For a chosen threshold value = 5 (cf. Eq. (7)), the in- version scheme converged after 5 iterations. Figure 4 shows the convergence of the C-responses. The recovered con- ductivity model in comparison to the (laterally averaged) target model is shown in Fig. 5. Lateral averaged conduc- tivity here denotes the arithmetic mean of the conductivity of all cells in the respective layer. The results indicate that the inversion scheme is able to accurately recover mantle conductivity at all depths. Although the conductivity of the initial model is very different from the target conductivity structure, the ﬁnal model agrees well with the target model. Due to the applied smoothing, the recovered model does not comprise the large jumps in conductivity that are apparent in the target model at depths of 400 km and 700 km. Such large jumps in conductivity are, however, not likely for true Earth.
The study of lateral variability in physical properties of Earth’s mantle using geophysical methods is a topic of mod- ern fundamental science as it gives insight into geodynamic processes such as mantle convection, the fate of subducting slabs and the origin of continents. Global seismic tomogra- phy (cf. Li and Romanowicz, 1995; Woodhouse and Tram- pert, 1995; Su and Dziewonski, 1997; Ritsema et al., 1999; Bijwaard and Spakman, 2000; Deschamps et al., 2002) pro- vides today a variety of three-dimensional (3-D) mantle ve- locity models which can be interpreted in terms of cratonic roots, mantle plumes and slab graveyards.
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Most of these methods work in the frequency domain, for which the EM induction equation is solved at discrete time-harmonics. The time-domain approaches introduced by Hamano (2002) and Vel´ımsk´y and Martinec (2005) al- low to model EM induction due to transient excitation. This paper presents the development of a 3-D time-domain inver- sion scheme tailored for the upcoming Swarm multisatellite mission as part of the Swarm Satellite Constellation Appli- cation and Research Facility (Olsen et al., 2013, SCARF). The algorithm uses the time-series of external ﬁeld Gauss coefﬁcients, and their induced counterparts, obtained by the comprehensive inversion (Sabaka et al., 2013, CI) of Swarm satellite and ground observatory data, and inverts them in terms of 3-D electrical conductivity structure in the Earth’s mantle.
The earth dynamic system is one of the key scientific questions on the earth science. The thermodynamic behavior and gravity force of the earth and the rheology nature of the mantle prove that mantle convection is the main power source leading the lithosphere to break and move. Yet the directivity of both the structures in the crust and plate movement reminds of the earth rotation. Here we demonstrate that the mantle convection and inertia force of the earth rotation affect each other, the former being the power source of lithosphere plate break and motion, and the latter determining the direction of the mantle convection and plate motion. The sense of plate motion depends on the mantle upwells, whose trends are controlled by the earth rotation. The geometric shapes of the plate boundaries can adjust the direction of plate movement.
Mapping the three-dimensional (3-D) electrical conductivity of Earth’s mantle has been identiﬁed as one of the primary scientiﬁc objectives for the Swarm satellite mission. We present a 3-D frequency domain inversion scheme to recover mantle conductivity from satellite magnetic data. The scheme is based on an inversion of time spectra of internal (induced) spherical harmonic coefﬁcients of the magnetic potential due to magnetospheric sources. Time series of internal and external (inducing) coefﬁcients, whose determination is a prerequisite for this formulation, will be available as a Swarm Level-2 data product. An iterative gradient-type (quasi-Newton) optimization method is chosen to solve our 3-D non-linear inverse problem. In order to make the inversion tractable, we elaborate an adjoint approach for a fast and robust calculation of the data misﬁt gradient. We verify our approach with synthetic, but realistic time spectra of internal coefﬁcients, obtained by simulating induction due to a realistic magnetospheric source in a 3-D conductivity model of the Earth. In these model studies, both shape and conductivity of a large-scale conductivity anomaly in the mid-mantle are recovered very well. The inversion scheme also shows to be robust with respect to noise and is therefore ready to process Swarm data. Key words: 3-D electromagnetic induction, 3-D inversion, mantle conductivity anomalies, frequency domain.
