Triangulated spherical splines for geopotential reconstruction |
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| Authors: | M J Lai C K Shum V Baramidze P Wenston |
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| Institution: | (1) Department of Mathematics, The University of Georgia, Athens, GA 30602, USA;(2) School of Earth Sciences, Ohio State University, Columbus, OH 43210, USA;(3) Department of Mathematics, Western Illinois University, Macomb, IL 61455, USA |
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| Abstract: | We present an alternate mathematical technique than contemporary spherical harmonics to approximate the geopotential based
on triangulated spherical spline functions, which are smooth piecewise spherical harmonic polynomials over spherical triangulations.
The new method is capable of multi-spatial resolution modeling and could thus enhance spatial resolutions for regional gravity
field inversion using data from space gravimetry missions such as CHAMP, GRACE or GOCE. First, we propose to use the minimal
energy spherical spline interpolation to find a good approximation of the geopotential at the orbital altitude of the satellite.
Then we explain how to solve Laplace’s equation on the Earth’s exterior to compute a spherical spline to approximate the geopotential
at the Earth’s surface. We propose a domain decomposition technique, which can compute an approximation of the minimal energy
spherical spline interpolation on the orbital altitude and a multiple star technique to compute the spherical spline approximation
by the collocation method. We prove that the spherical spline constructed by means of the domain decomposition technique converges
to the minimal energy spline interpolation. We also prove that the modeled spline geopotential is continuous from the satellite
altitude down to the Earth’s surface. We have implemented the two computational algorithms and applied them in a numerical
experiment using simulated CHAMP geopotential observations computed at satellite altitude (450 km) assuming EGM96 (n
max = 90) is the truth model. We then validate our approach by comparing the computed geopotential values using the resulting
spherical spline model down to the Earth’s surface, with the truth EGM96 values over several study regions. Our numerical
evidence demonstrates that the algorithms produce a viable alternative of regional gravity field solution potentially exploiting
the full accuracy of data from space gravimetry missions. The major advantage of our method is that it allows us to compute
the geopotential over the regions of interest as well as enhancing the spatial resolution commensurable with the characteristics
of satellite coverage, which could not be done using a global spherical harmonic representation.
The results in this paper are based on the research supported by the National Science Foundation under the grant no. 0327577. |
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| Keywords: | Geopotential Spherical splines Minimal energy interpolation Domain decomposition technique |
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