scholarly journals Gravity Field Theory

2021 ◽  
Author(s):  
Ahmed Shehab Ahmed Al-Banna
Keyword(s):  
Field Theory ◽  
Gravity Field ◽  
Geophysical Methods ◽  
The Other ◽  
Earth Surface ◽  
Gravity Method ◽  
Geophysical Model ◽  
The Earth ◽  
Figure Of The Earth ◽  
Model Understanding

Gravity keep all things on the earth surface on the ground. Gravity method is one of the oldest geophysical methods. It is used to solve many geological problems. This method can be integrated with the other geophysical methods to prepare more accepted geophysical model. Understanding the theory and the principles concepts considered as an important step to improve the method. Chapter one attempt to discuss Newton’s law, potential and attraction gravitational field, Geoid, Spheroid and geodetically figure of the earth, the gravity difference between equator and poles of the earth and some facts about gravity field.

scholarly journals Accuracy Analysis of Gravity Field Changes from Grace RL06 and RL05 Data Compared to in Situ Gravimetric Measurements in the Context of Choosing Optimal Filtering Type

2020 ◽  
Vol 55 (3) ◽  
pp. 100-117
Author(s):  
Viktor Szabó ◽  
Dorota Marjańska
Keyword(s):  
Gravity Field ◽  
Ocean Circulation ◽  
Gravity Data ◽  
The Other ◽  
Subsurface Water ◽  
Satellite Gravity ◽  
Absolute Gravimetry ◽  
The Earth ◽  
Gravity Measurements ◽  
Gravity Recovery

AbstractGlobal satellite gravity measurements provide unique information regarding gravity field distribution and its variability on the Earth. The main cause of gravity changes is the mass transportation within the Earth, appearing as, e.g. dynamic fluctuations in hydrology, glaciology, oceanology, meteorology and the lithosphere. This phenomenon has become more comprehensible thanks to the dedicated gravimetric missions such as Gravity Recovery and Climate Experiment (GRACE), Challenging Minisatellite Payload (CHAMP) and Gravity Field and Steady-State Ocean Circulation Explorer (GOCE). From among these missions, GRACE seems to be the most dominating source of gravity data, sharing a unique set of observations from over 15 years. The results of this experiment are often of interest to geodesists and geophysicists due to its high compatibility with the other methods of gravity measurements, especially absolute gravimetry. Direct validation of gravity field solutions is crucial as it can provide conclusions concerning forecasts of subsurface water changes. The aim of this work is to present the issue of selection of filtration parameters for monthly gravity field solutions in RL06 and RL05 releases and then to compare them to a time series of absolute gravimetric data conducted in quasi-monthly measurements in Astro-Geodetic Observatory in Józefosław (Poland). The other purpose of this study is to estimate the accuracy of GRACE temporal solutions in comparison with absolute terrestrial gravimetry data and making an attempt to indicate the significance of differences between solutions using various types of filtration (DDK, Gaussian) from selected research centres.

scholarly journals Mach–Zehnder fiber interferometer test of the anisotropy of the speed of light

2009 ◽  
Vol 87 (9) ◽  
pp. 999-1008 ◽  
Author(s):  
Victor de Haan
Keyword(s):  
Optical Fiber ◽  
Phase Difference ◽  
Main Direction ◽  
The Other ◽  
Earth Surface ◽  
Temperature Stabilization ◽  
Speed Of Light ◽  
The Earth ◽  
Better Than ◽  
Phase Differences

Two optical fiber Mach–Zehnder interferometers were constructed in an environment with a temperature stabilization of better than 1 mK per day. One interferometer consisted of a length of 12 m optical fiber in each arm, with the main direction of the arms perpendicular to each other while the other consisted of a length of 2 m optical fiber in each arm, where the main direction of the arms are parallel, and served as a control. In each arm, 1 m of fiber was wound around a ring made of piezo material, enabling the control of the length of the arms by means of an applied voltage. The influence of the temperature on the optical phase difference between the interferometer arms was measured. The temperature change induced a variation of the interaction region of the optical fiber couplers. Further, the influence of rotation of the interferometers at the Earth surface on the observed phase differences was determined. For one interferometer (with the long and perpendicular arms), it was found that the phase difference depends on the azimuth of the interferometer. For the other one (with the short and parallel arms), no relevant dependence on the azimuth has been measured.

scholarly journals Reducing filter effects in GRACE-derived polar motion excitations

2020 ◽  
Author(s):  
Franziska Göttl ◽  
Michael Murböck ◽  
Michael Schmidt ◽  
Florian Seitz
Keyword(s):  
Gravity Field ◽  
Polar Motion ◽  
Grid Point ◽  
Ocean Model ◽  
Earth System ◽  
Satellite Mission ◽  
Geophysical Model ◽  
The Earth ◽  
Mass Redistribution ◽  
Filter Effects

