Constraining stress magnitudes using petroleum exploration data in the Cooper–Eromanga Basins, Australia

The magnitude of the in situ stresses in the Cooper–Eromanga Basins have been determined using an extensive petroleum exploration database from over 40 years of drilling. The magnitude of the vertical stress (S_v) was calculated based on density and velocity checkshot data in 24 wells. Upper and lower bound values of the vertical stress magnitude are approximated by S_v = (14.39 × Z)^1.12 and S_v = (11.67 × Z)^1.15 functions respectively (where Z is depth in km and S_v is in MPa). Leak-off test data from the two basins constrain the lower bound estimate for the minimum horizontal stress (S_hmin) magnitude to 15.5 MPa/km. Closure pressures from a large number of minifrac tests indicate considerable scatter in the minimum horizontal stress magnitude, with values approaching the magnitude of the vertical stress in some areas. The magnitude of the maximum horizontal stress (S_Hmax) was constrained by the frictional limits to stress beyond which faulting occurs and by the presence of drilling-induced tensile fractures in some wells. The maximum horizontal stress magnitude can only be loosely constrained regionally using frictional limits, due to the variability of both the minimum horizontal stress and vertical stress estimates. However, the maximum horizontal stress and thus the full stress tensor can be better constrained at individual well locations, as demonstrated in Bulyeroo-1 and Dullingari North-8, where the necessary data (i.e. image logs, minifrac tests and density logs) are available. The stress magnitudes determined indicate a predominantly strike-slip fault stress regime (S_Hmax > S_v > S_hmin) at a depth of between 1 and 3 km in the Cooper–Eromanga Basins. However, some areas of the basin are transitional between strike-slip and reverse fault stress regimes (S_Hmax > S_v ≈ S_hmin). Large differential stresses in the Cooper–Eromanga Basins indicate a high upper crustal strength for the region, consistent with other intraplate regions. We propose that the in situ stress field in the Cooper–Eromanga Basins is a direct result of the complex interaction of tectonic stresses from the convergent plate boundaries surrounding the Indo-Australian plate that are transmitted into the center of the plate through a high-strength upper crust.     

Stress tensor analysis of the 1998–1999 tectonic swarm of northern Quito related to the volcanic swarm of Guagua Pichincha volcano, Ecuador

The phreatic activity and the subsequent dacitic dome growth in 1998–1999 at Guagua Pichincha volcano, Ecuador, were associated with two seismic swarms: one located in the northern part of Quito (population: 1,500,000) and another one, just below the active volcano, about 15–20 km SW from the first one. Quito swarm tectonic events have high frequencies (from 1 to 10–15 Hz). We registered more than 3200 events (among which 2354 events of 1.4≤M_L≤4.2) between June 1998 and December 1999 at the −2- and −17-km depth. The volcanic events below the Guagua Pichincha caldera have high (from 1 to 10–15 Hz) and low (less than 3 Hz) frequencies. Approximately, 130,000 events were registered between September 1998 and December 1999 at the +2.4- and −3.5-km depth. Here, we study the stress tensors of these two swarms deduced from the polarities of P first motions and compare them to the regional stress tensor deduced from CMT Harvard focal mechanisms. The Quito swarm stress tensor is relatively close to the regional stress tensor (the σ₁ axis was oriented N117°E close to the N102°E direction of the plate motion found by the GPS measurement, and σ₃ is nearly vertical). The difference may be due to the action of the closely active Guagua Pichincha volcano. The Guagua Pichincha stress tensor is very different from the regional tectonic one. The σ₁ axis of the volcano is oriented N214°E, almost perpendicular to the σ₁ of the swarm of Quito and σ₃ is almost horizontal. Even if these two tensors are different, they can be explained in a more general tectonic scheme. The almost horizontal direction of σ₃ just below the volcano is compatible with an extensional horizontal direction that may be expected in the shallow extrados part of a compressional region and consistent with an opening of the top of the Guagua Pichincha volcano. The movement of the fluids (magma, gas and/or groundwater) produced by the closely active Guagua Pichincha volcano seems to have an influence in the acceleration of the generation of seismic events.     

