws were intermediate between open fractures and filled fractures, the fracture response may be worth exploring. In this work, the effect of the filling property of sandstone with partial filling flaws on the fracture behavior was systematically investigated based on three-point bending tests and the numerical approach of discrete element method (DEM). In the laboratory, semi-circular three-point bending tests were carried out with partial filling flaws of various filling strengths. Based on this, numerical simulations were used to further investigate the effect of the filling ratio and the inclination of the partial filling flaw on the mechanical and fracture responses, and the effect of the partial filling flaw under mixed-mode loading on the fracture mechanism was elucidated coupled with acoustic emission (AE) characteristics. The obtained results showed that the increase in filling strength and filling ratio of partial filling flaw led to an increase in peak strength, with a decreasing trend in peak strength with the inclination of partial filling flaw. In terms of crack propagation pattern, the increasing filling strength of the partial filling flaw induced the transformation of the fracture mechanism toward deflection, with a tortuosity path, while the filling ratio and inclination of partial filling flaw led to fracture mechanism change from deflection to penetration and attraction, accompanied with a larger AE event source in filler. Accordingly, the b-value based on the Gutenberg-Richter equation fluctuated between 5 and 4 at low filling ratio and inclination and remained around 5 at high filling ratio and inclination of partial filling flaw. Related results may provide an application prospective for reservoir stimulation using the natural fracture system.

Insights into Temporal Evolution of Induced Earthquakes in the Southern Delaware Basin Using Calibrated Relocations from the TXAR Catalog (2009–2016)

Abstract The Texas Seismological Network (TexNet) has enabled real-time monitoring of induced earthquakes since 2017. Before 2017, location uncertainties and temporal gaps in seismic data obscure correlations across Texas between seismicity and saltwater disposal or hydraulic fracturing. Depth biases also complicate linking anthropogenic stress changes to faults. We relocate 73 M 1.5+ earthquakes from the TXAR catalog (2009–2016) relative to the centroid of a calibrated core cluster consisting of 116 earthquakes from the TexNet catalog post-2020, in the southern Delaware basin south of the Grisham fault zone. Hypocentroidal decomposition relocation reduces spatial uncertainties of the TXAR events to <5 km and provides updated depths. The core cluster has uncertainties less than <300 m and depth constrained from near-source stations and S−P differential times. The majority of relocated TXAR events indicate the triggering of northwest-trending faults at a mean depth of 1 km below sea level, suggesting a causal connection with shallow saltwater disposal and consistency with post-2017 seismicity. Spatiotemporal patterns of pre-2017 seismicity and saltwater disposal highlight initial triggering via pore-pressure stress perturbations from nearby low-volume injections and later from southeastward pressure diffusion along permeable anisotropic conduits and fracture zones. The comparison between pre- and post-2017 seismicity indicates shallow fault reactivation through similar triggering mechanisms since 2009.

Cross-Validation of Metabolic Phenotypes in SARS-CoV-2 Infected Subpopulations Using Targeted Liquid Chromatography-Mass Spectrometry (LC-MS).

To ensure biological validity in metabolic phenotyping, findings must be replicated in independent sample sets. Targeted workflows have long been heralded as ideal platforms for such validation due to their robust quantitative capability. We evaluated the capability of liquid chromatography-mass spectrometry (LC-MS) assays targeting organic acids and bile acids to validate metabolic phenotypes of SARS-CoV-2 infection. Two independent sample sets were collected: (1) Australia: plasma, SARS-CoV-2 positive (n = 20), noninfected healthy controls (n = 22) and COVID-19 disease-like symptoms but negative for SARS-CoV-2 infection (n = 22). (2) Spain: serum, SARS-CoV-2 positive (n = 33) and noninfected healthy controls (n = 39). Multivariate modeling using orthogonal projections to latent structures discriminant analyses (OPLS-DA) classified healthy controls from SARS-CoV-2 positive (Australia; R2 = 0.17, ROC-AUC = 1; Spain R2 = 0.20, ROC-AUC = 1). Univariate analyses revealed 23 significantly different (p < 0.05) metabolites between healthy controls and SARS-CoV-2 positive individuals across both cohorts. Significant metabolites revealed consistent perturbations in cellular energy metabolism (pyruvic acid, and 2-oxoglutaric acid), oxidative stress (lactic acid, 2-hydroxybutyric acid), hypoxia (2-hydroxyglutaric acid, 5-aminolevulinic acid), liver activity (primary bile acids), and host-gut microbial cometabolism (hippuric acid, phenylpropionic acid, indole-3-propionic acid). These data support targeted LC-MS metabolic phenotyping workflows for biological validation in independent sample sets.

