Gravitational Potential Variations Research Articles

Analysis of non-tidal ocean loading for gravitational potential observations in northern Europe

With the progress in clock technology heading towards a relative clock accuracy of 10−18, geodetic applications become feasible, such as determining gravity potential differences over large distances at the level of 0.1 m2 s−2. In this context, the effect of temporal gravity field variations on the new observable has to be considered. This paper studies non-tidal ocean loading effects on the gravitational potential around the North Sea with respect to signal strength and temporal behavior. Ten years of gravitational potential variations caused by non-tidal ocean loading are calculated for five locations in Germany and France using the Green's function approach. The potential variations are discussed with respect to a static gravity field, the effect of different measurement durations and the differences between two locations. The gravitational potential variations reach values of 0.2–0.5 m2 s−2 in coastal areas and decrease with increasing distance from the coast. Analyzing the potential variations for increasing measurement durations from 1 h to 48 h shows a decrease in magnitude. All investigated locations are strongly correlated. They differ mostly due to different magnitudes of the gravitational potential variations.

Identification of prominent spatio-temporal signals in GRACE derived terrestrial water storage for India

Abstract. Fresh water is a necessity of the human civilization. But with the increasing global population, the quantity and quality of available fresh water is getting compromised. To mitigate this subliminal problem, it is essential to enhance our level of understanding about the dynamics of global and regional fresh water resources which include surface and ground water reserves. With development in remote sensing technology, traditional and much localized in-situ observations are augmented with satellite data to get a holistic picture of the terrestrial water resources. For this reason, Gravity Recovery And Climate Experiment (GRACE) satellite mission was jointly implemented by NASA and German Aerospace Research Agency – DLR to map the variation of gravitational potential, which after removing atmospheric and oceanic effects is majorly caused by changes in Terrestrial Water Storage (TWS). India also faces the challenge of rejuvenating the fast deteriorating and exhausting water resources due to the rapid urbanization. In the present study we try to identify physically meaningful major spatial and temporal patterns or signals of changes in TWS for India. TWS data set over India for a period of 90 months, from June 2003 to December 2010 is use to isolate spatial and temporal signals using Principal Component Analysis (PCA), an extensively used method in meteorological studies. To achieve better disintegration of the data into more physically meaningful components we use a blind signal separation technique, Independent Component Analysis (ICA).

The period of a free-swinging pendulum in adiabatic and non-adiabatic gravitational potential variations

An experiment aimed at the determination of the Newtonian constant of gravitation G is in progress at the Politecnico di Torino. This experiment is based on measurement of the period of a simple pendulum, when its gravitational potential is forced to cycle by moving two source masses between two positions, respectively, near and far from the oscillation plane. In previous papers various geometrical and physical effects were analysed, including internal, environmental and technical ones. Most effects are made irrelevant at the desired level of uncertainty (10−4) by the common mode rejection provided by the differential measurement scheme. The remaining effects were shown to impose reasonable constraints of symmetry and geometrical accuracy, and are quickly reviewed here. In this paper the energy exchange between the oscillating mass and the gravitational potential is analysed, and its effect on the period is evaluated. It is shown that the uncertainty contribution of the latter does not constitute a problem for the desired 10−4 accuracy of G determination.

Testing gravity against the early time integrated Sachs-Wolfe effect

A generic prediction of general relativity is that the cosmological linear density growth factor D is scale independent. But in general, modified gravities do not preserve this signature. A scale dependent D can cause time variation in gravitational potential at high redshifts and provides a new cosmological test of gravity, through early time integrated Sachs-Wolfe (ISW) effect-large scale structure (LSS) cross correlation. We demonstrate the power of this test for a class of f(R) gravity, with the form f(R) = {lambda}{sub 1}H{sub 0}{sup 2} exp(-R/{lambda}{sub 2}H{sub 0}{sup 2}). Such f(R) gravity, even with degenerate expansion history to {Lambda}CDM, can produce detectable ISW effect at z {approx}> 3 and l {approx}> 20. Null-detection of such effect would constrain {lambda}{sub 2} to be {lambda}{sub 2} > 1000 at > 95% confidence level. On the other hand, robust detection of ISW-LSS cross correlation at high z will severely challenge general relativity.