Tectonic analysis of an oceanic transform fault zone based on fault-slip data and earthquake focal mechanisms: the Húsavík–Flatey Fault zone, Iceland

The Húsavík–Flatey Fault (HFF) is an oblique dextral transform fault, part of the Tjörnes Fracture Zone (TFZ), that connects the North Volcanic Zone of Iceland and the Kolbeinsey Ridge. We carry out stress inversion to reconstruct the paleostress fields and present-day stress fields along the Húsavík–Flatey Fault, analysing 2700 brittle tectonic data measured on the field and about 700 earthquake focal mechanisms calculated by the Icelandic Meteorological Office. This allows us to discuss the Latest Cenozoic finite deformations (from the tectonic data) as well as the present-day deformations (from the earthquake mechanisms). In both these cases, different tectonic groups are reconstructed and each of them includes several distinct stress states characterised by normal or strike-slip faulting. The stress states of a same tectonic group are related through stress permutations (σ₁−σ₂ and σ₂−σ₃ permutations as well as σ₁−σ₃ reversals). They do not reflect separate tectonic episodes. The tectonic groups derived from the geological data and the earthquake data have striking similarity and are considered to be related. The obliquity of the Húsavík–Flatey Fault implies geometric accommodation in the transform zone, resulting mainly from a dextral transtension along an ENE–WSW trend. This overall mechanism is subject to slip partitioning into two stress states: a Húsavík–Flatey Fault-perpendicular, NE–SW trending extension and a Húsavík–Flatey Fault-parallel, NW–SE trending extension. These three regimes occur in various local tectonic successions and not as a regional definite succession of tectonic events. The largest magnitude earthquakes reveal a regional stress field tightly related to the transform motion, whereas the lowest magnitude earthquakes depend on the local stress fields. The field data also reveal an early extension trending similar to the spreading vector. The focal mechanism data do not reflect this extension, which occurred earlier in the evolution of the HFF and is interpreted as a stage of structural development dominated by the rifting process.     

Cenozoic post-collisional brittle tectonic history and stress reorientation in the High Zagros Belt (Iran, Fars Province)

The Zagros fold-and-thrust belt of SW-Iran is among the youngest continental collision zones on Earth. Collision is thought to have occurred in the late Oligocene–early Miocene, followed by continental shortening. The High Zagros Belt (HZB) presents a Neogene imbricate structure that has affected the thick sedimentary cover of the former Arabian continental passive margin. The HZB of interior Fars marks the innermost part of SE-Zagros, trending NW–SE, that is characterised by higher elevation, lack of seismicity, and no evident active crustal shortening with respect to the outer (SW) parts. This study examines the brittle structures that developed during the mountain building process to decipher the history of polyphase deformation and variations in compressive tectonic fields since the onset of collision. Analytic inversion techniques enabled us to determine and separate different brittle tectonic regimes in terms of stress tensors. Various strike–slip, compressional, and tensional stress regimes are thus identified with different stress fields. Brittle tectonic analyses were carried out to reconstruct possible geometrical relationships between different structures and to establish relative chronologies of corresponding stress fields, considering the folding process. Results indicate that in the studied area, the main fold and thrust structure developed in a general compressional stress regime with an average N032° direction of σ₁ stress axis during the Miocene. Strike–slip structures were generated under three successive strike–slip stress regimes with different σ₁ directions in the early Miocene (N053°), late Miocene–early Pliocene (N026°), and post-Pliocene (N002°), evolving from pre-fold to post-fold faulting. Tensional structures also developed as a function of the evolving stress regimes. Our reconstruction of stress fields suggests an anticlockwise reorientation of the horizontal σ₁ axis since the onset of collision and a significant change in vertical stress from σ₃ to σ₂ since the late stage of folding and thrusting. A late right-lateral reactivation was also observed on some pre-existing belt-parallel brittle structures, especially along the reverse fault systems, consistent with the recent N–S plate convergence. However, this feature was not reflected by large structures in the HZB of interior Fars. The results should not be extrapolated to the entire Zagros belt, where the deformation front has propagated from inner to outer zones during the younger events.     

