It is well accepted that the lithosphere may exhibit nonzero mechanical strength over geological time and space scales, associated with the existence of non-lithostatic (deviatoric) stress. The parameter that characterizes the apparent strength of the lithosphere is the flexural rigidity D, which is commonly expressed through the effective elastic thickness (Te) of the litho-sphere. Estimates of Te for oceanic lithosphere approximately follow the depth to a specific iso-therm (-600°C), which marks the base of the mechanical lithosphere. The physical meaning and significance of the effective elastic thickness for continents are still enigmatic, because for continental lithosphere estimates of Te bear little relation to specific geological or physical boundaries. Although high observed values of Te (70-90 km for cratons) can be partly explained by the present day temperature gradients, the low values (10-20 km), in general, cannot. In addition, the elastic plate models are self-inconsistent in that they mostly predict intraplate stresses high enough to lead to inelastic (brittle or ductile) deformation, according to data of rock mechanics. To provide a basis for a physically consistent unified interpretation of the observed variations of Te for continental and oceanic lithosphere, we developed an analytical and numerical approach that allows direct treatment of Te in terms of the lithospheric rheology, thermal structure, and strain/stress distribution. Our technique is based on finding true inelastic and equivalent (effective) elastic solutions for the problem of deformation of the lithosphere with realistic brittle-elasto-ductile rheology. We show that the thermal state (thermotectonic age) of the lithosphere is only one of at least three equally important properties that determine apparent values of Te. These other properties are the state of the crust-mantle interface (decoupling of crust and mantle), the thickness and proportions of the mechanically competent crust and mantle, and the local curvature of the plate, which is directly related to the bending stresses. The thickness of the mechanically competent crust and the degree of coupling or decoupling is generally controlled by composition of the upper and lower crust, total thickness of the crust, and by the crustal geotherm. If decoupling takes place, it permits as much as 50% decrease of Te, compared with Te implied from conventional thermal profiles. Comparison of the theoretically predicted Te with inferred values for different regions suggests that the lower crust of most continental plates has a low-temperature activation rheology (such as quartz) which permits crust and mantle decoupling. The curvature of the plate depends on the theological structure and on the distribution of external loads applied to the plate (e.g., surface topography, sediment fill, and plate-boundary forces). Bending stresses created by major mountain belts are large enough to cause inelastic deformation (brittle failure and a ductile flow) in the underlying plate, which, in turn, leads to a 30 to 80% decrease of Te beneath such belts and less beneath the adjacent regions. The boundary forces and moments (e.g., due to the slab pull, etc.) lead to more localized but even stronger reductions in Te (e.g., plate necking in subduction zones). Our approach provides a feedback between the "observed" Te and rheology, allowing to constrain the lithospheric structure from estimates of Te.

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The effective elastic thickness (Te) of continental lithosphere: What does it really mean?

Focal mechanisms of 32 North American midplate earthquakes (mo = 3.8-6.5) were evaluated to determine if slip is compatible with a broad-scale regional stress field derived from plate-driving forces and, if so, under what conditions (stress regime, pore pressure, and frictional coefficient). Using independent information on in situ stress orientations from well bore breakout and hydraulic fracturing data and assuming that the regional principal stresses are in approximately horizontal and vertical planes (_ 10o), the constraint that the slip vector represents the direction of maximum resolved shear stress on the fault plane was used to calculate relative stress magnitudes defined by the parameterb = (S2 - S3)/(S - S3) from the fault/stress geometry. As long as the focal mechanism has a component of oblique slip (i.e., the B axis does not coincide with the intermediate principal stress direction), this calculation identifies which of the two nodal planes is a geometrically possible slip plane (Gephart, 1985). Slip in a majority of the earthquakes (25 of 32) was found to be geometrically compatible with reactivation of favorably oriented preexisting fault planes in response to the broad-scale uniform regional stress field. Slip in five events was clearly inconsistent with the regional stress field and appears to require a localized stress anomaly to explain the seismicity. Significantly, all five of these events occurred prior to 1970 (when many regional networks were installed), and their focal mechanisms are inconsistent with more recent solutions of nearby smaller events. The frictional likelihood of the geometrically possible slip on the selected fault planes was evaluated in the context of conventional frictional faulting theory. The ratio of shear to normal stress on the fault planes at hypocentral depth was calculated relative to an assumed regional stress field. Regional stress magnitudes were determined from (1) S/S3 ratios based on the frictional strength of optimally oriented faults (the basis for the linear brittle portion of lithospheric strength profiles), (2) the computed relative stress magnitude (b) values, and (3) a vertical principal stress assumed equal to the lithostat. Two end-member possibilities were examined to explain the observed slip in these less than optimally oriented fault planes. First, the frictional coefficient was held constant on all faults, hydrostatic pore pressure was assumed regionally, and the fault zone pore pressure was determined. Since pore pressure is a measurable quantity with real limits in the crust (P0 < S3), this end-member case was used to determine which of the geometrically possible slip planes were frictionally likely slip planes. Alternately, pore pressure was fixed at hydrostatic everywhere, and the required relative lowered frictional coefficient of the fault zone was computed. Slip in 23 of the 25 geometrically compatible earthquakes was determined to also be frictionally likely in response to an approximately horizontal and vertical regional stress field derived from plate-driving forces whose magnitudes are constrained by the frictional strength of optimally oriented faults (assuming hydrostatic pore pressure regionally). The conditions for slip on these 23 relatively "well-oriented" earthquake faults were determined relative to this regional crustal strength model and require only moderate increases in pore pressure (between about 0.4-0.8 of lithostatic, hydrostatic is about 0.37 of lithostatic) or, alternately, moderate lowering (<50%) of the frictional coefficient on the faults which slipped. Superlithostatic pore pressures are not required. Focal mechanisms for the two other earthquakes with slip vectors geometrically consistent with the regional stress field, however, did require pore pressures far exceeding the least principal stress (or extremely low coefficients of friction). These events may reflect either local stress rotations undetected with current sampling or poorly constrained focal mechanisms. The analysis also confirmed a roughly north to south contrast in stress regime between the central eastern United States and southeastern Canada previously inferred from a contrast in focal mecha- nisms between the two areas: most central eastern United States earthquakes occur in response to a strike-slip stress regime, whereas the southeastern Canadian events require a thrust faulting stress regime. This contrast in stress regime, with a constant maximum horizontal stress orientation determined by far-field plate-driving forces, requires a systematic lateral variation in relative stress magnitudes. Superposition of stresses due to simple flexural models of glacial rebound stresses are of the correct sense to explain the observed lateral variation, but maximum computed rebound-related stress magnitude changes are quite small (about 10 MPa) and do not appear large enough to account for the stress regime change if commonly assumed stress magnitudes determined from frictional strength apply to the crust at seismogenic depths.