Modelling of crust and mantle heterogeneity effects in the theory of Earth tides

General relations are obtained for the determination of radial and tangential components of displacements and gravitational potential variations at the Earth's surface due to tidal forces for a model with a horizontally inhomogeneous distributions of elastic moduli. Model calculations are performed to estimate the eects of local and regional inhomogeneities of elastic moduli specified in regions of simple configurations on tidal variations in gravity, tilts and deformations. As distinct from gravity data, data on tidal tilts and deformations can provide significant constraints on local inhomogeneities of elastic moduli in the immediate vicinity of an observation point. Results of model calculations show that the phases and amplitudes of tidal tilts and deformations change by 10-15% in the vicinity of a soft inclusion in which the shear modulus is smaller than its value in the surrounding medium by 20-30%. Anomalies of such a contrast can be detected over several months of continuous tidal observations.

Mercury's tides and interior structure

An accurate tide‐generating potential series for Mercury has been calculated on the basis of VSOP87 ephemerides for the solar system planets. Due to the 3:2 spin‐orbit resonance, the tides on Mercury cannot be divided into the three classically known tidal frequency bands for the Earth: the diurnal, semidiurnal, and long‐period tides. Instead, the tides all have periods of the order of one Mercury day, or, equivalently, one Mercury year, and their amplitudes have been calculated with an accuracy of 10−5 m2s−2. Basic Mercury models with varying inner and outer core radii and core sulfur concentration have been constructed in order to test the sensitivity of tides to these parameters. To determine the reaction of Mercury to the tidal forcing, the Love numbers h, l, and k and the gravimetric factor δ were calculated for the interior models. Tidal displacements, gravity variations, and external gravitational potential variations have also been calculated for the models. It is shown that especially the measurement of the external potential variations will be extremely useful for constraining the inner and outer core.

Tidally induced surface displacements, external potential variations, and gravity variations on Mars

We have used and extended Roosbeek’s tidal potential for Mars to calculate tidal displacements, gravity variations, and external gravitational potential variations. The tides on Mars are caused by the Sun, and to a lesser degree by the natural satellites Phobos (8%, relative to the Sun) and Deimos (0.08%, relative to the Sun). To determine the reaction of Mars to the tidal forcing, the Love numbers h, l, and k and the gravimetric factor δ were calculated for interior models of Mars with different state, density, and radius of the core and for models which include mantle anelasticity. The latitude dependence and frequency dependence of the Love numbers have been taken explicitly into account. The Love numbers are about three times smaller than those for the Earth and are very sensitive to core changes; e.g., a difference of about 30% is found between a model with a liquid core and an otherwise similar model with a solid core. Tidal displacements on Mars are much smaller than on Earth due to the smaller tidal potential, but also due to the smaller reaction of Mars (smaller Love numbers). For both the tidal diplacement and the tidal external potential perturbations, the tidal signal is at the limit of detection and is too small to permit properties of Mars’s interior to be inferred. On the other hand, the Phobos tidally induced gravity changes, which are subdiurnal with typical periods shorter than 12 h, can be measured very precisely by the very broad band seismometer with thermal control of the seismological experiment SEIS of the upcoming NetLander mission. It is shown that the Phobos-induced gravity tides could be used to study the Martian core.

Gravitational Potential Variations of the Sun and Moon for Estimation of Reservoir Compressibility

Summary Total compressibility in a fractured reservoir is estimated using the pressure response due to gravitational potential variations. Both the lunar and the solar gravitational potentials are fully accounted for by inclusion of longer-period components. The semidiurnal and diurnal pressure data show substantial long-term variations. The gravitational potential also contains the same variation trend: the ratio between the potential and pressure has a fairly uniform value over successive cycles. The computed total compressibility is also fairly constant and independent of the cycle.