A new method of estimating the ratio between in situ rock stresses and tectonics based on empirical and probabilistic analyses

This paper describes a new procedure for assessing the ratio between in situ stresses in rock masses by means of K (K = σ_H / σ_v, being σ_H and σ_v principal stress) and tectonics for purposes of engineering geology and rock mechanics. The method combines the use of the logic decision tree and the empirical relationship between the Tectonic Stress Index, TSI, and a series of K in situ values obtained from an extensive database. The decision tree considers geological and geophysical factors affecting stress magnitudes both on the regional and local scale. The TSI index is defined by geological and geomechanical parameters. The method proposed provides an assessment of the magnitude of horizontal stresses of tectonic origin. Results for several regions of Europe are presented and the possible applications of the procedure are discussed.     

European continuous active tectonic strain–stress map

This paper shows a new continuous strain–stress map for Europe obtained from the direct inversion of earthquake focal mechanisms calculated from the centroid tensor method. A total of 1608 focal mechanisms have been selected with several quality criteria from different catalogues (CMT Harvard, ETH, Med-Net, I.G.N. and I.A.G.) from 1973 to the present day. Values for the maximum horizontal shortening direction and brittle strain–stress regime defined by the k′ ratio (e_y/e_z, horizontal maximum/vertical strain) have been calculated following in Europe and Pannonian Basin the slip model of tri-axial deformation. The individual results including Dey and the shape of the active brittle strain ellipsoid have been interpolated to a final 15′ regular grid taking into account the relationship between the tectonic horizontal strain–stress value and the vertical load. Both continuous strain regime and maximum horizontal shortening (Dey) maps show a good correlation with the primary tectonic forces generated along the plate boundaries, plate kinematics and also some local perturbations related with main crustal heterogeneities and topography, as well as significant spatial variations in integrated crustal strength.     

Stress field in the Northern Rhine area, Central Europe, from earthquake fault plane solutions

Fault plane solutions (FPS) from 110 earthquakes in the northern Rhine area with local magnitudes, ranging from 1.0 to 6.1, and occurring between 1976 and 2002 are determined. FPS are retrieved from P-wave first motions using a grid search approach allowing a detailed exploration of the parameter space. The influence of the 1D velocity model on take-off angles and resulting FPS is examined. All events were relocated with a recently developed minimum 1D model of the velocity structure [J. Geophys. Res. (2003)]. Rose diagrams of the orientation of P, T and B axes show a clear preference of trends of P and T axes at N292°E and N27°E, respectively. The majority of B axes trend in northerly directions. Plunges of P and T axes are mostly around 45° while most B axes are subhorizontal. The main direction of the maximum horizontal stress directly inferred from the fault plane solutions is N118°E.To calculate the orientations of the principal stress axes and the shape of the stress tensor, the inversion method of Gephard and Forsyth [J. Geophys. Res. 89 (1984) 9305] was applied to the whole data set and to several subsets of data. The subsets were formed by grouping events from various geological and tectonic areas and by grouping events into different depth ranges. The subset areas include the Lower Rhine Embayment, the Rhenish Massif, the middle Rhine area, the Neuwied Basin and the area known as the Stavelot–Venn Massif. Inversion of the entire data set shows some ambiguity between a strike-slip and extensional stress regime, with a vertical axis for the medium principal stress and a trend of N305°E and N35°E for the σ₁ and σ₃ axis, respectively, as the best fitting tensor. Earthquakes from the Lower Rhine Embayment and, to some degree, from the middle Rhine area indicate an extensional stress regime. In the Lower Rhine Embayment, plunge and trend of the σ₁ axis are 76° and N162°E and for the σ₃ axis 7° and N42°E. The best fitting solution for the area of the Stavelot–Venn Massif is a strike-slip regime with subhorizontal σ₁ and σ₃ axes with a trend of N316°E and N225°E, respectively. Stress orientations found here agree overall with the results from earlier studies based on smaller data sets. The directions of the maximum and minimum horizontal stresses inverted from focal mechanisms agree well with the stress field predicted by the European Stress Map. This confirms earlier interpretations that the stress field of the Rhine Graben system is controlled by plate driving forces acting on the plate boundaries. However, amplitudes of the stresses change on a local scale and with depth. Estimates of the absolute magnitude of principal stresses favor a normal faulting regime in the shallow crust (above 12-km depth) and a strike-slip regime in the lower crust.     

