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At least 127 records · Page 7

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.↗

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.↗

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.↗

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.↗

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.↗

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↗

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↗

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.↗

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.↗

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.↗

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.↗

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.↗

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.↗

Does Mercury have a molten core

A feasible nonseismic observational experiment is proposed for determining the existence and extent of a conducting molten core within Mercury. This experiment would utilize the effects of a liquid core on the dynamics of Mercury's rotation; two necessary conditions for performing it are that the core must not follow the mantle's forced librations in longitude but must follow the mantle on the timescale of the 250,000-yr precession. A method is developed by assuming these conditions to be satisfied, and bounds are established on the core viscosity for which they are satisfied. It is shown that the value of the ratio of the moment of inertia of the mantle to the largest principal moment of inertia of the entire planet would indicate whether the core is most probably solid, partially fluid, or entirely fluid. Techniques are suggested for determining the unknowns required to compute the necessary ratio.

Peale, S. J.↗

The Tethered Moon

A reasonable initial condition on Earth after the Moonforming impact is that it begins as a hot global magma ocean1,2. We therefore begin our study with the mantle as a liquid ocean with a surface temperature on the order of 3000- 4000 K at a time some 100-1000 years after the impact, by which point we can hope that early transients have settled down. A 2nd initial condition is a substantial atmosphere, 100-1000 bars of H2O and CO2, supplemented by smaller amounts of CO, H2, N2, various sulfur-containing gases, and a suite of geochemical volatiles evaporated from the magma. Third, we start the Moon with its current mass at the relevant Roche limit. The 4th initial condition is the angular momentum of the Earth-Moon system. Canonical models hold this constant, whilst some recent models begin with considerably more angular momentum than is present today. Here we present a ruthlessly simplified model of Earth's cooling magmasphere based on a full-featured atmosphere and including tidal heating by the newborn Moon. Thermal blanketing by H2O-CO2 atmospheres slows cooling of a magma ocean. Geochemical volatiles - chiefly S, Na, and Cl - raise the opacity of the magma ocean's atmosphere and slow cooling still more. We assume a uniform mantle with a single internal (potential) temperature and a global viscosity. The important "freezing point" is the sharp rheological transition between a fluid carrying suspended crystals and a solid matrix through which fluids percolate. Most tidal heating takes place at this "freezing point" in a gel that is both pliable and viscous. Parameterized convection links the cooling rate to the temperature and heat generation inside the Earth. Tidal heating is a major effect. Tidal dissipation in the magma ocean is described by viscosity. The Moon is entwined with Earth by the negative feedback between thermal blanketing and tidal heating that comes from the temperature-dependent viscosity of the magma ocean. Because of this feedback, the rate that the Moon's orbit evolves is limited by the modest radiative cooling rate of Earth's atmosphere, which in effect tethers the Moon to the Earth. Consequently the Moon's orbit evolves orders of magnitude more slowly than in conventional models. Slow orbital evolution promotes capture by orbital resonances that may have been important in the Earth-Moon system

Earth-Moon system↗

Volatile solubities in magmas - Transport of volatiles from mantles to planet surfaces

The solubility of CO2, CO, CH4, H2, and H2O in melts of NaAlSi3O8 composition was measured at the mantle conditions of pressure (10-20 Kb) and temperature (1200 C). The melt volatiles were found to have dramatically lower H2/H2O and higher CO/CO2 ratios than the fluid, due to large variations in relative solubilities of volatile species in the melt. Partial melting of source regions of either high or low oxygen fugacity (fO2) will result in magmas with intermediate fO2. This means that volcanic gases can be either more, or less reducing than their source regions and that a volcanic gas composition cannot be used to directly estimate either the fO2 or the volatile composition of the source region. The results suggest that volcanic gases will usually lie in the 'neutral' range, with the fO2 values near those of the quartz-fayalite-magnetite buffer. These gases are predominately H2O with minor CO2, CO, CH4, and H2. These conclusions should apply to earth, Mars, and Venus mantles, in which the magmas produced by partial melting have moderate silica contents, but will probably not apply to very low silica magmas, such as kimberlites, because of the very high solubility of CO2 in those magmas.

Holloway, J. R.↗

Surface topography due to convection in a variable viscosity fluid - Application to short wavelength gravity anomalies in the central Pacific Ocean

Finite difference calculations of thermal convection in a fluid layer with a viscosity exponentially decreasing with temperature are performed in the context of examining the topography and gravity anomalies due to mantle convection. The surface topography and gravity anomalies are shown to be positive over regions of ascending flow and negative over regions of descending flow; at large Rayleigh numbers the amplitude of surface topography is inferred to depend on Rayleigh number to the power of 7/9. Compositional stratifications of the mantle is proposed as a mechanism for confining small-scale convection to a thin layer. A comparative analysis of the results with other available models is included.

Lin, J.↗

The pole tide in deep oceans

The fluid-dynamical theory of the pole tide is examined by describing the oceanic response to the Chandler wobble and assessing its implications for mantle anelasticity and low-frequency ocean dynamics. The Laplace tide equations accounting for bottom friction are given, and a spherical harmonic approach is delineated in which the time-independent portion of the tide height is expanded. Pole-tide height and related inertia products are linearly proportional to wobble amplitude, and the final equations are modified to account for mantle elasticity and oceanic loading. Results for pole tide effects are given for various earth models with attention to the role of boundary constraints. A dynamic effect is identified which lengthens the Chandler period by about 1 day more than static lengthening, a contribution that suggests a vigorous low-frequency response. The values derived are shown to agree with previous models that do not incorporate the effects of the pole tide.

Dickman, S. R.↗