Potential Theory and the Static Gravity Field of the Earth

Jekeli, Christopher

doi:10.1016/b978-0-444-53802-4.00056-7

Cited by 11 publications

(9 citation statements)

References 48 publications

(28 reference statements)

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“…To evaluate the solutions derived from different kinematic empirical parameters processing strategies, the comparison in terms of equivalent water height (EWH) was also conducted. The same postprocessing procedure was applied as follows: (1) the P4M6 decorrelation filtering was applied to remove the correlated noise by fitting and subtracting a fourth‐order polynomial to even and odd coefficient pairs at spherical harmonic orders six and above (Swenson & Wahr, ), (2) the Gaussian filter with a radius of 300 km was implemented to reduce the high‐degree errors (Jekeli, ), (3) a global gridded 1° × 1° surface mass change field in terms of EWHs was calculated from each of the GRACE solutions, following the equations defined by Wahr et al (). The annual amplitudes and yearly trends in terms of EWH were then computed.…”

Section: Results Based On Grace Datamentioning

confidence: 99%

Impact of Different Kinematic Empirical Parameters Processing Strategies on Temporal Gravity Field Model Determination

et al. 2018

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During temporal gravity field model determination, the kinematic empirical parameters are mainly designed to remove the strong bias, drift, and 1‐cycle per revolution variations in range‐rates. In practice, two different strategies are commonly used to process these empirical parameters. One is to determine the empirical parameters before solving spherical harmonic coefficients, called Pure Predetermined Strategy (PPS). The other is to simultaneously determine the empirical parameters and spherical harmonic coefficients, called Pure Simultaneous Strategy (PSS). In this study, apart from these two strategies, a novel processing strategy called Filter Predetermined Strategy (FPS) is also discussed. These different processing strategies may result in different solutions. With the Gravity Recovery and Climate Experiment Level 1B data spanning 2005 to 2010, the impacts of different kinematic empirical parameters processing strategies were assessed in detail. The numerical results indicate that (1) using three different processing strategies and their hybrids can determine the temporal gravity field model, while (2) the solutions via PPS present apparent temporal signal attenuation, which is approximately 15% lower in annual amplitude in Amazon River Basin, and 15% lower in yearly trend in Greenland, and (3) the signal‐to‐noise ratios of the solutions via PPS are generally smaller than those of the solutions via FPS and PSS, and (4) the performance of FPS is superior in terms of postfit range‐rates, but compatible with PSS in terms of other cross comparisons. According to comprehensive comparison results in terms of temporal signals and noise, the performance of our Huazhong University of Science and Technology models determined via FPS is in excellent accordance with other representative temporal gravity field models, such as CSR RL05, GFZ RL05a, and JPL RL05.

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Section: Results Based On Grace Datamentioning

confidence: 99%

Impact of Different Kinematic Empirical Parameters Processing Strategies on Temporal Gravity Field Model Determination

et al. 2018

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“…The [2, m ] Q quadrupoles are closely related to the inertia tensor [ Chao and Gross , ]. In particular, the [2, 0] Q quadrupole represents the dynamic oblateness of the Earth; its corresponding Stokes coefficient is larger by at least 2 orders of magnitude than the next in order [e.g., Jekeli , ]. That is obviously true for any radius within the Earth.…”

Section: Statics Of the Micg Systemmentioning

confidence: 99%

Dynamics of axial torsional libration under the mantle‐inner core gravitational interaction