Weak tidal correlation of NW-Bohemia/Vogtland earthquake swarms

We analyze the possible effect of solid Earth tidal stresses upon a vertical strike-slip fault in NW-Bohemia/Vogtland, central Europe, typical by occurrence of swarm earthquakes. The horizontal components of solid Earth tidal stresses were found strongly to prevail and to reach the level of 2 kPa. We examined tidal triggering as influence of tidal stresses to launching the swarm activity in relative absence of other stress disturbances. The onset times of 46 swarms of mostly M_L < 3 earthquakes that occurred in the period 1991–2005 displayed an increased occurrence near the fortnightly maximum of tidal extensive normal stress. The statistical test however did not prove a statistically significant correlation indicating a triggering effect of fault extension due to tidal loading. We also examined tidal effects to the already running seismic activity of the prominent 2000 swarm by comparing the tidal stress distribution in the investigated period with the distribution of tidal stresses in the occurrence times of each earthquake. The results show that these distributions are almost similar, which indicates that individual earthquakes occur independent of tidal stresses. The unclear tidal correlation of the swarm seismicity may be interpreted by small amplitudes and rates of tidal stress changes compared to the amplitudes and rates of coseismic stress perturbations and of pressure bursts of deep generated fluids.     

Paleo-deviatoric stress magnitudes from calcite twins and related structural permeability evolution in minor faults: Example from the toarcian shale of the French Causses Basin, Aveyron, France

The relationship between deformation and so-called fluid paleotransfers in minor faults has been analysed in an argillaceous formation located in the Causses Basin in France. The fluid paleotransfers are related to the fault activity to a large extent. We attempt to estimate the intensity of paleo-deviatoric stress magnitudes under which the fault activity may have occurred and consequently, the change in the structural fault permeability. The paleo-deviatoric stress magnitudes were calculated with the inverse method of Etchecopar applied to calcite twinning. The measured crystals are contained within the core zone of minor faults and this study is based on a previous complete microtectonic and microstructural analysis of the faults. In this paper, analysis of calcite twinning has been applied for the first time to vein fillings associated small faults in a context of relatively weak deformation, a condition ensured by the tectonic and structural analysis. Calculation and discussion of the paleo-deviatoric stress tensors in relation to the evolution of the structural fault permeability and to the hydraulic behaviour of the faults are the aim of this paper. The analysed faults, created and active during the same tectonic event, were permeable under a (σ₁–σ₃) mean value of 40–50 MPa. On the other hand, the reactivation of faults during a second tectonic event implies mean (σ₁–σ₃) value higher than 40–50 MPa, especially for the faults that are poorly oriented with respect to the principal tectonic stress directions. The core zone of these faults remained sealed and impermeable or became permeable by development of microcracks inside the pre-existing fillings.     

The representation and calculation of the deviatoric component of the geological stress tensor

A new diagram for the representation of stress states is proposed and compared with Nadai's stress diagram. The diagram is a graph whose axes are labelled as the differences of the principal stresses (σ₂-σ₃ as ordinate axis, σ₁-σ₂ as the abscissa; where σ₁ > σ₂ > σ₃ are the principal stresses). The design of the plot has been deliberately modelled on that of the ‘log Flinn’ diagram which is used to represent finite strain ellipsoids. The position of the plotted stress state on this diagram depends on the nature of the deviatoric (non-hydrostatic) component of the stress tensor. The distance of the plotted stress from the origin corresponds broadly to the departure of the stress from a hydrostatic state and the parameter R, defined as the gradient of the line joining the plotted state to the origin, expresses the type of symmetry possessed by the stress tensor.It is explained how the diagram can be used to represent calculated palaeostresses and, in particular, how the parameter R can be found directly from some existing methods of stress analysis currently in use.Besides its proposed function to represent the results of such analyses it is felt that the use of the diagram may make clear the essential elements of the definitions of well-known terms used to describe particular stress states (e.g. plane stress, triaxial stress, axial compression, etc.).     

