Inversion of GRACE Gravity for Global Surface Mass Variations
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Spatial and Temporal Antarctic Ice Sheet Mass Trends, Glacio-Isostatic Adjustment, and Surface Processes from a Joint Inversion of Satellite Altimeter, Gravity, and GPS Data
We present spatiotemporal mass balance trends for the Antarctic Ice Sheet from a statistical inversion of satellite altimetry, gravimetry, and elastic-corrected GPS data for the period 2003-2013. Our method simultaneously determines annual trends in ice dynamics, surface mass balance anomalies, and a time-invariant solution for glacio-isostatic adjustment while remaining largely independent of forward models. We establish that over the period 2003-2013, Antarctica has been losing mass at a rateof -84 +/- 22 Gt per yr, with a sustained negative mean trend of dynamic imbalance of -111 +/- 13 Gt per yr. West Antarctica is the largest contributor with -112 +/- 10 Gt per yr, mainly triggered by high thinning rates of glaciers draining into the Amundsen Sea Embayment. The Antarctic Peninsula has experienced a dramatic increase in mass loss in the last decade, with a mean rate of -28 +/- 7 Gt per yr and significantly higher values for the most recent years following the destabilization of the Southern Antarctic Peninsula around 2010. The total mass loss is partly compensated by a significant mass gain of 56 +/- 18 Gt per yr in East Antarctica due to a positive trend of surface mass balance anomalies.
Martin-Espanol, Alba↗
Evidence for active hotspots on Venus from analysis of Magellan gravity data
The 500-Myr average crater retention age for Venus has raised questions about the present-day level of tectonic activity. In this study we examine the relationship between the gravity and topography of four large volcanic swells, Beta, Atla, Bell, and Western Eistla Regiones, for clues about their stage evolution. The Magellan line-of-sight gravity data are inverted using a point mass model of the anomalous mass to solve for the local vertical gravity field. Spectral admittance calculated from both the local gravity inversions and a spherical harmonic model is compared to three models of compensation: local compensation, a 'flexural' model with local and regional compensation of surface and subsurface loads, and a 'hotspot' model of compensation that includes top loading by volcanoes and subsurface loading due to a deep, low density mass anomaly. The coherence is also calculated in each region, but yields an elastic thickness estimate only at Bell Regio. In all models, the long wavelengths are compensated locally. Our results may indicate a relatively old, possibly inactive plume.
Smrekar, Suzanne E.↗
Effect of nonlinear interactions on p-mode frequencies and line widths
We calculate the effect of nonlinear interactions among solar acoustic modes upon the modal frequencies and energy loss rates (or line widths). The frequency shift for a radial p-mode of frequency 3 mHz is found to be about -0.5 microHz. The magnitude of nonlinear frequency shift increases more rapidly with frequency than the inverse mode mass (mode mass is defined as the ratio of energy in the mode to its surface velocity amplitude squared). This frequency shift is primarily due to nonresonant three-mode interactions and is dominated by high l surface gravity waves (f-modes) and p-modes. The line width of a radial p-mode of frequency 3 mHz, due to resonant nonlinear interactions, is about 0.3 microHz. This result is consistent with that of Kumar and Goldreich (1989). We also find, in agreement with these authors, that the most important nonlinear interactions of trapped p-modes involve f-modes and high-frequency p-modes (frequency greater than about 5 mHz) which propagate in the solar photosphere. Thus, using the arguments advanced by Kumar & Goldreich (1989), we conclude that nonlinear couplings cannot saturate the overstable solar p-modes at their small observed amplitudes. Both the nonlinear frequency shifts and line widths, at a fixed frequency, are proportional to the inverse of mode mass which for modes of degree greater than about 100 is approximately l(exp 0.8). Therefore, the frequency of an f-mode of l = 1000, due to nonlinear interactions, is decreased by approximately 0.4%.
