Abstract
In the Earth gravity-field model, potential coefficients are projections of the Earth gravitational potential on the corresponding spherical harmonics by degree and order. These coefficients reflect the spectral composition of the Earth gravitational potential in the whole space, but they cannot reflect the spectral composition in a local area. In this study, the Earth gravitational potential was projected on spherical harmonics in a local area using a window function introduced to facilitate the mathematical expressions. Then a model for the spectral structure of the Earth gravitational potential in the local area was established. The model can reflect the signal strength of any gravity-field spectrum component in the local area, which adds information for the description of the gravity field of the Earth, and which has great significance for Earth-sciences research and satellite gravity measurements. Taking the third-degree coefficients, for example, the signal-strength distributions of potential coefficients were computed. The data show that the signal-strength distributions of third-degree coefficients on the sphere surface are independent of the longitude. Among the third-degree coefficients, the zero-order, first-order and second-order coefficients are stronger near the two poles of the Earth, while the third-order coefficient is stronger near the equator.
Highlights
The Earth gravity field is one of basic physical fields of the Earth, and it reflects information relating to matter distribution inside the Earth and affects physical events on the Earth and in the neighboring space
By projecting gravitational potential on spherical harmonic functions in the global area, i.e., using spherical harmonic analysis (SHA), a conventional gravity model can be obtained, and one potential coefficient reflects the total energy of the corresponding spherical harmonic in the global area
In our method, the gravitational potential in a local area is directly projected on the spherical harmonic functions, not on the spherical cap harmonic functions, which compared to spherical cap harmonic analysis (SCHA), can obtain more potential coefficients and a more comprehensive spectrum structure for the local area, the computation cost will increase
Summary
The Earth gravity field is one of basic physical fields of the Earth, and it reflects information relating to matter distribution inside the Earth and affects physical events on the Earth and in the neighboring space. In the present study, based on the results in Slepian and Pollak [1961], the Earth gravitational potential was projected onto spherical harmonic functions in a local area, and by appropriate mathematical expressions, the signal-strength model for the gravity potential spectral component in a local space was established.
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