An asymptotic solution of hydrodynamic equations at the mid-plane of a plume in the earths mantle

From the partial differential equations of hydrodynamics governing the movements in the Earth's mantle of a Newtonian fluid with a pressure- and temperature-dependent viscosity, considering the bilateral symmetry of velocity and temperature distributions at the mid-plane of the plume, an analytical solution of the governing equations near the mid-plane of the plume was found by the method of asymptotic analysis. The vertical distribution of the upward velocity, viscosity and temperature at the mid-plane, and the temperature excess at the centre of the plume above the ambient mantle temperature were then calculated for two sets of Newtonian rheological parameters. The results obtained show that the temperature at the mid-plane and the temperature excess are nearly independent of the rheological parameters. The upward velocity at the mid-plane, however, is strongly dependent on the rheological parameters.

Magma Extraction from the Mantle Wedge at Convergent Margins Through Dikes: A Parametric Sensitivity Analysis

We address under what conditions a magma generated by partial melting at 100 km depth in the mantle wedge above a subduction zone can reach the crust in dikes before stalling. We also address under what conditions primitive basaltic magma (Mg # >60) can be delivered from this depth to the crust. We employ linear elastic fracture mechanics with magma solidification theory and perform a parametric sensitivity analysis. All dikes are initiated at a depth of 100 km in the thermal core of the wedge, and the Moho is fixed at 35 km depth. We consider a range of melt solidus temperatures (800-1100 degrees C), viscosities (10-100 Pa s), and densities (2400-2700 kg m(-3)). We also consider a range of host rock fracture toughness values (50-300 MPa m(1/2)) and dike lengths (2-5 km) and two thermal structures for the mantle wedge (1260 and 1400 degrees C at 100 km depth and 760 and 900 degrees C at 35 km depth). For the given parameter space, many dikes can reach the Moho in less than a few hundred hours, well within the time constraints provided by U series isotope disequilibria studies. Increasing the temperature in the mantle wedge, or increasing the dike length, allows additional dikes to propagate to the Moho. We conclude that some dikes with vertical lengths near their critical lengths and relatively high solidus temperatures will stall in the mantle before reaching the Moho, and these may be returned by corner flow to depths where they can melt under hydrous conditions. Thus, a chemical signature in arc lavas suggesting partial melting of slab basalts may be partly influenced by these recycled dikes. Alternatively, dikes with lengths well above their critical lengths can easily deliver primitive magmas to the crust, particularly if the mantle wedge is relatively hot. Dike transport remains a viable primary mechanism of magma ascent in convergent tectonic settings, but the potential for less rapid mechanisms making an important contribution increases as the mantle temperature at the Moho approaches the solidus temperature of the magma.

Thermal regime of the Southeast Indian Ridge between 88°E and 140°E: Remarks on the subsidence of the ridge flanks

The flanks of the Southeast Indian Ridge are characterized by anomalously low subsidence rates for the 0-25 Ma period: less than 300 m Ma(-1/2) between 101 degrees E and 120 degrees E and less than 260 m Ma(-1/2) within the Australian-Antarctic Discordance (AAD), between 120 degrees E and 128 degrees E. The expected along-axis variation in mantle temperature (similar to 50 degrees C) is too small to explain this observation, even when the temperature dependence of the mantle physical properties is accounted for. We successively analyze the effect on subsidence of different factors, such as variations in crustal thickness; the dynamic contribution of an old, detached slab supposedly present within the mantle below the AAD; and depletion in phi(m), a parameter here defined as the "ubiquitously distributed melt fraction" within the asthenosphere. These effects may all contribute to the observed, anomalously low subsidence rate of the ridge flanks, with the most significant contribution being probably related to the depletion in phi(m). However, these effects have a deep-seated origin that cannot explain the abruptness of the transition across the fracture zones that delineate the boundaries of the AAD, near 120 degrees E and near 128 degrees E, respectively.