Kumar, Pawan↗
Constraining Venus and Mars Internal Structures from the Gravity Response to Atmospheric Loading
The gravity fields of celestial bodies that possess an atmosphere are periodically perturbed by the redistribution of fluid mass associated with the atmospheric dynamics. A component of this perturbation is due to the gravitational response of the body to the deformation of its surface induced by the atmospheric pressure loading. The magnitude of this effect depends on the relation between the loading and the response in terms of geopotential variations measured by the load Love numbers. In this work, we simulate and analyze the gravity field generated by the atmospheres of Venus and Mars by accounting for different models of their internal structure. By precisely characterizing the phenomena that drive the mass transportation in the atmosphere through general circulation models, we determine the effect of the interior structure on the response to the atmospheric loading. An accurate estimation of the time-varying gravity field, which measures the atmospheric contribution, may provide significant constraints on the interior structure through the measurement of the load Love numbers. A combined determination of tidal and load Love numbers would enhance our knowledge of the interior of planetary bodies, providing further geophysical constraints in the inversion of internal structure models.The gravity fields of celestial bodies that possess an atmosphere are periodically perturbed by the redistribution of fluid mass associated with the atmospheric dynamics. A component of this perturbation is due to the gravitational response of the body to the deformation of its surface induced by the atmospheric pressure loading. The magnitude of this effect depends on the relation between the loading and the response in terms of geopotential variations measured by the load Love numbers. In this work, we simulate and analyze the gravity field generated by the atmospheres of Venus and Mars by accounting for different models of their internal structure. By precisely characterizing the phenomena that drive the mass transportation in the atmosphere through general circulation models, we determine the effect of the interior structure on the response to the atmospheric loading. An accurate estimation of the time-varying gravity field, which measures the atmospheric contribution, may provide significant constraints on the interior structure through the measurement of the load Love numbers. A combined determination of tidal and load Love numbers would enhance our knowledge of the interior of planetary bodies, providing further geophysical constraints in the inversion of internal structure models.
Mars↗
Satellite and surface geophysical expression of anomalous crustal structure in Kentucky and Tennessee
An equivalent layer magnetization model is discussed. Inversion of long wavelength satellite magnetic anomaly data indicates a very magnetic source region centered in south central Kentucky. Refraction profiles suggest that the source of the gravity anomaly is a large mass of rock occupying much of the crustal thickness. The outline of the source delineated by gravity contours is also discernible in aeromagnetic anomaly patterns. The mafic plutonic complex, and several lines of evidence are consistent with a rift association. The body is, however, clearly related to the inferred position of the Grenville Front. It is bounded on the north by the fault zones of the 38th Parallel Lineament. It is suggested that such magnetization levels are achieved with magnetic mineralogies produced by normal oxidation and metamorphic processes and enhanced by viscous build-up, especially in mafic rocks of alkaline character.
Mayhew, M. A.↗
Simulation gravity modeling to spacecraft-tracking data - Analysis and application
It is proposed that line-of-sight gravity measurements derived from spacecraft-tracking data can be used for quantitative subsurface density modeling by suitable orbit simulation procedures. Such an approach avoids complex dynamic reductions and is analogous to the modeling of conventional surface gravity data. This procedure utilizes the vector calculations of a given gravity model in a simplified trajectory integration program that simulates the line-of-sight gravity. Solutions from an orbit simulation inversion and a dynamic inversion on Doppler observables compare well (within 1% in mass and size), and the error sources in the simulation approximation are shown to be quite small. An application of this technique is made to lunar crater gravity anomalies by simulating the complete Bouguer correction to several large young lunar craters. It is shown that the craters all have negative Bouguer anomalies.