Seasonal Modulation of Crustal Seismicity in Northeastern Japan Driven by Snow Load

AbstractNumerous studies have reported that surface hydrological loading can seasonally modulate seismicity rates at crustal depths. For example, substantial winter snow accumulation occurs across the Japanese Islands, and these snowy regions appear to have seasonally modulated the occurrence of previous large inland earthquakes. Therefore, it is important to investigate the impact of seasonal stress changes on crustal seismicity to deepen our understanding of earthquake generation. Here we constrain seasonal changes in the surface load across northeastern Japan using Global Navigation Satellite System surface displacements and evaluate the potential relationship between temporal trends in inland seismicity and estimated seasonal stress changes. The spatial distribution of the seasonal surface load is consistent with snow depth along the Sea of Japan. The inland seismicity beneath northeastern Japan is modestly modulated by the seasonal stress changes that are induced by the annual snow load. However, this seasonal response is weaker than that in other regions. This weak modulation may be due to the small surface‐load‐induced stress perturbation relative to the long‐term‐averaged stressing rate and/or the limited presence of crustal fluids to trigger seismicity in Japan.

On the role of poroelastic stressing and pore pressure diffusion in discrete fracture and fault system in triggering post-injection seismicity in enhanced geothermal systems

Injection-induced seismicity has become one of the most critical challenges for the widespread deployment of Enhanced Geothermal Systems (EGS). In particular, some EGS development projects have led to large, damaging earthquakes that unexpectedly occurred far off the stimulated reservoir region and, in particular, after stopping fluid injection. Yet, the causative mechanisms of these seismicity patterns remain highly elusive. Here, we identify a combination of mechanisms that could explain delayed seismicity in EGS sites by conducting fully-coupled hydromechanical simulations of the hydraulic stimulation of a naturally-fractured granitic reservoir. The model comprises a sparse network of long, variably-oriented fractures interacting with a nearby, critically-oriented fault. The results show that the presence of fractures introduces notable nonlinearities in the flow field and rock deformation and significantly expands the rock volume affected by fluid injection. First, the stimulated fracture network provides highly-permeable conduits for communicating elevated pore pressure over long distances. Second, the anisotropic expansion of fractures generates shear stress that is transmitted almost instantaneously across the reservoir. The pore pressure and stress perturbations can not only cause slip along fractures, inducing (micro)seismicity during injection, but also affect the stability of nearby faults, which may not necessarily be pressurized during injection. The transferred poroelastic stresses can increase or decrease the slip tendency along different fault segments. However, the fault may reactivate only after several months following injection when a progressive pore pressure diffusion modulated by the transient fault permeability evolution brings a critically-stressed fault segment to failure conditions. We also find that the spatiotemporal evolution of seismicity depends largely on the nearby fault orientation, hydromechanical properties, and hydraulic connection with the fracture network, as well as the initial state of stress. We conclude that accurate subsurface characterization and continuous monitoring during and after injection should allow for managing the risks posed by injection-induced seismicity and safely unlocking the immense potential for clean and sustainable geothermal energy.

Impact of faults on the remote stress state

Abstract. The impact of faults on the contemporary stress field in the upper crust has been discussed in various studies. Data and models clearly show that there is an effect, but so far, a systematic study quantifying the impact as a function of distance from the fault is lacking. In the absence of data, here we use a series of generic 3-D models to investigate which component of the stress tensor is affected at which distance from the fault. Our study concentrates on the far field, located hundreds of metres from the fault zone. The models assess various techniques to represent faults, different material properties, different boundary conditions, variable orientation, and the fault's size. The study findings indicate that most of the factors tested do not have an influence on either the stress tensor orientation or principal stress magnitudes in the far field beyond 1000 m from the fault. Only in the case of oblique faults with a low static friction coefficient of μ=0.1 can noteworthy stress perturbations be seen up to 2000 m from the fault. However, the changes that we detected are generally small and of the order of lateral stress variability due to rock property variability. Furthermore, only in the first hundreds of metres to the fault are variations large enough to be theoretically detected by borehole-based stress data when considering their inherent uncertainties. This finding agrees with robust stress magnitude measurements and stress orientation data. Thus, in areas where high-quality and high-resolution data show gradual and continuous stress tensor rotations of &gt;20∘ observed over lateral spatial scales of 10 km or more, we infer that these rotations cannot be attributed to faults. We hypothesize that most stress orientation changes attributed to faults may originate from different sources such as density and strength contrasts.

Mesh size effect on finite source inversion with 3-D finite-element modelling

SUMMARY Three-dimensional finite-element models, which can handle the stress perturbations caused by subsurface mechanical heterogeneities and fault interactions, have been combined with the finite source inversion to estimate the coseismic slip distribution over the fault plane. However, the mesh grid for discretizing the governing equations in the finite-element model significantly affects the numerical accuracy. In this study, we performed kinematic finite source inversion with idealized (regular observation point array; M1A–M1D) and regional (GEONET, GPS Earthquake Observation Network System stations in Japan; M2A–M2H) models with different mesh sizes to quantitatively analyse the effect of the mesh grid size around the fault plane on the inverted fault slip distribution. Synthetic observation data vectors obtained from the finest models (M1A and M2A) are compared with those from the coarser models (M1B–M1D and M2B–M2H), which were adopted to construct Green's function matrix. We found that the coarser mesh models derived a smaller surface displacement, leading to a decrease in the norm of Green's function matrix, which in turn influences the fault slip magnitude from the finite source inversion. Finally, we performed the source inversion for the fault slip distribution of the 2011 Mw 9.0 Tohoku–Oki earthquake using the coseismic surface displacements recorded at the GEONET and seafloor stations and finite-element modelling. By reducing the mesh size on the fault, we confirmed that the estimated magnitude of fault slip converged to approximately 80 m, which is consistent with the range of fault slip amounts from previous studies based on the Okada model. At least 0.88 million total domain elements and a 6.7 km2 mesh size on the fault plane with an area of 240 × 720 km2 are required for the convergence of the fault slip. Furthermore, we found that the location of the maximum fault slip is less sensitive to the mesh size, implying that source inversion based on a coarse mesh model (i.e. less than 0.5 million elements and &amp;gt; ∼60 km2 mesh size) can quickly provide the rough fault slip distribution.