The Southeast Indian Ridge between 88°E and 118°E: Gravity anomalies and crustal accretion at intermediate spreading rates

Although slow spreading ridges characterized by a deep axial valley and fast spreading ridges characterized by an axial bathymetric high have been extensively studied, the transition between these two modes of axial morphology is not well understood. We conducted a geophysical-survey of the intermediate spreading rate Southeast Indian Ridge between 88 degrees E and 118 degrees E, a 2300-km-long section of the ridge located between the Amsterdam hot spot and the Australian-Antarctic Discordance where satellite gravity data suggest that the Southeast Indian Ridge (SEIR) undergoes a change from an axial high in the west to an axial valley in the east. A basic change in axial morphology is found near 103 degrees 30'E in the shipboard data; the axis to the west is marked by an axial high, while a valley is found to the east. Although a well-developed axial high, characteristic of the East Pacific Rise (EPR), is occasionally present, the more common observation is a rifted high that is lower and pervasively faulted, sometimes with significant (> 50 m throw) faults within a kilometer of the axis. A shallow axial valley (< 700 m deep) is observed from 104 degrees E to 114 degrees E with a sudden change to a deep (>1200 m deep) valley across a transform at 114 degrees E. The changes in axial morphology along the SEIR are accompanied by a 500 m increase in near-axis ridge flank depth from 2800 m near 88 degrees E to 3300 m near 114 degrees E and by a 50 mGal increase in the regional level of mantle Bouguer gravity anomalies over the same distance, The regional changes in depth and mantle Bouguer anomaly (MBA) gravity can be both explained by a 1.7-2.4 km change in crustal thickness or by a mantle temperature change of 50 degrees C-90 degrees C. In reality, melt supply (crustal thickness) and mantle temperature are linked, so that changes in both may occur simultaneously and these estimates serve as upper bounds. The along-axis MBA gradient is not uniform. Pronounced steps in the regional level of the MBA gravity occur at 103 degrees 30'E-104 degrees E and at 114 degrees E-116 degrees E and correspond to the changes in the nature of the axial morphology and in the amplitude of abyssal hill morphology suggesting that the different forms of morphology do not grade into each other but rather represent distinctly different forms of axial (s)tructure and tectonics with a sharp transition between them. The change from an axial high to an axial valley requires a threshold effect in which the strength of the lithosphere changes quickly. The presence or absence of a quasi-steady state magma chamber may provide such a mechanism. The different forms of axial morphology are also associated with different intrasegment MBA gravity patterns. Segments with an axial high have an MBA low located at a depth minimum near the center of the segment, At EPR-like segments, the MBA low is about 10 mGal with along-axis gradients of 0.15-0.25 mGal/km, similar to those observed at the EPR, Rifted highs have a shallower low and lower gradients suggesting an attenuated composite magma chamber and a reduced and perhaps episodic melt supply. Segments with a shallow axial valley have very flat along-axis MBA profiles with little correspondence between axial depth and axial MBA gravity.

The Southeast Indian Ridge between 88°E and 118°E: Variations in crustal accretion at constant spreading rate

The temperature of the mantle and the rate of melt production are parameters which play important roles in controlling the style of crustal accretion along mid-ocean ridges. To investigate the variability in crustal accretion that develops in response to variations in mantle temperature, we have conducted a geophysical investigation of the Southeast Indian Ridge (SEIR) between the Amsterdam hotspot and the Australian-Antarctic Discordance (88 degrees E-118 degrees E). The spreading center deepens by 2100 m from west to east within the study area. Despite a uniform, intermediate spreading rate (69-75 mm yr-l), the SEIR exhibits the range in axial morphology displayed by the East Pacific Rise and the Mid-Atlantic Ridge (MAR) and usually associated with variations in spreading rate. The spreading center is characterized by an axial high west of 102 degrees 45'E, whereas an axial valley is prevalent east of this longitude. Both the deepening of the ridge axis and the general evolution of axial morphology from an axial high to a rift valley are not uniform. A region of intermediate morphology separates axial highs and MAR-like rift valleys. Local transitions in axial morphology occur in three areas along the ridge axis. The increase in axial depth toward the Australian-Antarctic Discordance may be explained by the thinning of the oceanic crust by similar to 4 km and the change in axial topography. The long-wavelength changes observed along the SEIR can be attributed to a gradient in mantle temperature between regions influenced by the Amsterdam and Kerguelen hot spots and the Australian-Antarctic Discordance. However, local processes, perhaps associated with an heterogeneous mantle or along-axis asthenospheric flow, may give rise to local transitions in axial topography and depth anomalies.