Phillips, R. J.↗
The inverse gravimetric problem in gravity modelling
One of the main purposes of geodesy is to determine the gravity field of the Earth in the space outside its physical surface. This purpose can be pursued without any particular knowledge of the internal density even if the exact shape of the physical surface of the Earth is not known, though this seems to entangle the two domains, as it was in the old Stoke's theory before the appearance of Molodensky's approach. Nevertheless, even when large, dense and homogeneous data sets are available, it was always recognized that subtracting from the gravity field the effect of the outer layer of the masses (topographic effect) yields a much smoother field. This is obviously more important when a sparse data set is bad so that any smoothing of the gravity field helps in interpolating between the data without raising the modeling error, this approach is generally followed because it has become very cheap in terms of computing time since the appearance of spectral techniques. The mathematical description of the Inverse Gravimetric Problem (IGP) is dominated mainly by two principles, which in loose terms can be formulated as follows: the knowledge of the external gravity field determines mainly the lateral variations of the density; and the deeper the density anomaly giving rise to a gravity anomaly, the more improperly posed is the problem of recovering the former from the latter. The statistical relation between rho and n (and its inverse) is also investigated in its general form, proving that degree cross-covariances have to be introduced to describe the behavior of rho. The problem of the simultaneous estimate of a spherical anomalous potential and of the external, topographic masses is addressed criticizing the choice of the mixed collection approach.
Sanso, F.↗
GRAIL Refinements to Lunar Seismic Structure
Joint interpretation of disparate geophysical datasets helps to reduce drawbacks that can result from analyzing them individually. The Apollo seismic network was situated on the lunar nearside surface in a roughly equilateral triangle having sides approximately 1000 km long, with stations 12/14 nearly co‐located at one corner. Due to this limited geographical extent, near‐surface ray coverage from moonquakes is low, but increases with depth. In comparison, gravity surveys and their resulting gravity anomaly maps have traditionally offered optimal resolution at crustal depths. Gravimetric maps and seismic data sets are therefore well suited to joint inversion, since the complementary information reduces inherent model ambiguity. Previous joint inversions of the Apollo seismic data (seismic phase arrival times) and Clementine‐ or Lunar Prospector‐derived gravity data (mass and moment of inertia) attempted to recover the subsurface structure of the Moon by focusing on hypothetical lunar compositions that explore the density/velocity relationship. These efforts typically search for the best fitting thermodynamically calculated velocity/density model, allowing variables like core size, velocity, and/or composition to vary freely. Seismic velocity profiles previously derived from the Apollo seismic data through inversion of travel times vary both in the depth of the crust and mantle layers, and the seismic velocities and densities assigned to those layers. The lunar mass and moment of inertia likewise only constrain gross variations in the density profile beyond that of a uniform density sphere. As a result, composition and structure models previously obtained by jointly inverting these data retain the original uncertainties inherent in the input data sets. We will perform a joint inversion of Apollo seismic delay times and gravity data collected by the GRAIL lunar gravity mission, in order to recover seismic velocities and density as a function of latitude, longitude, and depth within the Moon. We will relate density to seismic velocity using a linear relationship that is allowed to be depth‐dependent. The corresponding coefficient (B) can reflect a variety of material properties that vary with depth, including temperature and composition. The inversion seeks to recover the set of density, velocity, and B‐coefficient perturbations that minimize (in a least‐squares sense) the difference between the observed and calculated data.
