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NASA NTRS1994

Linear stability of a layered fluid with mobile surface plates

We develop a general method of calculating the linear stability of a fluid with homogeneous layers that is heated from below. The method employs a propagator technique to obtain expressions for the fluid velocity, stress, and temperature. The principal advantage of the method is the ease with which solutions are adapted to a wide variety of boundary conditions and fluid properties. We demonstrate the utility of the method using three examples which quantify the effects of (1) rheological layering, (2) mobile plates at the surface, and (3) multiple phase transitions. Each example is presented in the context of Earth's mantle. In the first example, we predict that convection becomes confined to the upper mantle once the viscosity increase between the upper and lower mantle exceeds a factor of 2000, consistent with the nonlinear calculations of Davies (1977). In the second example we find that the heat flux variations in a convecting fluid with variably sized, surface plates can be attributed, in part, to changes in the critical Rayleigh number. The linear stability of a fluid with multiple phase transitions is significantly affects by the locations of the transitions. We find that phase transitions have their largest effect when they are located at the center of the fluid layer and become much less important when they are located near the exterior boundaries.

Buffett, B. A.↗

NASA NTRS2014

Recycling of Oceanic Lithosphere: Water, fO2 and Fe-isotope Constraints

Spinel peridotite and garnet pyroxenite xenoliths from Hawaii provide important clues about the composition of the oceanic lithosphere, and can be used to assess its contribution to mantle heterogeneity upon recycling. The peridotites have lower bulk H2O (approximately 70-114 ppm) than the MORB source, qualitatively consistent with melt depletion. The garnet pyroxenites (high pressure cumulates) have higher H2O (200-460 ppm, up to 550 ppm accounting for phlogopite) and low H2O/Ce ratios (less than 100). The peridotites have relatively light Fe-isotopes (delta Fe -57 = -0.34 to 0.13) that decrease with increasing depletion, while the pyroxenites are significantly heavier (delta Fe-57 up to 0.3). The observed xenolith, as well as MORB and OIB total Fe-isotope variability is larger that can be explained by existing melting models. The high H2O and low H2O/Ce ratios of pyroxenites are similar to estimates of EM-type OIB sources, while their heavy delta Fe-57 are similar to some Society and Cook-Austral basalts. Therefore, recycling of mineralogically enriched oceanic lithosphere (i.e. pyroxenites) may contribute to OIB sources and mantle heterogeneity. The Fe(3+)/Sigma systematics of these xenoliths also suggest that there might be lateral redox gradients within the lithosphere, between juxtaposed oxidized spinel peridotites (deltaFMQ = -0.7 to 1.6, at 15 kb) and more reduced pyroxenites (deltaFMQ = -2 to -0.4, at 20-25kb). Such mineralogically and compositionally imposed fO2 gradients may generate local redox melting due to changes in fluid speciation (e.g. reduced fluids from pyroxenite encountering more oxidized peridotite). Formation of such incipient, small degree melts could further contribute to metasomatic features seen in peridotites, mantle heterogeneity, as well as the low velocity and high electrical conductivity structures near the base of the lithosphere and upper mantle.

Bizmis, M.↗

NASA NTRS2001

Influence of a Fluid Lunar Core on the Moons Orientation

Oblateness of and dissipation at the lunar liquid-core/solid-mantle boundary affects the precession of core and mantle. Analysis of Lunar Laser ranges gives a weak detection of oblateness and a strong determination of dissipation. Additional information is contained in the original extended abstract.

Williams, J. G.↗

NASA NTRS1973

Convection in the earth's mantle

The computer is used to solve for thermal convection within the earth's mantle. A review of the knowledge of surface displacements and of the present understanding of the mantle and its relevant physical and chemical properties is contained in the paper. Applicable equations assume a Newtonian fluid layer heated from below and within, with gravity acting downward. The numerical method employs finite differences and was constructed with a view toward the faithful simulation of coupling mechanisms. It enables surveying the effect of a parameter using a relatively coarse computing mesh. Some of the results obtained are presented.

