Earth's Density Research Articles

Reassessment of Birch's Law on hcp‐Fe From Ultrasonic Sound Velocity Measurement and Implications on the Velocity Profiles of Earth's Inner Core

AbstractWe performed in situ X‐ray diffraction and ultrasonic sound velocity measurements on hcp‐Fe up to 15 GPa, 873 K in a multi‐anvil apparatus. The elastic moduli and their pressure and temperature derivatives were determined by fitting the velocity and density data to the third‐order finite strain equations, yielding KS0 = 169.0(57) GPa, KS0′ = 5.4(6), (∂KS/∂T)P = −0.031(3) GPa/K, G0 = 104.5(27) GPa, G0′ = 1.7(2), (∂G/∂T)P = −0.060(2) GPa/K. Within the experimental P‐T range, we find significant temperature effect on the density‐velocity (ρ − VP or S) relations and caution the use of the temperature‐independent Birch's law for extrapolation to core conditions. Furthermore, temperature‐induced velocity decrease is more significant in VS than in VP, offering a possible explanation for the high Poisson's ratio in the core. Extrapolations based on our results together with previous experimental data suggest that VP of hcp‐Fe aligns with PREM at Earth's core conditions, while Vs and density are approximately 10% and 2.7% higher than PREM, respectively.

A proposed method for calculating the voltage and current distributions of grounded and isolated networks subjected to line‐to‐ground faults

AbstractOne crucial objective of this article is to present simplified and accurate approaches to study the current distribution and ground surface potential around the area surrounding an earthed and isolated system in case of a line‐to‐earth fault. The present study is done in the case of uniform and two‐layer soils. Suggested models for calculating the distribution of the earth's surface current density, step, and touch voltages in grounded and isolated systems are presented, discussed, and adapted. The contact and arc resistances of line to ground faulty conductors are considered. Rods and/or grounding grids usually do grounded systems. The impact of both step and touch potentials and current density are investigated in this article. The methods of the calculations are based on the electrical concepts, the charge simulation method, and the imaging procedure for the grounding system. The suggested method can be considered a novel and simple technique for calculating the current distributions of the ground surface during line to ground fault. The results agree with those obtained by others, with the advantage of the proposed algorithm for its ease of application and simplicity. 3‐D dimensions’ contours of the current density and the electric potential on the earth surface around the faulty point are presented in case of homogeneous and two layers’ soil. Finally, this article's novelty is to devise a method for calculating the step and touch potentials and current density around the point of contact of the conductor carrying the electric voltages in the event of faults occurring in the electrical network, whether the network is grounded or isolated. Such faults of electrical networks may cause human hazards.

Climatology, Long‐Term Trend and Solar Response of Na Density Based on 28 Years (1990–2017) of Midlatitude Mesopause Na Lidar Observation

AbstractThe climatology of earth's Na density over Fort Collins, CO (41°N, 105°W) based on nocturnal Na lidar observations between 1990 and 1999 was reported by She et al. (2000, https://doi.org/10.1029/2000gl003825). Based on a continued 28‐year data set between 1990 and 2017 with the latter part observed over Logan, UT (42N, 112W), we update the seasonal variations between 80 and 110 km. This data set is also used to deduce long‐term responses of Na density (profile) between 75 and 110 km, showing a positive linear trend between 75 and 93 km (with maximum ∼2.87 × 108 m−3/decade at 87 km); it turns negative before approaching zero at 110 km (with minimum ∼−2.96 × 107 m−3/decade at 100 km). The associated solar response is also positive for the altitude range in question (with maximum ∼5.20 × 106 m−3/SFU at 91 km). We also derived the 28‐year mean Na layer column abundance, centroid altitude, and root mean square width to be 3.92 ± 2.14 1013 m−2, 91.3 ± 1.0 km, and 4.62 ± 0.56 km, respectively, and deduced long‐term trend and solar cycle responses of column abundance and centroid altitude, respectively to be 7.81 ± 1.63%/decade and 16.9 ± 2.8%/100SFU, and −355 ± 35 m/decade and −1.94 ± 0.69 m/SFU. We explained conceptually how positive long‐term responses in Na density led to positive responses in column abundance and negative responses in centroid altitude.