Weber, Renee C.↗
GRAIL Refinements to Lunar Seismic Structure
Joint interpretation of disparate geophysical datasets helps reduce drawbacks that can result from analyzing them individually. The Apollo seismic network was situated on the lunar nearside surface in a roughly equilateral triangle having sides approximately 1000 km long, with stations 12/14 nearly co-located at one corner. Due to this limited geographical extent, near-surface ray coverage from moonquakes is low, but increases with depth. In comparison, gravity surveys and their resulting gravity anomaly maps have traditionally offered optimal resolution at crustal depths. Gravimetric maps and seismic data sets are therefore well suited to joint inversion, since the complementary information reduces inherent model ambiguity. Previous joint inversions of the Apollo seismic data (seismic phase arrival times) and Clementine- or Lunar Prospector-derived gravity data (mass and moment of inertia) attempted to recover the subsurface structure of the Moon by focusing on hypothetical lunar compositions that explored the density/velocity relationship. These efforts typically searched for the best fitting thermodynamically calculated velocity/density model, and allowed variables like core size, velocity, and/or composition to vary freely. Seismic velocity profiles derived from the Apollo seismic data through travel time inversion vary both in the depth of the crust and mantle layers, and the seismic velocities and densities assigned to those layers. The lunar mass and moment of inertia likewise only constrain gross variations in the density profile beyond that of a uniform density sphere. As a result, composition and structure models previously obtained by jointly inverting these data retain the original uncertainties inherent in the input data sets. We perform a joint inversion of Apollo seismic delay times and gravity data collected by the GRAIL lunar gravity mission, in order to recover seismic velocity and density as a function of latitude, longitude, and depth within the Moon. We relate density (p) to seismic velocity (v) using a depth-dependent linear relationship. The corresponding coefficient (B) can reflect a variety of material properties, including temperature and composition. The inversion seeks to recover the set of p, v, and B perturbations that minimize (in a least-squares sense) the difference between the observed and calculated data.
Weber, Renee C.↗
Combustion of solid carbon rods in zero and normal gravity
In order to investigate the mechanism of carbon combustion and to assess the importance of gravitational induced convection on the process, zero and normal gravity experiments were conducted in which spectroscopic carbon rods were resistance ignitied and burned in dry oxygen environments. In the zero-gravity drop tower tests, a blue flame surrounded the rod, showing that a gas phase reaction in which carbon monoxide was oxidized to carbon dioxide was taking place. The ratio of flame diameter to rod diameter was obtained as a function of time. It was found that this ratio was inversely proportional to both the oxygen pressure and the rod diameter. In the normal gravity tests, direct mass spectrometric sampling was used to measure gas phase concentrations. The gas sampling probe was positioned near the circumference of a horizontally mounted 0.615 cm diameter carbon rod, either at the top or at angles of 45 deg to 90 deg from the top, and yielded concentration profiles of CO2, CO, and O2 as a function of distance from the surface. The mechanism controlling the combustion process was found to change from chemical process control at the 90 deg and 45 deg probe positions to mass transfer control at the 0 deg probe position at the top of the rod. Under the experimental conditions used, carbon combustion was characterized by two surface reactions, 2C + O2 yields 2CO and CO2 + C yields 2CO, and a gas phase reaction, 2CO + O2 yields 2CO2.
Spuckler, C. M.↗
Asteroseismic Inversions of Mixed Acoustic-Gravity Modes to Probe the Stellar Core Structure
The discovery of mixed acoustic-gravity modes of oscillations of moderate mass stars opens a unique opportunity to infer the structure of the inner energy-generating cores and thus test the stellar evolution theory. The mixed modes have properties of internal gravity waves (g-modes) in the convectively stable helium core and properties of acoustic modes outside the core. We select several sets of the oscillation mode frequencies in the mass range from about 1.3 to 1.6 solar masses from the Kepler Legacy database, and apply the optimally localized averaging inversion technique previously developed for low-degree helioseismology. The inversion technique takes into account the uncertainties in the determination of the mass and radius of the stars, as well as the surface effects. The methodology provides sensitivity kernels for various structure properties, including the sound speed, density, and Ledoux parameter of convective stability, and, thus, the direct relationship between the stellar properties and the deviation of observed frequencies from the reference models. The inversion results reveal significant deviations in the core structure from the reference models calculated using the MESA evolutionary code for the stellar parameters obtained by the asteroseismic model grid fitting. Our analysis shows that the best resolution of the inner helium core and surrounding shell is achieved in inversions for the Ledoux parameter.