<p><span>Polar motion is caused by mass redistribution and motion within the Earth system. The GRACE satellite mission observed variations of the Earth’s gravity field which are caused by mass redistribution. Therefore GRACE time variable gravity field models are a valuable source to estimate individual geophysical mass-related excitations of polar motion. Since GRACE observations contain erroneous meridional stripes, filtering is essential in order to retrieve meaningful information about mass redistribution within the Earth system. However filtering reduces not only the noise but also smooths the signal and induces leakage of neighboring subsystems into each other.</span></p><p><span><span>We present a novel approach to reduce these filter effects in GRACE-derived equivalent water heights and polar motion excitation functions which is based on once and twice filtered gravity field solutions. The advantages of this method are that it is independent from geophysical model information, works on global grid point scale and can therefore be used for mass variation estimations of several subsystems of the Earth (e.g. continental hydrosphere, oceans, Antarctica and Greenland). In order to validate this new method, we perform a closed-loop simulation based on a realistic orbit scenario and error assumptions for instruments and background models, apply it to real GRACE data (GFZ RL06) and show comparisons with ocean model results from ECCO and MPIOM.</span></span></p>

scholarly journals An account of experiments for determining the variation in the length of the pendulum vibrating seconds, at the principal stations of the trigonometrical survey of Great Britain

1833 ◽  
Vol 2 ◽  
pp. 117-118
Keyword(s):  
Great Britain ◽  
Centrifugal Force ◽  
The Other ◽  
The Earth ◽  
Constant Quantity ◽  
Figure Of The Earth ◽  
The Difference

In this communication Captain Kater, having noticed the circumstances to which his researches owe their origin, proceeds to detail his investigations, and to describe the implements and apparatus employed in his various inquiries; the construction of the pendulum and its appendages is minutely explained, as also the rate of its expansion for each thermometric degree, whence is deduced the corresponding correction to be applied to the number of its vibrations. The operations at each station, with their results, are enumerated at length, and illustrated by numerous tables. The length of the seconds pendulum for the latitude of London is 39·13722 inches in parts of the scale which forms the basis of the trigonometrical survey; for the latitude of Unst 39·16939 inches, of Portsay 39·15952, of Leith Fort 39·15347, of Clifton 39·14393, of Arbury Hill 39·14043, and of Shanklin Farm 39·13407 inches. The calculation of the latitude of each of these stations is given at length, to afford the opportunity of any further examination desirable on that subject; but these and the other details relating to calculation do not admit of abridgement. Captain Kater concludes this paper with some observations respecting the figure of the earth. It having been shown by Clairaut that the sum of the two fractions, expressing the ellipticity and the diminution of gravity, from the pole to the equator, is always a constant quantity, and equal to 5/2 of the fraction, expressing the ratio of centrifugal force, find that of gravity at the equator, it follows that if the decrease of gravity from the pole to the equator be subtracted from this constant quantity, the remaining fraction will express the ellipticity of the spheroid. The diminution of gravity may be known by finding the difference of the length of two pendulums, vibrating in equal times at the equator and pole, which are to each other directly as gravitation; but as such experiments cannot be made at the pole, Captain Kater proceeds to describe the means of obtaining the desired result by observations at intermediate stations; whence it appears that the length of the seconds pendulum at the equator, deduced from the observations at Unst and Dunnose, is 39·00527 inches, and gravitation at the equator 16·040 feet; hence the centrifugal force at the equator is 1/288 of gravitation, or 1/282 of gravity, which last being multiplied by 5/2 gives ·0086505 for the sum of the fractions, expressing the ellipticity of the earth and diminution of gravity from the pole to the equator.

scholarly journals Reducing filter effects in GRACE-derived polar motion excitations

2019 ◽  
Vol 71 (1) ◽  
Author(s):  
Franziska Göttl ◽  
Michael Murböck ◽  
Michael Schmidt ◽  
Florian Seitz
Keyword(s):  
Gravity Field ◽  
Polar Motion ◽  
Grid Point ◽  
Earth System ◽  
Satellite Mission ◽  
Geophysical Model ◽  
The Earth ◽  
Novel Approach ◽  
Mass Redistribution ◽  
Filter Effects