The strain and textural history of thin-skinned tectonic zones: examples from the Assynt region of the Moine thrust zone, NW Scotland

The Moine thrust zone at Assynt is a classical example of a foreland propagating, thin-skinned thrust zone, ideal for an examination of thrust-related folds, deformation textures and strains and complex incremental strain history. Divergent transport directions, oblique trending folds, duplex zones and extensional strains normal to the main transport direction may all be explained in terms of thrust propagation, leading to the development of oblique to lateral ramps. The majority of thrusts cut up section from basement to cover in the transport direction but there is also localised extensional flow and thinning of the thrust sheets. In northern Assynt, the thrust zone involves a wide vertical zone of sinistral shear, within which forethrusts, backthrusts and associated folds and cleavages are oblique to the general transport direction. It is suggested that north of this shear, the thrusts moved further, probably under a thicker cover, while to the south, movement was more intermittent, probably under a thinner cover. This variation is probably due to a change in thrust geometry in the Moines, east of the Moine thrust zone, causing a variation in gravitational potential along the length of the Moine thrust.

On oscillations of the Earth's fluid core

Summary. In the conventional spheroidal and toroidal representation, the differential equations governing long-period free oscillations of the Earth’s fluid core form an infinitely coupled system. Because of the mathematical complexity, solutions of this system are customarily attempted by numerical integration. The approach, however, necessitates a severe truncation of the coupling chain and this, in turn, renders it difficult to interpret the results. An alternative approach is sought in this work. By invoking the ‘solenoidal flow’ approximation which neglects the dilatation, and the ‘subseismic’ approximation which neglects the flow pressure respectively, we have succeeded in developing analytic solutions for the inertial and gravitational oscillations. This results in a significant simplification of the eigenvalue problem because the infinitely coupled system of differential equations is now reduced to an algebraic one. More importantly, the analytic solutions reveal immediately the roles played by the rotation and density stratification in core dynamics. We find that the inertial oscillations, which arise from the Earth’s rotation, are essentially independent of the core’s density stratification. Thus the fluid core can be approximated by a homogeneous, incompressible and non-gravitating inviscid Newtonian fluid with only minor modifications. The gravitational oscillations, on the other hand, are governed by both the rotation and density stratification. In a non-rotating earth, gravitational oscillations are not possible for neutrally or unstably stratified cores. Because of rotation, however, gravitational oscillations become possible for any density stratification in the core, and the eigenfrequencies are divided into alternating allowed and forbidden zones. We show that in each allowed zone, there exist an infinite number of gravitational oscillations with their eigenfrequencies approaching asymptotically the eigenfrequency of a corresponding inertial oscillation. Both the solenoidal flow and subseismic approximations ignore the fluid flow arising from the variation in gravitational potential. To correct for this neglect, as well as taking into account the deformation in the solid part of the Earth, an asymptotic formulation is developed. It is shown that the eigenfrequencies can be determined without explicitly solving for the ‘correction’

Geophysical data and long-wave heterogeneities of the Earth's mantle

To investigate the presence and nature of the lateral heterogeneities in the earth's mantle, geophysical data with global distribution are analyzed and correlated. Surface heat flow, seismic travel-time residuals, and crustal thickness data are expanded in spherical harmonics. Using these, and the coefficients of similar expansions of surface topography of the earth, and the gravitational potential variations as revealed by satellite data, both total and degree correlation coefficients are obtained. From the interpretation of these results, jointly with available laboratory data on velocity-density relationships and the temperature coefficient of velocity, the following are concluded: (1) Lateral mass anomalies and/or density variations in the earth's mantle are larger by at least an order of magnitude from what is required to explain the satellite data. Earth's surface topography and crustal structure introduce loads which are compensated in the upper, and perhaps lower, mantle giving rise to lateral density anomalies in the mantle. (2) Surface heat flow variations are controlled primarily by the shallow structure and tectonic features of the earth. (3) At long wavelengths (n ≤ 6), gravitational, heat flow, and seismic travel-time variations are not correlated with topographic elevations.