scholarly journals Revisiting the Light Time Correction in Gravimetric Missions Like GRACE and GRACE Follow-On

2020 ◽  
Author(s):  
Yihao Yan ◽  
Vitali Müller ◽  
Gerhard Heinzel ◽  
Min Zhong
Keyword(s):  
Gravity Field ◽  
Electromagnetic Waves ◽  
Classical Method ◽  
Relativistic Effects ◽  
Gravity Field Recovery ◽  
Iterative Equations ◽  
General Relativistic ◽  
Time Correction ◽  
The Difference ◽  
Lower Noise

<p>The satellite gravimetry missions GRACE (Gravity Recovery and Climate Experiment) and GRACE Follow-On provide the global and monthly gravity field for almost 17 years, which plays an irreplaceable role in understanding the mass transport of the Earth system. The key observation is the biased inter-satellite range, which is measured primarily by a K-Band Ranging system (KBR) in GRACE and GRACE Follow-On. The GRACE Follow-On satellites are additionally equipped with a Laser Ranging Interferometer (LRI), which provides measurements with lower noise compared to the KBR. However, the measured biased range which is directly measured by the inter-satellite ranging systems differs from the instantaneous biased range which is usually required for gravity field recovery. The difference is called the Light Time Correction (LTC) and arises from the non-zero travel time of electromagnetic waves between the spacecraft. We re-analyzed the LTC calculation from first principles considering general relativistic effects and state-of-the-art models of Earth’s potential field, and different types of orbital data. By analyzing the iterative equations in the LTC calculation of KBR and LRI, a novel analytical expression method is obtained to avoid the numerical limitation of the classical method. The dependency of the LTC on geopotential models and on the parameterization is further studied, and afterwards the results are compared against the LTC provided in the official datasets of GRACE and GRACE Follow-On. It is shown that the new approach has significantly lower noise, well below the instrument noise of current instruments, especially relevant for the LRI, and even if used with kinematic orbit products. This allows calculating the LTC accurate enough even for the next generation of gravimetric missions.</p>

scholarly journals Revisiting the light time correction in gravimetric missions like GRACE and GRACE follow-on

2021 ◽  
Vol 95 (5) ◽  
Author(s):  
Yihao Yan ◽  
Vitali Müller ◽  
Gerhard Heinzel ◽  
Min Zhong
Keyword(s):  
Gravity Field ◽  
Center Of Mass ◽  
Precise Orbit Determination ◽  
Relativistic Effects ◽  
Gravity Field Recovery ◽  
General Relativistic ◽  
Time Correction ◽  
The Difference ◽  
Electro Magnetic ◽  
Lower Noise

AbstractThe gravity field maps of the satellite gravimetry missions Gravity Recovery and Climate Experiment (GRACE ) and GRACE Follow-On are derived by means of precise orbit determination. The key observation is the biased inter-satellite range, which is measured primarily by a K-Band Ranging system (KBR) in GRACE and GRACE Follow-On. The GRACE Follow-On satellites are additionally equipped with a Laser Ranging Interferometer (LRI), which provides measurements with lower noise compared to the KBR. The biased range of KBR and LRI needs to be converted for gravity field recovery into an instantaneous range, i.e. the biased Euclidean distance between the satellites’ center-of-mass at the same time. One contributor to the difference between measured and instantaneous range arises due to the nonzero travel time of electro-magnetic waves between the spacecraft. We revisit the calculation of the light time correction (LTC) from first principles considering general relativistic effects and state-of-the-art models of Earth’s potential field. The novel analytical expressions for the LTC of KBR and LRI can circumvent numerical limitations of the classical approach. The dependency of the LTC on geopotential models and on the parameterization is studied, and afterwards the results are compared against the LTC provided in the official datasets of GRACE and GRACE Follow-On. It is shown that the new approach has a significantly lower noise, well below the instrument noise of current instruments, especially relevant for the LRI, and even if used with kinematic orbit products. This allows calculating the LTC accurate enough even for the next generation of gravimetric missions.

