Magnitude Of Deviatoric Stress Research Articles

Constraint on the background stress in the source region of the 2016 Kumamoto earthquake sequence based on temporal changes in elastic strain energies and coseismic stress rotation

Summary We investigated the deviatoric stress magnitude of the background stress fields before the 2016 Kumamoto earthquake sequence in Japan based on temporal changes in elastic strain energies caused by the mainshock and coseismic stress rotation. We modelled the six components of background stress fields from stress orientations together with the parameter of effective friction coefficients (μ’ = 0.3, 0.15, 0.1, 0.05, and 0.03) using the 3-D Mohr diagram. We computed the absolute stress fields immediately following the primary events (the largest foreshock and mainshock) of the earthquake sequence by combining coseismic stress change fields with background stress fields. The total amount of elastic strain energy released by the mainshock increased with the effective friction coefficient. Considering the energy balance in which some part of the released energy must be consumed as radiated energy, we understood that the model with μ’ = 0.03 was unrealistic. We also examined the dependence of coseismic stress rotation on the effective friction coefficient. Furthermore, we applied a stress inversion method to moment tensor data of earthquakes to directly estimate coseismic stress rotation. Comparing the theoretical and estimated coseismic stress rotations, we concluded that the models with μ’ = 0.3 and 0.15 were more consistent with the observations than those with μ’ < 0.1. In the reasonable models, the deviatoric stress magnitudes were 37–65 and 39−70 MPa at a depth of 10 km on the northern and southern source faults, respectively.

Dynamical Modeling of Fault Slip Rates at the New Zealand Plate Boundary Indicates Fault Weakness

AbstractWe construct a thin‐sheet dynamical model of the New Zealand plate boundary that includes faults. Our model fits fault slip rates, style of distributed deformation, and is constrained by relative plate boundary motion. We assume a pseudo‐plastic rheology and achieve a best fit to slip rate observations with a deviatoric stress magnitude of 20 MPa. Modeled local forces are significant at Puysegur and Hikurangi subduction zones, and smaller forces are related to mantle downwelling beneath South Island and Havre Trough mantle upwelling. Modeled tractions on faults are mostly 5–20 MPa, similar to or slightly smaller than stress magnitudes adjacent to faults. Modeled shear tractions are generally 2–10 MPa, comparable to stress drops during earthquakes. Modeled stress orientations and fault dips suggest that many faults are not optimally oriented for their style of faulting. Notably small traction magnitudes of <5 MPa and shear tractions of <0.5 MPa are modeled for faults in the central North Island Dextral Fault Belt (NIDFB), which we infer to be very poorly oriented. Friction coefficients on faults (ratio of shear stress to effective normal stress) are in the range 0.1–0.3 for major crustal faults such as the Alpine Fault and Marlborough faults, but subduction zones and the NIDFB have values <0.1. We propose that low values of long‐term fault strength, shear stress resolved onto the fault, and overall magnitudes of deviatoric stress in the crust are a consequence of dynamic weakening of faults during fault slip.

Failure mechanism and stability control of surrounding rock in mining roadway with gentle slope and close distance

In this study, theoretical analysis, numerical simulation and field measurement were adopted to analyze the difficult problem of controlling the stability of surrounding rock in gently inclined and close-distance coal seam mining roadways. The results showed that: (1) According to the properties and stress environment of the roadway roof, to determine the specific spatial range of the original roof stage, transition stage and regeneration roof stage of the roadway, and corresponding to the distribution of plastic zones in the spatial stages, was an important basis for analyzing the deformation mechanism of the roadway and proposing a phased collaborative control plan. (2) Under the influence of mining, the plastic zone of the transportation roadway expanded violently by about 10 m ahead of the working face. Within the range of roadway passing the overlying goaf, the plastic zone of the surrounding rock between the layers runed through, especially extending to the roof and two shoulder corners of the roadway. The roof and two shoulder corners of the roadway became the key parts for the stability control of the surrounding rock. (3) The mechanical mechanism of asymmetric expansion of the plastic zone was obtained as follows: the range was determined by the magnitude of the deviatoric stress and the orientation was dominated by the direction of the principal stress. The combined effect of the magnitude of deviatoric stress and the angle of principal stress caused asymmetric expansion of the plastic zone. (4) A phased collaborative control scheme was proposed, and numerical simulation and industrial verification were carried out on the proposed scheme. The deformation of the surrounding rock of the roadway at the engineering site was less than 150 mm, and the control effect of the surrounding rock was good, ensuring the safe and efficient recovery of the fully mechanized mining face. The present study revealed the mechanical mechanism of failure and instability of the surrounding rock of the gently inclined close distance coal seam mining roadway and proposed a phased collaborative control scheme, which could provide valuable information for mining research.

