To date, more than 7300 in situ stress orientations have been compiled as part of the World Stress Map project. Of these, over 4400 are considered reliable tectonic stress indicators, recording horizontal stress orientations to within <±25°. Remarkably good correlation is observed between stress orientations deduced from in situ stress measurements and geologic observations made in the upper 1–2 km, well bore breakouts extending to 4–5 km depth and earthquake focal mechanisms to depths of ∼20 km. Regionally uniform stress orientations and relative magnitudes permit definition of broad-scale regional stress patterns often extending 20–200 times the approximately 20–25 km thickness of the upper brittle lithosphere. The “first-order” midplate stress fields are believed to be largely the result of compressional forces applied at plate boundaries, primarily ridge push and continental collision. The orientation of the intraplate stress field is thus largely controlled by the geometry of the plate boundaries. There is no evidence of large lateral stress gradients (as evidenced by lateral variations in stress regime) which would be expected across large plates if simple resistive or driving basal drag tractions (parallel or antiparallel to absolute motion) controlled the intraplate stress field. Intraplate areas of active extension are generally associated with regions of high topography: western U.S. Cordillera, high Andes, Tibetan plateau, western Indian Ocean plateau. Buoyancy stresses related to crustal thickening and/or lithospheric thinning in these regions dominate the intraplate compressional stress field due to plate-driving forces. These buoyancy forces are just one of several categories of “second-order” stresses, or local perturbations, that can be identified once the first-order stress patterns are recognized. These second-order stress fields can often be associated with specific geologic or tectonic features, for example, lithospheric flexure, lateral strength contrasts, as well as the lateral density contrasts which give rise to buoyancy forces. These second-order stress patterns typically have wavelengths ranging from 5 to 10+ times the thickness of the brittle upper lithosphere. A two-dimensional analysis of the amount of rotation of regional horizontal stress orientations due to a superimposed local stress constrains the ratio of the magnitude of the horizontal regional stress differences to the local uniaxial stress. For a detectable rotation of 15°, the local horizontal uniaxial stress must be at least twice the magnitude of the regional horizontal stress differences. Examples of local rotations of SHmax orientations include a 75°–85° rotation on the northeastern Canadian continental shelf possibly related to margin-normal extension derived from sediment-loading flexural stresses, a 50°–60° rotation within the East African rift relative to western Africa due to extensional buoyancy forces caused by lithospheric thinning, and an approximately 90° rotation along the northern margin of the Paleozoic Amazonas rift in central Brazil. In this final example, this rotation is hypothesized as being due to deviatoric compression oriented normal to the rift axis resulting from local lithospheric support of a dense mass in the lower crust beneath the rift (“rift pillow”). Estimates of the magnitudes of first-order (plate boundary force-derived) regional stress differences computed from modeling the source of observed local stress rotations magnitudes can be compared with regional stress differences based on the frictional strength of the crust (i.e., “Byerlee's law”) assuming hydrostatic pore pressure. The examples given here are too few to provide a definitive evaluation of the direct applicability of Byerlee's law to the upper brittle part of the lithosphere, particularly in view of uncertainties such as pore pressure and relative magnitude of the intermediate principal stresses. Nonetheless, the observed rotations all indicate that the magnitude of the local horizontal uniaxial stresses must be 1–2.5+ times the magnitude of the regional first-order horizontal stress differences and suggest that careful evaluation of such local rotations may be a powerful technique for constraining the in situ magnitude stress differences in the upper, brittle part of the lithosphere.

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First‐ and second‐order patterns of stress in the lithosphere: The World Stress Map Project

splitting observations are interpreted in terms of the strain-induced lattice preferred orientation of mantle minerals, especially olivine. We consider three hypotheses concerning the origin of the continental anlsotropy: (1) strain associated with absolute plate motion, as in the oceanic upper mantle, (2) crustal stress, and (3) the past and present internal deformation of the subcontinental upper mantle by tectonic episodes. It is found that the last hypothesis is the most successful, namely that the most recent significant episode of internal deformation appears to be the best predictor of q. For stable continental regions, this is interpreted as "fossil" anisotropy, whereas for presently active regions, such as Alaska, the anisotropy reflects present-day tectonic activity. In the stable portion of North America there is a good correlation between delay time and lithospheric thickness; this is consistent with the anisotropy being localized in the subcontinental lithosphere and suggests that intrinsic anisotropy is approximately constant. The acceptance of this hypothesis has several implications for subcontinental mantle deformation. First, it argues for coherent deformation of the continental lithosphere (crust and mantle) during orogenies. This implies that the anisotropic portion of the lithosphere was present since the deformational episode and rules out the addition of undeformed material to this layer by subsequent "underplating" or conductive growth of the thermal boundary layer. One of the most important issues in the study of orogenies is the need to reconcile the formation of thickened lithosphere with the paradoxically high mantle temperatures often associated with orogenic episodes. Most efforts to date have focussed on modes of deformation whereby the cold lithospheric mantle is removed (by convective instability or delamination) and replaced by warm asthenosphere. These models, however, are incompatible with the evidence for preserved coherent lithospheric deformation; rather, the deformed mantle appears to have been heated in place. We suggest that the elevated mantle temperatures may be due to the strain heating accompanying the deformation.