Neotectonic evolution of the Central Betic Cordilleras (Southern Spain)

Paleostress orientations were calculated from fault-slip data of 36 sites located along a traverse through the Central Betic Cordilleras (southern Spain). Heterogeneous fault sets, which are frequent in the area, have been divided into homogeneous subsets by cross-cutting relationships observed in the field and by a paleostress stratigraphy approach applied on each individual fault population. The state of stress was sorted according to main tectonic events and a new chronology is presented of the Miocene to Recent deformation in the central part of the Betic Cordilleras. The deviatoric stress tensors fall into four distinct groups that are regionally consistent and correlate with three Late Oligocene–Aquitanian to Recent major tectonic events in the Betic Cordilleras. The new chronology of the neotectonic evolution includes, from oldest to youngest, the following main tectonic phases:

(1) Late Oligocene–Aquitanian to Early Tortonian: σ₁ subhorizontal N–S, partly E–W directed, σ₃ subvertical; compressional structures (thrusting of nappes, large-scale folding) and strike-slip faulting in the Alborán Domain and the External Zone of the Betic Cordilleras;

(2) Early Tortonian to Pliocene–Pleistocene: σ₁ subvertical, σ₃ subhorizontal NW–SE, partly N–S directed or E–W-directed (radial extension); large-scale normal faulting in the Central Betic Cordilleras and in the oldest Neogene formations of the Granada Basin related to the gravitational collapse of the Betic Cordilleras and the exhumation of the intensely metamorphosed rock series of the Internal Zones, at the same time formation of the Alborán Basin and intramontane basins such as the Granada Basin;

(3) Pleistocene to Recent: (3a) σ₁ subvertical, σ₃ subhorizontal NE–SW with prominent normal faulting, but coevally; (3b) σ₁ subhorizontal NW directed, σ₃ NE–SW subhorizontal with strike-slip faulting. Extensional structures and strike-slip faulting are related to the ongoing convergence of the Eurasian and African Plates and coeval uplift of the Betic Cordilleras. Reactivation of pre-existing fractures and faults was frequently observed. Phase 3 is interpreted as periodic strike-slip and normal faulting events due to a permutation of the principal stress axes, mainly σ₁ and σ₂.

Structural and stress analysis based on fault-slip data in the Amman area, Jordan

This study presents a structural analysis based on hundreds of striated small faults (fault-slip data) in the Amman area east of the Dead Sea Transform System. Stress inversion of the fault-slip data was performed using an improved Right-Dihedral method, followed by rotational optimization (TENSOR Program, Delvaux, 1993). Fault-slip data (totaling 212) include fault planes, striations and sense of movements, are obtained from the Turonian Wadi As Sir Formation, distributed mainly along the southern side of the Amman – Hallabat structure in Jordan the study area. Results show that σ1 (SHmax) and σ3 (SHmin) are generally sub-horizontal and σ2 is sub-vertical in 8 of 11 paleostress tensors, which are belonging to a major strike-slip system with σ1 swinging around N to NW direction. The other three stress tensors show σ2 (SHmax), σ1 vertical and σ3 is NE oriented. This situation explained as permutation of stress axes σ1 and σ2 that occur during tectonic events and partitioned strike slip deformation. NW compressional stresses affected the area and produced the major Amman – Hallabat strike-slip fault and its related structures, e.g., NW trending normal faults and NE trending folds in the study area.The new paleostress results related with the active major stress field of the region the Dead Sea Stress Field (DSS) during the Miocene to Recent.     

Stress fields about strike-slip faults inferred from stylolites and tension gashes

In general, the long axis of the tension gashes and stylolitic columns developed in limestones during a single phase of compressional deformation occur parallel to the direction of the maximum compressive stress (σ₁). This is the case in the Languedoc for structures developed in the Jurassic limestones during the N-S Pyrenean compression. Exceptionnally, however, these microstructures turn in direction and become oblique (even orthogonal) one to the other, probably as a consequence of a variation in intensity and direction of the stress field at the end of a microfault. This mechanism also occurs in a larger scale structure involving segments of pre-tectonic joints that act as “en échelon” microfaults in a brittle “kink-band” equivalent to a peculiar type of potential wrench-fault.     

