Covariance Functions Set Derived from Radial Multipoles Potentials: Theory and Some Results for Regional Gravity Field in Central Europe

1995 ◽  
pp. 296-303
Author(s):  
Alexander Marchenko ◽  
Oleg Abrikosov
Keyword(s):  
Gravity Field ◽  
Central Europe ◽  
Covariance Functions ◽  
Regional Gravity

GRACE Follow-On Gravity Field Recovery from Combined Laser Ranging Interferometer and Microwave Ranging System Measurements

2021 ◽  
Author(s):  
Saniya Behzadpour ◽  
Andreas Kvas ◽  
Torsten Mayer-Gürr
Keyword(s):  
Gravity Field ◽  
Laser Ranging ◽  
Measurement Technology ◽  
Additional Measurement ◽  
Covariance Functions ◽  
Gravity Field Recovery ◽  
Global Gravity ◽  
Least Squares Adjustment ◽  
Noise Covariance ◽  
Component Estimation

<p>Besides a K-Band Ranging System (KBR), GRACE-FO carries a Laser Ranging Interferometer (LRI) as a technology demonstration to provide measurements of inter-satellite range changes. This additional measurement technology provides supplementary observations, which allow for cross-instrument diagnostics with the KBR system and, to some extent, the separation of ranging noise from other sources such as noise in the on-board accelerometer (ACC) measurements.</p><p>The aim of this study is to incorporate the two ranging systems (LRI and KBR) observations in ITSG-Grace2018 gravity field recovery. The two observation groups are combined in an iterative least-squares adjustment with variance component estimation used to determine the unknown noise covariance functions for KBR, LRI, and ACC measurements. We further compare the gravity field solutions obtained from the combined solutions to KBR-only results and discuss the differences with a focus on the global gravity field and LRI calibration parameters.</p>

Towards an updated, enhanced regional gravity field solution for Antarctica

2021 ◽  
Author(s):  
Mirko Scheinert ◽  
Philipp Zingerle ◽  
Theresa Schaller ◽  
Roland Pail ◽  
Martin Willberg
Keyword(s):  
Gravity Anomaly ◽  
Gravity Field ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Data Set ◽  
Gravity Field Model ◽  
Terrestrial Gravity ◽  
Field Solution ◽  
Gravity Disturbances ◽  
Regional Gravity

<p>In the frame of the IAG Subcommission 2.4f “Gravity and Geoid in Antarctica” (AntGG) a first Antarctic-wide grid of ground-based gravity anomalies was released in 2016 (Scheinert et al. 2016). That data set was provided with a grid space of 10 km and covered about 73% of the Antarctic continent. Since then a considerably amount of new data has been made available, mainly collected by means of airborne gravimetry. Regions which were formerly void of any terrestrial gravity observations and have now been surveyed include especially the polar data gap originating from GOCE satellite gravimetry. Thus, it is timely to come up with an updated and enhanced regional gravity field solution for Antarctica. For this, we aim to improve further aspects in comparison to the AntGG 2016 solution: The grid spacing will be enhanced to 5 km. Instead of providing gravity anomalies only for parts of Antarctica, now the entire continent should be covered. In addition to the gravity anomaly also a regional geoid solution should be provided along with further desirable functionals (e.g. gravity anomaly vs. disturbance, different height levels).</p><p>We will discuss the expanded AntGG data base which now includes terrestrial gravity data from Antarctic surveys conducted over the past 40 years. The methodology applied in the analysis is based on the remove-compute-restore technique. Here we utilize the newly developed combined spherical-harmonic gravity field model SATOP1 (Zingerle et al. 2019) which is based on the global satellite-only model GOCO05s and the high-resolution topographic model EARTH2014. We will demonstrate the feasibility to adequately reduce the original gravity data and, thus, to also cross-validate and evaluate the accuracy of the data especially where different data set overlap. For the compute step the recently developed partition-enhanced least-squares collocation (PE-LSC) has been used (Zingerle et al. 2021, in review; cf. the contribution of Zingerle et al. in the same session). This method allows to treat all data available in Antarctica in one single computation step in an efficient and fast way. Thus, it becomes feasible to iterate the computations within short time once any input data or parameters are changed, and to easily predict the desirable functionals also in regions void of terrestrial measurements as well as at any height level (e.g. gravity anomalies at the surface or gravity disturbances at constant height).</p><p>We will discuss the results and give an outlook on the data products which shall be finally provided to present the new regional gravity field solution for Antarctica. Furthermore, implications for further applications will be discussed e.g. with respect to geophysical modelling of the Earth’s interior (cf. the contribution of Schaller et al. in session G4.3).</p>