The re-analysis on the raw data processing of KBR and LRI on GRACE-FO

2021 ◽  
Author(s):  
Yihao Yan ◽  
Changqing Wang ◽  
Vitali Müller ◽  
Min Zhong ◽  
Lei Liang ◽  
...  
Keyword(s):  
Gravity Field ◽  
Science Data ◽  
Raw Data ◽  
Gravity Field Recovery ◽  
Offset Correction ◽  
Instrument Noise ◽  
Time Correction ◽  
Gravity Recovery ◽  
Temporal Gravity ◽  
Good Agreement

<div> <p>The KBR (K-Band ranging instrument) and LRI (Laser Interferometer) are used to measure the distance variations between the twin spacecraft, which is one of the most important observations used for temporal gravity field recovery. The data pre-processing from raw or so-called Level-1A into the Level-1B format, which is suited for gravity field recovery, is a key step. Although Level-1B files are made publicly available by the GRACE-FO Science Data System (SDS), it has been shown that alternative Level-1B datasets may yield improved the results of gravity field<sup>[1]</sup>. Investigations of the pre-processing may allow us to improve the gravity recovery strategy and are essential to support developments of gravimetric satellite missions in China, such as TianQin-2 project. The pre-processing normally includes the time-tag synchronization, filtering and resampling, and other corrections, e.g. light-time correction for both instruments and antenna offset correction for KBR. We re-processed the Level-1A data of KBR and LRI to the Level1B using code developed at IGG/Wuhan. The results show good agreement in case of the RL04 KBR data, i.e. the differences between IGG-KBR1B and SDS-KBR1B are about three orders of magnitude lower than the instrument noise level for KBR. For the LRI, we found that phase jumps are not removed completely in the SDS-LRI1B products. As shown by Abich<sup>[2]</sup>, these phase jumps in the LRI phase observations are mainly coincident with thruster activations. Our work will analyze the impacts of different processing methods of the raw data on post-fit residuals and the gravity field recovery based on IGG-KBR1B and IGG-LRI1B datasets.</p> <p> </p> <div> <p>[1] Wiese, D.: SDS Level-2/-3 JPL, GRACE/GRACE-FO Science Team Meeting 2020, online, 27 October–29 Oct 2020, GSTM2020-75, https://doi.org/10.5194/gstm2020-75, 2020.</p> <p>[2]    Abich K, Abramovici A, Amparan B, et al. In-Orbit Performance of the GRACE Follow-on Laser Ranging Interferometer [J]. Phys Rev Lett, 2019, 123(3): 031101, https://doi.org/10.1103/PhysRevLett.123.031101.</p> </div> </div><p> </p>

REFLECTION COEFFICIENT OF AN ELECTROMAGNETIC WAVE IN CONDUCTIVE MEDIA

2018 ◽  
pp. 100-106
Author(s):  
M. S. Sudakova ◽  
M. L. Vladov ◽  
M. R. Sadurtdinov
Keyword(s):  
Reflection Coefficient ◽  
Ground Penetrating Radar ◽  
Electromagnetic Waves ◽  
Water Contamination ◽  
Survey Design ◽  
Direct And Inverse Problems ◽  
The Difference ◽  
Ground Penetrating ◽  
Ideal Dielectric

Within the ground penetrating radar bandwidth the medium is considered to be an ideal dielectric, which is not always true. Electromagnetic waves reflection coefficient conductivity dependence showed a significant role of the difference in conductivity in reflection strength. It was confirmed by physical modeling. Conductivity of geological media should be taken into account when solving direct and inverse problems, survey design planning, etc. Ground penetrating radar can be used to solve the problem of mapping of halocline or determine water contamination.

Beyond the Schwarzschild Metric

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Gravitational Waves ◽  
Test Particle ◽  
Direct Detection ◽  
Relativistic Effects ◽  
Big Bang ◽  
Clusters Of Galaxies ◽  
General Relativistic ◽  
The Universe

General relativity explains much more than the spacetime around static spherical masses.We briefly assess general relativity in the larger context of physical theories, then explore various general relativistic effects that have no Newtonian analog. First, source massmotion gives rise to gravitomagnetic effects on test particles.These effects also depend on the velocity of the test particle, which has substantial implications for orbits around black holes to be further explored in Chapter 20. Second, any changes in the sourcemass ripple outward as gravitational waves, and we tell the century‐long story from the prediction of gravitational waves to their first direct detection in 2015. Third, the deflection of light by galaxies and clusters of galaxies allows us to map the amount and distribution of mass in the universe in astonishing detail. Finally, general relativity enables modeling the universe as a whole, and we explore the resulting Big Bang cosmology.

scholarly journals Earth’s Time-Variable Gravity from GRACE Follow-On K-Band Range-Rates and Pseudo-Observed Orbits

