A Model for the polar motion of the deformable Earth adequate for astrometric data

Refined analytical expressions for the frequencies corresponding to the Chandler motion of the pole and the diurnal rotation of the deformable Earth are derived. Numerical estimates of the period and amplitude of the polar oscillations are presented. The trajectory of the Chandler polar motion derived via numerical modeling is in qualitative and quantitative agreement with experimental data from the International Earth Rotation Service (IERS). An evolutionary model describing slow variations in the Earth’s rotation parameters under the action of the dissipative moments of the tidal gravitational forces on time scales considerably longer than the precession period of the Earth’s axis is constructed. The axis of the Earth’s figure tends to approach the angular momentum vector of the proper rotation.     

High-accuracy forecasting of the Earth’s polar motion

The fundamental astrometrical problem of high-accuracy interpolation of the trajectory of the Earth’s pole and construction of an adequate theoretical model for associated complex multifrequency oscillations are considered. Measurements of the Earth-rotation parameters demonstrate the possibility of adjusting the filtering algorithm to make it suitable for practical navigational applications associated with a need for reliable high-accuracy predictions over the required time scales (short-and medium-terms). Numerical simulations and tests of the procedure used to optimize the adjustment parameters are presented.     

A gravitational-tidal mechanism for the Earth’s polar oscillations

Perturbed, rotational-oscillational motions of the Earth induced by the gravitational torques exerted by the Sun and Moon are studied using a linear mechanical model for a viscoelastic rigid body. A tidal mechanism is identified for the excitation of polar oscillations, i.e., for oscillations of the angular-velocity vector specified in a fixed coordinate frame, attributed to the rotational-progressive motion of the barycenter of the Earth-Moon “binary planet” about the Sun. The main features of the oscillations remain stable and do not change considerably over time intervals significantly exceeding the precessional period of the Earth’s axis. A simple mathematical model containing two frequencies, namely, the Chandler and annual frequencies, is constructed using the methods of celestial mechanics. This model is adequate to the astrometric measurements performed by the International Earth Rotation Service (IERS). The parameters of the model are identified via least-squares fitting and a spectral analysis of the IERS data. Statistically valid interpolations of the data for time intervals covering from several months to 15–20 yr are obtained. High-accuracy forecasting of the polar motions for 0.5–1 yr and reasonably trustworthy forecasting for 1–3 yr demonstrated by observations over the last few years are presented for the first time. The results obtained are of theoretical interest for dynamical astronomy, geodynamics, and celestial mechanics, and are also important for astrometrical, navigational, and geophysical applications.     

Nonlinear stochastic correlation models for the pole’s motion of a deformable Earth

A combined stochastic correlation model for the pole’s motion of a deformable Earth is constructed using the data of the International Earth Rotation Service and dynamical Euler equations taking into account tidal deformations. The deterministic component of the model describes the main regular dynamical effects, while its stochastic component describes irregular effects obeying statistical laws. Linear differential (requiring solutions of ordinary differential equations), and finite (assuming integrated characteristics) correlation models are constructed for both Gaussian and non-Gaussian random parameters. The stochastic oscillations and trend of the Earth’s proper angular velocity are analyzed, as well as nonlinear stochastic oscillations and the trend of the pole. This approach can be considered quite novel.     

On climate changes in polar zones of the Earth in the twentieth and twenty-first centuries

Doklady Earth Sciences -     

The break-up of Rodinia,birth of Gondwana,true polar wander and the snowball Earth