Earth shaped by primordial H2 atmospheres.

Earth's water, intrinsic oxidation state and metal core density are fundamental chemical features of our planet. Studies of exoplanets provide a useful context for elucidating the source of these chemical traits. Planet formation and evolution models demonstrate that rocky exoplanets commonly formed with hydrogen-rich envelopes that were lost over time1. These findings suggest that Earth may also have formed from bodies with hydrogen-rich primary atmospheres. Here we use a self-consistent thermodynamic model to show that Earth's water, core density and overall oxidation state can all be sourced to equilibrium between hydrogen-rich primary atmospheres and underlying magma oceans in its progenitor planetary embryos. Water is produced from dry starting materials resembling enstatite chondrites as oxygen from magma oceans reacts with hydrogen. Hydrogen derived from the atmosphere enters the magma ocean and eventually the metal core at equilibrium, causing metal density deficits matching that of Earth. Oxidation of the silicate rocks from solar-like to Earth-like oxygen fugacities also ensues as silicon, along with hydrogen and oxygen, alloys with iron in the cores. Reaction with hydrogen atmospheres and metal-silicate equilibrium thus provides a simple explanation for fundamental features of Earth's geochemistry that is consistent with rocky planet formation across the Galaxy.

Effect of matter density in T2HK and DUNE

CP phase determination for the near future long baseline experiments, T2HK and DUNE, will require precise measurements of the oscillation probabilities. However, the uncertainty in the Earth's density must be considered in determining these oscillation probabilities. Therefore, in this study, we update the individual sensitivities of these experiments for determining the current unknowns in the standard three flavor scenario considering the latest configuration and also the complementarity between them while considering the uncertainty in the density. Our study showed that this uncertainty has a non-negligible impact on the precision of the CP phase determination particularly for DUNE.

Solar Rotation Effects in Earth's and Mars' Thermospheric Densities as Revealed by Concurrent MAVEN, Swarm‐C, and GOES Observations

AbstractThe responses of Earth's and Mars' thermospheric densities to quasi‐periodic (∼27‐day) solar rotation variations in flux were measured contemporaneously by the Mars Atmosphere and Volatile EvolutioN, Geostationary Operational Environmental Satellites, and Swarm‐C satellites. While large solar rotation variability is found in both planetary thermospheres, correlation analyses performed on over 6 years of observations reveal that, independently of extreme ultraviolet flux level, Earth's daytime density response is about 10%–50% larger than Mars' at a similar density level. Important altitude dependencies in the density sensitivity to the solar rotation in solar flux are found in the Martian thermosphere, while the terrestrial thermosphere is shown to exhibit only small (±5%) day/night and latitude variations in the response. Detailed analyses focused on correlative periods in 2015–2016 and 2020 indicate important solar cycle effects in the sensitivities of both planetary thermospheres, with increased slopes under low solar flux conditions. These results provide important new insights into processes relevant to the interpretation of the sources of short‐term density variability in Mars' and Earth's thermospheres associated with solar drivers and point to the need for targeted modeling efforts along with dedicated data analyses to help resolve current unknowns in thermal balance processes.

Geomorphology of contractional salt tectonics along the Kuqa fold-thrust belt, northwestern China: Testing pre-kinematic diapir versus source-fed thrust and detachment fold models