SMD↗
Estimation and Validation of Oceanic Mass Circulation from the GRACE Mission
Since the launch of the Gravity Recovery And Climate Experiment (GRACE) in March 2002, the Earth's surface mass variations have been monitored with unprecedented accuracy and resolution. Compared to the classical spherical harmonic solutions, global high-resolution mascon solutions allows the retrieval of mass variations with higher spatial and temporal sampling (2 degrees and 10 days). We present here the validation of the GRACE global mascon solutions by comparing mass estimates to a set of about 100 ocean bottom pressure (OSP) records, and show that the forward modelling of continental hydrology prior to the inversion of the K-band range rate data allows better estimates of ocean mass variations. We also validate our GRACE results to OSP variations modelled by different state-of-the-art ocean general circulation models, including ECCO (Estimating the Circulation and Climate of the Ocean) and operational and reanalysis from the MERCATOR project.
Boy, J.-P.↗
Combustion of solid carbon rods in zero and normal gravity
In order to investigate the mechanism of carbon combustion, spectroscopic carbon rods were resistance ignited and burned in an oxygen environment in normal and zero gravity. Direct mass spectrometric sampling was used in the normal gravity tests to obtain concentration profiles of CO2, CO, and O2 as a function of distance from the carbon surface. The experimental concentrations were compared to those predicted by a stagnant film model. Zero gravity droptower tests were conducted in order to assess the effect of convection on the normal gravity combustion process. The ratio of flame diameter to rod diameter as a function of time for oxygen pressures of 5, 10, 15, and 20 psia was obtained for three different diameter rods. It was found that this ratio was inversely proportional to both the oxygen pressure and the rod diameter.
Spuckler, C. M.↗
Geomagnetic Variability and Predictability
The Earth's magnetic field varies on time scales from seconds to millions of years. These variations can be measured directly by ground observatories and satellites, and indirectly through laboratories. They are from different electromagnetic processes in magnetosphere and ionosphere (external), ocean and crust (surface), and deep in the Earth's fluid outer core (internal). Of the measured magnetic signals, 95% is from the core, and is called the core field, or internal field. Variation of the core field, often called the geomagnetic secular variation (SV), is the manifestation of the magnetohydrodynamic processes in the core. Therefore, SV provides rich information on the core dynamical state that is then critical for understanding the geophysical mechanisms of the SV, the core-mantle interactions, and contribution of mass transport inside the core on Earth's gravity variation. Traditionally, the core state is probed via two independent methodologies: core flow inversion from the observed SV, and pure numerical dynamo simulation. The former is driven by observations, but does not include necessary interactions among physical variables; the latter is dynamically consistent, but is not constrained by any observation. Therefore, both are very limited in providing appropriate estimates of the core state. To avoid these limitations, a new approach, geomagnetic data assimilation, appears recently. In this approach, simulation results (model forecasts) are constantly corrected with observations, the corrected solutions (analysis), are then used as the initial conditions to make more accurate forecasts of future. Recent studies have demonstrated successfully that assimilation solutions are different from those of free running models. These new solutions are better estimates of the core state, and have been used to provide accurate prediction of SV for the period from 2010 to 2015. This prediction is part of the IGRF field model for international community applications.
Kuang, Weijia↗
Combustion of solid carbon rods in zero and normal gravity
In order to investigate the mechanism of carbon combustion, normal and zero gravity experiments were conducted in which spectroscopic carbon rods were resistance ignited and burned in an oxygen environment. Direct mass spectrometric sampling was used in the normal gravity tests to measure gas phase concentrations. The gas sampling probe was positioned near the circumference of the horizontally mounted carbon rods, either at the top or at angles of 45 or 90 deg from the top, and yielded concentration profiles of CO2, CO, and O2 as a function of distance from the carbon surface. The experimental concentrations were compared to those predicted by a stagnant film model. Zero gravity droptower tests were conducted in order to assess the effect of convection on the normal gravity combustion process. The ratio of flame diameter to rod diameter as a function of time for oxygen pressures of 5, 10, 15, and 20 psia was obtained for three different diameter rods. It was found that this ratio was inversely proportional to both the oxygen pressure and the rod diameter.