2021 ◽  
Vol 13 (9) ◽  
pp. 1766
Author(s):  
Igor Koch ◽  
Mathias Duwe ◽  
Jakob Flury ◽  
Akbar Shabanloui
Keyword(s):  
Gravity Field ◽  
Time Variable ◽  
Time Variable Gravity ◽  
Gravity Field Recovery ◽  
Variable Gravity ◽  
Earth’S System ◽  
Grace Mission ◽  
Insight Into ◽  
K Band

During its science phase from 2002–2017, the low-low satellite-to-satellite tracking mission Gravity Field Recovery And Climate Experiment (GRACE) provided an insight into Earth’s time-variable gravity (TVG). The unprecedented quality of gravity field solutions from GRACE sensor data improved the understanding of mass changes in Earth’s system considerably. Monthly gravity field solutions as the main products of the GRACE mission, published by several analysis centers (ACs) from Europe, USA and China, became indispensable products for quantifying terrestrial water storage, ice sheet mass balance and sea level change. The successor mission GRACE Follow-On (GRACE-FO) was launched in May 2018 and proceeds observing Earth’s TVG. The Institute of Geodesy (IfE) at Leibniz University Hannover (LUH) is one of the most recent ACs. The purpose of this article is to give a detailed insight into the gravity field recovery processing strategy applied at LUH; to compare the obtained gravity field results to the gravity field solutions of other established ACs; and to compare the GRACE-FO performance to that of the preceding GRACE mission in terms of post-fit residuals. We use the in-house-developed MATLAB-based GRACE-SIGMA software to compute unconstrained solutions based on the generalized orbit determination of 3 h arcs. K-band range-rates (KBRR) and kinematic orbits are used as (pseudo)-observations. A comparison of the obtained solutions to the results of the GRACE-FO Science Data System (SDS) and Combination Service for Time-variable Gravity Fields (COST-G) ACs, reveals a competitive quality of our solutions. While the spectral and spatial noise levels slightly differ, the signal content of the solutions is similar among all ACs. The carried out comparison of GRACE and GRACE-FO KBRR post-fit residuals highlights an improvement of the GRACE-FO K-band ranging system performance. The overall amplitude of GRACE-FO post-fit residuals is about three times smaller, compared to GRACE. GRACE-FO post-fit residuals show less systematics, compared to GRACE. Nevertheless, the power spectral density of GRACE-FO and GRACE post-fit residuals is dominated by similar spikes located at multiples of the orbital and daily frequencies. To our knowledge, the detailed origin of these spikes and their influence on the gravity field recovery quality were not addressed in any study so far and therefore deserve further attention in the future. Presented results are based on 29 monthly gravity field solutions from June 2018 until December 2020. The regularly updated LUH-GRACE-FO-2020 time series of monthly gravity field solutions can be found on the website of the International Centre for Global Earth Models (ICGEM) and in LUH’s research data repository. These operationally published products complement the time series of the already established ACs and allow for a continuous and independent assessment of mass changes in Earth’s system.

scholarly journals GRACETOOLS—GRACE Gravity Field Recovery Tools

Geosciences ◽  
2018 ◽  
Vol 8 (9) ◽  
pp. 350 ◽  
Author(s):  
Neda Darbeheshti ◽  
Florian Wöske ◽  
Matthias Weigelt ◽  
Christopher Mccullough ◽  
Hu Wu
Keyword(s):  
Open Source ◽  
Gravity Field ◽  
Transition Matrix ◽  
State Transition ◽  
Satellite Observations ◽  
Gravity Field Recovery ◽  
Grace Data ◽  
Range Rate ◽  
Analysis Platform ◽  
Recovery Tools

This paper introduces GRACETOOLS, the first open source gravity field recovery tool using GRACE type satellite observations. Our aim is to initiate an open source GRACE data analysis platform, where the existing algorithms and codes for working with GRACE data are shared and improved. We describe the first release of GRACETOOLS that includes solving variational equations for gravity field recovery using GRACE range rate observations. All mathematical models are presented in a matrix format, with emphasis on state transition matrix, followed by details of the batch least squares algorithm. At the end, we demonstrate how GRACETOOLS works with simulated GRACE type observations. The first release of GRACETOOLS consist of all MATLAB M-files and is publicly available at Supplementary Materials.

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>

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