An improved sampling rule for mapping geopotential functions of a planet from a near polar orbit

authored by: Matthias Weigelt, Nico Sneeuw, E. J.O. Schrama, Pieter N.A.M. Visser
Abstract: One of the limiting factors in the determination of gravity field solutions is the spatial sampling. Especially during phases, when the satellite repeats its own track after a short time, the spatial resolution will be limited. The Nyquist rule-of-thumb for mapping geopotential functions of a planet, also referred to as the Colombo-Nyquist rule-of-thumb, provides a limit for the maximum achievable degree of a spherical harmonic development for repeat orbits. We show in this paper that this rule is too conservative, and solutions with better spatial resolutions are possible. A new rule is introduced which limits the maximum achievable order (not degree!) to be smaller than the number of revolutions if the difference between the number of revolutions and the number of nodal days is of odd parity and to be smaller than half the number of revolutions if the difference is of even parity. The dependence on the parity is reflected in the eigenvalue spectrum of the normal matrix and becomes especially important in the presence of noise. The rule is based on applying the Nyquist sampling theorem separately in North-South and East-West direction. This is only possible for satellites in highly inclined orbits like champ and grace. Tables for these two satellite missions are also provided which indicate the passed and (in case of grace) expected repeat cycles and possible degradations in the quality of the gravity field solutions.
Organisation(s): Institute of Geodesy
External Organisation(s): University of Stuttgart
Delft University of Technology
Type: Article
Journal: Journal of geodesy
Volume: 87
Pages: 127-142
No. of pages: 16
ISSN: 0949-7714
Publication date: 02.2013
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Geophysics, Geochemistry and Petrology, Computers in Earth Sciences
Electronic version(s): https://doi.org/10.1007/s00190-012-0585-0 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{21125f93482a425dbcd5c014c0e7bf46,
title = "An improved sampling rule for mapping geopotential functions of a planet from a near polar orbit",
abstract = "One of the limiting factors in the determination of gravity field solutions is the spatial sampling. Especially during phases, when the satellite repeats its own track after a short time, the spatial resolution will be limited. The Nyquist rule-of-thumb for mapping geopotential functions of a planet, also referred to as the Colombo-Nyquist rule-of-thumb, provides a limit for the maximum achievable degree of a spherical harmonic development for repeat orbits. We show in this paper that this rule is too conservative, and solutions with better spatial resolutions are possible. A new rule is introduced which limits the maximum achievable order (not degree!) to be smaller than the number of revolutions if the difference between the number of revolutions and the number of nodal days is of odd parity and to be smaller than half the number of revolutions if the difference is of even parity. The dependence on the parity is reflected in the eigenvalue spectrum of the normal matrix and becomes especially important in the presence of noise. The rule is based on applying the Nyquist sampling theorem separately in North-South and East-West direction. This is only possible for satellites in highly inclined orbits like champ and grace. Tables for these two satellite missions are also provided which indicate the passed and (in case of grace) expected repeat cycles and possible degradations in the quality of the gravity field solutions.",
keywords = "champ, grace, Nyquist rule-of-thumb, Space-borne gravimetry, Spatial sampling",
author = "Matthias Weigelt and Nico Sneeuw and Schrama, {E. J.O.} and Visser, {Pieter N.A.M.}",
year = "2013",
month = feb,
doi = "10.1007/s00190-012-0585-0",
language = "English",
volume = "87",
pages = "127--142",
journal = "Journal of geodesy",
issn = "0949-7714",
publisher = "Springer Verlag",
number = "2",
}