Transient creep and semibrittle behavior of crystalline rocks

We review transient creep and semibrittle behavior of crystalline solids. The results are expected to be pertinent to crystalline rocks undergoing deformation in the depth range 5 to 20 km, corresponding to depths of focus of many major earthquakes. Transient creep data for crystalline rocks at elevated temperatures are analyzed but are poorly understood because of lack of information on the deformation processes which, at low to moderate pressure, are likely to be semibrittle in nature. Activation energies for transient creep at high effective confining pressure are much higher than those found for atmospheric pressure tests in which thermally-activated microfracturing probably dominates the creep rate. Empirical transient creep equations are extrapolated at 200° to 600°C, stresses from 0.1 to 1.0 kbar, to times ranging from 3.17×10² to 3.17×10⁸ years. At the higher temperatures, appreciable transient creep strains may take place but the physical significance of the results is in question because the flow mechanisms have not been determined. The purpose of this paper is to stimulate careful research on this important topic.     

Stress in the lithosphere: Inferences from steady state flow of rocks

Mechanical data and flow processes from steady state deformation experiments may be used to infer the state of stress in the lithosphere and asthenosphere. Extrapolations of flow equations to a representative geologic strain rate of 10^–14/sec. for halite, marble, quartzite, dolomite, dunite and enstatolite are now warranted because the steady state flow processes in the experiments are identical to those in rocks and because the geotherms are reasonably well established. More direct estimates are obtained from free dislocation densities, subgrain sizes and recrystallized grain sizes all of which are functions only of stress. Using the last of these techniques, we have estimated stress profiles as a function of depth from xenoliths in basalts and kimberlites, whose depths of equilibration were determined by pyroxene techniques, from four different areas of subcontinental and suboceanic upper mantle. The results are similar and indicate stress differences of about 200 to 300 bars at 40 to 50 km, decaying to a few tens of bars at depths betow 100 km. These stresses are reasonable and are in accord with extrapolations of the mechanical data provided that allowance is made for a general increase in strain rate and decrease in viscosity with depth.     

First cosmogenic 10Be age constraint on the timing of Younger Dryas glaciation and ice cap thickness,western Scottish Highlands

We use cosmogenic ¹⁰Be surface exposure age techniques at a locality close to Rannoch Moor, western Scottish Highlands, in order to establish the age and chronology of its most recent glaciation. Glacial erratics and an in situ bedrock quartz vein sampled from this site—the summit of Beinn Inverveigh—have yielded zero‐erosion exposure ages of 12.9 ± 1.5 ka to 11.6 ± 1.0 ka, implying complete ice cover of the mountain during the Younger Dryas, or Loch Lomond Stadial. These results fit closely with published ¹⁴C dates that bracket the maximum (lateral) extent of ice cap outlet glaciers, and are the first internally consistent ages to specifically address this period of glaciation in Scotland. Furthermore, the dates imply that previous palaeoglaciological reconstructions for this area may have underestimated both the thickness of the former ice cap and, by implication, its volume. © British Geological Survey/Natural Environment Research Council copyright 2007. Reproduced with the permission of BGS/NERC. Published by John Wiley & Sons, Ltd.     

Controls on biochemical oxygen demand in the upper Klamath River,Oregon

A series of 30-day biochemical oxygen demand (BOD) experiments were conducted on water column samples from a reach of the upper Klamath River that experiences hypoxia and anoxia in summer. Samples were incubated with added nitrification inhibitor to measure carbonaceous BOD (CBOD), untreated to measure total BOD, which included demand from nitrogenous BOD (NBOD), and coarse-filtered to examine the effect of removing large particulate matter. All BOD data were fit well with a two-group model, so named because it considered contributions from both labile and refractory pools of carbon: BOD_t = a₁(1 ? e^? a₀t) + a₂t. Site-average labile first-order decay rates a₀ ranged from 0.15 to 0.22/day for CBOD and 0.11 to 0.29/day for BOD. Site-average values of refractory zero-order decay rates a₂ ranged from 0.13 to 0.25 mg/L/day for CBOD and 0.01 to 0.45 mg/L/day for BOD; the zero-order CBOD decay rate increased from early- to mid-summer. Values of ultimate CBOD for the labile component a₁ ranged from 5.5 to 28.8 mg/L for CBOD, and 7.6 to 30.8 mg/L for BOD. Two upstream sites had higher CBOD compared to those downstream. Maximum measured total BOD₅ and BOD₃₀ during the study were 26.5 and 55.4 mg/L; minimums were 4.2 and 13.6 mg/L. For most samples, the oxygen demand from the three components considered here were: labile CBOD > NBOD > refractory CBOD, though the relative importance of refractory CBOD to oxygen demand increased over time. Coarse-filtering reduced CBOD for samples with high particulate carbon and high biovolumes of Aphanizomenon flos-aquae. There was a strong positive correlation between BOD, CBOD, and the labile component of CBOD to particulate C and N, with weaker positive correlation to field pH, field dissolved oxygen, and total N. The refractory component of CBOD was not correlated to particulate matter, instead showing weak but statistically significant correlation to dissolved organic carbon, UV absorbance at 254 nm, and total N. Particulate organic matter, especially the alga A.flos-aquae, is an important component of oxygen demand in this reach of the Klamath River, though refractory dissolved organic matter would continue to exert an oxygen demand over longer time periods and as water travels downstream.     