Turcotte, D. L.↗

NASA NTRS1981

Postseismic rebound due to creep of the lower lithosphere and asthenosphere

Postseismic surface deformations are attributed to the inelastic flow of the subcrustal regions of the Earth following an earthquake. A multilayer representation of the Earth's rheological properties is used in conjunction with a finite element computational scheme to calculate time dependent displacements and strains subsequent to a strike slip earthquake. The deviatoric stress strain relations for the uppermost layer is assumed elastic. Lower layers are assumed to be, in order of increasing depth, a standard, linear, three element, viscoelastic solid; a linear viscoelastic fluid; and another elastic solid. Physically these layers correspond to the upper lithosphere, lower lithosphere, asthenosphere, and lower mantle, respectively. Elastic dilatational properties are assumed throughout. Appreciable postseismic displacements, possibly approaching meters, for large earthquakes, arise from viscoelastic relaxation following sudden coseismic slip. Furthermore, compared to the simpler case of an elastic lithosphere over a viscoelastic asthenosphere and the near fault postseismic shear, strain is increased, by a factor of two or more in some cases, by the presence of a viscoelastic lower lithosphere. Also, the duration of postseismic straining is increased by the relatively slow relaxation of this layer.

Cohen, S. C.↗

NASA NTRS1988

Viscous relaxation of impact crater relief on Venus - Constraints on crustal thickness and thermal gradient

Models for the viscous relaxation of impact crater topography are used to constrain the crustal thickness (H) and the mean lithospheric thermal gradient beneath the craters on Venus. A general formulation for gravity-driven flow in a linearly viscous fluid has been obtained which incorporates the densities and temperature-dependent effective viscosities of distinct crust and mantle layers. An upper limit to the crustal volume of Venus of 10 to the 10th cu km is obtained which implies either that the average rate of crustal generation has been much smaller on Venus than on earth or that some form of crustal recycling has occurred on Venus.

Grimm, Robert E.↗

NASA NTRS1989

Long-wavelength variations in earth's geoid - Physical models and dynamical implications

Seismic tomography and fluid dynamical models are extended to include a detailed and realistic parameterization of the viscosity structure of the mantle. The model also includes the effects of heterogeneity inferred from surface-wave studies of upper-mantle structure. It is found that about 90 percent of the observed geoid may be explained by density anomalies inferred from tomography, a model of subducted slabs, and an earth model with a low-viscosity asthenosphere over a moderate-viscosity lower mantle.

Hager, B. H.↗

NASA NTRS1992

Steady induction effects in geomagnetism. Part 1A: Steady motional induction of geomagnetic chaos

Geomagnetic effects of magnetic induction by hypothetically steady fluid motion and steady magnetic flux diffusion near the top of Earth's core are investigated using electromagnetic theory, simple magnetic earth models, and numerical experiments with geomagnetic field models. The problem of estimating a steady fluid velocity field near the top of Earth's core which induces the secular variation indicated by broad-scale models of the observed geomagnetic field is examined and solved. In Part 1, the steady surficial core flow estimation problem is solved in the context of the source-free mantle/frozen-flux core model. In the first paper (IA), the theory underlying such estimates is reviewed and some consequences of various kinematic and dynamic flow hypotheses are derived. For a frozen-flux core, fluid downwelling is required to change the mean square normal magnetic flux density averaged over the core-mantle boundary. For surficially geostrophic flow, downwelling implies poleward flow. The solution of the forward steady motional induction problem at the surface of a frozen-flux core is derived and found to be a fine, easily visualized example of deterministic chaos. Geomagnetic effects of statistically steady core surface flow may well dominate secular variation over several decades. Indeed, effects of persistent, if not steady, surficially geostrophic core flow are described which may help explain certain features of the present broad-scale geomagnetic field and perhaps paleomagnetic secular variation.