Chao

2017

JGR Solid Earth

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The aims of this paper are (i) formulating the dynamics of the mantle‐inner core gravitational (MICG) interaction in terms of the spherical‐harmonic multipoles of mass density. The modeled MICG system is composed of two concentric rigid bodies (mantle and inner core) of near‐spherical but otherwise heterogeneous configuration, with a fluid outer core in between playing a passive role. We derive the general equation of motion for the vector rotation but only focus on the polar component that describes the MICG axial torsional libration. The torsion constant and hence the square of the natural frequency of the libration is proportional to the product of the equatorial ellipticities of the mantle and inner‐core geoid embodied in their multipoles (of two different types) of degree 2 and order 2 (such as the Large Low‐Shear‐Velocity Provinces above the core‐mantle boundary) and (ii) studying the geophysical implications upon equating the said MICG libration to the steady 6 year oscillation that are observed in the Earth's spin rate or the length‐of‐day variation (ΔLOD). In particular, the MICG torsion constant is found to be Γtrue˜z = CIC σz2 ≈ 6.5 × 1019 N m, while the inner core's (BIC − AIC) ≈ 1.08 × 1031 kg m2 gives the inner core triaxiality (BIC − AIC)/CIC ≈ 1.8 × 10−4, about 8 times the whole‐Earth value. It is also asserted that the required inner‐core ellipticity amounts to no more than ~140 m in geoid height, much smaller than the sensitivity required for the seismic wave travel time to resolve the variation of the inner core.

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“…The coordinates of CM in a Cartesian coordinates system are defined by a volume integral of product of an infinitesimal mass element d m and its location in each coordinate axis (i.e., linear moment) over the Earth, for example,

X_{normalC normalM} ≡ \frac{1}{M} true \int X normald m

for the X axis. It can be shown that the CM coordinates are directly related to the “degree 1” gravitational potential field as follows [e.g., Jekeli , ]:

X_{normalC normalM} ≡ \frac{1}{M} true \int X normald m = \sqrt{3} a {\overset{true¯}{C}}_{1,1},

Y_{normalC normalM} ≡ \frac{1}{M} true \int Y normald m = \sqrt{3} a {\overset{true¯}{S}}_{1,1},

Z_{normalC normalM} ≡ \frac{1}{M} true \int Z normald m = \sqrt{3} a {\overset{true¯}{C}}_{1,0},

where

{\overset{true¯}{C}}_{1,0}

{\overset{true¯}{C}}_{1,1}

, and

{\overset{true¯}{S}}_{1,1}

are the degree 1 gravitational potential coefficients. The coefficients are dimensionless and normalized following the convention in Heiskanen and Moritz [].…”

Section: Center Of Mass Of the Earth's Systemmentioning

confidence: 99%

Seasonal clockwise gyration and tilt of the Australian continent chasing the center of mass of the Earth's system from GPS and GRACE

Han

2016

JGR Solid Earth

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As atmosphere, ocean, ice, and terrestrial water are redistributed, the center of mass (CM) of the Earth's system moves and the accompanying loading yields global surface deformation. In Australia, when GPS surface displacements were corrected for local mass change (hydrology, atmosphere, and ocean) with Gravity Recovery And Climate Experiment (GRACE) data, the residual GPS data reveal a peculiar seasonal mode of continental deformation. During the southern summer, the entire continent coherently shifts northwest by ~1 mm and the southeastern part is uplifted, while the northwestern part is subsided by 2–3 mm and the opposite patterns of deformation are observed during the southern winter. Such characteristic deformation could be understood to be a result of the Earth's elastic response to globally averaged surface mass load, generally heavier in Europe during southern summer and in the South Pacific Ocean during southern winter. It was found that such deformation is even larger than local hydrology‐induced loading effects in horizontal motion over Australia. A simple method of determining locations of the CM was developed by combining GPS and GRACE data; the latter being insensitive to the CM motion but sufficiently accurate to remove the local hydrologic and atmospheric effects in GPS data. The CM signals are pronounced over systematic errors in GPS and GRACE data. The CM coordinates estimated by inversion of the Australian GPS data set and GRACE agree with the geocenter motions determined by satellite tracking analysis. This study suggests an independent way of monitoring the CM motion entirely based on two distinct geodetic measurements of GPS and GRACE.

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Potential Theory and the Static Gravity Field of the Earth

Cited by 11 publications

References 48 publications

Impact of Different Kinematic Empirical Parameters Processing Strategies on Temporal Gravity Field Model Determination

Impact of Different Kinematic Empirical Parameters Processing Strategies on Temporal Gravity Field Model Determination

Dynamics of axial torsional libration under the mantle‐inner core gravitational interaction

Seasonal clockwise gyration and tilt of the Australian continent chasing the center of mass of the Earth's system from GPS and GRACE

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