Distributions of temperature, velocity and viscosity at symmetrical axis of cylindrical plume in earth's mantle with variable viscosity

The parameters at the symmetrical axis of a cylindrical plume characterize the strength of this plume and provide a boundary condition which must be given to investigate the structure of a plume. For Newtonian fluid with a temperature-and pressure-dependence viscosity, an asymptotical solution of hydrodynamic equations at the symmetrical axis of the plume is found in the present paper. The temperature, upward velocity and viscosity at the symmetrical axis have been obtained as functions of depth, The calculated results have been given for two typical sets of Newtonian rheological parameters. The results obtained show that the temperature distribution along the symmetrical axis is nearly independent of the theological parameters. The upward velocity at the symmetrical axis, however, is strongly dependent on the rheological parameters.

Three-dimensional models of mantle convection : influence of phase transitions and temperature-dependent viscosity

Two of the most important questions in mantle dynamics are investigated in three separate studies: the influence of phase transitions (studies 1 and 2), and the influence of temperature-dependent viscosity (study 3).

(1) Numerical modeling of mantle convection in a three-dimensional spherical shell incorporating the two major mantle phase transitions reveals an inherently three-dimensional flow pattern characterized by accumulation of cold downwellings above the 670 km discontinuity, and cylindrical 'avalanches' of upper mantle material into the lower mantle. The exothermic phase transition at 400 km depth reduces the degree of layering. A region of strongly-depressed temperature occurs at the base of the mantle. The temperature field is strongly modulated by this partial layering, both locally and in globally-averaged diagnostics. Flow penetration is strongly wavelength-dependent, with easy penetration at long wavelengths but strong inhibition at short wavelengths. The amplitude of the geoid is not significantly affected.

(2) Using a simple criterion for the deflection of an upwelling or downwelling by an endothermic phase transition, the scaling of the critical phase buoyancy parameter with the important lengthscales is obtained. The derived trends match those observed in numerical simulations, i.e., deflection is enhanced by (a) shorter wavelengths, (b) narrower up/downwellings (c) internal heating and (d) narrower phase loops.

(3) A systematic investigation into the effects of temperature-dependent viscosity on mantle convection has been performed in three-dimensional Cartesian geometry, with a factor of 1000-2500 viscosity variation, and Rayleigh numbers of 10^5-10^7. Enormous differences in model behavior are found, depending on the details of rheology, heating mode, compressibility and boundary conditions. Stress-free boundaries, compressibility, and temperature-dependent viscosity all favor long-wavelength flows, even in internally heated cases. However, small cells are obtained with some parameter combinations. Downwelling plumes and upwelling sheets are possible when viscosity is dependent solely on temperature. Viscous dissipation becomes important with temperature-dependent viscosity.

The sensitivity of mantle flow and structure to these various complexities illustrates the importance of performing mantle convection calculations with rheological and thermodynamic properties matching as closely as possible those of the Earth.

Controls of mantle potential temperature and lithospheric thickness on magmatism in the North Atlantic Igneous Province.

FUNDING This study was funded by University of Aberdeen. SUPPLEMENTARY DATA Supplementary data for this paper are available at Journal of Petrology online. ACKNOWLEDGEMENTS The authors wish to thank Claude Herzberg, Estaban Gazel and an anonymous reviewer for thoughtful and constructive reviews.

Mechanical and thermal structure of a cylindrical plume in the earth's mantle

A mantle plume is understood as a hot, narrow, upwelling flow in the earth's mantle and accompanied by an efficient transfer of mass and energy from deep to upper layer of the earth. The cylindrical plume in earth's mantle plays an important role in explaining the origin of the surface hot spots and linear island chains. From the basic hydrodynamical equations, the detailed mechanical and thermal structure of a cylindrical plume of Newtouian fluids with temperature and pressure-dependent viscosity are given in the present paper. For two sets of rheological parameters the radial profiles of upward velocity, temperature and viscosity in the plume and radiuses of the plume at various depths have been calculated.