Variations in the present-day stress field and its implications for hydrocarbon development in the Hassi Terfa field, Hassi Messaoud, Algeria

Understanding the contemporary stress field and its variations is important in hydrocarbon production. These fluctuations are significant for borehole stability and trajectory, hydraulic stimulation, fault reactivation, and optimal well completion. In this study, we provide the first geomechanical model to determine the orientation and magnitude of the present-day stress of the Hassi Terfa field using geophysical logs to understand the origin of the spatial variation of the stress state. The breakouts from acoustic image logs provide an average maximum horizontal stress (SHmax) orientation of N115°, consistent with the Africa–Eurasia plate motion, which imposes the largest first-order stress source. However, our analysis demonstrates local stress perturbations near faults. This may mean that the stress field in the Hassi Terfa is superimposed by a third-order source of stress (<100 km). Our model demonstrates variations in stress magnitude with depth interpreted to be lithology-dependent, which act as a natural barrier against fracture propagation. We propose a new approach to quantify these perturbations via the stress regime index R′, using the magnitude of the principal stress components. The results demonstrate different layer-to-layer faulting regimes. These perturbations will limit the vertical propagation of hydraulic fracturing to the overlying formation, which enables it to access a larger reservoir volume and improve production. In general, a strike–slip regime with a slight normal slip component is interpreted for the study area. We develop the first-ever quantitative stress map using the relative principal stress magnitude parameter (Aϕ) to present the lateral variation of the stress regime throughout the Saharan platform. Results demonstrate a consistent strike–slip to normal/strike–slip regime with a uniform SHmax orientation. This map will help operators achieve optimal well direction and optimize hydraulic stimulation. Our results have considerable implications for hydrocarbon production in the central and southeastern Saharan platform.

Delayed and fractional-order dynamics of a model for earthquake induced by stress perturbations

Fractional calculus and time delay provide a powerful tool to model complex systems with memory and fractal systems and, the viscoelastic systems. Earthquakes are both complex systems with long-memory and some of their faults have fractal properties and, the rocks constituting faults have viscoelastic behavior. In this paper, we examined the dynamics of the spring-block considering the fractional viscous damping force and interaction between the blocks. The shear stress response is studied using the harmonic balance method and the numerical simulations are performed through Adams-Bashforth-Moulton scheme. The effects of the fractional-order and time delay on the amplitude-frequency curves and on the transition between steady state and seismic regime are investigated. The system response shows the existence of the resonance and anti-resonance. It is appears that the resonance amplitude and resonance frequency are strongly dependent on the time delay and fractional-order. This resonance phenomenon results in an accumulation of energy which can lead to the destabilization of the fault system. At the anti-resonance the system response has minimum amplitude, and the blocks move without accumulated energy. The results show that the delay and fractional viscous can affect the properties of the rock, which is characterized by the modified linear stiffness coefficient, modified linear damping coefficient and the modified linear friction coefficient. The stability and hopf bifurcation are investigated and the critical value of the time delay for the occurrence of Hopf bifurcation is determined. The transition from stationary state to the periodic orbit and vice-versa through the hopf bifurcation is observed in the system.

Transient and Steady‐State Friction in Non‐Isobaric Conditions

AbstractThe frictional properties of faults control the initiation and propagation of earthquakes and the associated hazards. Although the ambient temperature and instantaneous slip velocity controls on friction in isobaric conditions are increasingly well understood, the role of normal stress on steady‐state and transient frictional behaviors remains elusive. The friction coefficient of rocks exhibits a strong dependence on normal stress at typical crustal depths. Furthermore, rapid changes in normal stress cause a direct effect on friction followed by an evolutionary response. Here, we derive a constitutive friction law that consistently explains the yield strength of rocks from atmospheric pressure to gigapascals while capturing the transient behavior following perturbations in normal stress. The model explains the frictional strength of a variety of sedimentary, metamorphic, and igneous rocks and the slip‐dependent response upon normal stress steps of Westerly granite bare contact and synthetic gouges made of quartz and a mixture of quartz and smectite. The nonlinear normal stress dependence of the frictional resistance may originate from the distribution of asperities that control the real area of contact. The direct and transient effects may be important for induced seismicity by hydraulic fracturing or for naturally occurring normal stress perturbations within fault zones in the brittle crust.