Convergence of Liapunov series for Huygens–Roche Figures

According to the classical theory of equilibrium figures, surfaces of equal density, potential and pressure concur (let us call them isobars). Isobars can be represented by means of Liapunov power series in small parameter q, up to the first approximation coinciding with the centrifugal to gravitational force ratio at the equator. Liapunov has proved the existence of the universal convergence domain: the above mentioned series converge for all bodies (satisfying a natural condition that the density ρ decreases from the center to the surface) if |q| < q*. Using Liapunov’s algorithm and symbolic manipulation tools, we have found q*= 0.000370916. Evidently, the convergence radius q* may be much greater in common situations. To comfirm it it is reasonable to consider two limiting and one or two intermediate cases for the density behaviour: ρ is a constant, the Dirac’s δ-function, linear function of the distance from the center, etc. And indeed, in the previous paper we find a three orders of magnitude greater value for homogeneous figures. In the present paper we find that in the opposite case of Huygens-Roche figures (a point-mass surrounded by a weightless atmosphere) the convergence radius is unexpectedly large and coincides with the well-known biggest possible value q*= 0.541115598 for such a class of figures. To ascertain it we ought to use numerical calculations, so our main result is demonstrated by means of a computer assisted proof. This revised version was published online in July 2006 with corrections to the Cover Date.     

The compressibility of Fe- and Al-bearing phase D to 30 GPa

High-pressure in situ X-ray diffraction experiment of Fe- and Al-bearing phase D (Mg_0.89Fe_0.14Al_0.25Si_1.56H_2.93O₆) has been carried out to 30.5 GPa at room temperature using multianvil apparatus. Fitting a third-order Birch–Murnaghan equation of state to the P–V data yields values of V ₀ = 86.10 ± 0.05 ų; K ₀ = 136.5 ± 3.3 GPa and K′ = 6.32 ± 0.30. If K′ is fixed at 4.0 K ₀ = 157.0 ± 0.7 GPa, which is 6% smaller than Fe–Al free phase D reported previously. Analysis of axial compressibilities reveals that the c-axis is almost twice as compressible (K _c  = 93.6 ± 1.1 GPa) as the a-axis (K _a  = 173.8 ± 2.2 GPa). Above 25 GPa the c/a ratio becomes pressure independent. No compressibility anomalies related to the structural transitions of H-atoms were observed in the pressure range to 30 GPa. The density reduction of hydrated subducting slab would be significant if the modal amount of phase D exceeds 10%.     

Interaction of peridotite with Ca-rich carbonatite melt at 3.1 and 6.5 GPa: Implication for merwinite formation in upper mantle,and for the metasomatic origin of sublithospheric diamonds with Ca-rich suite of inclusions

We performed an experimental study, designed to reproduce the formation of an unusual merwinite?+?olivine-bearing mantle assemblage recently described as a part of a Ca-rich suite of inclusions in sublithospheric diamonds, through the interaction of peridotite with an alkali-rich Ca-carbonatite melt, derived from deeply subducted oceanic crust. In the first set of experiments, we studied the reaction between powdered Mg-silicates, olivine and orthopyroxene, and a model Ca-carbonate melt (molar Na:K:Ca?=?1:1:2), in a homogeneous mixture, at 3.1 and 6.5 GPa. In these equilibration experiments, we observed the formation of a merwinite?+?olivine-bearing assemblage at 3.1 GPa and 1200 °C and at 6.5 GPa and 1300–1400 °C. The melts coexisting with this assemblage have a low Si and high Ca content (Ca#?=?molar 100?×?Ca/(Ca?+?Mg)?>?0.57). In the second set of experiments, we investigated reaction rims produced by interaction of the same Ca-carbonate melt (molar Na:K:Ca?=?1:1:2) with Mg-silicate, olivine and orthopyroxene, single crystals at 3.1 GPa and 1300 °C and at 6.5 GPa and 1400 °C. The interaction of the Ca-carbonate melt with olivine leads to merwinite formation through the expected reaction: 2Mg₂SiO₄ (olivine)?+?6CaCO₃ (liquid)?=?Ca₃MgSi₂O₈ (merwinite)?+?3CaMg(CO₃)₂ (liquid). Thus, our experiments confirm the idea that merwinite in the upper mantle may originate via interaction of peridotite with Ca-rich carbonatite melt, and that diamonds hosting merwinite may have a metasomatic origin. It is remarkable that the interaction of the Ca-carbonate melt with orthopyroxene crystals does not produce merwinite both at 3.1 and 6.5 GPa. This indicates that olivine grain boundaries are preferable for merwinite formation in the upper mantle.     

