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Cambridge, United Kingdom

The geochemical variations within the Skaergaard intrusion provide an opportunity to discover what features of the intrusion can be understood using the simplest form of the equations governing the two-phase flow of melt and matrix. The equations governing the conservation of mass, momentum and energy are first simplified by using the extended Boussinesq approximation, and then solved numerically to study the time-dependent behaviour of a compacting solidifying layer at the base of a magma chamber when variations in the horizontal plane can be neglected. The most important result is that the concept of a trapped liquid fraction, which has been widely used to model the bulk composition of layered intrusions, is a useful concept to describe the steady-state behaviour of compacting layers. This result is at first sight surprising, because there is relative movement between the melt and crystals during compaction, and the system is therefore open. The reason why it is useful is because both the melt and the crystals are moving downwards in a frame fixed to the upper surface of the compacting layer. Because the mass of all elements must be conserved, what goes into the top of the layer as melt and solid must come out of its bottom as a solid when the behaviour is not time dependent. However, when time-dependent behaviour occurs, the concept of a trapped liquid fraction ceases to be useful.The governing equations are used to model the concentration of phosphorus, uranium and rubidium in the lower part of the Skaergaard intrusion, where they behave incompatibly. The observed behaviour requires the viscosity of the solid part of the compacting layer to have a value of ~1017 Pa s. © The Author 2011. Published by Oxford University Press. All rights reserved. Source


McKenzie D.,Bullard Labs | Yi W.,TU Munich | Rummel R.,TU Munich
Earth and Planetary Science Letters | Year: 2014

The cold upper part of the lithosphere can support the elastic stresses that govern rigid plate movements and support the Earth's topography. In many regions the thickness T e of the layer involved can be estimated from the relationship between surface gravity measurements and topography. However, there are extensive regions of the continents where the topography is well determined, but the gravity field is not. The obvious solution to this problem is to use the satellite, rather than the surface, gravity field. The wavelength range of interest, 200-500 km, requires a satellite with a low orbit. The first satellite to satisfy this requirement is the Gravity field and steady state OCean Explorer (GOCE). Measurements of the elements of the gravity gradient tensor and determinations of the spherical harmonic coefficients of the gravity field based on GOCE observations are used to estimate T e. For Hawaii these estimates are 18.4 km and 21.4 km respectively, and agree well with a value of 18.2 km obtained from the surface gravity field determined from altimetry. An attempt to estimate the value of T e of the central North Atlantic using GOCE data was not successful, whereas surface data gives a value of about 4 km. Estimates for Tibet and surrounding regions, where the gravity field from surface measurements is poorly determined, are 25-32 km. The NW part of S. America gives 17-24 km. The difference in the values of T e from the two regions probably results from the difference in lithospheric thicknesses. Estimates of T e from central and southern Africa, of 31-34 km, are less well constrained than are those from Tibet and S. America. These results show that the data from GOCE can be used to estimate the value of T e where it is poorly determined from surface measurements, is greater than ~15 km, and where large topographic loads produce large gravity anomalies. © 2014 Elsevier B.V. Source


McKenzie D.,Bullard Labs | Yi W.,TU Munich | Yi W.,Intelligent Group | Rummel R.,TU Munich
Earth and Planetary Science Letters | Year: 2015

Satellite-only gravity fields and surface gravity obtained from altimetric measurements now agree well at wavelengths greater than ~180 km. Satellite gravity fields can therefore be used to estimate the elastic thickness Te in regions where surface observations are sparse. They are used for this purpose in a number of continental regions, of India, Africa, and Antarctica, where the topography is sufficiently rough, and also in regions of the USA, China, Australia and Siberia, where there are surface measurements. Estimates of Te for Antarctica depend on measurements of ice thickness, which are now available for much of the continent. Values of Te are obtained using two methods: from the admittance between the free air gravity and the topography, and from the coherence between Bouguer gravity anomalies and the topography. The first, but not the second, gives values of Te that are everywhere less than the seismogenic thickness. Where there is sufficient topography, estimates of Te from PreCambrian shields are all greater than 10 km and do not correlate with the lithospheric thickness. They are probably are governed by variations in crustal heat generation rates. Values for regions strongly affected by Phanerozoic tectonics are all less than 7 km, and all such regions are underlain by thin lithosphere. © 2015 Elsevier B.V. Source


McKenzie D.,Bullard Labs
Earth and Planetary Science Letters | Year: 2010

The effective elastic thickness, Te, of continental lithosphere can be estimated from the relationship between gravity and topography in the spectral domain. Two methods have been used, one of which depends on the coherence between Bouguer gravity anomalies and topography, whereas the other uses the transfer function, commonly known as the admittance, between the free air gravity and topography. The two methods give estimates of Te which differ by as much as an order of magnitude in those continental regions where variations in elevation are small. This problem has led to much controversy. An important concern is the extent to which estimates of Te are affected by dynamically maintained gravity and topography, arising from mantle convection and postglacial recovery. Unlike elastically supported anomalies, these processes can generate gravity and topographic long wavelength (>500km) anomalies. If such anomalies are modelled as being supported by elastic forces, the resulting values of Te are overestimated, often by a large amount. © 2010. Source


McKenzie D.,Bullard Labs | Priestley K.,Bullard Labs
Earth and Planetary Science Letters | Year: 2016

Surface wave tomography using Rayleigh waves has shown that Tibet and the surrounding mountain ranges that are now being shortened are underlain by thick lithosphere, of similar thickness to that beneath cratons. Both their elevation and lithospheric thickness can result from pure shear shortening of normal thickness continental lithosphere by about a factor of two. The resulting thermal evolution of the crust and lithosphere is dominated by radioactive decay in the crust. It raises the temperature of the lower part of the crust and of the upper part of the lithosphere to above their solidus temperatures, generating granites and small volumes of mafic alkaline rocks from beneath the Moho, as well as generating high temperature metamorphic assemblages in the crust. Thermal models of this process show that it can match the P, T estimates determined from metamorphic xenoliths from Tibet and the Pamirs, and can also match the compositions of the alkaline rocks. The seismological properties of the upper part of the lithosphere beneath northern Tibet suggest that it has already been heated by the blanketing effect and radioactivity of the thick crust on top. If the crustal thickness is reduced by erosion alone to its normal value at low elevations, without any tectonic extension, over a time scale that is short compared to the thermal time constant of thick lithosphere, of ~250 Ma, thermal subsidence will produce a basin underlain by thick lithosphere. Though this simple model accounts for the relevant observations, there is not yet sufficient information available to be able to model in detail the resulting thermal evolution of the sediments deposited in such cratonic basins. © 2015 Elsevier B.V.. Source

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