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The geomagnetic field one can measure at the Earth’s surface or on board satellites is the sum of contributions from many different sources. These sources have different physical origins and can be found both below (in the form of electrical currents and magnetized material) and above (only in the form of electrical currents) the Earth’s surface. Each source happens to produce a contribution with rather specific spatio-temporal properties. This fortunate situation is what makes the identification and investigation of the contribution of each source possible, provided appropriate observational data sets are available and analyzed in an adequate way to produce the so-called geomagnetic field models. Here we provide a general overview of the various sources that contribute to the observed geomagnetic field, and of the modern data that enable their investigation via such procedures. The Earth has a large and complicated magnetic field, a major part of which is produced by a self-sustaining dynamo operating in the fluid outer core. What is measured at or near the surface of the Earth, however, is the superposition of the core field and of additional fields caused by magnetized rocks in the Earth’s crust, by electric currents flowing in the ionosphere, magnetosphere and oceans, and by currents induced in the Earth by the time-varying external fields. The sophisticated separation of these various fields and the accurate determination of their spatial and temporal structure based on magnetic field observations is a significant challenge, which requires advanced modeling techniques (see e.g., Hulot et al. 2007). These techniques rely on a number of mathematical properties which we review in the accompanying chapter by Sabaka et al. (2010), entitled “Mathematical Properties Relevant to Geomagnetic Field Modelling”. But as many of those properties have been derived by relying on assumptions motivated by the nature of the various sources of the Earth’s magnetic field and of the available observations, it is important that a general overview of those sources and observations be given. This is precisely the purpose of the present chapter. It will first describe the various sources that contribute to the Earth’s magnetic field (Sect. 1) and next discuss the observations currently available to investigate them (Sect. 2). Special emphasis is given on data collected by satellites, since these are extensively used for modeling the present magnetic field. We will conclude with a few words with respect to the way the fields those sources produce can be identified and investigated, thanks to geomagnetic field modeling. E-mail: nio@space.dtu.dk

The research project LOTSE-CHAMP/GRACE (Long time series of consistently reprocessed high-accuracy CHAMP/GRACE data products) has the overall goal to reprocess all CHAMP and GRACE gravity, magnetic and atmospheric mission data. The reprocessing will provide a 10 years long, consistent and high-quality time series of (a) static and time variable gravity field models describing the mass distribution and mass variation in the system Earth, (b) atmospheric parameters such as mean global temperatures or tropopause altitudes and (c) the state and change in the Earth’s outer core and lithospheric magnetic field during the CHAMP (2000–2010) and/or GRACE (since 2002) mission life time. These consistent data sets are used by the national and international user community as a valuable and complementary source of information for global change analysis such as monitoring of the continental hydrological cycle, polar ice mass loss, sea level change or monitoring of global temperature variations, as well as for geological and tectonic studies.

The D\(^{\prime \prime }\) region, which lies in the lowermost few hundred kilometres of the mantle, is a central cog in the Earth’s heat engine, influencing convection in the underlying core and overlying mantle. In recent years dense seismic networks have revealed a wealth of information about the seismic properties of this region, which are distinct from those of the mantle above. Here we review observations of seismic anisotropy in this region. In the past it has been assumed that the region exhibits a simple form of transverse isotropy with a vertical symmetry axis (VTI anisotropy). We summarise new methodologies for characterising a more general style of anisotropy using observations from a range of azimuths. The observations can be then used to constrain the mineralogy of the region and its style of deformation by a lattice preferred orientation (LPO) of the constituent minerals. Of specific interest is the recent discovery of the stability of the post-perovskite phase in this region, which might explain many enigmatic properties of D\(^{\prime \prime }\). Mantle flow models based on density models derived from global tomographic seismic velocity models can be used to test plausible mineralogies, such as post-perovskite, and their deformation mechanisms. Here we show how linked predictions from mineral physics, geodynamical modelling and seismic observations can be used to better constrain the dynamics, mineralogy and physical properties of the lowermost mantle.

The solar system formed about 4.6 billion years ago. The Earth and other terrestrial planets are believed to have formed by gathering together the so-called planetesimals. Planetesimals are formed by the coalescence of fine- or coarse-grained mineral matters, metals, and gases of various kinds (such as mentioned in the previous chapter). As planetesimals stuck together mostly by gravity and the body thus formed grew larger, it became a precursor of terrestrial planet. Some of these bodies were smashed by other bodies, and their fragments became meteorites. Hence, studies of meteorites would provide a lot of insight into the formation and the earlier state of the Earth.

