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Cited by 41Geophysics and Gravity MeasurementsGeophysics and Sensor TechnologyGeophysical and Geoelectrical Methods

Evaluation of high-degree series expansions of the topographic potential to higher-order powers

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Hirt, Christian, Kuhn, Michael·2012·Journal of Geophysical Research: Solid Earth
DOI 10.1029/2012jb009492
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Abstract

Mass associated with surface topography makes a significant contribution to the Earth's gravitational potential at all spectral scales. Accurate computation in spherical harmonics to high degree requires calculations of multiple integer powers of the global topography. The purpose of this paper is to analyze the contributions of Earth's topography to its potential to the tenth power of the topography, and quantify truncation errors resulting from neglecting higher‐order powers. To account for the effect of gravity attenuation with height, we use series expansions for gravity upward‐continuation to the Earth's surface. With degree‐2160 expansions, limitation to the first three powers of the topography, as often done in practice, may give rise to maximum truncation errors exceeding 100 mGal at a reference sphere, and ∼25 mGal at the topography. Aiming for a maximum truncation error of 1 mGal we found that higher‐order terms to the seventh power are required over the Himalaya Mountains as example of Earth's most rugged land region. Upward‐continuation of topographic gravity effects with mGal‐precision from the sphere to the Earth's surface is accomplished with a series expansion of fifth order. As a key finding, the accurate conversion of topography to gravity effects at the Earth's surface is governed by two similar yet not identical series expansions. For degree‐2160 expansions, we recommend that the powers of Earth's topography be used up to seventh order to accurately evaluate the topographic potential to the mGal‐level, as required, e.g., for the construction of high‐resolution Bouguer gravity anomaly maps in spherical harmonics.

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  • GOCE series global gravity models can reach an accuracy level of 1 cm or higher but with a poor resolution of 1 degree by 1 degree.

    “For instance, the GOCE series models (see, e.g., [13]); also see the products released from ESA (www.esa.int(accessed on 10 March 2023)) and the International Centre for Global Earth Models (icgem.gfz-potsdam.de/ICGEM(accessed on 10 March 2023)) can reach an accuracy level of 1 cm (even higher) but with a poor resolution of 1 • × 1 • .”

    From Unification of a Global Height System at the Centimeter-Level Using Precise Clock Frequency Signal Links (2023) · cites this paper as [13]

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Related

Authors
Hirt, C., & Kuhn, M.
Affiliations
Curtin University (AU)
ORCID
Hirt, Christian
Venue
Journal of Geophysical Research: Solid Earth
Publisher
American Geophysical Union (AGU)
Published
2012-12
Volume
117
Issue
B12
ISSN
0148-0227 (ISSN-L)
DOI
10.1029/2012jb009492
OpenAlex
W1999058978
Cited by
41
References
48
Citations by year
2026: 3 · 2024: 2 · 2023: 2 · 2021: 1 · 2020: 3 · 2019: 3 · 2018: 3 · 2017: 8 · 2016: 7 · 2015: 2 · 2014: 3 · 2013: 3 · 2012: 1
FWCI
2.13
Type
journal article
Language
en
Open access
Licence
Locations
  • Journal of Geophysical Research Atmospheres (publishedVersion)
  • eSpace (Curtin University) (submittedVersion)
  • mediaTUM (Technical University of Munich) (submittedVersion, other-oa)
Funders
  • Institute for Geoscience Research
  • Australian Research Council
Topics
  • Physical Sciences › Earth and Planetary Sciences › Oceanography › Geophysics and Gravity Measurements
  • Physical Sciences › Engineering › Ocean Engineering › Geophysics and Sensor Technology
  • Physical Sciences › Earth and Planetary Sciences › Geophysics › Geophysical and Geoelectrical Methods
Keywords
topographic gravity, truncation error, upward continuation, Bouguer gravity anomalies, Himalaya, gravity field

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