Statistics and Data Analysis in Geology

The concept of strength envelopes, developed in the 1970s, allowed quantitative predictions of the strength of the lithosphere based on experimentally determined constitutive equations. Initial strength envelopes used an empirical relation for frictional sliding to describe deformation along brittle faults in the upper portion of the lithosphere and power law creep equations to estimate the plastic flow strength of rocks in the deeper part of the lithosphere. In the intervening decades, substantial progress has been made both in understanding the physical mechanisms involved in lithospheric deformation and in refining constitutive equations that describe these processes. The importance of a regime of semibrittle behavior is now recognized. Based on data from rocks without added pore fluids, the transition from brittle deformation to semibrittle flow can be estimated as the point at which the brittle fracture strength equals the peak stress to cause sliding. The transition from semibrittle deformation to plastic flow can be approximated as the stress at which the pressure exceeds the plastic flow strength. Current estimates of these stresses are on the order of a few hundred megapascals for relatively dry rocks. Knowledge of the stability of sliding along faults and of the onset of localization during brittle fracture has improved considerably. If the depth to the bottom of the seismogenic zone is determined by the transition to the stable frictional sliding regime, then that depth will be considerably more shallow than the depth of the transition to the plastic flow regime. Major questions concerning the strength of rocks remain. In particular, the effect of water on strength is critical to accurate predictions. Constitutive equations which include the effects of water fugacity and pore fluid pressure as well as temperature and strain rate are needed for both the brittle sliding and semibrittle flow regimes. Although the constitutive equations for dislocation creep and diffusional creep in single-phase aggregates are more robust, few data exist for plastic deformation in two-phase aggregates. Despite the fact that localization is ubiquitous in rocks deforming both in brittle and plastic regimes, only a limited amount of accurate experimental data are available to constrain predictions of this behavior. Accordingly, flow strengths now predicted from laboratory data probably overestimate the actual rock strength, perhaps by a significant amount. Still, the predictions are robust enough that uncertainties in geometry, mineralogy, loading conditions and thermodynamic state are probably the limiting factors in our understanding. Thus, experimentally determined rheologies can be applied to understand a broad range of topical problems in regional and global tectonics both on the Earth and on other planetary bodies.

Strength of the lithosphere: Constraints imposed by laboratory experiments

https://www.whoi.edu/fileserver.do?id=180587&pt=2&p=59967

Water in the oceanic upper mantle: implications for rheology, melt extraction and the evolution of the lithosphere

Slab breakoff: A model of lithosphere detachment and its test in the magmatism and deformation of collisional orogens

In this manuscript we review experimental constraints for the viscosity of the upper mantle. We first analyze experimental data to provide a critical review of flow law parameters for olivine aggregates and single crystals deformed in the diffusion creep and dislocation creep regimes under both wet and dry conditions. Using reasonable values for the physical state of the upper mantle, the viscosities predicted by extrapolation of the experimental flow laws compare well with independent estimates for the viscosity of the oceanic mantle, which is approximately 10 19 Pa s at a depth of ∼100 km. The viscosity of the mantle wedge of subduction zones could be even lower if the flux of water through it can result in olivine water contents greater than those estimated for the oceanic asthenosphere and promote the onset of melting. Calculations of the partitioning of water between hydrous melt and mantle peridotite suggest that the water content of the residue of arc melting is similar to that estimated for the asthenosphere. Thus, transport of water from the slab into the mantle wedge can continually replenish the water content of the upper mantle and facilitate the existence of a low viscosity asthenosphere.

Rheology of the Upper Mantle and the Mantle Wedge: A View from the Experimentalists

The experimental deformation of dunite

New microstructural data on experimentally deformed “wet” and “dry” natural olivine rocks (Anita Bay and Aheim dunite), together with the other reliable experimental data, indicate that the experimental stress-recrystallized grain size relationship in olivine-rocks is largely independent of water content and temperature, and is only slightly dependent on the flow properties of the material. The experimental data cover a stress range of 30–300 MPa, water contents from <30 ppm to 300 ppm, and temperatures in the range 1100–1650°C. Local melt contents of up to 10 volume% cannot be demonstrated to have a significant effect on the stress—grain size relationship.

Relationships between dynamically recrystallized grain size and deformation conditions in experimentally deformed olivine rocks

High-temperature transient creep in olivine rocks

https://www.geokniga.org/bookfiles/geokniga-crystallographic-preferred-orientations-and-misorientations-some-olivine-ro.pdf

Crystallographic preferred orientations and misorientations in some olivine rocks deformed by diffusion or dislocation creep

Research over the last 10 years has indicated that Australia has a significant geothermal energy resource. Regions of high crustal temperature at depths ≤5km may be economic targets for hot dry rock technology. A new database of temperature measurements made in 5722 wells across Australia has been used to construct improved maps of the spatial distribution of temperature in the Australian crust. The new database, Austherm04, builds upon the earlier work of Somerville et al. (1994) by greatly improving data quality control and by including temperature data from a further 1430 wells. Whilst there has been some enhancement of the overall spatial coverage when compared with the earlier work, the bulk of the new data are still largely clustered within the same provinces that dominate the Somerville et. al. dataset. As a result, data distribution across the continent still tends to be rather patchy and irregular with some regions well represented and others not. An Arc/Info GIS coverage has been built from the Austherm04 database. This coverage was intersected with GIS grids (constructed from Australian mean surface temperature data provided by the Australian Bureau of Meteorology and depth to basement estimates provided by Geoscience Australia) to interpolate the mean surface temperature and depth-to-basement for each well location. Calculations of the crustal temperature at a depth of 5 kilometres at each well location were then made using measured or estimated thermal gradients, the surface temperature estimates and the depth to basement information. In the absence of specific data, a uniform gradient of 25oC/km was assumed for basement rocks. The calculated crustal temperatures at 5 km depth were used to interpolate grids of cell size equal to 0.02 degrees. Interpolation was performed across the continental dataset using geostatistical ‘kriging. A variety of semivariogram error-modelling approaches have been tested. To date best results have been obtained with an exponential model.

Prame Chopra

Papers

The experimental deformation of dunite

Relationships between dynamically recrystallized grain size and deformation conditions in experimentally deformed olivine rocks

High-temperature transient creep in olivine rocks

Crystallographic preferred orientations and misorientations in some olivine rocks deformed by diffusion or dislocation creep

A GIS Analysis of Temperature in the Australian Crust