HR: 1340h
AN: G33C-0060    [Abstracts]
TI: Spherical Spline Interpolation for Geopotential Reconstruction
AU: * Lai, M
EM: mjlai@math.uga.edu
AF: Department of Mathematics, University of Georgia, Athens, GA 30602 United States
AU: Shum, C
EM: ckshum@osu.edu
AF: Laboratory for Space Geodesy and Remote Sensing, Ohio State University, Columbus, OH 43210 United States
AU: Wenston, P
EM: paul@math.uga.edu
AF: Department of Mathematics, University of Georgia, Athens, GA 30602 United States
AU: Han, S
EM: han.104@osu.edu
AF: Laboratory for Space Geodesy and Remote Sensing, Ohio State University, Columbus, OH 43210 United States
AU: Baramidze, V
EM: vbaramid@math.uga.edu
AF: Department of Mathematics, University of Georgia, Athens, GA 30602 United States
AU: Xie, J
EM: xie.32@osu.edu
AF: Laboratory for Space Geodesy and Remote Sensing, Ohio State University, Columbus, OH 43210 United States
AB: We describe how to approximate the geopotential near the surface of the Earth using spherical spline functions. Spherical splines are smooth piecewise spherical harmonic polynomials over spherical triangulations. First, we propose a multiple star technique to compute a minimal energy spherical spline interpolation of a given set of geopotential measurements at the orbital surface of the satellite. Then we explain how to solve an inverse problem: using the solution expression of Laplace's equation on the exterior of a spherical surface around the Earth to compute a spherical spline approximation of the geopotential on the spherical surface. We prove that the spline interpolant constructed by means of the multiple star technique converges to the global minimal energy spline interpolant. The convergence of the minimal energy interpolating splines implies that the global minimal energy spline interpolant converges to the geopotential over the orbital surfacec of the satellite. We then prove that the linear system associated with the inverse problem is invertible and the spline geopotential on the spherical surface around the earth approximates the geopotential on that surface. Finally we use the spherical splines and apply our computational methods to contemporary space gravimetry measurements from GRACE for gravity field modeling. We will present some numerical experiments to demonstrate our methods.
DE: 0520 Data analysis: algorithms and implementation
DE: 0545 Modeling (4255)
DE: 1214 Geopotential theory and determination (0903)
SC: Geodesy [G]
MN: Fall Meeting 2005