Voorhies, Coerte V.↗

NASA NTRS2002

Phosphorus Equilibria Among Mafic Silicate Phases

Phosphorus incorporation in major rock-forming silicate minerals has the following implications: (1) Reactions between phosphorus-hosting major silicates and accessory phosphates, which are also major trace element carriers, may control the stability of the latter and thus may affect the amount of phosphorus and other trace elements released to the coexisting melt or fluid phase. (2) Less of a phosphate mineral is needed to account for the bulk phosphorus of planetaty mantles. (3) During partial melting of mantle mineral assemblages or equilibrium fractional crystallization of basaltic magmas, and in the absence or prior to saturation with a phosphate mineral, silicate melts may become enriched in phosphorus, especially in the geochemically important low melt fraction regime, Although the small differences in the ionic radii of IVp5+, IVSi4+, and IV Al3+ makes phosphoms incorporation into crystalline silicates perhaps unsurprising, isostructural silicate and phosphate crystalline solids do not readily form solutions, e.g., (Fe, Mg)2SiO4 vs. LiMgPO4, SiO)2 VS. AlPO4. Nonetheless, there are reports of, poorly characterized silico-phosphate phases in angrites , 2-4 wt% P2O5 in olivine and pyroxene grains in pallasites and reduced terestrial basalts which are little understood but potentially useful, and up to 17 wt% P2O5 in olivine from ancient slags. However, such enrichments are rare and only underscore the likelihood of phosphoms incorporation in silicate minerals. The mechanisms that allow phosphorus to enter major rock-forming silicate minerals (e.g., Oliv, Px, Gt) remain little understood and the relevant data base is limited. Nonetheless, old and new high-pressure (5-10 GPa) experimental data suggest that P2O5 wt% decreases from silica-poor to silica-rich compositions or from orthosilicate to chain silicate structures (garnet > olivine > orthopyroxene) which implies that phosphorus incorporation in silicates is perhaps more structure-than site-specific. The data also indicate that DXVliQP2O5 decrease in the same order, but DOVLiQP2O5 and DOpx/LiQP205 are likely constant, respectively equal to 0.08(3) and 0.007(4), in contrast, DG1ILiQP205 increases from 0.15(3) to 0.36(10) as garnet becomes majoritic, thus silica-enriched, and may also depend on liquid composition (SiO2, P2O5 and Na2O wt%).

Berlin, Jana↗

NASA NTRS1990

An analytic model of axisymmetric mantle plume due to thermal and chemical diffusion

An analytic model of axisymmetric mantle plumes driven by either thermal diffusion or combined diffusion of both heat and chemical species from a point source is presented. The governing equations are solved numerically in cylindrical coordinates for a Newtonian fluid with constant viscosity. Instead of starting from an assumed plume source, constraints on the source parameters, such as the depth of the source regions and the total heat input from the plume sources, are deduced using the geophysical characteristics of mantle plumes inferred from modelling of hotspot swells. The Hawaiian hotspot and the Bermuda hotspot are used as examples. Narrow mantle plumes are expected for likely mantle viscosities. The temperature anomaly and the size of thermal plumes underneath the lithosphere can be sensitive indicators of plume depth. The Hawaiian plume is likely to originate at a much greater depth than the Bermuda plume. One suggestive result puts the Hawaiian plume source at a depth near the core-mantle boundary and the source of the Bermuda plume in the upper mantle, close to the 700 km discontinuity. The total thermal energy input by the source region to the Hawaiian plume is about 5 x 10(10) watts. The corresponding diameter of the source region is about 100 to 150 km. Chemical diffusion from the same source does not affect the thermal structure of the plume.

Liu, Mian↗

NASA NTRS1991

Contributions from geomagnetic inverse theory to the study of hydromagnetic conditions near the core-mantle boundary

The Final Report on contributions from geomagnetic inverse theory to the study of hydromagnetic conditions near the core-mantle boundary (CMB) is presented. The original proposal was to study five questions concerning what the surface and satellite magnetic data imply about hydromagnetic and electromagnetic conditions near the CMB. The five questions are: (1) what do the surface and satellite data imply about the geomagnetic field B near the surface of the earth; (2) how does one extrapolate B down through the conducting mantle to the CMB; (3) if B on the CMB is visible, how accurately does it satisfy the frozen-flux approximation; (4) if frozen flux is a good approximation on the CMB, what can be inferred about the fluid velocity v in the upper core; and (5) if v at the CMB is visible, does it suggest any dynamical properties of the core, such as vertical advection, Alfven-inertial waves, link instabilities, or mantle effects. A summary of the research is provided.

Backus, George E.↗

NASA NTRS1982

Investigation of geomagnetic field forecasting and fluid dynamics of the core

Progress in the development, testing, and evaluation of kinematic geomagnetic forecast models and their utility in magnetic prediction of the core-mantle boundary of the Earth and in determination of the core radius is reported. The GFSC 9/80 model, which uses MAGSAT data, was determined to be of high quality.