Fault slip analysis of Quaternary faults in southeastern Korea

The Quaternary stress field has been reconstructed for southeast Korea using sets of fault data. The subhorizontal direction of the maximum principal stress (σ₁) trended ENE and the direction of the minimum principal stress (σ₃) was nearly vertical. The stress ratio (Φ = (σ₂ − σ₃) / (σ₁ − σ₃)) value was 0.65. Two possible interpretations for the stress field can be made in the framework of eastern Asian tectonics; (1) The σ_Hmax trajectory for southeast Korea fits well with the fan-shaped radial pattern of maximum principal stress induced by the India–Eurasia collision. Thus, we suggest that the main source for this recent stress field in southeast Korea is related to the remote India–Eurasia continental collision. (2) The stress field in Korea shows a pattern similar to that in southwestern Japan. The origin for the E–W trending σ_Hmax in Japan is known to be related to the mantle upwelling in the East China Sea. Thus, it is possible that Quaternary stress field in Korea has evolved synchronously with that in Japan. We suggest further studies (GPS and in situ stress measurement) to test these hypotheses.     

Late Cenozoic stress evolution along the Karasu Valley, SE Turkey

This study defines the Mio-Pliocene to present-day stress regime acting at the northeastern corner of the eastern Mediterranean region along the Karasu Valley (i.e., the Amanos Range), taking in the Antakya, Osmaniye and Kahramanmaras provinces. The inversion slip vectors measured on fault planes and chronologies between striations indicate that the stress regime varied from transpressional initially to transtensional, having consistent NW- and NE-trending σ_Hmax (σ₁) and σ_Hmin (σ₃) axes, respectively; there are significantly different mean stress-ratio (R_m) values however. The older mean stress state is characterized by N151±11°E-trending σ₁ and N59±12°E-trending σ₃ axes, and by a mean arithmetic R_m value of 0.76, indicating that the regional stress regime is transpressional. The younger stress regime is characterized by N154±8°E-trending σ₁ and N243±8°E-trending σ₃ axes, and by a mean arithmetic R_m value of 0.17, indicating a transtensional character for this regional stress regime. The low R values of the stress deviators related to the recent stress state reflect normal-component slips. The earthquake focal mechanism inversions confirm that the younger stress regime continues into the Recent. The inversion identifies a transtensional stress regime representing strike-slip and an extensional stress state with a consistent NE-trending σ_Hmin (σ₃) axis. These stress states are characterized by N66°E and N249°E-trending σ₃ axes, respectively. Both significant regional stress regimes induce left-lateral displacement along the southern part of the East Anatolian Fault (EAF, or Amanos Fault). The temporal change, probably in Quaternary time, within the regional stress regime—from transpression to transtension—resulted from the coeval influences of subduction processes in the west–southwest (i.e., along the Cyprus arc), continental collision in the east, and westward escape of the Anatolian block.     

Geometry of the fault zone of the 2003 Ms = 7.5 Chuya earthquake and associated stress fields, Gorny Altai

The co-seismic deformations produced during the September 27, 2003 Chuya earthquake (Ms = 7.5) that affected the Gorny Altai, Russia, are described and discussed along a 30 km long segment. The co-seismic deformations have manifested themselves both in unconsolidated sediments as R- and R′-shears, extension fractures and contraction structures, and in bedrock as the reactivation of preexisting schistosity zones and individual fractures, as well as development of new ruptures and coarse crushing zones. It has been established that the pattern of earthquake ruptures represents a typical fault zone trending NW–SE with a width reaching 4–5 km and a dextral strike–slip kinematics. The initial stress field that produced the whole structural pattern of co-seismic deformations during the Chuya earthquake, is associated with a transcurrent regime with a NNW–SSE, almost N–S, trending of compressional stress axis (σ₁), and a ENE–WSW, almost E–W, trending of tensional stress axis (σ₃). The state of stress in the newly-formed fault zone is relatively uniform. The local stress variations are expressed in insignificant deviation of σ₁ from N–S to NW–SE or NE–SW, in short-term fluctuations of relative stress values in keeping their spatial orientations, or in a local increase of the plunge angle of the σ₁. The geometry of the fault zone associated with the Chuya earthquake has been compared with the mechanical model of fracturing in large continental fault zones with dextral strike–slip kinematics. It is apparent that the observed fracture pattern corresponds to the late disjunctive stage of faulting when the master fault is not fully developed but its segments are already clearly defined. It has been shown that fracturing in widely different rocks follows the common laws of the deformation of solid bodies, even close to the Earth surface, and with high rates of movements.     