Abstract Polar motion is caused by mass redistribution and motion within the Earth system. The GRACE (Gravity Recovery and Climate Experiment) satellite mission observed variations of the Earth’s gravity field which are caused by mass redistribution. Therefore GRACE time variable gravity field models are a valuable source to estimate individual geophysical mass-related excitations of polar motion. Since GRACE observations contain erroneous meridional stripes, filtering is essential to retrieve meaningful information about mass redistribution within the Earth system. However filtering reduces not only the noise but also smoothes the signal and induces leakage of neighboring subsystems into each other. We present a novel approach to reduce these filter effects in GRACE-derived equivalent water heights and polar motion excitation functions which is based on once- and twice-filtered gravity field solutions. The advantages of this method are that it is independent from geophysical model information, works on global grid point scale and can therefore be used for mass variation estimations of several subsystems of the Earth. A closed-loop simulation reveals that due to application of the new filter effect reduction approach the uncertainties in GRACE-derived polar motion excitations can be decreased from 12–48% to 5–29%, especially for the oceanic excitations. Comparisons of real GRACE data with model-based oceanic excitations show that the agreement can be improved by up to 15 percentage points.

scholarly journals Spacetime coordinates in the geocentric reference frame

1986 ◽  
Vol 114 ◽  
pp. 269-276 ◽  
Author(s):  
M. Fujimoto ◽  
E. Grafarend
Keyword(s):  
Solar System ◽  
Gravity Field ◽  
Reference Frame ◽  
Relative Velocity ◽  
Proper Time ◽  
Frame Of Reference ◽  
Earth Surface ◽  
Riemann Geometry ◽  
The Earth ◽  
Integrating Factors

A geocentric relativistic reference frame is established which is close to the conventional non-relativistic equatorial frame of reference. Within post-Newtonian approximation the worldline of the geocentre is used to connect points by spacelike geodesics on the equal proper time hypersurface and to establish a properly chosen tetrad reference frame. Points on the earth surface and near the earth-space are coordinated making use of the Frobenius matrix of integrating factors which connects the geocentric orthonormal tetrad with the tangent spacetime of relativistic pseudo-Riemann geometry. The gravity field of the earth and its relative velocity with respect to the solar system barycentre cause coordinate effects of the order of 10 cm for topocentric point positioning.

II. On the precession of the equinoxes

1807 ◽  
Vol 97 ◽  
pp. 57-82
Keyword(s):  
Natural Philosophy ◽  
The Other ◽  
The Sun ◽  
Sir Isaac Newton ◽  
Isaac Newton ◽  
The Third ◽  
The Earth ◽  
Figure Of The Earth ◽  
The Subject ◽  
Theory Of Gravity

Perhaps the solution of no other problem, in natural philo­sophy, has so often baffled the attempts of mathematicians as that of determining the precession of the equinoxes, by the theory of gravity. The phenomenon itself was observed about one hundred and fifty years before the Christian æra, but Sir Isaac Newton was the first who endeavoured to estimate its magnitude by the true principles of motion, combined with the attractive influence of the sun and moon on the spheroidal figure of the earth. It has always been allowed, by those competent to judge, that his investigations relating to the subject evince the same transcendent abilities as are displayed in the other parts of his immortal work, the mathematical Principles of natural Philosophy, but, for more than half a century past, it has been justly asserted that he made a mistake in his process, which rendered his conclusions erro­neous. Since the detection of this error, some of the most eminent mathematicians in Europe have attempted solutions of the problem. Their success has been various; but their investi­gations may be arranged under three general heads. Under the first of these may be placed such as lead to a wrong conclusion, in consequence of a mistake committed in some part of the proceedings. The second head may be allotted to those in which the conclusions may be admitted as just, but rendered so by the counteraction of opposite errors. Such may be ranked under the third head as are conducted without error fatal to the conclusion, and in which the result is as near the truth as the subject seems to admit.

Note on Selection of Coordinate Systems for Geodynamics

1975 ◽  
Vol 26 ◽  
pp. 395-407
Author(s):  
S. Henriksen
Keyword(s):  
Sea Level ◽  
The Other ◽  
Coordinate Systems ◽  
Mean Sea Level ◽  
The Earth ◽  
The One ◽  
Static Systems ◽  
Selection Of

The first question to be answered, in seeking coordinate systems for geodynamics, is: what is geodynamics? The answer is, of course, that geodynamics is that part of geophysics which is concerned with movements of the Earth, as opposed to geostatics which is the physics of the stationary Earth. But as far as we know, there is no stationary Earth – epur sic monere. So geodynamics is actually coextensive with geophysics, and coordinate systems suitable for the one should be suitable for the other. At the present time, there are not many coordinate systems, if any, that can be identified with a static Earth. Certainly the only coordinate of aeronomic (atmospheric) interest is the height, and this is usually either as geodynamic height or as pressure. In oceanology, the most important coordinate is depth, and this, like heights in the atmosphere, is expressed as metric depth from mean sea level, as geodynamic depth, or as pressure. Only for the earth do we find “static” systems in use, ana even here there is real question as to whether the systems are dynamic or static. So it would seem that our answer to the question, of what kind, of coordinate systems are we seeking, must be that we are looking for the same systems as are used in geophysics, and these systems are dynamic in nature already – that is, their definition involvestime.

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