Three-dimensional benchmark for variable-density flow and transport simulation: matching semi-analytic stability modes for steady unstable convection in an inclined porous box

This benchmark for three-dimensional (3D) numerical simulators of variable-density groundwater flow and solute or energy transport consists of matching simulation results with the semi-analytical solution for the transition from one steady-state convective mode to another in a porous box. Previous experimental and analytical studies of natural convective flow in an inclined porous layer have shown that there are a variety of convective modes possible depending on system parameters, geometry and inclination. In particular, there is a well-defined transition from the helicoidal mode consisting of downslope longitudinal rolls superimposed upon an upslope unicellular roll to a mode consisting of purely an upslope unicellular roll. Three-dimensional benchmarks for variable-density simulators are currently (2009) lacking and comparison of simulation results with this transition locus provides an unambiguous means to test the ability of such simulators to represent steady-state unstable 3D variable-density physics.     

Hydrostatic pore water pressure revisited

Hydrostatic or “normal” pressure can be easily visualized as a water column with pressure given by ρgh and any departures classified as abnormal pressure. This is the basis for commonly used hydrostatic pressure depth trends in sedimentary basins that are constructed on assumptions of constant gradients and are datumed at mean sea level or ground level. But the straightforward water column concept does not upscale in a simple way to sedimentary basins where the zones of interest are several thousands of metres below the land or sea surface. Sedimentary basins are heterogeneous, including stacked, confined reservoirs and variations in pore water composition. It is possible to construct pressure-depth profiles that honour the geology and hydrostratigraphy of a basin and these give different hydrostatic baselines from simple constant gradients hung from familiar local datums such as ground level. Key steps are using a reservoir-specific datums such as the water table or potentiometric surface relevant to that unit, then building a pressure-depth trend that represents the pore fluid salinity variation and density profile throughout the reservoir unit. At a given depth, this version of hydrostatic may predict pressures several hundred psi different from a single density gradient hung from a datum local to the well, and exhibit a notched profile reflecting the geological and hydrological stratigraphy. This construct redefines normal and abnormal pore fluid pressures in sedimentary basins. The impacts of this alternative approach to sedimentary basin hydrostatics, even if data are limited and pressure profiles have to be framed probabilistically, extend to many aspects of studying and interacting with fluid systems in sedimentary basins including basin modelling, petroleum systems analysis, well planning and well operations.     

General sky models for illuminating terrains

Sky models are quantitative representations of natural luminance of the sky under various atmospheric conditions. They have been used extensively in studies of architectural design for nearly a century, and more recently for rendering objects in the field of computer graphics. The objectives of this paper are to (1) describe sky models, (2) demonstrate how map designers can render terrain under various sky models in a typical geographic information system (GIS), (3) illustrate potential enhancements to terrain renderings using sky models, and (4) discuss how sky models, with their well-established standards from a different discipline, might contribute to a virtual geographic environment (VGE).

Current GIS hill-shading tools use the Lambertian assumption which can be related to a simple point light source at an infinite distance to render terrain. General sky models allow the map designer to choose from a gamut of sky models standardized by the International Commission on Illumination (CIE). We present a computer application that allows the map designer to select a general sky model and to use existing GIS tools to illuminate any terrain under that model. The application determines the orientations and weights of many discrete point light sources that, in the aggregate, approximate the illumination provided by the chosen sky model. We discuss specific enhancements to terrains that are shaded and shadowed with these general sky models, including additional detail of secondary landforms with soft shadows and more realistic shading contrasts. We also illustrate how non-directional illumination models result in renderings that lack the perceptual relief effect. Additionally, we argue that this process of creating hill-shaded visualizations of terrain with sky models shows parallels to other geo-simulations, and that basing such work on standards from the computer graphics industry shows potential for its use in VGE.