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>

scholarly journals Thickness and Basal Configuration of Lower Blue Glacier, Washington, Determined by Gravimetry

1965 ◽  
Vol 5 (41) ◽  
pp. 637-650 ◽  
Author(s):  
Charles E. Corbató
Keyword(s):  
Gravity Field ◽  
Three Dimensional ◽  
Successive Approximations ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Gravity Measurements ◽  
Computational Errors ◽  
Terrain Corrections ◽  
Seismic Reflections ◽  
Regional Gravity

AbstractGravity measurements at 146 stations on lower Blue Glacier were used to determine the subglacial bedrock configuration. The gravity values, station elevations and density contrast were carefully measured, and terrain corrections thoroughly evaluated to insure accuracy of the Bottguer anomalies. A series of successive approximations results in evaluation of the regional gravity field and a three-dimensional model of the glacier whose gravimetric effects fit the range of the observational and computational errors. Comparison with bore holes and seismic reflections indicates no significant errors in the model and accuracies of 5–10 per cent in the calculated thicknesses of the glacier.

Reply by author to discussion by N. F. Uren

Geophysics ◽  
1970 ◽  
Vol 35 (1) ◽  
pp. 161-161
Author(s):  
M. K. Paul
Keyword(s):  
Differential Equation ◽  
Gravity Field ◽  
The Difference ◽  
Regional Gravity ◽  
Considerable Detail

I thank Mr. N. F. Uren for his interest in my paper. Mr. Uren’s discussion mainly concerns the appropriateness of the difference / differential equation that the regional gravity field, [Formula: see text], has been implied in my paper to satisfy. I think that this point has been discussed in considerable detail in my reply to an earlier discussion on this paper (Geophysics, June 1969, p. 483–485), which can, however, be summarized as follows.

scholarly journals Globally covering a-priori regional gravity covariance models

2003 ◽  
Vol 1 ◽  
pp. 143-147 ◽  
Author(s):  
D. Arabelos ◽  
C. C. Tscherning
Keyword(s):  
Gravity Anomaly ◽  
Covariance Function ◽  
Signal To Noise Ratio ◽  
A Priori ◽  
Scale Factor ◽  
Covariance Functions ◽  
Covariance Models ◽  
Free Air Gravity ◽  
Regional Gravity ◽  
Degree Variances

Abstract. Gravity anomaly data generated using Wenzel’s GPM98A model complete to degree 1800, from which OSU91A has been subtracted, have been used to estimate covariance functions for a set of globally covering equal-area blocks of size 22.5° × 22.5° at Equator, having a 2.5° overlap. For each block an analytic covariance function model was determined. The models are based on 4 parameters: the depth to the Bjerhammar sphere (determines correlation), the free-air gravity anomaly variance, a scale factor of the OSU91A error degree-variances and a maximal summation index, N, of the error degree-variances. The depth of Bjerhammar-sphere varies from -134km to nearly zero, N varies from 360 to 40, the scale factor from 0.03 to 38.0 and the gravity variance from 1081 to 24(10µms-2)2. The parameters are interpreted in terms of the quality of the data used to construct OSU91A and GPM98A and general conditions such as the occurrence of mountain chains. The variation of the parameters show that it is necessary to use regional covariance models in order to obtain a realistic signal to noise ratio in global applications.Key words. GOCE mission, Covariance function, Spacewise approach`

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