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Shear wave splitting and subcontinental mantle deformation

The ubiquity of dykes in the Earth's crust is evidence that the transport of magma by fluid-induced fracture of the lithosphere is an important phenomenon. Magma fracture transports melt vertically from regions of production in the mantle to surface eruptions or near-surface magma chambers and then laterally from the magma chambers in dykes and sills. In order to investigate the mechanics of magma fracture, the driving and resisting pressures in a propagating dyke are estimated and the dominant physical balances between these pressures are described. It is shown that the transport of magma in feeder dykes is characterized by a local balance between buoyancy forces and viscous pressure drop, that elastic forces play a secondary role except near the dyke tip and that the influence of the fracture resistance of crustal rocks on dyke propagation is negligible. The local nature of the force balance implies that the local density difference controls the height of magma ascent rather than the total hydrostatic head and hence that magma is emplaced at its level of neutral buoyancy (LNB) in the crust. There is a small overshoot beyond this level which is calculated to be typically a few kilometres. Magma accumulating at the LNB will be intruded in lateral dykes and sills which are directed along the LNB by buoyancy forces since the magma is in gravitational equilibrium at this level. Laboratory analogue experiments demonstrate the physical principle of buoyancy-controlled propagation to and along the LNB. The equations governing the dynamics of magma fracture are solved for the cases of lithospheric ascent and of lateral intrusion. Volatiles are predicted to be exsolved from the melt at the tips of extending fractures due to the generation of low pressures by viscous flow into the tip. Chilling of magma at the edges of a dyke inhibits cross-stream propagation and concentrates the downstream flow into a wider dyke. The family of theoretical solutions in different geometries provides simple models which describe the relation between the elastic and fluid-mechanical phenomena and from which the lengths, widths and rates of propagation can be calculated. The predicted dimensions are in broad agreement with geological observations.

Fluid‐mechanical models of crack propagation and their application to magma transport in dykes

Reservoir Geomechanics: Frontmatter

Global crustal stress pattern based on the World Stress Map database release 2008

Regional patterns of present-day tectonic stress can be used to evaluate the forces acting on the lithosphere and to investigate intraplate seismicity. Most intraplate regions are characterized by a compressional stress regime; extension is limited almost entirely to thermally uplifted regions. In several plates the maximum horizontal stress is subparallel to the direction of absolute plate motion, suggesting that the forces driving the plates also dominate the stress distribution in the plate interior.

Global patterns of tectonic stress

The World Stress Map Project is a global cooperative effort to compile and interpret data on the orientation and relative magnitudes of the contemporary in situ tectonic stress field in the Earth's lithosphere. Horizontal stress orientations show regionally uniform patterns throughout many continental intraplate regions. These regional intraplate stress fields are consistent over regions 1000-5000 km wide or ca. 100 times the thickness of the upper brittle part of the lithosphere (ca. 20 km) and about 10-15 times the thickness of typical continental lithosphere (ca. 150-200 km). Relative stress magnitudes or stress regimes in the lithosphere are inferred from direct in situ stress measurements and from the style of active faulting. The intraplate stress field in both the oceans and continents is largely compressional with one or both of the horizontal stresses greater than the vertical stress. The regionally uniform horizontal intraplate stress orientations are generally consistent with either relative or absolute plate motions indicating that plate-boundary forces dominate the stress distribution within the plates. Since most regions of normal faulting occur in areas of high elevation, the extensional stress regimes in these areas can be attributed to superimposed bouyancy forces related to crustal thickening and/or lithosphere thinning; stresses derived from these bouyancy forces locally exceed midplate compressional stresses. Evaluating the effect of viscous drag forces acting on the plates is difficult. Simple driving or resisting drag models (with shear tractions acting parallel or antiparallel to plate motion) are consistent with stress orientation data; however, the large lateral stress gradients across broad plates required to balance these tractions are not observed in the relative stress magnitude data. Current models of stresses due to whole mantle flow inferred from seismic tomography models (and with the inclusion of the effect of high density slabs) predict a general compressional stress state within continents but do not match the broad-scale horizontal stress orientations. The broad regionally uniform intraplate stress orientations are best correlated with compressional plate-boundary forces and the geometry of the plate boundaries.

Stress Magnitudes in the Crust: Constraints from Stress Orientation and Relative Magnitude Data

The Stress Map of North America , constructed on four 42 inch by 55 inch sheets, plots modern maximum horizontal stress (SHmax) orientations for North America inferred from a variety of geophysical and geologic data. These data are described and discussed in the companion DNAG volume Neotectonics of North America. A brief description of the various stress indicators is given in the legend.

Stress Map of North America

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M. Magee

Papers

Global patterns of tectonic stress

Stress Magnitudes in the Crust: Constraints from Stress Orientation and Relative Magnitude Data

Stress Map of North America

Wellbore breakout analysis for determining tectonic stress orientations in Washington State