Extended Applicability of the Spherical-Harmonic and Point-Mass Modeling of the Gravity Field,

1980 ◽  
Author(s):  
Georges Blaha
Keyword(s):  
Gravity Field ◽  
Spherical Harmonic ◽  
Point Mass

Gravity Field Recovery and Observation Noise Separation from Simultaneous Laser Ranging Interferometer and K-Band Ranging System Measurements

2020 ◽  
Author(s):  
Andreas Kvas ◽  
Saniya Behzadpour ◽  
Torsten Mayer-Guerr
Keyword(s):  
Gravity Field ◽  
Spherical Harmonic ◽  
Uncertainty Propagation ◽  
Stochastic Modelling ◽  
Laser Ranging ◽  
Polar Regions ◽  
Data Types ◽  
Covariance Functions ◽  
Gravity Field Recovery ◽  
K Band

<p>The unique instrumentation of GRACE Follow-On (GRACE-FO) offers two independent inter-satellite ranging systems with concurrent observations. Next to a K-Band Ranging System (KBR), which has already been proved during the highly-successfully GRACE mission, the GRACE-FO satellites are equipped with an experimental Laser Ranging Interferometer (LRI), which features a drastically increased measurement precision compared to the KBR. Having two simultaneous ranging observations available allows for cross-calibration between the instruments and, to some degree, the separation of ranging noise from other sources such as noise in the on-board accelerometer (ACC) measurements.  </p> <p>In this contribution we present a stochastic description of the two ranging observation types provided by GRACE-FO, which also takes cross-correlations between the two observables into account. We determine the unknown noise covariance functions through variance component estimation and show that this method is, to some extent, capable of separating between KBR, LRI, and ACC noise. A side effect of this stochastic modelling is that the formal errors of the spherical harmonic coefficients fit very well to empirical estimates, which is key for combination with other data types and uncertainty propagation. We further compare the gravity field solutions obtained from a combined least-squares adjustment to KBR-only and LRI-only results and discuss the differences between the time series with a focus on gravity field and calibration parameters. Even though, at the moment, global statistics only show a minor improvement when using LRI ranging measurements instead of KBR observations, some parts of the spectrum and geographic regions benefit significantly from the increased measurement accuracy of the LRI. Specifically, we see a higher signal-to-noise ratio in low spherical harmonic orders and the polar regions.</p>

Subtleties in spherical harmonic synthesis of the gravity field

2020 ◽  
Author(s):  
Ropesh Goyal ◽  
Sten Claessens ◽  
Will Featherstone ◽  
Onkar Dikshit
Keyword(s):  
Gravity Field ◽  
Spherical Harmonic ◽  
Gravitational Constant ◽  
Angular Rate ◽  
Physical Geodesy ◽  
Major Axis ◽  
Gravity Potential ◽  
Semi Major Axis ◽  
The Earth ◽  
Spherical Harmonic Synthesis

<p>Spherical harmonic synthesis (SHS) can be used to compute various gravity functions (e.g., geoid undulations, height anomalies, deflections of vertical, gravity disturbances, gravity anomalies, etc.) using the 4pi fully normalised Stokes coefficients from the many freely available Global Geopotential Models (GGMs).  This requires a normal ellipsoid and its gravity field, which are defined by four parameters comprising (i) the second-degree even zonal Stokes coefficient (J2) (aka dynamic form factor), (ii) the product of the mass of the Earth and universal gravitational constant (GM) (aka geocentric gravitational constant), (iii) the Earth’s angular rate of rotation (ω), and (iv) the length of the semi-major axis (a). GGMs are also accompanied by numerical values for GM and a, which are not necessarily identical to those of the normal ellipsoid.  In addition, the value of W<sub>0,</sub> the potential of the geoid from a GGM, needs to be defined for the SHS of many gravity functions. W<sub>0</sub> may not be identical to U<sub>0</sub>, the potential on the surface of the normal ellipsoid, which follows from the four defining parameters of the normal ellipsoid.  If W<sub>0</sub> and U<sub>0</sub> are equal and if the normal ellipsoid and GGM use the same value for GM, then some terms cancel when computing the disturbing gravity potential.  However, this is not always the case, which results in a zero-degree term (bias) when the masses and potentials are different.  There is also a latitude-dependent term when the geometries of the GGM and normal ellipsoids differ.  We demonstrate these effects for some GGMs, some values of W<sub>0</sub>, and the GRS80, WGS84 and TOPEX/Poseidon ellipsoids and comment on its omission from some public domain codes and services (isGraflab.m, harmonic_synth.f and ICGEM).  In terms of geoid heights, the effect of neglecting these parameters can reach nearly one metre, which is significant when one goal of modern physical geodesy is to compute the geoid with centimetric accuracy.  It is also important to clarify these effects for all (non-specialist) users of GGMs.</p>

scholarly journals Monthly spherical harmonic gravity field solutions determined from GRACE inter-satellite range-rate data alone

2006 ◽  
Vol 33 (2) ◽  
Author(s):  
S. B. Luthcke ◽  
D. D. Rowlands ◽  
F. G. Lemoine ◽  
S. M. Klosko ◽  
D. Chinn ◽  
...  
Keyword(s):  
Gravity Field ◽  
Spherical Harmonic ◽  
Rate Data ◽  
Range Rate

scholarly journals High-frequency analysis of Earth gravity field models based on terrestrial gravity and GPS/levelling data: a case study in Greece

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
T. D. Papanikolaou ◽  
N. Papadopoulos
Keyword(s):  
Gravity Field ◽  
Spherical Harmonic ◽  
Gravity Models ◽  
Earth Gravity Field ◽  
Earth Gravity ◽  
Gravity Field Recovery ◽  
High Degree ◽  
Spherical Harmonic Synthesis ◽  
Gravity Field Models ◽  
Terrestrial Data

AbstractThe present study aims at the validation of global gravity field models through numerical investigation in gravity field functionals based on spherical harmonic synthesis of the geopotential models and the analysis of terrestrial data. We examine gravity models produced according to the latest approaches for gravity field recovery based on the principles of the Gravity field and steadystate Ocean Circulation Explorer (GOCE) and Gravity Recovery And Climate Experiment (GRACE) satellite missions. Furthermore, we evaluate the overall spectrum of the ultra-high degree combined gravity models EGM2008 and EIGEN-6C3stat. The terrestrial data consist of gravity and collocated GPS/levelling data in the overall Hellenic region. The software presented here implements the algorithm of spherical harmonic synthesis in a degree-wise cumulative sense. This approach may quantify the bandlimited performance of the individual models by monitoring the degree-wise computed functionals against the terrestrial data. The degree-wise analysis performed yields insight in the short-wavelengths of the Earth gravity field as these are expressed by the high degree harmonics.

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