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data from the plasma mantle, some conditions are consequently implemented to remove magnetosheath, cusp and polar cap data. The polar cap is usually associated with low-energy ions in contrast to the plasma mantle composed mainly of ener- getic solar particles, meaning these two regions can be distinguished by the ratio between the thermal pressure and the magnetic pressure called the plasma β . In the polar cap, plasma β is typically around 0.05 and conse- quently our constraint is β > 0.1 to avoid polar cap data (see e.g. Liao et al. 2010, 2015; Haaland et al. 2017). More- over, several studies, such as Nilsson et al. (2006), Kistler et al. (2006), Slapak et al. (2017), have shown that the plasma sheet and plasma mantle populations have similar plasma β but can be distinguished by their density and temperature. Thus, we excluded the plasma sheet popula- tion by setting the proton perpendicular temperature to T ⊥ (H
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Neither Davies (1988), Sleep (1990), nor King and Allen (2014) attempted to answer what would seem to be a key question: just how much hotter are plumes? McKenzie (1984) estimated that the Hawaiian plume needed to be some 200 °C hotter than mantle beneath mid-ocean ridges to produce the volume of basalt observed. Klein and Langmuir (1987) showed that MORB chemistry, specifically sodium and iron contents that are sensitive to the degree and depth of melting, correlated with ridge depth such that high extents and greater depths of melting were associated with shallower ridge depths. They concluded that both the Na and Fe variations resulted from variations in mantle temperatures of as much as 250 °C beneath the mid-ocean ridges. The highest temperatures were invariably associated with near hot spots such as Iceland. Wyllie (1988) estimated that the Hawaiian plume was perhaps 300 °C hotter than mantle beneath mid-ocean ridges. A decade later, Herzberg and O’Hara (1998) estimated that the Hawaiian plume was “200 to 250 °C hotter than present day ridges” while Iceland was only 100 to 150 °C hotter. Putirka et al. (2007) used a recalibrated olivine geothermom- eter to calculate melt temperatures and then derive mantle potential tempera- ture. They found the mantle potential temperature beneath mid-ocean ridges is 1454±81 °C and that the potential temperature of the Hawaiian and Samoan plumes are identical at 1722 °C and the Iceland plume has a potential tempera- ture of 1616 °C. These translate into excess temperatures of 268 °C and 162 °C, respectively, in overall good agreement with earlier studies. Niu et al. (2011) argued that at least some of the difference between the estimated temperatures between Iceland and Hawaii was due to differences in lithospheric thickness between Iceland and the other hot spots because this thickness controls the depth of last equilibration between mantle and melts. Herzberg et al. (2007) found lower potential temperatures for ambient mantle, in the range of 1280-1400 °C, but nevertheless conclude that plumes are typically 200-300 °C hotter. Herzberg and Asimow (2008) estimated mantle excess potential temperatures for a variety of other plumes and found that they fell, with scatter, between those for Hawaii (~200 °C) and Iceland (~100 °C). These estimates are generally in good agree- ment with studies that use entirely different approaches, such as the width of the geochemical anomaly along ridges (Schilling, 1991) and melt production, excess topography and geoid height (Watson and McKenzie, 1991).
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data are required to examine low frequency variations. Sec- ond, simultaneous data from many stations are required to make global analyses. Third, station locations should be distributed as uniformly as possible over the Earth. Loca- tions of stations considered in this paper are given in Table 1, and their distribution is shown in Fig. 1. Unfortunately, the third requirement is by no means satisfied as is evident by no entry from good stations existing in Australia, because of more emphasis on the other two requirements, which are more important in the present study.
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that observed. This suggested that the sub-IBM arc crust and uppermost mantle may be composed of these lithol- ogies, which have evolved through the processes shown in Fig. 4. In this case, the Moho discontinuity, which de- fines the boundary between the crust and mantle, may be the boundary between the remaining basaltic, initial arc crust and the restite of crustal melting following the extraction of rhyolitic melts. However, this interpretation requires the crustal component, which is a restite of crustal melting and thus originally forms within the crust (above the Moho), to be transferred to the upper mantle and consequently crossing, and then distributed below the Moho. If so, this confirms the previous sug- gestion of Tatsumi et al. (2008) that the sub-arc Moho is not a rigid material boundary between crust and mantle materials but is chemically transparent and permeable to crustal components.
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Many studies, using full dynamic models of mantle con- vection, have demonstrated that the mineralogical solid- solid endothermic phase transition at 660 km depth and/or exothermic phase transition at 410 km depth have a signif- icant inﬂuence on the behavior of convection in the Earth’s mantle. Their studies have been done in convection models with the uniform or pressure- (depth-) dependent viscosity (e.g., Christensen and Yuen, 1985; Machetel and Weber, 1991; Peltier and Solheim, 1992; Zhao et al., 1992; Tack- ley et al., 1993; Steinbach et al., 1993; Weinstein, 1993; Honda et al., 1993; Tackley et al., 1994; Steinbach and Yuen, 1994; Nakakuki and Fujimoto, 1994; Yuen et al., 1994; Solheim and Peltier, 1994a, 1994b; Ita and King, 1994; Monnereau and Rabinowicz, 1996; Tackley, 1996b; Bunge et al., 1997; Steinbach and Yuen, 1997; Cserepes and Yuen, 1997; Cserepes and Yuen, 2000; Cserepes et al., 2000), and the temperature-dependent viscosity, (e.g., Zhong and Gurnis, 1994; Nakakuki et al., 1994; King and Ita, 1995; Steinbach and Yuen, 1995, 1997; Brunet and Ma- chetel, 1998; Brunet and Yuen, 2000). Because of the na- ture of uniform or weakly temperature-dependent viscos- ity, they have shown that the cold downwelling plumes fre- quently arise from surface boundary layer of the convecting vessel and easily deﬂect at the endothermic 660 km phase
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With the widening of the expansion belt, the lithogenetic new oceanic crust is like a carrying pole, which car- ries two old oceanic crusts. Due to that the oceanic crust is in total submergence, the diagenesis of new oceanic crust stops the magma of the earth’s mantle from uplifting. Under the buoyancy influence of the high-density magma of the earth’s mantle, it will generate two consequences for the new oceanic crust, one is that the old oceanic crusts on the two sides of the expansion belt uplift, thus forming the upheaval of the expansion belt, which is called the oceanic ridge; the other is that the new oceanic crust body bends under stress, thus entering the phase of top mounting.