Effect of initial deviatoric stress on anisotropy of marine clay during principal stress rotation

The effect of the initial deviatoric stress direction and magnitude of deviatoric stress q on the strain components and non-coaxial behavior of soft marine clay during principal stress rotation was experimentally examined. The strain components and pore water pressure depended considerably on the deviatoric stress direction and q. Through polar diagrams, a notable non-coaxiality was observed between the orientations of the major principal strain increment and major principal stress, and the non-coaxial angle fluctuated with variations in the initial deviatoric stress direction and q. The results can provide an experimental basis for constitutive modeling of continuous major principal stress axes for ocean engineering.

Mechanism for Deep Crustal Seismicity: Insight From Modeling of Deformation Processes at the Main Ethiopian Rift

AbstractWe combine numerical modeling of lithospheric extension with analysis of seismic moment release and earthquake b‐value in order to elucidate the mechanism for deep crustal seismicity and seismic swarms in the Main Ethiopian Rift (MER). We run 2‐D numerical simulations of lithospheric deformation calibrated by appropriate rheology and extensional history of the MER to simulate migration of deformation from mid‐Miocene border faults to ∼30 km wide zone of Pliocene to recent rift floor faults. While currently the highest strain rate is localized in a narrow zone within the rift axis, brittle strain has been accumulated in a wide region of the rift. The magnitude of deviatoric stress shows strong variation with depth. The uppermost crust deforms with maximum stress of 80 MPa, at 8–14 km depth stress sharply decreases to 10 MPa and then increases to a maximum of 160 MPa at ∼18 km depth. These two peaks at which the crust deforms with maximum stress of 80 MPa or above correspond to peaks in the seismic moment release. Correspondingly, the drop in stress at 8–14 km correlates to a low in seismic moment release. At this depth range, the crust is weaker and deformation is mainly accommodated in a ductile manner. We therefore see a good correlation between depths at which the crust is strong and elevated seismic deformation, while regions where the crust is weaker deform more aseismically. Overall, the bimodal depth distribution of seismic moment release is best explained by the rheology of the deforming crust.

Local stress perturbations associated with the 2008 Wenchuan M 8.0 earthquake near the Longmenshan fault zone in the eastern margin of the Tibetan Plateau

The 2008 Wenchuan M 8.0 earthquake induced local stress perturbations near the Longmenshan (LMS) fault zone. Using in situ measurements and stress tensor inversions from focal mechanisms, we investigated the post-earthquake perturbed stress field at shallow depths (≤1.2 km), in the upper crust above a basal attachment (~5–18 km) as well as in the middle crust beneath a basal attachment (~19–32 km). At shallow depths in the Beichuan-Jiangyou section, the maximum principal stress (σ1) orientations changed from a pre-earthquake orientation of NWW to a post-earthquake orientation of NEE. However, near the Baoxing-An'xian and Qingchuan-Mianxian sections, the pre-earthquake σ1 orientation of NW-NWW was largely unaltered. Before the mainshock, in the upper crust above the basal detachment, the entire LMS fault zone exhibited a consistent σ1 orientation of NW-NWW. However, after the earthquake, some sections, such as the Beichuan-Nanba section, achieved σ1 orientations of NEE that were distinctly different from the pre-seismic stress field. In the middle crust beneath the basal detachment, the stress field was mostly unchanged. The crust beneath the basal detachment, along the eastern margin of the Tibetan Plateau, is dominated by NWW-oriented maximum principle stress and strain directions and a thrust faulting stress regime along the entire LMS fault zone; these observations are representative of the southeastward motion of the Bayan Har block and its ongoing collision with the South China block along the LMS thrust belt. The spatially heterogeneous stress field that occurred in the upper crust (≤18 km) after the mainshock was most likely caused by the co-seismic static stress changes associated with the Wenchuan earthquake. Prior to the onset of seismic activity, the deviatoric stress magnitudes were estimated at less than 22 MPa and 4 MPa at depths of 10 km and 20 km, respectively, suggesting that the mainshock fault zone has a relatively low fault strength to overcome, in order to initiate significant co-seismic rupture and aftershocks, especially in the crust beneath the basal detachment. These smaller deviatoric magnitudes are indicative of the weaker fault materials that resides in the LMS region.