The Kuqa fold-thrust belt arguably hosts Earth's highest density of diverse surface salt structures, including salt-cored anticlines, strike-slip faults that double as salt walls, salt domes, and salt thrusts. Key aspects of the structural development of the range are unresolved. In particular, it is unclear whether the fold-thrust belt developed via forward-propagating salt-cored detachment folds which locally nucleated late thrust faults, or if such detachment folds grew interspersed with either (i) long-lived pre-kinematic salt diapirs that evolved into local salt thrusts and/or (ii) source-fed thrust faults and associated folds. Detachment folds and hanging wall anticlines of source-fed thrusts feature gradual lateral propagation during growth, whereas diapirs either lack lateral propagation or involve irregular propagation and dramatic strain gradients. Therefore, we test the hypotheses by examining potential geomorphological records of lateral ridge propagation along the frontal Kuqa fold-thrust belt. A particular focus is the Quele salt thrust, because it spans one tenth of the length of the frontal belt and it is commonly hypothesized to represent a deformed diapir or a source-fed thrust fault. We find that all ridges along the frontal Kuqa fold-thrust belt feature (1) bow-shaped along-strike topography, with decreasing relief from the topographic crest to the plunging ends of the ridges, (2) curved wind and water gaps, (3) asymmetric fan-shaped and forked-shaped tributaries, and (4) drainage basin maturity decreases towards lateral ridge terminations. These features are consistent with lateral fold propagation. At the Quele salt thrust, such evidence indicates that the hanging wall developed as two distinct anticlines which merged into a composite anticlinorium. Our findings indicate that the frontal Kuqa fold-thrust belt developed either by detachment folding with local late thrust fault formation, or via such structures interspersed with source-fed thrust faults.

On the nonlinear three-dimensional models in equatorial ocean flows

<p style='text-indent:20px;'>The paper focusses on some of the recent breakthroughs in the development of models for nonlinear, three-dimensional Equatorial oceanic flows by Constantin and Johnson. The unique character of the formulations is in the systematic approach followed, while making approximations as required, and consequently assessing the implications. These Constantin-Johnson type of models are general enough, as effects such as that of Earth's rotation, Coriolis term, stratification, thermocline, pycnocline, density variations and vertical velocities can be accounted for. Exact solutions based on the use of singular perturbation theory have been obtained for several different cases and situations. The novelty in the models lies in the introduction of a quasi-stream-function which facilitates the derivation of the solutions. Analytical results are supplemented with some numerical illustrations to provide a flavour of the complex flow structures involved. Insights are provided into the velocity field and flow paths, indicating the presence of cellular structures, upwelling/downwelling and subsurface ocean 'bridges'.</p>

Estimation of Rock Characteristics Based on Polarization Spectra: Surface Roughness, Composition, and Density

Surface polarization characteristics provide crucial structural information of the Earth's surface. As two key elements of the natural geographical environment, rocks and soils play an important role in the study of surface processes. Inherent surface characteristics, such as surface roughness, composition, and density are critical parameters for the remote monitoring of land surfaces as they affect the polarization characteristics of scattered light waves. In this study, we investigated the relationship between surface roughness, composition, and density, and the polarization spectra of limestone-dolomite series rock. Results reveal a power function relationship between the surface roughness and the degree of polarization peaks among different detection zenith and azimuth angles. The depth and position of the absorbing waveband are significantly correlated with the characteristic component contents. The rock density was determined via the polarized reflection spectra, with the Earth's surface density calculations associated with a 2.6% divergence from the current recognized data. Our results demonstrate the ability of polarized spectra to retrieve surface roughness, composition, and density, with potential for further development in future work.

INCREASE: An updated model suite to study the INfluence of Cosmic Rays on Exoplanetary AtmoSpherEs

AbstractExoplanets are as diverse as they are fascinating. They vary from ultrahot Jupiter‐like low‐density planets to presumed gas‐ice‐rock mixture worlds such as GJ 1214b or worlds as LHS 1140b, which features twice the Earth's bulk density. Regarding the great diversity of exoplanetary atmospheres, much remains to be explored. For a few selected objects such as GJ1214b, Proxima Centauri b, and the TRAPPIST‐1 planets, the first observations of their atmospheres have already been achieved or are expected in the near future with the launch of the James Webb Space Telescope envisaged in October 2021. However, in order to interpret these observations, model studies of planetary atmospheres that account for various processes—such as atmospheric escape, outgassing, climate, photochemistry, as well as the physics of air showers and the transport of stellar energetic particles and galactic cosmic rays through the stellar astrospheres and planetary magnetic fields—are necessary. Here, we present our model suite INCREASE, a planned extension of the model suite discussed in Herbst, Grenfell, et al. (2019).