The thermal and mechanical structure of a two-dimensional plume in the earths mantle

On the condition that the distribution of velocity and temperature at the mid-plane of a mantle plume has been obtained (pages 213–218, this issue), the problem of determining the lateral structure of the plume at a given depth is reduced to solving an eigenvalue problem of a set of ordinary differential equations with five unknown functions, with an eigenvalue being related to the thermal thickness of the plume at this depth. The lateral profiles of upward velocity, temperature and viscosity in the plume and the thickness of the plume at various depths are calculated for two sets of Newtonian rheological parameters. The calculations show that the precondition for the existence of the plume, δT/L 1 (L = the height of the plume, δT = lateral distance from the mid-plane), can be satisfied, except for the starting region of the plume or near the base of the lithosphere. At the lateral distance, δT, the upward velocity decreases to 0.1 – 50% of its maximum value at different depths. It is believed that this model may provide an approach for a quantitative description of the detailed structure of a mantle plume.

Regional variations in upper mantle structure beneath North America

Several types of seismological data, including surface wave group and phase velocities, travel times from large explosions, and teleseismic travel time anomalies, have indicated that there are significant regional variations in the upper few hundred kilometers of the mantle beneath continental areas. Body wave travel times and amplitudes from large chemical and nuclear explosions are used in this study to delineate the details of these variations beneath North America.

As a preliminary step in this study, theoretical P wave travel times, apparent velocities, and amplitudes have been calculated for a number of proposed upper mantle models, those of Gutenberg, Jeffreys, Lehman, and Lukk and Nersesov. These quantities have been calculated for both P and S waves for model CIT11GB, which is derived from surface wave dispersion data. First arrival times for all the models except that of Lukk and Nersesov are in close agreement, but the travel time curves for later arrivals are both qualitatively and quantitatively very different. For model CIT11GB, there are two large, overlapping regions of triplication of the travel time curve, produced by regions of rapid velocity increase near depths of 400 and 600 km. Throughout the distance range from 10 to 40 degrees, the later arrivals produced by these discontinuities have larger amplitudes than the first arrivals. The amplitudes of body waves, in fact, are extremely sensitive to small variations in the velocity structure, and provide a powerful tool for studying structural details.

Most of eastern North America, including the Canadian Shield has a Pn velocity of about 8.1 km/sec, with a nearly abrupt increase in compressional velocity by ~ 0.3 km/sec near at a depth varying regionally between 60 and 90 km. Variations in the structure of this part of the mantle are significant even within the Canadian Shield. The low-velocity zone is a minor feature in eastern North America and is subject to pronounced regional variations. It is 30 to 50 km thick, and occurs somewhere in the depth range from 80 to 160 km. The velocity decrease is less than 0.2 km/sec.

Consideration of the absolute amplitudes indicates that the attenuation due to anelasticity is negligible for 2 hz waves in the upper 200 km along the southeastern and southwestern margins of the Canadian Shield. For compressional waves the average Q for this region is > 3000. The amplitudes also indicate that the velocity gradient is at least 2 x 10^-3 both above and below the low-velocity zone, implying that the temperature gradient is < 4.8°C/km if the regions are chemically homogeneous.

In western North America, the low-velocity zone is a pronounced feature, extending to the base of the crust and having minimum velocities of 7.7 to 7.8 km/sec. Beneath the Colorado Plateau and Southern Rocky Mountains provinces, there is a rapid velocity increase of about 0.3 km/sec, similar to that observed in eastern North America, but near a depth of 100 km.

Complicated travel time curves observed on profiles with stations in both eastern and western North America can be explained in detail by a model taking into account the lateral variations in the structure of the low-velocity zone. These variations involve primarily the velocity within the zone and the depth to the top of the zone; the depth to the bottom is, for both regions, between 140 and 160 km.

The depth to the transition zone near 400 km also varies regionally, by about 30-40 km. These differences imply variations of 250 °C in the temperature or 6 % in the iron content of the mantle, if the phase transformation of olivine to the spinel structure is assumed responsible. The structural variations at this depth are not correlated with those at shallower depths, and follow no obvious simple pattern.