A comparative study of the stress-dependence of dynamic and static moduli for sandstones

Understanding the differences between the static and dynamic elastic moduli of reservoir rocks is essential for the successful exploration and production of hydrocarbon reservoirs. However, the controlling factors on the dynamic-static discrepancy for sandstones remain ambiguous. Consequently, we have purposely selected three outcrop sandstone samples with large porosity contrast to investigate the effects of the stress state, magnitude, and load-unload history on the dynamic and static moduli through laboratory measurements. The results suggest that the dynamic moduli are systematically larger than the static moduli at almost any hydrostatic or deviatoric stress magnitude. In contrast, the static moduli are much more sensitive to the stress variations than the dynamic ones, leading to the decreasing dynamic-static difference upon hydrostatic loading and the increasing dynamic-static difference upon deviatoric loading. When the maximum stress in a cycle is initially reversed, the dynamic-static ratio tends to approach one, whatever the bulk modulus under hydrostatic pressure condition or the Young’s modulus under triaxial stress condition. Under the subsequent unloading process, the static bulk modulus is always higher than that derived during loading. However, the unloading static Young’s modulus is larger than the loading Young’s modulus only at a relatively high deviatoric stress magnitude greater than 30 MPa, while showing an opposite trend at a low-stress condition of less than 25 MPa. From the microstructural viewpoint, it is believed that the static tests accumulate the elastic, viscoelastic, and nonelastic properties within a certain stress or strain range. In contrast to the dynamic modulus, the static modulus exhibits greater sensitivity to the pressure or stress changes under hydrostatic and deviatoric stress conditions. The strong stress dependence makes it important to consider the in situ stress conditions when establishing dynamic-static modulus relations.

Stress and deformation mechanisms at a subduction zone: insights from 2-D thermomechanical numerical modelling

SUMMARY Numerous processes such as metamorphic reactions, fluid and melt transfer and earthquakes occur at a subducting zone, but are still incompletely understood. These processes are affected, or even controlled, by the magnitude and distribution of stress and deformation mechanism. To eventually understand subduction zone processes, we quantify here stresses and deformation mechanisms in and around a subducting lithosphere, surrounded by asthenosphere and overlain by an overriding plate. We use 2-D thermomechanical numerical simulations based on the finite difference and marker-in-cell method and consider a 3200 km wide and 660 km deep numerical domain with a resolution of 1 km by 1 km. We apply a combined visco-elasto-plastic deformation behaviour using a linear combination of diffusion creep, dislocation creep and Peierls creep for the viscous deformation. We consider two end-member subduction scenarios: forced and free subduction. In the forced scenario, horizontal velocities are applied to the lateral boundaries of the plates during the entire simulation. In the free scenario, we set the horizontal boundary velocities to zero once the subducted slab is long enough to generate a slab pull force large enough to maintain subduction without horizontal boundary velocities. A slab pull of at least 1.8 TN m–1 is required to continue subduction in the free scenario. We also quantify along-profile variations of gravitational potential energy (GPE). We evaluate the contributions of topography and density variations to GPE variations across a subduction system. The GPE variations indicate large-scale horizontal compressive forces around the trench region and extension forces on both sides of the trench region. Corresponding vertically averaged differential stresses are between 120 and 170 MPa. Furthermore, we calculate the distribution of the dominant deformation mechanisms. Elastoplastic deformation is the dominant mechanism in the upper region of the lithosphere and subducting slab (from ca. 5 to 60 km depth from the top of the slab). Viscous deformation dominates in the lower region of the lithosphere and in the asthenosphere. Considering elasticity in the calculations has an important impact on the magnitude and distribution of deviatoric stress; hence, simulations with increased shear modulus, in order to reduce elasticity, exhibit considerably different stress fields. Limiting absolute stress magnitudes by decreasing the internal friction angle causes slab detachment so that slab pull cannot be transmitted anymore to the horizontal lithosphere. Applying different boundary conditions shows that forced subduction simulations are stronger affected by the applied boundary conditions than free subduction simulations. We also compare our modelled topography and gravity anomaly with natural data of seafloor bathymetry and free-air gravity anomalies across the Mariana trench. Elasticity and deviatoric stress magnitudes of several hundreds of MPa are required to best fit the natural data. This agreement suggests that the modelled flexural behaviour and density field are compatible with natural data. Moreover, we discuss potential applications of our results to the depth of faulting in a subducting plate and to the generation of petit-spot volcanoes.