Because of the smallest period of CoRoT-7b found for a planet around another star the temperatures will be extremely high on its surface. Estimations for the temperatures on the day side (Schneider ) lead to a temperature of about 2000 K depending on the rotation of the planet; due to the vicinity to the star a bounded rotation is very probable. This would mean that the silicate surface consists of lava and the planets’ atmosphere of evaporated silicates. On the contrary the far side could be in the temperature range such that water could be liquid or even be present on its surface in form of ice. In Fig. 19 there is a sketch of this planet where bounded rotation because of the acting tides of the star is assumed. This –
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∂t + ( u · ∇) p = −γ · p ∇ u , (5) where γ and g are the specific heat ratio of the gas and the gravitational acceleration of a planet, respectively. Boldface symbols in the text and equations denote vector quantities. Our code is based on the algorithm CIP (Cubic Interpolated Propagation: Yabe and Aoki, 1991; Yabe et al., 1991). The CIP scheme is a kind of semi-Lagrangean finite dif- ference scheme. In this scheme, the hydrodynamic equa- tions (3)–(5) are split into two phases, the advection phase and the non-advection phase, with respect to the physical values (ρ, p and u) and their spatial derivatives. The ad- vection phase is solved by propagating an upstream profile which is constructed inside the grid cell with a cubic poly- nomial. This scheme can solve hyperbolic equations with third-order accuracy in time and space and capture a sharp shock wave very well with the smaller grid number and less diffusion. The feasibility of this method has been demon- strated by applying it to various fluid flow problems, such as laser-induced evaporation and vapor expansion (Yabe et al., 1995; Ohkubo et al., 2003) and shock wave genera- tion (Takewaki and Yabe, 1987). In the field of planetary science, the break-up of Shoemaker-Levy 9 entering the Jovian atmosphere was studied with this method (Yabe et al., 1994). Our code was tested with two typical strong- shockwave problems: a 1-D shock-tube problem and the Sedov blast wave problem. Compared with the analytic so- lution of the 1-D shock-tube problem, the relative errors are 4.9% for the velocity, 3.5% for the pressure and 5.2% for the density.
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Although the possibility of tidal locking of an Earth- like planet within the habitable zone of a Sun-like star is low, the existence of Venus shows that a slow rotating planet is possible. As mentioned in the “Introduction”, Yang et al. (2014) demonstrated that very slowly rotating and tidally locked planets located at a distance of 0.7 AU from a Sun-like star can maintain an Earth-like atmos- phere despite their close distance to the parent star. Their models were designed for tropospheric simulations and lacked the full stratospheric chemistry and resolution available in CESM1(WACCM). Furthermore, several past studies of tidally locked exoplanets orbiting M stars used models with solar spectrums and atmospheric compo- sitions similar to that of the PDE (Merlis and Schneider
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modulus in magnitudes). The colored regions represent contours of equal goodness of fit compared to a transiting planet model, with the 3σ contour indicated in white. Blends inside this contour give acceptable fits to the Kepler photometry, and are considered viable. They all involve eclipsing binaries that are up to ∼5.5 mag fainter than the target (dashed green line in the figure). Other constraints can potentially rule out additional blends. For example, blends in the blue-hatched areas have overall colors for the combined light that are either too red (left) or too blue (right) compared to the measured color of the target (r−Ks = 1.475 ± 0.022, taken from the KIC; Brown et al. 2011), at the 3σ level. For this particular kind of blend these constraints are not helpful however, as those scenarios are already ruled out by BLENDER. False positives that are in the green-hatched area correspond to secondary components that are less than 1 mag fainter than the target, and which we consider to be also ruled out because such stars would usually have been detected in our spectroscopic observations, as a second set of lines. Once again this constraint is redundant with the BLENDER results. The one-mag limit is very conservative, as stars down to 2 or 3 mag fainter than the target would also most likely have been seen in our high-resolution, high signal-to-noise ratio Keck spectra.