Spuckler, C. M.↗
Kelt-16b: A Highly Irradiated, Ultra-Short Period Hot Jupiter Nearing Tidal Disruption
We announce the discovery of KELT-16b, a highly irradiated, ultra-short period hot Jupiter transiting the relatively bright (visual magnitude equals 11.7) star TYC 2688-1839-1/KELT-16. A global analysis of the system shows KELT-16 to be an F7V star with effective temperature equal to 6236 plus or minus 54 degrees Kelvin, log g (sub asterisk) equal to 4.253 from plus 0.031 to minus 0.036, [Fe/H] equal to minus 0.002 from plus 0.086 to minus 0.085, mass (sub asterisk) equal to 1.211 from plus 0.043 to minus 0.046 times the solar mass, and radius (sub asterisk) equal to 1.360 from plus 0.064 o minus 0.053 times the solar radius. The planet is a relatively high-mass inflated gas giant with planetary mass equal to 2.75 from plus 0.016 to minus 0.15 times Jupiter's mass, planetary radius equal to 1.415 from plus 0.084 to minus 0.067 times Jupiter's radius, density planetary rho equal to 1.20 plus or minus 0.18 grams per cubic centimeter, surface gravity, log planetary gravity equal to 3.530 from plus 0.042 to minus 0.049, and equatorial temperature equal to 2453 from plus 55 to minus 47 degrees Kelvin. The best-fitting linear ephemeris is T(sub C) equal to 22457247.24791 plus or minus 0.00019 BJD (sub TDB) and P equal to 0.9689951 plus or minus 0.0000024 day. KELT-16b joins WASP-18b, -19b, -43b, -103b, and HATS-18b as the only giant transiting planets with periodicity P less than 1 day. Its ultra-short period and high irradiation make it a benchmark target for atmospheric studies by the Hubble Space Telescope, Spitzer, and eventually the James Webb Space Telescope. For example, as a hotter, higher-mass analog of WASP-43b, KELT-16b may feature an atmospheric temperature-pressure inversion and day-to-night temperature swing extreme enough for TiO to rain out at the terminator. KELT-16b could also join WASP-43b in extending tests of the observed mass-metallicity relation of the solar system gas giants to higher masses. KELT-16b currently orbits at a mere approximately 1.7 Roche radii from its host star, and could be tidally disrupted in as little as a few times 10 (sup 5) years (for a stellar tidal quality factor of Q (sup prime) (sub asterisk) equal to 10 (sup 5). Finally, the likely existence of a widely separated bound stellar companion in the KELT-16 system makes it possible that Kozai-Lidov (KL) oscillations played a role in driving KELT-16b inward to its current precarious orbit.
Oberst, Thomas E.↗
On the Inversion for Mass (Re)Distribution from Global (Time-Variable) Gravity Field
The well-known non-uniqueness of the gravitational inverse problem states the following: The external gravity field, even if completely and exactly known, cannot Uniquely determine the density distribution of the body that produces the gravity field. This is an intrinsic property of a field that obeys the Laplace equation, as already treated in mathematical as well as geophysical literature. In this paper we provide conceptual insight by examining the problem in terms of spherical harmonic expansion of the global gravity field. By comparing the multipoles and the moments of the density function, we show that in 3-S the degree of knowledge deficiency in trying to inversely recover the density distribution from external gravity field is (n+l)(n+2)/2 - (2n+l) = n(n-1)/2 for each harmonic degree n. On the other hand, on a 2-D spherical shell we show via a simple relationship that the inverse solution of the surface density distribution is unique. The latter applies quite readily in the inversion of time-variable gravity signals (such as those observed by the GRACE space mission) where the sources over a wide range of the scales largely come from the Earth's Surface.
Chao, Benjamin F.↗