Benton, E. R.↗

DOE OSTI2021

The stability of subducted glaucophane with the Earth’s secular cooling

The blueschist to eclogite transition is one of the major geochemical–metamorphic processes typifying the subduction zone, which releases fluids triggering earthquakes and arc volcanism. Although glaucophane is an index hydrous mineral for the blueschist facies, its stability at mantle depths in diverse subduction regimes of contemporary and early Earth has not been experimentally determined. Here, we show that the maximum depth of glaucophane stability increases with decreasing thermal gradients of the subduction system. Along cold subduction geotherm, glaucophane remains stable down ca. 240 km depth, whereas it dehydrates and breaks down at as shallow as ca. 40 km depth under warm subduction geotherm or the Proterozoic tectonic setting. Our results imply that secular cooling of the Earth has extended the stability of glaucophane and consequently enabled the transportation of water into deeper interior of the Earth, suppressing arc magmatism, volcanism, and seismic activities along subduction zones.

58 GEOSCIENCES↗

NASA NTRS2003

Magmatic Processes That Produced Lunar Fire Fountains

Reanalysis of the Apollo 15 A, B, and C green glass beads from slide 15426,72, led to the discovery of patchy, highly vesicular glass rims adhering to beads. These rims are high in S and Ni and low in MgO, but otherwise compositionally similar to the green glasses. We find that these rims represent a unique melt composition that places constraints on lunar magmatic processes. Combining the compositional data for the vesicular glass rims with new minor element data for the green glass beads leads us to hypothesize that the vesicular rim fluid originated near the green glass source, at about 2.2 GPa. These findings support the theory of a heterogeneous lunar mantle, and suggest that sulfur did not drive the eruption from depth, but that degassing volatiles into the vacuum did drive the final fire fountain eruption.

Elkins-Tanton, Linda T.↗

NASA NTRS1975

The Igwisi Hills extrusive 'kimberlites'

The petrography and mineral chemistry of volcanic rocks from the Igwisi Hills in Tanzania are discussed. There is considerable evidence to suggest that the Igwisi rocks are extrusive kimberlites: a two-component nature with high P-T minerals in a low P-T matrix; the presence of chrome pyrope, Al enstatite, chrome diopside, chromite and olivine; a highly oxidized, volatile-rich matrix with serpentine, calcite, magnetite, perovskite; high Sr, Zr, and Nb contents; occurrence in a narrow isolated vent within a stable shield area. The Igwisi rocks differ from kimberlite in the lack of magnesian ilmenite, the scarcity of matrix phlogopite, and the overall low alkali content. They apparently contain material from phlogopite-bearing garnet peridotites with a primary mineral assemblage indicative of equilibrium at upper mantle temperatures and pressures. This primary assemblage was brought rapidly to the surface in a gas-charged, carbonate-rich fluid. Rapid upward transport, extrusion, and rapid cooling have tended to prevent reaction between inclusions and the carbonate-rich matrix that might otherwise have yielded a more typical kimberlite.