Geodynamic evolution of southwestern North America since the Late Eocene

Slab rollback, lithospheric body forces, or evolution of plate boundary conditions are strongly debated as possible lithospheric driving mechanisms for Cenozoic extension in southwestern North America. By incorporating paleo-topography, lithospheric structure, and paleo-boundary conditions, we develop a complete geodynamic model that quantifies lithospheric deviatoric stresses and predicts extension and shear history since Late Eocene. We show that lithospheric body forces together with influence of change-over from subduction to transtensional boundary conditions from Late Eocene to Early Miocene were the primary driving factors controlling direction and magnitude of extensional deviatoric stresses that produced topographic collapse. After paleo-highlands collapsed, influence of Pacific-North America plate motion and associated deformation style along the plate boundary became increasingly important from Middle Miocene to present. Smaller-scale convection stress effects from slab rollback and associated mantle flow played only a minor role. However, slab rollback guided deformation rate through introduction of melts and fluids that impacted rheology.

Mechanism of Microstructural Variation Under Cyclic Shearing of Shantou Marine Clay: Experimental Investigation and Model Development

Soil microstructure has been extensively studied in recent years, because it can provide insights into macro behaviour. Previous studies in this area mainly focus on the change in soil microstructure during isotropic and one-dimensional consolidation. The principal objective of this study is to investigate the mechanism of microstructure evolution of soft marine clay under cyclic shearing. Cyclic triaxial tests were carried out at various confining pressures, cyclic deviatoric stresses and over-consolidation ratios (OCR). Soil microstructure was determined using the scanning electron microscope (SEM). Artificial neural networks (ANN) were used to develop a model for understanding the interaction effects of different parameters (number of cycles, cyclic deviatoric stress) on axial strain at different confining pressures (60, 80, 100 and 150 kPa). It was found that there is a threshold cyclic deviatoric stress, above which soil specimen shows significant strain and eventually fails. The threshold value is found to increase almost linearly with an increase in confining pressure and also, increases with increasing OCR. On the other hand, the change of soil microstructure during the subsequent cyclic shearing depends on the magnitude of cyclic deviatoric stress. When the cyclic deviatoric stress is below a threshold value, the soil microstructure maintains almost unchanged. When the cyclic deviatoric stress exceeds the threshold value, some large pores appear even though the total pore volume is kept constant (undrained condition under cyclic loads). With an increase in pore non-uniformity, soil skeleton becomes weaker and eventually collapses.

Stress Field in the 2016 Kumamoto Earthquake (M 7.3) Area

AbstractWe used 1‐D and 3‐D velocity models to determine focal mechanism solutions (FMSs) of 349 crustal earthquakes (M 2.7–7.3) and stress tensors in the source area of the 2016 Kumamoto earthquake (M 7.3) that occurred on the Futagawa‐Hinagu fault zone in Kyushu, Southwest Japan. There are some differences in the FMSs determined with the 1‐D and 3‐D velocity models. The use of the 3‐D velocity model leads to better results of stress tensors, which are determined by inverting the FMSs. The orientation of the minimum stress (σ3) axis is more accurately determined, which trends NNW‐SSE to N‐S nearly horizontally. In contrast, the axes of the maximum and intermediate stresses (σ1 and σ2) trend WSW‐ENE to E‐W with wide ranges. Significant spatiotemporal variations of the stress field are revealed in the Kumamoto source zone, indicating a small magnitude of deviatoric stress. The friction coefficient of the faults is estimated to be relatively small (~0.4), indicating that the seismogenic faults in central Kyushu are weak. The fault weakening may be caused by fluids beneath the source area and arc magma under the nearby Aso active volcano.