A major global plate reorganisation occurred between ∼750 and ∼550 Ma. Gondwana was assembled following the dispersal of Rodinia, a supercontinent centred on Laurentia in existence since ∼1050 Ma. The reorganisation began when tectonic elements, later composing East Gondwana, rotated piecemeal away from the Pacific margin of Laurentia. These elements swept across the ancestral Pacific (Mozambique) Ocean that lay between Laurentia and the combined African cratons of Congo and Kalahari, which were loosely joined after ∼820 Ma. Simultaneously, the Adamastor (Brasilide) Ocean closed by subduction bordering the West Gondwana cratons, drawing virtually all of Gondwana together by ∼550 Ma. The final assembly of Gondwana occurred contemporaneously with the separation of Laurentia from West Gondwana.It has been postulated that the imprint of Rodinia's long-lived existence on lower mantleconvection produced a prolate ellipsoidal geoid figure. This could give rise to episodic inertial interchange true polar wander (IITPW), meaning that the entire silicate shell of the Earth (above the core-mantle boundary) rolled through 90° with respect to the diurnal spin axis in ∼15 Ma (equivalent to an apparent polar wander velocity of ∼66 cm a⁻¹. Although empirical arguments for IITPW of Cambrian age appear to be flawed, evidence for an ultra-fast ( > 40 cm a⁻¹) meridional component of apparent polar wander for Laurentia between 564 and 550 Ma suggests that IITPW might have occurred at that time.The break-up of Rodinia increased the continental margin area and preferential organic C burial globally, which is reflected by high δ¹³C values in seawater proxies. The consequent drawdown of CO₂ is implicated in a succession of runaway ice-albedo catastrophes between ∼750 and ∼570 Ma, during each of which the oceans completely froze over. Each “snowball” Earth event must have lasted for millions of years because their terminations depended on extreme CO₂ levels, built up by subaerial volcanic outgassing in the absence of sinks for C. A succession of ice-albedo catastrophes, each terminated under ultra-greenhouse conditions, must have imposed an intense environmental filter on the evolution of life. They may have triggered the radiation of Ediacaran fauna in the aftermath of the final snowball event. It is increasingly recognised that the Late Neoproterozoic was one of the most remarkable periods in Earth history, and it appears to exemplify the interplay of tectonics, the environment and biology in deep time.     

Simple shear of deformable square objects

Finite element models of square objects in a contrasting matrix in simple shear show that the objects deform to a variety of shapes. For a range of viscosity contrasts, we catalogue the changing shapes and orientations of objects in progressive simple shear. At moderate simple shear (γ=1.5), the shapes are virtually indistinguishable from those in equivalent pure shear models with the same bulk strain (R_S=4), examined in a previous study. In theory, differences would be expected, especially for very stiff objects or at very large strain. In all our simple shear models, relatively competent square objects become asymmetric barrel shapes with concave shortened edges, similar to some types of boudin. Incompetent objects develop shapes surprisingly similar to mica fish described in mylonites.     

波浪作用下考虑海床变形影响的溶质运移数值模拟

波浪会促进海水中溶质向海底沉积物运移,但已有研究大多未考虑海床（海底沉积物）变形效应的影响。为揭示波浪作用下海床土变形对溶质运移过程的影响机制,构建了考虑海床土变形影响的溶质运移计算模型,对波浪作用下溶质向砂质海底沉积物中的运移过程进行模拟。结果表明:海床土变形会增大孔隙水流速,进而增大溶质纵向水动力弥散系数,增强溶质运移的机械弥散作用,促进溶质向沉积物中运移;考虑海床变形时的溶质最大纵向水动力弥散系数可达不考虑海床变形时的8.5倍,约为分子扩散系数的545倍;海床土剪切模量越小,土体变形效应越明显,对溶质运移过程的影响越大;海床土饱和度的降低,会进一步加速波浪作用下溶质向海底沉积物的运移过程。     

Microplate motions in the hotspot reference frame

We have computed motions of the major plates (seven large plates and seven medium‐sized plates) and 38 microplates relative to the hotspot reference frame, and present velocities of these 52 plates. Moreover, using updated plate boundaries for the present, we have computed new geometrical factors for plates and microplates, useful for kinematic calculations and to obtain the net‐rotation of the lithosphere and plate velocities in the mean‐lithosphere reference frame. Instead of a continuum or gradational distribution of the plates by size, the plates clearly partition into three groups each having their own characteristics. For the seven large plates, rotation poles generally lie in high latitudes; the seven medium‐sized plates have rotation poles in a restricted equatorial area; the 38 small plates show the greatest scatter. Moreover subsets of the 52 plates reveal differing fractal behaviour: the large, middle and small groupings each have a characteristic fractal dimension, suggestive of microplate clustering. The highest angular velocities occur for some of the smallest plates, with the location of their rotation poles closeby. Terra Nova, 18, 276–281, 2006     

