Jean-Claude Mareschal

Constraints on the deep thermal structure of the Dharwar craton, India, from heat flow, shear wave velocities, and mantle xenoliths

[1]xa0We have used constraints from seismic shear wave vertical velocity profiles, geothermobarometry estimates on mantle xenoliths, and surface heat flux and heat production measurements to analyze the thermal regime of the deep lithosphere beneath India. In the Dharwar craton of southern India, the shear wave velocity gradient in the mantle, as well as xenolith geothermobarometry data, suggests a low mantle heat flux, 14–20 mW m−2, consistent with surface heat flux measurements. However, for standard cratonic mantle composition, seismic velocities require Moho and mantle temperatures to be about 300 K higher than inferred from heat flux and xenolith data. This discrepancy can be only resolved by changing the mantle composition, specifically by increasing the Fe number. The shear wave velocities are highest beneath north central India, where calculated S wave travel times are 2 s shorter than in the Dharwar craton. These differences in traveltime and the very steep gradient in the shear wave velocity profiles in north central India cannot be explained by variations in mantle temperature but require differences in mantle composition.

Thermal regime and post-orogenic extension in collision belts

In order to assess the conditions leading to post-orogenic extension, the temperature and strength of the lithosphere during continental collision are calculated. The calculations assume that heat is transported by conduction and either that the lithosphere is homogeneously thickened or that only the crust is thickened during the collision. Despite increased crustal thickness and heat production, the temperature does not increase if the rate of shortening is moderate (5 × 10−16s−1, leading to 100% increase in crustal thickness in 40 Myears). The temperature distribution is used to determine a rheological profile that is compared with the stress induced by compensated topography. The calculations show that, for homogeneous lithospheric thickening, the strength of the lithosphere increases and is higher than the tensile stress except in the shallow crust. The total strength of stable continental lithosphere at the end of shortening is on the order of 1013 N m−1; it is larger by one order than the force induced by compensated topography (1012 N m−1). It appears that homogeneous lithospheric thickening would not lead to post-orogenic extension unless the initial conditions are very special (with the lithosphere hotter than normal). For crustal thickening only, the strength of the lithosphere decreases slightly and is on the same order as the tensile stress. Extension does not necessarily follow from thickening of the crust only but it could take place for a relatively wide range of initial conditions (with initial surface heat-flow 60 mW m−2 or higher). Alternatively, an event such as rapid removal of the mantle lithosphere by delamination or small-scale convection would increase the tensile stress, heat rapidly the lithosphere, reduce its strength, and always trigger extension.

Intraplate seismicity and stress in the southeastern United States

Abstract The stress induced by topography and by density heterogeneities in the lithosphere has been computed for two seismic regions in the southeastern United States: the Southern Appalachian mountains and the South Carolina Coastal Plain. The lithosphere was assumed to be a three-dimensional layered elastic slab overlying an inviscid fluid. The calculations indicate that the local stress is of the same magnitude as the tectonic stress (tens of MPa); but contradictory conclusions are suggested by the comparison of stress differences and principal directions with earthquake locations and focal mechanisms. In the Southern Appalachians, the seismicity correlates well with the stress maximum and focal mechanisms agree with the calculations where regional stress is combined with locally induced stress. In South Carolina, a combination of regional and local stress can explain the orientation of focal mechanisms, but stress does not concentrate in the region of Charleston, and, thus, other factors must play a role in the Charleston seismicity.

Andrew Fowler: Mathematical Geoscience

The word model is one of the most used and often abused in the geosciences. It has taken several different meanings: when physicists talk about the Bohr–Sommerfeld or the standard models, they refer to fundamental explanations. When geoscientists refer to a model, they sometimes refer to a collection of data (gravity model xyz of the Earth’s gravity field, for instance, or seismic tomography model abc of the Earth’s mantle). A numerical model is really a set of numerical experiments. Mathematical modeling is a different thing, it is the formulation and solution of (geo)physical problems in mathematical terms usually with analytical solutions. It extracts the essence of a physical problem and reduces it to a tractable mathematical problem. Mathematical modeling requires technical skills, but, first and foremost, it is an art: it demands at least as much physical intuition as mathematical technique. Andrew Fowler, the author of Mathematical Geoscience, has been teaching applied mathematics for geoscientists at the University of Oxford. He has devoted most of his research career to mathematical modeling of different problems in the geosciences. He has a long and diverse experience in the field, and, most importantly, he is a great artist! Mathematical Geoscience covers many different topics related to the earth, oceans, and atmosphere, but one can see that they all belong to the very wide field of geophysical fluid dynamics. They include climate, atmospheric physics, oceanography, geomorphology, glaciology, petrology and volcanology and mantle convection. Geophysical fluid dynamics belongs to a British tradition in applied mathematics; a tradition based on the works of John Scott Russell, Lord Rayleigh, Sir Horace Lamb, Sir Harold Jeffreys, G.I. Taylor, Batchelor, and many others. One of the characteristics of the British school of applied mathematics is its empirical approach; these mathematicians can even devise experiments to refine their mathematical models.