On decadal time scales, there are three major physical processes in the Earth’s outer core that contribute to gravity variations: (i) the mass redistribution due to advection in the outer core, (ii) the mantle deformation in response to (i), and (iii) the (core) pressure loading on the core-mantle boundary. Except the last one, they cannot be evaluated from surface observations. In this paper we use MoSST core dynamics model and PREM model to understand the gravity anomalies from the three processes. Our numerical results show that, the gravity anomalies are comparable in magnitude, though that from the process (i) is in general the strongest. The gravity anomalies from the first two processes tend to offset each other (“mantle shielding”). Consequently the pressure loading effect contributes more to axisymmetric part of the net gravity variation, while the net effect from the first two processes is more important to non axisymmetric components.

This chapter deals with several applications of the basic thermodynamic relations developed so far to problems relating to the properties and processes in the Earth’s interior, from shallow crustal level to the lower mantle and core, supplemented by an overview of the interior of the Earth. The specific topics include thermal pressure with applications to the core of the Earth and magma-hydrothermal systems, relationship between elastic properties of solids and seismic wave velocities with applications to radial density variation in the Earth’s core and mantle, adiabatic flow processes with applications to geyser eruption and upwelling of material and melting in the Earth’s interior, and thermal effect of volatile ascent.

This is a report on first steps for a combination of two numerical models of the evolution of the Earth’s mantle: The first one, K3, is a new 2-D convection-fractionation model that simulates the growth of continents and of the geochemically complementary depleted mantle reservoir. The second model shows the 3-D generation of oceanic lithospheric plates and subducting sheet-like downwellings in a spherical-shell mantle. Based on the abundances of the present-day geochemical reservoirs of Hofmann (1988) we developed a numerical dynamical model of convection and of chemical differentiation in the Earth’s mantle. It is shown that a growing and additionally laterally moving continent and a growing depleted mantle evolved from an initially homogeneous primordial mantle. The internal heat production density of the evolving mantle depends on the redistribution of the radioactive elements by fractionation and convection. The fractionation generates separate geochemical reservoirs. However, the convection blurs the reservoirs by mixing. Although we take into account also the effects of the two phase transitions in 410 and 660 km depth, it is essentially the dependence of the viscosity on radius which guarantees the conservation of the major geochemical reservoirs. This model has no internal compulsory conditions. The principal idea of this first model is to compute the relative viscosity variations as a function of depth from observable quantities. We develop a self-consistent theory using the Helmholtz free energy, the Ullmann-Pan’kov equation of state, the free volume Gruneisen parameter and Gilvarry’s formulation of Lindemann’s law. In order to receive the relative variations of the radial factor of the viscosity, we insert the pressure, P, the bulk modulus, K, and ∂K/∂P from PREM. For mantle layers deeper than 771 km we used the perovskite melting curve by Zerr and Boehler (1993, 1994) in order to estimate the relative viscosity. For the calibration of the viscosity we have chosen the standard postglacial-uplift viscosity beneath the continental lithosphere. Furthermore, we took into account the dependence of the viscosity on temperature and on the degree of depletion of volatiles. An essential first new result of this paper is a high-viscosity transition layer and a second low-viscosity layer below it. Although our model mantle is essentially heated from within, we assume additionally a small heat flow at the CMB. This is necessary because of the dynamo theory of the outer core. The second main result of this first model is a more distinct bipartition of the mantle in a depleted upper part and a lower part rich in incompatible elements, yet. This result is rather insensitive to variations of the Rayleigh number and of the thermal boundary condition at CMB. The different parts of this paper are closely connected by the algorithm. The continuation of the first finding leads to a 3-D, up to now purely thermal model of mantle evolution and plate generation. This second model was used to carry out a series of three-dimensional compressible spherical-shell convection calculations with another new, but related viscosity profile, called eta3, that is derived from PREM and mineral physics, only. Here, the Birch-Murnaghan equation was used to derive the Gruneisen parameter as a function of depth. Adding the pressure dependence of the thermal expansion coefficient of mantle minerals, we derived the specific heats, c p and c v, too. Using the Gilvarry formulation, we found a new melting temperature of the mantle and the new viscosity profile, eta3. The features of eta3 are a high-viscosity transition layer, a second low-viscosity layer beginning under the 660-km discontinuity, and a strong viscosity maximum in the central parts of the lower mantle. The rheology is Newtonian but it is supplemented by a viscoplastic yield stress, ∂ y. A viscosity-level parameter, r n, and ∂ y have been varied. For a medium-sized Rayleigh-number-yield-stress area, eta3 generates a stable, plate-tectonic behavior near the surface and simultaneously thin sheet-like downwellings in the depth. Outside this area three other types of solution were found. The presence of two internal low-viscosity layers and of ∂y is obviously conducive for plateness and thin sheet-like downwellings. The distribution of the downwellings is more Earth-like if the yield stress is added. The outlines of a combination of the two models have been discussed.