Effects of principal stress rotation on stress–strain behaviors of saturated clay under traffic–load–induced stress path

A series of cyclic torsional shear tests using hollow cylinder apparatus (HCA) were performed to investigate the effect of principal stress rotation (PSR) on the stress–strain behaviors of saturated soft clay. The traffic–load–induced shear stress path was used in the cyclic test and the investigation mainly concerned the influence of PSR on the shear stiffness and non-coaxiality. It indicated that the effects of PSR substantially depends on the magnitude of deviatoric stress (q = {[(σ1 − σ2)2 + (σ2 − σ3)2 + (σ1 − σ3)2]/2}1/2) as well as the intermediate principal stress ratio (b = (σ2 − σ3)/(σ1 − σ3)). At low deviatoric stress, the trajectory envelope of deviatoric strain path translates with a nearly constant size, showing constant shear stiffness and strong non-coaxiality. However, at high deviatoric stress, the trajectory envelope of deviatoric strain rapidly expands towards instability, showing degenerating shear stiffness and weak non-coaxiality. Moreover, the excess pore water pressure increases and the shear stiffness decreases more rapidly as b value increases. The results can provide an experimental basis for constitutive modelling of clays under traffic–induced loadings.

A km-scale “triaxial experiment” reveals the extreme mechanical weakness and anisotropy of mica-schists (Grandes Rousses Massif, France)

The development of Andersonian faults is predicted, according to theory and experiments, for brittle/frictional deformation occurring in a homogeneous medium. In contrast, in an anisotropic medium it is possible to observe fault nucleation and propagation that is non-Andersonian in geometry and kinematics. Here, we consider post-metamorphic brittle/frictional deformation in the mechanically anisotropic mylonitic mica-schists of the Grandes Rousse Massif (France). The role of the mylonitic foliation (and of any other source of mechanical anisotropy) in brittle/frictional deformation is a function of orientation and friction angle. According to the relative orientation of principal stress axes and foliation, a foliation characterized by a certain coefficient of friction will be utilized or not for the nucleation and propagation of brittle/frictional fractures and faults. If the foliation is not utilized, the rock behaves as if it was isotropic, and Andersonian geometry and kinematics can be observed. If the foliation is utilized, the deviatoric stress magnitude is buffered and Andersonian faults/fractures cannot develop. In a narrow transition regime, both Andersonian and non-Andersonian structures can be observed. We apply stress inversion and slip tendency analysis to determine the critical angle for failure of the metamorphic foliation of the Grandes Rousses schists, defined as the limit angle between the foliation and principal stress axes for which the foliation was brittlely reactivated. This approach allows defining the ratio of the coefficient of internal friction for failure along the mylonitic foliation to the isotropic coefficient of friction. Thus, the study area can be seen as a km-scale triaxial experiment that allows measuring the degree of mechanical anisotropy of the mylonitic mica-schists. In this way, we infer a coefficient of friction μweak=0.14 for brittle-frictional failure of the foliation, or 20% of the isotropic coefficient of internal friction.

Spatial variation of stress orientations in NE Japan revealed by dense seismic observations

In order to investigate the spatial distribution of the crustal stress state across NE Japan, we determined 1370 focal mechanisms by picking P-wave polarities from seismograms observed by temporary and permanent seismic networks densely deployed in this area. We applied stress tensor inversions to these data, plus to those routinely determined. The results show that the stress state in NE Japan is heterogeneous in space, which is different from previous results that showed that the NE Japan arc is characterized by margin normal compression. The orientations of the maximum compressional stress (σ1.) axes are significantly different with 95% confidence limits between the arc–backarc region and the forearc region. The arc–backarc region is characterized by spatially uniform margin normal compression. However, the north and south parts of the forearc region have the σ1 axis oriented nearly N–S and vertical, respectively. The region in between has a similar stress orientation to the arc–backarc region. Moreover, the stress regime in the arc–backarc region varies spatially in response to change in the surface altitude. Beneath regions of relatively low altitudes, a reverse faulting stress regime is dominant. However, regions of higher altitudes are characterized by a strike–slip faulting stress regime. Numerical model calculations, in which gravitational and buoyancy forces caused by topography are incorporated, show that differential stresses of about 15–25MPa are needed to explain the lateral variation of the stress regime observed in the arc–backarc region. This suggests that the background deviatoric stress magnitude in NE Japan is very low.

