| Dedicated gravity field missions as GRACE sample the gravitational field
of the Earth only along the satellite ground-tracks. Usually, surface spherical harmonics
are used to interpolate from the graound track to the whole surface of the Earth.
Especially in a repeat-orbit situation, this spherical harmonics interpolation
contributes significantly to the undesired striping effect.
The gound track of an repeat orbit forms a pattern with diamond-shaped cells. The
graviational field is only known at the boundaries of these cells. An interpolation
from the boundary to the interior of the cells has to fulfill two requirements
1. reproduction of the values at the boundaries.
2. minimal "deformation energy" inside the cell.
The only function fulfilling this requirement is the solution of an boundary value problem
for the biharmonic equation.
The poster will show the discretization of the bihatmonic operator for a grid, which is parallel
to the boundaries of the cell. It will solve the boundary value problem by the method of finite
differences and will compare the solution with the usual surface spherical harmonics expansion. |