Local climate change induced by groundwater overexploitation in a high Andean arid watershed,Laguna Lagunillas basin,northern Chile

The Laguna Lagunillas basin in the arid Andes of northern Chile exhibits a shallow aquifer and is exposed to extreme air temperature variations from 20 to ?25 °C. Between 1991 and 2012, groundwater levels in the Pampa Lagunillas aquifer fell from near-surface to ~15 m below ground level (bgl) due to severe overexploitation. In the same period, local mean monthly minimum temperatures started a declining trend, dropping by 3–8 °C relative to a nearby reference station. Meanwhile, mean monthly maximum summer temperatures shifted abruptly upwards by 2.7 °C on average in around 1996. The observed air temperature downturns and upturns are in accordance with detected anomalies in land-surface temperature imagery. Two major factors may be causing the local climate change. One is related to a water-table decline below the evaporative energy potential extinction depth of ~2 m bgl, which causes an up-heating of the bare soil surface and, in turn, influences the lower atmosphere. At the same time, the removal of near-surface groundwater reduces the thermal conductivity of the upper sedimentary layer, which consequently diminishes the heat exchange between the aquifer (constant heat source of ~10 °C) and the lower atmosphere during nights, leading to a severe dropping of minimum air temperatures. The observed critical water-level drawdown was 2–3 m bgl. Future and existing water-production projects in arid high Andean basins with shallow groundwater should avoid a decline of near-surface groundwater below 2 m bgl and take groundwater-climate interactions into account when identifying and monitoring potential environmental impacts.     

In-depth improvement of soil at the base of roads on taliks

The article presents a new technological solution to improve the safety of embankment bases on taliks during construction periods. The use of geotextile-sleeved sand columns and geogrids on low-temperature permafrost is investigated. The correlations between mechanical and temperature processes under this in-depth base improvement method are calculated.     

Phase relations and melting of carbonated peridotite between 10 and 20 GPa: a proxy for alkali- and CO<Subscript>2</Subscript>-rich silicate melts in the deep mantle

We determined the melting phase relations, melt compositions, and melting reactions of carbonated peridotite on two carbonate-bearing peridotite compositions (ACP: alkali-rich peridotite + 5.0 wt % CO₂ and PERC: fertile peridotite + 2.5 wt % CO₂) at 10–20 GPa and 1,500–2,100 °C and constrain isopleths of the CO₂ contents in the silicate melts in the deep mantle. At 10–20 GPa, near-solidus (ACP: 1,400–1,630 °C) carbonatitic melts with < 10 wt % SiO₂ and > 40 wt % CO₂ gradually change to carbonated silicate melts with > 25 wt % SiO₂ and < 25 wt % CO₂ between 1,480 and 1,670 °C in the presence of residual majorite garnet, olivine/wadsleyite, and clinoenstatite/clinopyroxene. With increasing degrees of melting, the melt composition changes to an alkali- and CO₂-rich silicate melt (Mg# = 83.7–91.6; ~ 26–36 wt % MgO; ~ 24–43 wt % SiO₂; ~ 4–13 wt % CaO; ~ 0.6–3.1 wt % Na₂O; and ~ 0.5–3.2 wt % K₂O; ~ 6.4–38.4 wt % CO₂). The temperature of the first appearance of CO₂-rich silicate melt at 10–20 GPa is ~ 440–470 °C lower than the solidus of volatile-free peridotite. Garnet + wadsleyite + clinoenstatite + carbonatitic melt controls initial carbonated silicate melting at a pressure < 15 GPa, whereas garnet + wadsleyite/ringwoodite + carbonatitic melt dominates at pressure > 15 GPa. Similar to hydrous peridotite, majorite garnet is a liquidus phase in carbonated peridotites (ACP and PERC) at 10–20 GPa. The liquidus is likely to be at ~ 2,050 °C or higher at pressures of the present study, which gives a melting interval of more than 670 °C in carbonated peridotite systems. Alkali-rich carbonated silicate melts may thus be produced through partial melting of carbonated peridotite to 20 GPa at near mantle adiabat or even at plume temperature. These alkali- and CO₂-rich silicate melts can percolate upward and may react with volatile-rich materials accumulate at the top of transition zone near 410-km depth. If these refertilized domains migrate upward and convect out of the zone of metal saturation, CO₂ and H₂O flux melting can take place and kimberlite parental magmas can be generated. These mechanisms might be important for mantle dynamics and are potentially effective metasomatic processes in the deep mantle.     

Immiscible two-phase Darcy flow model accounting for vanishing and discontinuous capillary pressures: application to the flow in fractured porous media

Fully implicit time-space discretizations applied to the two-phase Darcy flow problem leads to the systems of nonlinear equations, which are traditionally solved by some variant of Newton’s method. The efficiency of the resulting algorithms heavily depends on the choice of the primary unknowns since Newton’s method is not invariant with respect to a nonlinear change of variable. In this regard, the role of capillary pressure/saturation relation is paramount because the choice of primary unknowns is restricted by its shape. We propose an elegant mathematical framework for two-phase flow in heterogeneous porous media resulting in a family of formulations, which apply to general monotone capillary pressure/saturation relations and handle the saturation jumps at rocktype interfaces. The presented approach is applied to the hybrid dimensional model of two-phase water-gas Darcy flow in fractured porous media for which the fractures are modelled as interfaces of co-dimension one. The problem is discretized using an extension of vertex approximate gradient scheme. As for the phase pressure formulation, the discrete model requires only two unknowns by degree of freedom.     