Relationship between tectonic overpressure, deviatoric stress, driving force, isostasy and gravitational potential energy

We present analytical derivations and 2-D numerical simulations that quantify magnitudes of deviatoric stress and tectonic overpressure (i.e. difference between the pressure, or mean stress, and the lithostatic pressure) by relating them to lateral variations in the gravitational potential energy (GPE). These predictions of tectonic overpressure and deviatoric stress associated with GPE differences are independent of rock rheology (e.g. viscous or elastic) and rock strength. We consider a simple situation with lowlands and mountains (plateau). We use a numerical two-layer model consisting of a crust with higher Newtonian viscosity than that in the mantle, and also a three-layer model in which the two-layer lithosphere overlies a much less viscous asthenosphere. Our results (1) explain why estimates for the magnitude of stresses in Tibet, previously published by different authors, vary by a factor of two, (2) are applied to test the validity of the thin sheet approximation, (3) show that the magnitude of the depth-integrated tectonic overpressure is equal to the magnitude of the depth-integrated deviatoric stress if depth-integrated shear stresses on vertical and horizontal planes within the lithosphere are negligible (the thin sheet approximation) and (4) show that under thin sheet approximation tectonic overpressure is required to build and support continental plateaus, such as in Tibet or in the Andes, even if the topography and the crustal root are in isostatic equilibrium. Under thin sheet approximation, the magnitude of the depth-integrated tectonic overpressure is equal to the depth-integrated horizontal deviatoric stress, and both are approximately 3.5 × 10 12 N m −1 for Tibet. The horizontal driving force per unit length related to lateral GPE variations around Tibet is composed of the sum of both tectonic overpressure and deviatoric stress, and is approximately 7 × 10 12 N m −1 . This magnitude exceeds previously published estimates for the force per unit length required to fold the Indo-Australian Plate south of India, and hence the uplift of the Tibetan plateau could have folded the Indian Plate. We also discuss the mechanical conditions that are necessary to achieve isostasy, for which the lithostatic pressure is constant at a certain depth. The results show that tectonic overpressure can exist at a certain depth even if all deviatoric stresses are zero at this depth, because this tectonic overpressure is related to horizontal gradients of vertical shear stresses integrated across the entire depth of the lithosphere. The magnitude of the depth-integrated tectonic overpressure of 3.5 × 10 12 N m −1 implies that the pressure estimated from observed mineral assemblages in crustal rocks is likely significantly different from the lithostatic pressure, and pressure recorded by crustal rocks is not directly related to depth. In case of significant weakening of the entire lithosphere by any mechanism our analytical and numerical studies provide a simple estimation of tectonic overpressure via variations in GPE.

Modification of fluid inclusions in quartz by deviatoric stress. III: Influence of principal stresses on inclusion density and orientation

Extraction of useful geochemical, petrologic and structural information from deformed fluid inclusions is still a challenge in rocks displaying moderate plastic strain. In order to better understand the inclusion modifications induced by deviatoric stresses, six deformation experiments were performed with a Griggs piston-cylinder apparatus. Natural NaCl–H2O inclusions in an oriented quartz crystal were subjected to differential stresses of 250–470 MPa at 700–900 °C and at 700–1,000 MPa confining pressure. Independently of the strain rate and of the crystallographic orientation of the quartz, the inclusions became dismembered and flattened within a crystallographic cleavage plane subperpendicular to σ 1. The neonate (newly formed) inclusions that result from dismemberment have densities that tend towards equilibrium with P fluid = σ 1 at T shearing. These results permit ambiguities in earlier deformation experiments on CO2–H2O–NaCl to be resolved. The results of the two studies converge, indicating that density changes in neonate inclusions are promoted by high differential stresses, long periods at high P and high T, and fluid compositions that maximize quartz solubility. Neonates spawned from large precursor inclusions show greater changes in density that those spawned from small precursors. These findings support the proposal that deformed fluid inclusions can serve as monitors of both the orientation and magnitude of deviatoric stresses during low-strain, ductile deformation of quartz-bearing rocks.