Plate motion and thermal instability in the asthenosphere

This paper investigates the effect of shear heating in the asthenosphere on the thermal structure of the upper mantle. Equations describing the motion of the lithosphere over the asthenosphere in the presence of a strongly temperature-dependent stress-strain rate relation are derived and solved with the help of several approximations. These approximations are shown to be valid under conditions appropriate for the earth.Two sets of solutions are found. For one set (the “subcritical” solutions) a normal shear stress—velocity relation is found for small stresses. The velocity increases as the stress increases, reaching a maximum velocity σ_c for a critical stress σ_c. The subcritical solutions have a negligible effect on the thermal structure of the earth, even at the critical stress. The other set of solutions (the “supercritical” solutions) has the bizarre property that a decrease of applied shear stress leads to an increase of velocity. Thus, as the shear stress goes to zero, the velocity becomes infinite. At larger shear stresses the velocity decreases until it reaches σ_c at a stress σ_c (the two sets of solutions share this point in common). There are no steady solutions of any kind for shear stresses in excess of σ_c. We discard the supercritical solutions as candidates for the thermal structure of the earth on the basis of their instability to small perturbations of applied stress and temperature.The realm of subcritical solutions (stress less than σ_c, velocity less than σ_c) thus defines a regime of plate motion in which the thermal effects of shear heating are negligible. If the shear stresses acting on plates exceed σ_c, however, new physical processes must come into play to dissipate the excess heat generated. Assuming that the velocities of plates on the earth today are less than σ_c, relative to the deep mantle, a strict upper limit of a few tens of bars can be derived for σ_c, corresponding to effective viscosities of ca. 10¹⁹ poise in the asthenosphere.     

Some limitations of the Rf/φ technique of strain analysis — Discussion

A recent note by De Paor (1980) suggests that finite strain cannot be decomposed into tectonic and compaction components on the basis of asymmetry of the R_fφ data about the mean φ trace. This is true if only the shape of the R_fφ data field is considered, but shown to be incorrect when the distribution of data within this field is considered.     

The importance of the effective intermediate principal stress (σ′2) to fault slip patterns

In normal faulting regimes, the magnitudes and orientations of the maximum and minimum principal compressive stresses may be known with some confidence. However, the magnitude of the intermediate principal compressive stress is generally much more difficult to constrain and is often not considered to be an important factor. In this paper, we show that the slip characteristics of faults and fractures with complex or nonoptimal geometry are highly sensitive to variation or uncertainty in the ambient effective intermediate principal stress (σ′₂). Optimally oriented faults and fractures may be less sensitive to such variations or uncertainties. Slip tendency (T_s) analysis provides a basis for quantifying the effects of uncertainty in the magnitudes and orientations of all principal stresses and in any stress regime, thereby focusing efforts on the most important components of the system. We also show, for a normal faulting stress regime, that the proportion of potential surfaces experiencing high slip tendency (e.g., T_s ≥ 0.6) decreases from a maximum of about 38% where σ′₂ = σ′₃, to a minimum of approximately 14% where σ′₂ is halfway between σ′₃ and σ′₁, and increases to another high of approximately 29% where σ′₂ = σ′₁. This analysis illustrates the influence of the magnitude of σ′₂ on rock mass strength, an observation previously documented by experimental rock deformation studies. Because of the link between fault and fracture slip characteristics and transmissivity in critically stressed rock, this analysis can provide new insights into stress-controlled fault transmissivity.     

Some source and medium properties of the Vrancea seismic region, Romania

Simple spectral theory of seismic sources was used to determine source parameters directly related to medium properties (stress drop, seismic efficiency and fracture energy) and quality factors of the Vrancea (Romania) seismic region. The results show an increase in maximum static stress drop, maximum seismic efficiency and fracture energy with depth. The seismic efficiency is magnitude independent, but the stress drop is magnitude independent only for events with M_L > 3.8; below this value, the logarithm of stress drop increases quasi-linearly with magnitude. In the depth interval 50–160 km the stress drop increases with a slope of about 2–3 bar/km. The fracture energy per unit area of the fault has values of the order of 10⁵–10⁸ erg/cm².The frequency independent quality factors indicate that the attenuation of P waves is generally higher than that of S waves and that Q_p values are in agreement with recent tectonic models for the Vrancea region: total decoupling of the slab now sinking gravitationally is present only in the southwestern part of the Vrancea region, as suggested by the spatial position of intermediate depth hypocenters.