Details
| Original language | English |
|---|---|
| Pages (from-to) | 127-142 |
| Number of pages | 16 |
| Journal | Journal of geodesy |
| Volume | 87 |
| Issue number | 2 |
| Publication status | Published - Feb 2013 |
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
ASJC Scopus subject areas
- Earth and Planetary Sciences(all)
- Geophysics
- Earth and Planetary Sciences(all)
- Geochemistry and Petrology
- Earth and Planetary Sciences(all)
- Computers in Earth Sciences
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In: Journal of geodesy, Vol. 87, No. 2, 02.2013, p. 127-142.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - An improved sampling rule for mapping geopotential functions of a planet from a near polar orbit
AU - Weigelt, Matthias
AU - Sneeuw, Nico
AU - Schrama, E. J.O.
AU - Visser, Pieter N.A.M.
PY - 2013/2
Y1 - 2013/2
N2 - 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.
AB - 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.
KW - champ
KW - grace
KW - Nyquist rule-of-thumb
KW - Space-borne gravimetry
KW - Spatial sampling
UR - http://www.scopus.com/inward/record.url?scp=84873319189&partnerID=8YFLogxK
U2 - 10.1007/s00190-012-0585-0
DO - 10.1007/s00190-012-0585-0
M3 - Article
AN - SCOPUS:84873319189
VL - 87
SP - 127
EP - 142
JO - Journal of geodesy
JF - Journal of geodesy
SN - 0949-7714
IS - 2
ER -