Nearly complete stress drop in the 2011 M w 9.0 off the Pacific coast of Tohoku Earthquake

Temporal change in the stress field after the 2011 Tohoku earthquake was observed by stress tensor inversions of focal mechanisms of earthquakes near the source region. The maximum compressive stress (σ1) axis before the earthquake has a direction toward the plate convergence, dipping oceanward at an angle of 25–30 degrees. Its dip angle significantly increased by 30–35 degrees after the earthquake, and σ1 axis came to intersect with the plate interface at a high angle of about 80 degrees. By using the observed rotation of σ1 axis, we estimated the ratio of mainshock stress drop to the background deviatoric stress Δτ/τ to be 0.9–0.95. This shows that the deviatoric stress causing the Mw 9.0 earthquake was mostly released by the earthquake, or the stress drop during the earthquake was nearly complete. Adopting the average stress drop obtained by GPS observation data, the deviatoric stress magnitude is estimated to be 21–22 MPa. This suggests the plate interface is weak. The nearly complete stress drop caused a high dip angle of σ1 axis, which is the reason why not a small number of normal fault type aftershocks have occurred.

The dynamics of the eastern Mediterranean and eastern Turkey

SUMMARY In this study we investigate the dynamics of the region that includes Greece, the Aegean Sea and Asia Minor. In a least-squares inversion we solve for a continuous strain rate field, and corresponding velocity field, that satisfies 872 GPS data. The estimate of the geodetic strain rate field provides constraints for our dynamic analysis. Next, we separately solve the depth integrated 3-D force balance equations for depth-integrated deviatoric stresses within the lithosphere, in which body force input comes from differences in vertically integrated vertical stress, or differences in gravitational potential energy per unit area (GPE). These GPE estimates calibrate the absolute magnitudes of deviatoric stresses that are acting within the lithosphere. Further, we investigate the sensitivity of our stress field solutions by using two different crustal structure models: one from compiled crustal structure estimates obtained primarily from relatively recent seismic observations and the other from the Crust 2.0 model. In an iterative least-squares inversion we then solve for stress field boundary conditions that, when added to the contribution of deviatoric stresses associated with GPE differences, provides a best fit to the directions of principal axes and relative magnitudes of the principal axes of the rates of strain obtained in the kinematic analysis. Robust features that arise from the boundary condition solution are NNE forcing along the southern boundary east of about 33° E (0.5–1.2 × 1012 N m−1), with a rapid anticlockwise rotation of forces to the west of this, along with an outward pulling force (∼0.4 × 1012 N m−1) directed SSW along the entire Hellenic Arc segment. This force system along the Hellenic Arc can be interpreted as a result of slab rollback. The total depth integrated 3-D deviatoric stresses in the final dynamic solution provides an excellent match to the deformation indicators throughout the region, with vertically integrated stress magnitudes of order 0.5–2.5 × 1012 N m−1. We use constraints from derived stress magnitudes, together with GPS-defined scalar values of strain rate magnitude, to define bulk effective viscosities of the lithosphere. Depth-averaged effective viscosities for the entire lithosphere are high within the Black Sea, of order 0.7–3 ×1023 Pa-s, relative to surrounding continental lithosphere. North Anatolian shear zone, northern Aegean Sea and Gulf of Corinth are characterized by low depth averaged viscosities of order 1–5 ×1021 Pa-s. Deviatoric stresses from GPE differences and boundary condition effects combine in surprising ways in some regions, resulting in near total stress cancellation in areas such as the southern Aegean Sea and portions of the central Anatolian block. GPE differences combine with boundary condition effects along the eastern segment of the North Anatolian Fault (NAF) in a way that is compatible with the hypothesis that motion on the NAF was facilitated by slab detachment beneath East Anatolia and dynamic uplift of East Anatolian Plateau. In general, GPE differences play a nearly equal role as boundary condition influences in their contribution to the total deviatoric stress field. The low depth integrated deviatoric stress magnitudes throughout the region suggest that zones of active deformation are facilitated by dramatic weakening mechanisms throughout the lithosphere.