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One of the significant discoveries of the present time is spotting extremely intense radiation at distances of up to several Earth’s radii . The intensity of this radiation is millions of times higher than that of the cosmic rays observed until recently in the terrestrial atmosphere. Later on, the zones, where particles captured by the geomagnetic field are concentrated, were given the name radiation belts. Low-energy electrons fill almost the whole magnetic sphere of the Earth. The outer boundary of the magnetic sphere is at a distance r ≥ 10 R . A little the studies into radiation detected a new physical phe- nomenon predicted by E. Parker: an ionized gas flow, referred to as the solar wind, travels from the Sun at a velocity ~ 400-600 km/sec and replenishes steadily the number of charged particles in the Earth atmosphere. At calm periods the intensity of electrons may be as high as J ~ 10 8 cm –2 ·sec –1 and their spatial concentration varies between several particles and several tens per 1 cm 3 . During magnetic radiations their variation comes to two orders. The inner part of the magnetic sphere lying a di- pole-like geomagnetic field (up to 3 ) is referred to as the plasma sphere. The concentration of “cold plasma” particles in the plasma sphere is ~10 4 cm – .
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We first show the overall features of the sounding curves. With periods shorter than about 500 s (Fig. 3), the apparent resistivity and phase in the major elements decrease with decreasing period, which suggests that the uppermost layer is relatively conductive, likely associated with the crust including a thick (~400 m) pelagic sedi- ment layer (Shinohara et al. 2008). The apparent resistivi- ties show a peak at around 500 s and then decrease with increasing period (Fig. 3). This feature is typical for oce- anic mantle that consists of cool, resistive lithosphere and underlying hotter, more conductive asthenosphere (e.g., Filloux 1977). The peak of the apparent resistivity is higher for Area B than for Area A (Fig. 3). The responses look similar between sites within each area, but the spatial variation tends differ somewhat between Area A and Area B. For example, the phase tensors at 5120 s tend to elon- gate in the northeast–southwest direction in Area A, but form a more circular shape in Area B (Fig. 4). These obser- vations suggest a difference in the upper mantle structure at a scale beyond the array size. Splitting between the off- diagonal elements suggests the effect/s of lateral hetero- geneity and/or anisotropic structure. This phenomenon is smaller for Area B, which is more distant from the coast- lines; therefore, the coast effect is likely a possible cause. In fact, our previous study showed that splitting in the responses for Area A is partly explained by the topogra- phy, including coastlines (Baba et al. 2013a). However, for Area A, the splitting tends to be slightly more significant at the western sites, NM01, NM02, and NM04 (Fig. 3; Addi- tional file 1: Figure S1), and this feature is not reproduced
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For each chunk, we therefore kept the RV measurements outside of the chunk, but fixed their value to zero, with error bars of 100 m s −1 . A similar analysis was performed for α Cen Bb (Dumusque et al. 2012) and Kepler-10 (Dumusque et al. 2014). In Figure 4, we show the periodogram for each chunk of data (blue and red) and the GLS periodogram for the entire data set (gray). The signal at 35 days is seen in the first and second halves of the data, which is expected for a signal induced by a planet or by stellar activity if 35 days is the stellar rotation period. However, when looking at the phase of the signal, illustrated in Figure 4 by small arrows above the 35-day peak, it is clear that the signal has the same phase in each chunk. Furthermore, this phase is consistent with the phase derived when analyzing the entire data set. The signal thus retains the same phase from season to season, which is a strong argument in favor of the planetary origin of the signal. A signal due to stellar activity would change its phase because of the evolution of active region configuration on the stellar surface.
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Although we know of thousands of these small transiting exoplanets, only a few of these currently have precise mass measurements (precision better than 20%) allowing us to distinguish between different compositional models. Precise masses and resulting bulk densities are especially important for small planets, since a wide diversity of planet compositions are possible including rocky terrestrial planets with compact atmospheres and rocky cores with significant fractions of volatiles, like water and methane, and/or extended hydrogen/helium envelopes. A transition from rocky to gaseous planets has been proposed to occur at planetary radii of around 1.5 − 1.7 R ⊕ by a number of authors
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L + n + L n L − n − (33) It should be noted here that the effect of reduction of the mass M of the Sun [see (11)] due to the energy emission has been fully neglected. This effect leads evidently to an increase of the energy of a moving planet, so it acts in direction opposite to the quantum decrease of energy presented in the paper. Physically this means that the energy decrease discussed above (Section 3 and Section 4) is more sound for the satellites of non-radiating planets than for the planets themselves.