The lower atmosphere of the polar regions

Alfred Wegener initiated the study of the free polar atmosphere with more than 100 kite and tether balloon soundings to above 3000 m at Danmarkshavn, North Greenland, during 1906–09. From this beginning polar aerology advanced through a series of similar point studies to the first full upper air network during the IGY (1957/8). While its replacement by satellite remote sensing is gradually taking shape, the accumulated polar information has been thoroughly analyzed; a series of comprehensive accounts is referenced. The aspects singled out for this review are themes that would have been of special interest to Wegener — the surface energy balance and the polar inversion, the katabatic winds and snow drift, and the aerosols of the polar atmosphere.

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Zusammenfassung Alfred Wegener begann das Studium der freien Polaratmosphäre mit über 100 Drachen- und Fesselballonaufstiegen auf Höhen über 3000 m bei Danmarkshavn in Nordgrönland während der Jahre 1906–1909. Von diesem Anfang entwickelte sich die Polaraerologie durch eine Reihe ähnlicher Lokalstudien bis zum ersten vollständigen Beobachtungsnetz der freien Atmosphäre während des IGY (1956–8). Während des allmählichen Ersatzes dieses Systems durch Fernmessungen von Satelliten aus wurde die angesammelte Polarinformation gründlich analysiert; eine Reihe von umfassenden Berichten wird angeführt. Die hier behandelten Studien wären für Wegener von besonderem Interesse gewesen, da sie die Energiebilanz der Oberfläche und die Polarinversion, den katabatischen Wind und das Schneetreiben, und das Aerosol der Polaratmosphäre betreffen.

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Résumé C'est Alfred Wegener qui a commencé l'étude de l'atmosphère polaire par des sondages à l'aide de cerfs-volants et de ballons attachés jusqu'à une hauteur de 3000 m. à Danmarks-Havn au Groenland nord, de 1906 à 1909. Après ce début l'aérologie polaire se développa sur la base d'études locales jusqu'à l'établissement d'un premier réseau de stations d'observations pendant l'année géophysique internationale 1957–58. La recherche exposée ici aurait probablement intéressé Wegener car elle se rapporte à la balance énergétique de surface et à l'inversion polaire, aux vents katabatiques, à le chasse neige et aux aérosols de l'atmosphère polaire.

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2011年度海洋与极地科学领域基金项目的受理与评审

12011年度申请项目受理和同行通讯评议情况 1．1项目受理情况2011年地球科学四处（资助范围：海洋科学与极地科学）共受理申请项目1193项,其中包括面上项目635项、青年基金项目551项和地区基金项目7项,申请项数比2010年增加21．5％。     

New theory of the Earth

From time to time the phrase ＇Theory of the Earth＇ occurs among titles in Earth science history. It usually happens after times of changing major scientific paradigms. A first peak occurred in the Renaissance at the time of the origin of modern science with the introduction of the word geology by Ulisse Aldrovandi in 1603; and the phrase moved around in the controversy about the origin of marine fossils found in mountains, with works by Alessandro degli Alessandri （about 1500）, Girolamo Cardano （1550）, Gabriele Falloppio （1564）, Bernard Palissy （1580）, Andrea Cesalpino （1596）, and Simeone Maioli （1597）.     