ГЕОДИНАМІКА

This study aims to derive the Earth’s temporally varying Earth’s tensor of inertia based on the dynamical ellipticity , the coefficients , from UT/CSR data. They allow to find the time-varying Earth’s mechanical and geometrical parameters during the following periods: (a) from 1976 to 2020 based on monthly and weekly solutions of the coefficient ; (b) from 1992 to 2020 based on monthly and weekly solutions of the non zero coefficients , related to the principal axes of inertia, allowing to build models their long-term variations. Differences between and , given in various systems, represent the average value , which is smaller than time variations of or , characterizing a high quality of UT/CSR solutions. Two models for the time-dependent dynamical ellipticity were constructed using long-term variations for the zonal coefficient during the past 44 and 27.5 years. The approximate formulas for the time-dependent dynamical ellipticity were provided by the additional estimation of each parameter of the Taylor series, fixing at epoch =J2000 according to the IAU2000/2006 precession-nutation theory. The potential of the time-dependent gravitational quadrupole according to Maxwell theory was used to derive the new exact formulas for the orientation of the principal axes , , via location of the two quadrupole axes. Hence, the Earth’s time-dependent mechanical and geometrical parameters, including the gravitational quadrupole, the principal axes and the principal moments of inertia were computed at each moment during the past 27.5 years from 1992 to 2020. However, their linear change in all the considered parameters is rather unclear because of their various behavior on different time-intervals including variations of a sign of the considered effects due to a jump in the time-series during the time-period 1998 – 2002. The Earth’s 3D and 1D density models were constructed based on the restricted solution of the 3D Cartesian moments inside the ellipsoid of the revolution. They were derived with conditions to conserve the time-dependent gravitational potential from zero to second degree, the dynamical ellipticity, the polar flattening, basic radial jumps of density as sampled for the PREM model, and the long-term variations in space-time mass density distribution. It is important to note that in solving the inverse problem, the time dependence in the Earth's inertia tensor arises due to changes in the Earth's density, but does not depend on changes in its shape, which is confirmed by the corresponding equations where flattening is canceled.

Tidal Geopotential Dependence on Earth Ellipticity and Seawater Density and Its Detection With the GRACE Follow‐On Laser Ranging Interferometer

AbstractOcean tides produce significant gravitational perturbations that affect near‐Earth orbiting spacecraft. The gravitational potential induced by tidal mass redistribution is routinely modeled for global gravity analysis and orbit determination, although generally by assuming a spherical Earth and a uniform seawater density. The inadequacy of these simplifications is here addressed. We have developed an accurate yet efficient algorithm to compute the ocean tidal geopotential, allowing for Earth's elliptical shape and variable seawater density. Using this new computation, we find that (1) the effect of ellipticity is several percent of the tide signal over mid to high‐latitude regions, which is comparable to elevation error in the state‐of‐the‐art ocean tide models; (2) the effect of seawater density variations on the potential is as large as 2–3 cm in water‐height equivalent, primarily in deep water where density increases 2%–3% from compressibility. Our analysis of new Gravity Recovery and Climate Experiment Follow‐On (GRACE‐FO) laser ranging interferometer measurements reveals evident errors when ellipticity and density variations are ignored. When accounted for, the GRACE‐FO residual tidal gravity perturbations are reduced by half, depending on the adopted tide model; only the remaining half likely represents actual model elevation error. The use of a spherical surface and a uniform seawater density is no longer tenable given the precision of gravity measurements from GRACE and GRACE‐FO satellites.