By using the realizable k-ɛ turbulence model and the SIMPLEC algorithm, numerical simulation was performed to investigate the vortices fields for the single, double and four round holes. The modified wall function method, two-layer model, was adopted to simulate the flow in the near-wall region and the outer core flow. We got the shear-layer vortices, the horseshoe vortices and the counter-rotating vortex pair (CVP) in different conditions. The results show that in the multiple jets, with sheltering from the former jet, the locations of the shear-layer vortices go up. The horseshoe vortices become appearing until the multiple jets merging into a new jet. As the shear-layer vortices break, the CVP forms. All the horseshoe vortices and wake vortices affect the developing of the CVP. After the multiple jets merging into a new jet, the shape of the CVP changes gradually and tends to be regular.

Population III (Pop III) stars are the first stars in the universe. They do not contain metals, and their formation and evolution may be different from that of stars of later generations. In fact, according to the theory of star formation, Pop III stars might have very massive components (~100-10000 M☉). In this paper, we compute the spherically symmetric gravitational collapse of these Pop III massive stars. We solve the general relativistic hydrodynamics and neutrino transfer equations simultaneously, treating neutrino reactions in detail. Unlike supermassive stars (105 M☉), the stars of concern in this paper become opaque to neutrinos. The collapse is simulated until after an apparent horizon is formed. We confirm that the neutrino transfer plays a crucial role in the dynamics of gravitational collapse and find also that the β-equilibration leads to a somewhat unfamiliar evolution of electron fraction. Contrary to the naive expectation, the neutrino spectrum does not become harder for more massive stars. This is mainly because the neutrino cooling is more efficient and the outer core is more massive as the stellar mass increases. Here the outer core is the outer part of the iron core falling supersonically. We also evaluate the flux of relic neutrinos from Pop III massive stars. As expected, the detection of these neutrinos is difficult for the currently operating detectors. However, if ever observed, the spectrum will enable us to obtain information on the formation history of Pop III stars. We investigate 18 models covering the mass range of 300-104 M☉, making this study the most detailed numerical exploration of spherically symmetric gravitational collapse of Pop III massive stars. This will also serve as an important foundation for multidimensional investigations.

Unlike proteins and polysaccharides, the lipids are not characterised by similarities in structure but by a commonly high hydrophobicity: they are therefore more or less insoluble in water, but exhibit good solubilities in hydrophobic organic solvents such as benzene, chloroform or ether. Thus, significant structural differences exist between the individual lipid groups.

The geodynamo, i.e. the process by which the Earth’s magnetic field is generated in the liquid outer core of the Earth, is generally regarded as one of the fundamental problems of geophysics. It is the prevailing opinion among geophysicists that thermal and chemical buoyancy originating in connection with the solidification of the inner core and the general cooling of the Earth cause convection flows in the outer core which consists of liquid iron together with some lighter elements. The mechanical energy of the convection flow provides the energy for the sustenance of the magnetic field against Ohmic losses. The mechanism by which this transfer of energy is accomplished is called a homogeneous dynamo in order to distinguish it from the common inhomogeneous dynamos used in technical applications.

Seismic data show that the Earth’s core consists of an outer part, which has all the properties of a liquid, and the inner core, which is solid. From cosmochemical, geophysical, and geochemcial considerations, the dominant species in the core has to be iron (over 90%). Although not experimentally shown, but based on the available data on the compressibility of iron, it appears that iron itself has a density higher than the density of the core. Shock-wave data demonstrate that the density of the outer core is 8-11% below that of Fe-Ni under similar pressure and temperature conditions, implying the presence of 5-16% of a light element. Sulfur (S) was suggested as a single light element of the core; but sulfur is a moderately volatile element and its abundance in the bulk Earth is related to the abundance of other similarly volatile elements. Arguments are presented that the content of sulfur in the bulk Earth is similar or even lower than that of zinc (Zn). This leads to an upper limit for the bulk Earth S-content of 0.56% and S-content for the core of 1.7%. This is not enough to decrease the density of pure iron at the pressures and temperatures of the Earth’s core. Therefore, the Earth’s core may contain several light elements. However, dilution of iron by addition of sulfur or another light element is not essential. The outer core is liquid because of the phase transformations in iron and its melting behavior. Thus, the problem of the Earth’s core condition is a problem of relationships of iron phases at high temperature and pressure.