Reid, A. M.↗

DOE OSTI2021

Intra-Molecular Isotope Study of Light Hydrocarbons

Light hydrocarbons (C 1 -C 10 ) are the largest fraction of petroleum hydrocarbons and some of the most ubiquitous and mobile fluids within sedimentary basins. It has been increasingly recognized that hydrocarbons of varying chain-lengths can be stable even under mantle conditions and that their fluxes may play a key role in the carbon dynamics of the Earth. Major formation mechanisms of these light hydrocarbons include microbial, thermogenic, and abiogenic origins. Despite their proven utility, conventional approaches using the bulk or global stable isotopes of light hydrocarbons are often not sufficient to distinguish their sources (particularly, biogenic vs. abiogenic), maturation stages/temperatures, and migration-degradation processes. Most natural compounds, including light hydrocarbons, are composed of a set of diverse isotopic molecules that differ in the number of isotopic substitutions and/or positions of isotopic substitution within a given molecules. Many of light hydrocarbon molecules contain hydrogen and carbon in energetically non-equivalent positions: isotopomers or position-specific (intra-molecular) isotope fractionation. Position-specific isotopic compositions can differ due either to equilibrium or to path-dependent kinetic or biological processes. Thus, the position-specific isotopic fractionation between different carbon and hydrogen positions within a single molecular compound could be used regardless of their reactants and other products. We hypothesize that the formation, transport and degradation processes of light hydrocarbons in the subsurface induce and control significant, perhaps unique position-specific 13 C/ 12 C and 2 H/ 1 H isotope fractionation. In this proposal, we propose to develop a new dimension in stable isotope geochemistry of light hydrocarbons: intra-molecular isotope study of light hydrocarbons. The specific objectives of our proposal include: (a) develop robust and routine quantitative nuclear magnetic resonance (NMR) methods for high-precision/high-accuracy isotopomer analysis of propane and other light hydrocarbons (C 3 -C 10 ), (b) gain a first clear picture on position-specific δ 2 H and δ 13 C values of select light hydrocarbons of both natural and industrial sources, including samples of natural gases (C 3 and possibly C 4 -C 5 ) collected from select sedimentary basins with conventional and unconventional reservoirs, (c) acquire information on position-specific 13 C/ 12 C and 2 H/ 1 H isotope fractionation of light hydrocarbons in key natural processes (thermogenic formation and oxidative degradation) based on well-controlled laboratory experiments, and (d) establish a general framework for interpreting/modeling position-specific 13 C/ 12 C and 2 H/ 1 H isotope compositions of light hydrocarbons. Intra-molecular isotope study of light hydrocarbons is expected to open up great potentials that the bulk and position-specific isotope fractionation of light hydrocarbons, in combination with mathematical/theoretical kinetic models, could provide unprecedented wealth of information on the sources, transport, and sinks of light hydrocarbons in sedimentary basins and deep Earth.

03 NATURAL GAS↗

NASA NTRS1988

Effect of a shallow low-viscosity zone on the formation of midplate swells

A finite-element numerical method is used here to analyze the effect of a low-viscosity zone on convection driven by heating from below in the upper mantle, in particular on the formation of midplate swells. The convective temperature and velocity solutions are calculated for different combinations of the viscosity in the top layer, the fluid layer thicknesses, and the Rayleigh number based on the viscosity in the bottom layer. The temperature solutions are used to calculate the geoid, topography, and heat flow anomalies, the elastic plate thickness, the depth of compensation, and an upper bound on the uplift time that result from the flow. The results are compared to data at the Hawaii, Bermuda, Cape Verde, and Marquesas swells. The magnitudes and the trend with age are consistent with theoretical and other estimates of the viscosity variation in the shallow upper mantle. Convective models can therefore explain the uplift and observed anomalies at midplate swells.

Robinson, E. M.↗

NASA NTRS1984

A reappraisal of Darwin's fission hypothesis and a possible limit to the primordial angular momentum of the Earth

G. H. Darwin proposed that the primordial Earth may have rotated fast enough that the solar tidal period was nearly resonant with the fundamental free oscillation period of a fluid Earth and that a large and unstable tidal oscillation split off to become the moon. Jeffreys argumented that dissipation during resonance would be sufficient to prevent such an unstable oscillation greater than the tidal frequency (period - 2.68 hr). It is considered that solar tides have extracted angular momentum from the Earth-Moon system over 4.5 b.y. The correspondence of the primordial tidal and resonant frequencies is nearly exact. (The effect of central condensation of the proto earth is to increase both frequencies by a similar amount, though the resonance is not precisely known. This result, was unknown to Darwin or Jeffreys. The effects of resonance were evaluated. The resonance is likely to be too damped for fission. This argument is more general than Jeffreys', who considered friction between the oscillating mantle and a rigid core. It is argued that the fact that Q must be so great for fission that equilibrium can not be maintained; the fluid proto Earth passes so quickly through resonance that maximum amplitude is not reached. It is suggested that solar resonant tides acted as a brake on the spin of the primordial partially molten Earth. Certain proposed origins for the Moon do not necessarily involve addition of substantial amounts of angular momentum to the Earth-Moon system. The primordial Earth-Moon system may have had nearly the same angular momentum as it has today.

Mckinnon, W. B.↗