Bayesian Inference of Mantle Viscosity From Whole‐Mantle Density Models

AbstractThe long‐wavelength geoid is sensitive to Earth's mantle density structure as well as radial variations in mantle viscosity. We present a suite of inversions for the radial viscosity profile using whole‐mantle models that jointly constrain the variations in density, shear‐ and compressional‐wavespeeds using full‐spectrum tomography. We use a Bayesian approach to identify a collection of viscosity profiles compatible with the geoid, while enabling uncertainties to be quantified. Depending on tomographic model parameterization and data weighting, it is possible to obtain models with either positive‐ or negative‐buoyancy in the large low shear velocity provinces. We demonstrate that whole‐mantle density models in which density and VS variations are correlated imply an increase in viscosity below the transition zone, often near 1,000 km. Many solutions also contain a low‐viscosity channel below 650 km. Alternatively, models in which density is less‐correlated with VS—which better fit normal mode data—require a reduced viscosity region in the lower mantle. This feature appears in solutions because it reduces the sensitivity of the geoid to buoyancy variations in the lowermost mantle. The variability among the viscosity profiles obtained using different density models is indicative of the strong nonlinearities in modeling the geoid and the limited resolving power of the geoid kernels. We demonstrate that linearized analyses of model resolution do not adequately capture the posterior uncertainty on viscosity. Joint and iterative inversions of viscosity, wavespeeds, and density using seismic and geodynamic observations are required to reduce bias from prior assumptions on viscosity variation and scalings between material properties.

Earth's ionosphere D-region vertical electron density profile data during March 1-31, 2017 according to high-latitudinal Tumanny observatory partial reflection radar measurements and Polar Geophysical Institute's model.

The Earth's high-latitudinal D-Region ionosphere measurements are rarely performed continuously and with high temporal resolution. This data article provides the observed and modelled data on D-Region electron density variations during March 1-31, 2017 with 1-minute resolution. Both datasets share the same data-files’ structure and naming conventions. D-Region electron density observations were performed with the ground-based vertical sounding medium frequency (MF) partial reflection radar located at Tumanny observatory (69.0°N, 35.7°E). Modelling of D-Region ionosphere electron density variations were performed for the same period using Polar Geophysical Institute's theoretical model of quiet-time D-Region ionosphere. These datasets are valuable (a) to validate and cross-compare existing models of the D-Region ionosphere, (b) to verify and improve HF-band radio-waves propagation models, and (c) in investigations of the Earth's-ionosphere waveguide properties in dependence on the features of the lower part of the waveguide, i.e., the D-Region (often referenced to as the D-Layer). Both datasets are required to gain the reproducibility of results reported by Gomonov and co-authors [2019, doi: 10.1051/epjconf/201922403011].

Reply to Comment by Tsurutani et al. on “First Observation of Mesosphere Response to the Solar Wind High‐Speed Streams”

AbstractIn our recent paper, Yi, Reid, Xue, Younger, Spargo, et al. (2017, https://doi.org/10.1002/2017JA024446, hereinafter Y17A), we presented a first analysis of 9‐ and 6.75‐day periodic oscillations observed in the Earth's neutral mesospheric density during 2005 and 2006. These observations reveal a direct coupling between the Sun's upper atmosphere and the Earth's mesosphere. Tsurutani et al. (2019, https://doi.org/10.1002/2016JA022499, hereinafter T19) have commented on T19 by way of suggesting possible physical mechanisms for Y17A's observations (Y17A do not address possible mechanisms in their paper).

Pedersen Ionic Contribution in Different Time Scales

AbstractPedersen conductivity is one of the main parameters in atmospheric electrodynamics, magnetosphere‐ionosphere‐thermosphere coupling, and several other geophysical processes. It is determined by the collision frequency between charged and neutral components and the Earth's magnetic field intensity through the gyrofrequency. This work analyzes the contribution of different ionic species to the variability of Pedersen conductance in time scales from hours to years within the period 1964–2008 based on the results of various atmospheric and ionospheric models. The main results are (1) there is a positive correlation between O+ density and Pedersen conductance, (2) Pedersen conductance of F layer has a larger increase with the solar activity than that of E layer, (3) Pedersen conductance has a long‐term trend that is determined by Earth's magnetic field intensity and electron density, and (4) at midlatitudes trends are mainly governed by the Earth's magnetic field and modulated by the electron density, while at high latitudes both are important.