The composition of the Earth

Compositional models of the Earth are critically dependent on three main sources of information: the seismic profile of the Earth and its interpretation, comparisons between primitive meteorites and the solar nebula composition, and chemical and petrological models of peridotite-basalt melting relationships. Whereas a family of compositional models for the Earth are permissible based on these methods, the model that is most consistent with the seismological and geodynamic structure of the Earth comprises an upper and lower mantle of similar composition, an Fe---Ni core having between 5% and 15% of a low-atomic-weight element, and a mantle which, when compared to CI carbonaceous chondrites, is depleted in Mg and Si relative to the refractory lithophile elements.The absolute and relative abundances of the refractory elements in carbonaceous, ordinary, and enstatite chondritic meteorites are compared. The bulk composition of an average CI carbonaceous chondrite is defined from previous compilations and from the refractory element compositions of different groups of chondrites. The absolute uncertainties in their refractory element compositions are evaluated by comparing ratios of these elements. These data are then used to evaluate existing models of the composition of the Silicate Earth.The systematic behavior of major and trace elements during differentiation of the mantle is used to constrain the Silicate Earth composition. Seemingly fertile peridotites have experienced a previous melting event that must be accounted for when developing these models. The approach taken here avoids unnecessary assumptions inherent in several existing models, and results in an internally consistent Silicate Earth composition having chondritic proportions of the refractory lithophile elements at 2.75 times that in CI carbonaceous chondrites. Element ratios in peridotites, komatiites, basalts and various crustal rocks are used to assess the abundances of both non-lithophile and non-refractory elements in the Silicate Earth. These data provide insights into the accretion processes of the Earth, the chemical evolution of the Earth's mantle, the effect of core formation, and indicate negligible exchange between the core and mantle throughout the geologic record (the last 3.5 Ga).The composition of the Earth's core is poorly constrained beyond its major constituents (i.e. an Fe---Ni alloy). Density contrasts between the inner and outer core boundary are used to suggest the presence ( 10 ± 5%) of a light element or a combination of elements (e.g., O, S, Si) in the outer core. The core is the dominant repository of siderophile elements in the Earth. The limits of our understanding of the core's composition (including the light-element component) depend on models of core formation and the class of chondritic meteorites we have chosen when constructing models of the bulk Earth's composition.The Earth has a bulk Fe/Al of 20 ± 2, established by assuming that the Earth's budget of Al is stored entirely within the Silicate Earth and Fe is partitioned between the Silicate Earth ( 14%) and the core ( 86%). Chondritic meteorites display a range of Fe/Al ratios, with many having a value close to 20. A comparison of the bulk composition of the Earth and chondritic meteorites reveals both similarities and differences, with the Earth being more strongly depleted in the more volatile elements. There is no group of meteorites that has a bulk composition matching that of the Earth's.     

Tectonic map of the Earth

The regions of continental and oceanic crust are marked on the tectonic map of the World compiled by the author. Within the limits of the former the author indicates the Alpine geosynclines; the Alpine platforms outside these regions are divided into parts according to the age of the folded basement.The platforms have anticlises and syneclises marked on them, as well as the regions of tectonic activisation. The author proceeds from the conception that the history of the Earth had two stages. The first one is the geosyncline-platform or the granite stage, and it is characterised by the formation of the granitic continental crust. The second or basalt stage is marked by the rise of overheated basalts from the deep layers of the mantle. On the surface it is manifested in tectonic activisation, in extrusions of plateau-basalts and in oceanisation, which is associated with the secondary transformation of the granite-basalt continental crust into the water-basalt oceanic crust.

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Zusammenfassung Auf der vom Verfasser aufgestellten tektonischen Karte der Welt sind die Gebiete mit Kontinental- und Ozeankruste angegeben. Im Rahmen der Gebiete mit Kontinentalkruste sind die alpidischen Geosynklinalen gezeigt; die außer diesen Gebieten liegenden alpidischen Plattformen sind nach dem Alter des gefalteten Grundgebirges aufgeteilt. Die Plattformen teilen sich in Antiklisen und Syneklisen; es sind auch die Gebiete der tektonischen Aktivierung gezeigt. Der Verfasser legt dabei die Vorstellung zugrunde, daß die Geschichte der Erdkugel in zwei Stadien zu teilen ist. Das erste Stadium, das als Geosynklinalen- und Plattform-Stadium oder Granitstadium bezeichnet werden kann, ist durch die Bildung der Kontinentalkruste aus Granit gekennzeichnet. Das zweite Stadium, das sog. Basaltstadium, besteht im Aufstieg überhitzter Basalte aus den tiefen Schichten des Mantels. Auf der Oberfläche kommt dieses Stadium in der tektonischen Aktivierung, im Erguß von Plateau-Basalten und in der Bildung der Ozeane zum Ausdruck, die die sekundäre Umwandlung von granit-basaltischer Kontinentalkruste in wasser-basaltische Ozeankruste begleiten.