Synthetic gravity tide parameters (amplitude factors and phase leads) have been computed for the waves MF, Q1, O1, P1, K1, N2, M2, S2 and K2 in a worldwide 1° x 1° grid at 26995 grid points located mainly on land. The gravity tide parameters have been derived from gravity tide amplitudes of the Tamura (1987) tidal potential referring to a rigid Earth model, body tide amplitude factors using a model of an ocean-free, elastic, rotating, isotropic and ellipsoidal Earth with liquid outer core (Wahr 1981, Dehant 1987), and from ocean tide gravitation and load using a 1° x 1° ocean tide model (Schwiderski 1980). The synthetic gravity tide parameters have been compared at 31 European gravity tide stations selected from the data base DB92 of the International Center for Earth Tides (Melchior 1994) and show rms differences of 0.79% and 0.87% for the amplitude factors and 0.24° and 0.48° for the phase leads of the main waves 01 and M2 resp.

The local air pressure series at Potsdam for the period 19741–990 is investigated with respect to persistent diurnal and semidiurnal waves as they appear in the gravity tides. The parameters of the diurnal air pressure waves show much more temporal variations than the semidiurnal ones. In that way gravity tidal waves near to the solar day may be influenced too.

The flow around a piston gliding in a rotating circular duct filled with a liquid is observed experimentally. For Re-numbers up to ≈ 1150 the flow is laminar and stationary. The streamline patterns in front and behind the body are 3-dimensional and of different structure. At increasing Re-numbers an oscillatory mode appears. It originates from the back wake of the body and is accompanied by a train of separated flow regions propagating slowty along the channel to the front wake where they disappear.

The first definitive measurements of EXAFS by monitoring the direct photoelectron emission as a function of photon energy have been made using the Mn 3p and F 2s core levels in evaporated films of MnF2 [1,2]. Good agreement is found with bulk transmission EXAFS obtained with the Mn Is level. This development is important because: (1) Almost all elements have suitable core levels of low binding energy. (2) Since photopeaks from adjacent core levels do not cross as the photon energy is varied, the limitation imposed on other EXAFS techniques by this interference is removed. Auger electrons, which have fixed kinetic energies and so can cross photo-peaks, will generally have low energies if they originate from the outer core levels and be unlikely to appear in the EXAFS region of kinetic energies, i. e., in excess of about 50 eV. (3) VUV light is used, which greatly extends the useable range of photon energies. (4) More than one element in a solid may be studied with the same monochromator.

The age of the earth is estimated through radiometric dating methods to be 4.6 billion years. In the time since its origin, the earth has undergone a continuous thermal evolution. The thermal state which it has now reached can be estimated by direct and indirect means. However the difficulties in estimating temperature increase rapidly with depth. At present it is difficult to plot an accurate temperature map for crustal depths of only 10 km even in well-studied areas. Given the uncertainty in calculating the exact present day thermal state, one can imagine the difficulties and uncertainties in describing the thermal evolution of our planet through its 4.6 billion-year history.

In the absence of internal energy sources and mechanical, gravitational or radiative interactions with other bodies, the solid parts of the Earth (i.e., crust, mantle and inner core) and the fluid parts (atmosphere, hydrosphere and outer core) would rotate together as a rigid body at a constant rate about its fixed axis of maximum moment of inertia through its centre of mass. Positional astronomers equipped with perfect telescopes and clocks (and the necessary life- support systems all, together with the astronomers, of zero mass!) would find no variation of the latitude of any station and the longitude of all fixed stars would change at a constant rate.

The interior of the Earth inaccessible to direct geological methods is studied by means of geophysical and geochemical techniques. The geophysical methods used include seismic, gravimetric, geothermic, geomagnetic, and geoelectric techniques. Geochemistry widely employs laboratory study of the properties of rocks at high temperatures and pressures. The behaviour of matter in conditions not amenable to experimental reproduction is studied on the basis of solid state theory.