Steered migration in hard rock environments

Hard rock seismic exploration normally has to deal with rather complex geological environments. These types of environments are usually characterized by a large number of local heterogeneity (e.g., faults, fracture zones, and steeply dipping interfaces). The seismic data from such environments often have a poor signal‐to‐noise ratio because of the complexity of hard rock geology. To be able to obtain reliable images of subsurface structures in such geological conditions, processing algorithms that are capable of handling seismic data with a low signal‐to‐noise ratio are required for a reflection seismic exploration. In this paper, we describe a modification of the 3D Kirchhoff post‐stack migration algorithm that utilizes coherency attributes obtained by the diffraction imaging algorithm in 3D to steer the main Kirchhoff summation. The application to a 3D synthetic model shows the stability of the presented steered migration to the presence of high level of the random noise. A test on the 3D seismic volume, acquired on a mine site located in Western Australia, reveals the capability of the approach to image steep and sharp objects such as fracture and fault zones and lateral heterogeneity.     

Local Holocene environmental indicators in Upper Mesopotamia: Pedogenic carbonate record vs. archaeobotanical data and archaeoclimatological models

It has been suggested that pedogenic carbonate coatings on stones in archaeological sites can be used to reconstruct late Quaternary environmental changes in the area of the Fertile Crescent. This research compares a pedogenic carbonate record from southeastern Turkey with three other local or regional sources of palaeoenvironmental information in order to evaluate the correlation of this new proxy with other independent data from the area: (1) ancient plant macroremains from archaeological sites as ecological indicators, (2) stable carbon isotope composition of ancient plant macroremains available in the literature and from our own investigations in six mid-Holocene archaeological sites, and (3) modelled Holocene precipitation and temperature changes in the northern Fertile Crescent. Comparison involved selected palynological and isotopic data from lacustrine sediments as well as speleothem isotopic records in Near Eastern locations available in the literature. Although the data show a certain amount of variation of proxy records on the regional scale, for the northern Fertile Crescent (Upper Mesopotamia) they suggest three pronounced features of the Holocene environmental history: (1) a trend toward warmer temperatures may have affected the area during the early Holocene (between ca. 10,000–6000 cal BP), (2) increased moisture availability and relatively high temperatures in the mid-Holocene (ca. between 5000 and 4000 cal BP), and (3) a significant decrease in moisture availability around 4000 cal BP.Further research is needed to enhance the chronological resolution of both pedogenic carbonate and plant macrofossil records. This study stresses the complexity of the Holocene palaeogeography of the Near East and underlines the need for careful analysis of local sources of palaeonvironmental information in the region.     

Atmospheric and Coupled Model Intercomparison in Terms of Amplitude Phase Characteristics of Surface Air Temperature Annual Cycle

A model intercomparison in terms of surface air temperature annual cycle ampitude-phase characteristics(SAT AC APC)is performed. The models included in the intercomparison belong to two groups:five atmospheric models with prescribed sea surface temperature and sea ice cover and four coupled models forced by the atmospheric abundances of anthropogenic consituents (in total six coupled model simulations). Over land, the models, simulating higher than observed time averaged SAT,also tend to simulate smaller than observed amplitude of its annual and semiannual harmonics and (outside the Tropics laterthan-observed spring and autumn moments. The models with larger(smaller) time averaged amplitudes of annual and semiannual harmonics also tend to simulate larger(smaller)interannual standard deviations. Over the oceans, the coupled models with larger interannual standard deviations of annual mean SAT tend to simulate larger interannual standard deviations of both annual and semiannual SAT harmonics amplitudes. Most model errors are located in the belts 60°-70°N and 60°-70°S and over Antarctica. These errors are larger for those coupled models which do not employ dynamical modules for sea ice.No systematic differences are found in the simulated time averaged fields of the surface air temperature annual cycle characteristics for atmospheric models on one hand and for the coupled models on the other. But the coupled models generally simulate interannual variability of SAT AC APC better than the atmospheric models (which tend to underestimate it). For the coupled models, the results are not very sensitive to the choice of the particular scenario of anthropogenic forcing.There is a strong linear positive relationship between the model simulated time averaged semiannual SAT harmonics amplitude and interannual standard deviation of annual mean SAT.It is stronger over the tropical oceans and is weaker in the extratropics. In the tropical oceanic areas, it is stronger for the coupled than for the atmospheric models.