The gradiometric-geodynamic boundary value problem

Abstract

The role of gravity gradients is investigated in the framework of geodetic-geodynamic boundary value problems. The time variation of the Eötvös tensor can be separated into three parts. The first part is a surface movement term, the second is the time variation of the gravity field in the original point, and the third is a coupling term. The first and third terms can be computed by a third order derivative tensor of the gravity potential. These terms can be formulated in spherical and planar approximation. Gravity gradients have the advantage over gravity measurements that certain gravity gradient combinations are insensitive to site movements, thereby allowing the time variation of the gravity field to be determined without repeated height measurements. The solution of the corresponding gradiometric-geodynamic boundary value problem is shown with repeated gravity gradient measurements of the torsion balance. Several test computations with a simple mass density model were performed in order to analyze the time variation of gravity gradients and give estimates of their respective magnitudes.