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Stress field constraints on intraplate seismicity in eastern North America

An air pollution control system for treating contaminated air generated by food processing apparatus. Moist air laden with impurities and odors during food treatment is withdrawn from a processing chamber, cooled to condense moisture and particulate matter out of the air, and returned to the processing chamber, without discharge into the atmosphere. The conditioned air is reheated, absorbing moisture from the food product and again fed into the system.

Stress in the Lithosphere and the Strength of Active Faults

SUMMARY Gravity data from Iceland and its surroundings are analysed and modelled with respect to seismic data. A Bouguer gravity map of Iceland is recomputed based on admittance between the topography and the gravity and with corrections for glacial ice sheets. From seismic data and with the help of relations between the residual topography and the depth to seismic boundaries we construct maps of the main seismic boundaries, including the Moho. By inversion calculations we recomputed these maps, assuming different density values for Seismic Layer 4 to fit the observed gravity field. We found that the average density of Layer 4 has to be in the range 3050‐3150 kg m −3 in order to fit both seismic and gravity data. Thus we conclude that Layer 4 is a transition zone between the mantle and the oceanic crust in Iceland. Furthermore by assuming that the upper-mantle density variations necessary to compensate for the gravity effect of crustal layers, are caused by thermal variations in the upper mantle, we calculate the depth to the 1200 ◦ C isotherm to be at 30‐50 km depth below Iceland but rising up to less than 20 km below parts of the volcanic zone in Northern Iceland. We conclude that the temperature within the Seismic Layer 4 is close to 600 ◦ C at its top, increasing to approximately 950 ◦ Ca t its bottom (Moho), which makes a widespread layer of partially molten material within Layer 4 unlikely. By use of cross spectral analysis of the gravity field and the external topographic load at short wavelengths, we conclude that the elastic plate thickness in Iceland can hardly exceed 6 km. In addition we point out that the residual isostatic anomalies have circular forms east of the eastern volcanic zone but are near parallel to the ridge axis on the western side. This form of the anomalies may be caused by pressure from the eastward moving mantle plume below the eastern volcanic zone.

Nature of the crust-mantle transition zone and the thermal state of the upper mantle beneath Iceland from gravity modelling

This paper describes a generalized approximate method for assessing the effect of topography on the state of stress at depth in the crust and applies it to the site of the Cajon Pass Scientific Drilling Project. While previous studies have addressed idealized topography with regular shapes, we develop a three-dimensional (3-D) method for arbitrary surface topography. The analysis leads to four sets of elastic boundary value problems that are solved by convolutional methods based on the Green's functions of Boussinesq's problem and Cerruti's problem. The effect of topography on the state of stress can be divided into two parts by the linear superposition theorem. The first part is the effect on gravitational stress in the crust. In this case the effect of the topography can be expressed by the summation of the zero-order vertical load and the first-order horizontal shear at the base of the relief. The second part is the effect of topography on tectonic stress. In this case the effect of topography involves only the first-order horizontal shear. The total effect of the topography on the state of stress in the crust can be obtained by adding the effect on gravitational stress with the effect on tectonic stress. The stresses caused by a simple case of 3-D topography are calculated with this approach to serve as illustration. The identity of this study with previous studies (McTigue and Mei, 1981; Savage et al., 1985) for the same two-dimensional case demonstrates the correctness of this method. In applying this technique to the Cajon Pass Scientific Drilling Project, we considered stresses induced by the topography associated with the San Gabriel and the San Bernadino mountains as a function of depth at the site. The regional topography induces stresses of several megapascals at the drilling site which decrease rapidly with depth. The induced maximum horizontal compressive stress is approximately in the N-S direction. If we assume that in the absence of topography there is little right-lateral shear stress acting on the San Andreas fault at depth (a weak fault assumption), the regional topography tends to cause a slight increase of right-lateral shear on the San Andreas fault at a shallow depth in the crust. On the other hand, if we assume the strong fault model, the topography has no effect on the sense of shear on the San Andreas fault at all. Therefore it is clear that the small amount of left-lateral shear stress on the San Andreas fault observed in the upper 3.5 km at the Cajon Pass site is not associated with the topographic effect.

Jian Kuang

Papers

Intraplate stresses and seismicity: The role of topography and density heterogeneities

Intraplate seismicity and stress in the southeastern United States