Stress relaxation experiments of olivine under conditions of subducted slab in Earth's deep upper mantle

Stress relaxation experiments of olivine were conducted under high-pressure and high-temperature conditions up to 10GPa and 1273K using a Kawai-type multi-anvil apparatus. A pre-sintered San Carlos olivine sample rod was inserted between two dense Al2O3 pistons to yield high stress at high-pressure within an octahedral pressure medium. Stress was determined from the two-dimensional diffraction pattern taken using monochromatic X-rays and an imaging-plate, and sample length was determined from an X-ray radiograph. In these experiments, pressure was first increased at room temperature, and then the temperature was increased and kept at 673, 873, 1073, and 1273K. Four relaxation cycles, in total, were carried out in two experimental runs. The magnitude of deviatoric stress was calculated from five diffraction peaks with the following hkls: 021, 101, 130, 131, and 112. The calculated deviatoric stress was significantly different depending on which diffraction peak was used (up to a factor of ∼2) due to plastic deformation within the polycrystalline sample. The deviatoric stress decreased with increasing temperature in all of relaxation cycles. At given temperatures, the final-state value of deviatoric stress increased with increasing pressure. The upper bound for the plastic strain rate in the final-state was determined to be 10−7s−1 based on a comparison between the total sample length determined from the radiograph and the d-spacings along the piston direction determined from X-ray diffraction. Present results suggest a positive activation volume for the low-temperature rheology of olivine.

Contribution of gravitational potential energy differences to the global stress field

SUMMARY Modelling the lithospheric stress field has proved to be an efficient means of determining the role of lithospheric versus sublithospheric buoyancies and also of constraining the driving forces behind plate tectonics. Both these sources of buoyancies are important in generating the lithospheric stress field. However, these sources and the contribution that they make are dependent on a number of variables, such as the role of lateral strength variation in the lithosphere, the reference level for computing the gravitational potential energy per unit area (GPE) of the lithosphere, and even the definition of deviatoric stress. For the mantle contribution, much depends on the mantle convection model, including the role of lateral and radial viscosity variations, the spatial distribution of density buoyancies, and the resolution of the convection model. GPE differences are influenced by both lithosphere density buoyancies and by radial basal tractions that produce dynamic topography. The global lithospheric stress field can thus be divided into (1) stresses associated with GPE differences (including the contribution from radial basal tractions) and (2) stresses associated with the contribution of horizontal basal tractions. In this paper, we investigate only the contribution of GPE differences, both with and without the inferred contribution of radial basal tractions. We use the Crust 2.0 model to compute GPE values and show that these GPE differences are not sufficient alone to match all the directions and relative magnitudes of principal strain rate axes, as inferred from the comparison of our depth integrated deviatoric stress tensor field with the velocity gradient tensor field within the Earth's plate boundary zones. We argue that GPE differences calibrate the absolute magnitudes of depth integrated deviatoric stresses within the lithosphere; shortcomings of this contribution in matching the stress indicators within the plate boundary zones can be corrected by considering the contribution from horizontal tractions associated with density buoyancy driven mantle convection. Deviatoric stress magnitudes arising from GPE differences are in the range of 1–4 TN m−1, a part of which is contributed by dynamic topography. The EGM96 geoid data set is also used as a rough proxy for GPE values in the lithosphere. However, GPE differences from the geoid fail to yield depth integrated deviatoric stresses that can provide a good match to the deformation indicators. GPE values inferred from the geoid have significant shortcomings when used on a global scale due to the role of dynamically support of topography. Another important factor in estimating the depth integrated deviatoric stresses is the use of the correct level of reference in calculating GPE. We also elucidate the importance of understanding the reference pressure for calculating deviatoric stress and show that overestimates of deviatoric stress may result from either simplified 2-D approximations of the thin sheet equations or the assumption that the mean stress is equal to the vertical stress.