Foraging for dark matter in large volume liquid scintillator neutrino detectors with multiscatter events

We show that dark matter with a per-nucleon scattering cross section $\gtrsim 10^{-28}~{\rm cm^2}$ could be discovered by liquid scintillator neutrino detectors like BOREXINO, SNO+, and JUNO. Due to the large dark matter fluxes admitted, these detectors could find dark matter with masses up to $10^{21}$ GeV, surpassing the mass sensitivity of current direct detection experiments (such as XENON1T and PICO) by over two orders of magnitude. We derive the spin-independent and spin-dependent cross section sensitivity of these detectors using existing selection triggers, and propose an improved trigger program that enhances this sensitivity by two orders of magnitude. We interpret these sensitivities in terms of three dark matter scenarios: (1) effective contact operators for scattering, (2) QCD-charged dark matter, and (3) a recently proposed model of Planck-mass baryon-charged dark matter. We calculate the flux attenuation of dark matter at these detectors due to the earth overburden, taking into account the earth's density profile and elemental composition, and nuclear spins.

Nitrogen Solubility in Core Materials

AbstractDuring accretion, nitrogen was distributed between metal melt, silicate melt, and the atmosphere and today's N deficit of bulk silicate Earth with respect to chondrites may be due to segregation into the core and/or atmospheric losses. To examine the former, we experimentally determined N solubilities in Fe‐dominated metal melts at 1200–1800 °C, 0.4–9.0 GPa. Results show that pressure has a strong positive influence on N solubility, increasing from 1.0 to 7.4 wt% at 1–9 GPa (1400 °C) while temperature has the inverse effect, N solubility decreasing from 1.3 to 0.6 wt% at 1200–1800 °C (1 GPa). The solubility data are parameterized as function of pressure and temperature. Our results suggest that core‐forming metal melts can dissolve large quantities of N, and the potential N contribution to the Earth's core density deficit could hence be much larger than previously assumed. Most importantly, N in the deep reduced mantle should be stored in the small metal fractions and not in silicates.

Matter density profile shape effects at DUNE

Quantum mechanical interactions between neutrinos and matter along the path of propagation, the Wolfenstein matter effect, are of particular importance for the upcoming long-baseline neutrino oscillation experiments, specifically the Deep Underground Neutrino Experiment (DUNE). Here, we explore specifically what about the matter density profile can be measured by DUNE, considering both the shape and normalization of the profile between the neutrinos' origin and detection. Additionally, we explore the capability of a perturbative method for calculating neutrino oscillation probabilities and whether this method is suitable for DUNE. We also briefly quantitatively explore the ability of DUNE to measure the Earth's matter density, and the impact of performing this measurement on measuring standard neutrino oscillation parameters.

Hamilton’s principle and normal mode coupling in an aspherical planet with a fluid core

Seismic free oscillations, or normal modes, provide a convenient tool to calculate low-frequency seismograms in heterogeneous Earth models. A procedure called ‘full mode coupling’ allows the seismic response of the Earth to be computed. However, in order to be theoretically exact, such calculations must involve an infinite set of modes. In practice, only a finite subset of modes can be used, introducing an error into the seismograms. By systematically increasing the number of modes beyond the highest frequency of interest in the seismograms, we investigate the convergence of full-coupling calculations. As a rule-of-thumb, it is necessary to couple modes 1–2 mHz above the highest frequency of interest, although results depend upon the details of the Earth model. This is significantly higher than has previously been assumed. Observations of free oscillations also provide important constraints on the heterogeneous structure of the Earth. Historically, this inference problem has been addressed by the measurement and interpretation of splitting functions. These can be seen as secondary data extracted from low frequency seismograms. The measurement step necessitates the calculation of synthetic seismograms, but current implementations rely on approximations referred to as self- or group-coupling and do not use fully accurate seismograms. We therefore also investigate whether a systematic error might be present in currently published splitting functions. We find no evidence for any systematic bias, but published uncertainties must be doubled to properly account for the errors due to theoretical omissions and regularization in the measurement process. Correspondingly, uncertainties in results derived from splitting functions must also be increased. As is well known, density has only a weak signal in low-frequency seismograms. Our results suggest this signal is of similar scale to the true uncertainties associated with currently published splitting functions. Thus, it seems that great care must be taken in any attempt to robustly infer details of Earth's density structure using current splitting functions.