     

Analysis of a deformable fracture in permeable material

The response of deformable fractures to changes in fluid pressure controls phenomena ranging from the flow of fluids near wells to the propagation of hydraulic fractures. We developed an analysis designed to simulate fluid flows in the vicinity of asperity‐supported fractures at rest, or fully open fractures that might be propagating. Transitions between at‐rest and propagating fractures can also be simulated. This is accomplished by defining contact aperture as the aperture when asperities on a closing fracture first make contact. Locations on a fracture where the aperture is less than the contact aperture are loaded by both fluid pressure and effective stress, whereas locations where the aperture exceeds the contact aperture are loaded only by fluid pressure. Fluid pressure and effective stress on the fracture are determined as functions of time by solving equations of continuity in the fracture and matrix, and by matching the global displacements of the fracture walls to the local deformation of asperities. The resulting analysis is implemented in a numerical code that can simulate well tests or hydraulic fracturing operations. Aperture changes during hydraulic well tests can be measured in the field, and the results predicted using this analysis are similar to field observations. The hydraulic fracturing process can be simulated from the inflation of a pre‐existing crack, to the propagation of a fracture, and the closure of the fracture to rest on asperities or proppant. Two‐dimensional, multi‐phase fluid flow in the matrix is included to provide details that are obscured by simplifications of the leakoff process (Carter‐type assumptions) used in many hydraulic fracture models. Execution times are relatively short, so it is practical to implement this code with parameter estimation algorithms to facilitate interpretation of field data. Copyright © 2006 John Wiley & Sons, Ltd.     

The motions of galaxies in the field of the cosmic vacuum

The general solution and general integral of the equations of motion in the field of the cosmic vacuum are constructed. It is shown that the resulting motions of galaxies are along either hyperbolic or rectilinear paths. The laws of motion of galaxies in the field of the cosmic vacuum are formulated. Various forms of the Hubble law are considered. A strict adherence to the Hubble law is not possible for most initial conditions in the sense of the Lebesgue measure. Therefore, it becomes meaningless to search for explanations to deviations from the Hubble law due to any physical factor, apart from the repulsive force of the cosmic vacuum. Phase portraits for the galaxy motions are constructed. It is shown that the Hubble constant should be determined observationally using the most distant galaxies, since the accuracy of the result will be reduced otherwise.     

Deformation of particles developed around rigid and deformable nuclei

The deformation of particles developed around rigid and deformable nuclei e.g., oolites, is investigated theoretically by considering the motion of the viscous fluid within the particles during deformation. It is postulated that the deformed shapes of these particles are influenced by the development of stagnation points around the nuclei. The shape changes of these particles are studied experimentally using an ethyl cellulose—benzyl alcohol solution to represent both the matrix and the particles developed around rigid or highly viscous nuclei. The models were subjected to pure-shear, simple-shear and irrotational non-plane strain deformation and the experimental model deformation is compared with naturally deformed particles. The deformed shapes of particles with nuclei of different competencies differ greatly from that of particles without nuclei; the differences depending on the viscosity difference of the two media and the relative size of the nuclei as compared to the size of the particles enclosing it. For both pure-shear and simple-shear deformation, the shapes of these particles would approximate to that of constrictional (prolate) ellipsoids. Irrotational non-plane strain deformation could, depending on the deformation paths, result in these particles having shapes which are more flattened (oblate) or more constrictional (prolate) than homogeneous particles subjected to the same deformation.     

Effects of instability of the Earth and celestial coordinate systems on Earth orientation parameters

Unknown secular and long-term changes in the Earth orientation parameters attributed to instability (possible rotation) of both the Earth and celestial coordinate systems (ECS and CCS) are studied. Rotation of the CCS due to changes in the coordinates of extragalactic sources resulting from gravitational lensing can lead to errors of the order of several microarcseconds in the orientation parameters. The rotation of the ECS due to the crust pressing on the mantle diminishes the tidal retardation of the Earth's rotation and produces long-term variations in the duration of the day (with a period of about 1500 years) and in the motion of the pole relative to the Earth's surface.