The computer programs used in this study are described in the Appendices. The program TTINV (Appendix IV) fits spherically symmetric earth models to observed travel time data. The method, described in Appendix III, resembles conventional least-square fitting, using partial derivatives of the travel time with respect to the model parameters to perturb an initial model. The usual ill-conditioned nature of least-squares techniques is avoided by a technique which minimizes both the travel time residuals and the model perturbations.

Spherically symmetric earth models, however, have been found inadequate to explain most of the observed travel times in this study. TVT4, a computer program that performs ray theory calculations for a laterally inhomogeneous earth model, is described in Appendix II. Appendix I gives a derivation of seismic ray theory for an arbitrarily inhomogeneous earth model.

Thermochronology of central Ribeira Fold Belt, SE Brazil: Petrological and geochronological evidence for long-term high temperature maintenance during Western Gondwana amalgamation

The studied sector of the central Ribeira Fold Belt (SE Brazil) comprises metatexites, diatexites, charnockites and blastomylonites. This study integrates petrological and thermochronological data in order to constrain the thermotectonic and geodynamic evolution of this Neoproterozoic-Ordovician mobile belt during Western Gondwana amalgamation. New data indicate that after an earlier collision stage at similar to 610 Ma (zircon, U-Pb age), peak metamorphism and lower crust partial melting, coeval with the main regional high grade D(1) thrust deformation, occurred at 572-562 Ma (zircon, U-Pb ages). The overall average cooling rate was low (<5 degrees C/Ma) from 750 to 250 degrees C (at similar to 455 Ma; biotite-WR Rb-Sr age), but disparate cooling paths indicate differential uplift between distinct lithotypes: (a) metatexites and blastomylonites show a overall stable 3-5 degrees C/Ma cooling rate; (b) charnockites and associated rocks remained at T>650 degrees C during sub-horizontal D(2) shearing until similar to 510-470 Ma (garnet-WR Sm-Nd ages) (1-2 degrees C/Ma), being then rapidly exhumed/cooled (8-30 degrees C/Ma) during post-orogenic D(3) deformation with late granite emplacement at similar to 490 Ma (zircon, U-Pb age). Cooling rates based on garnet-biotite Fe-Mg diffusion are broadly consistent with the geochronological cooling rates: (a) metatexites were cooled faster at high temperatures (6 degrees C/Ma) and slowly at low temperatures (0.1 degrees C/Ma), decreasing cooling rates with time; (b) charnockites show low cooling rates (2 degrees C/Ma) near metamorphic peak conditions and high cooling rates (120 degrees C/Ma) at lower temperatures, increasing cooling rates during retrogression. The charnockite thermal evolution and the extensive production of granitoid melts in the area imply that high geothermal gradients were sustained fora long period of time (50-90 Ma). This thermal anomaly most likely reflects upwelling of asthenospheric mantle and magma underplating coupled with long-term generation of high HPE (heat producing elements) granitoids. These factors must have sustained elevated crustal geotherms for similar to 100 Ma, promoting widespread charnockite generation at middle to lower crustal levels. (C) 2010 Elsevier B.V. All rights reserved.

Temperature dependent growth and inorganic ion composition of haemolymph of juvenile Sepia officinalis, 2006

B Body wet weight and mantle length of juvenile Sepia officinalis were monitored over a peroid of five weeks. The animals had hatched in our aquarium system in Bremerhaven, Germany at 16°C and were descendants of individuals collected in the Oosterschelde estuary, Netherlands. Animals were kept in natural sea water at 10 or 17°C and fed small live shrimp (Palaemonetes varians) ad libitum daily. At the end of the experiment some animals kept at 17°C were sacrificed using ethanol. Haemolymph was withdrawn from the head vein using syringe and needle. Haemolymph samples were stored at -20°C until Na+, Cl-, K+, Mg2+, Ca2+ and SO42- concentrations were determined using ion chromatography. Mean body weight more that tripled at 17°C during the investigation period, while growth was impared by exposue to 10°C. Haemolymph ion concentrations were similar to those in sea water, except for sulphate. The concentration of this ion in the haemolymph was more that ten times lower than in sea water.