The free boundary value problem of physical geodesy and its uniqueness
Abstract
From the expansion into spherical harmonics of the gravitational potential in the external space, a determinant condition for the uniqueness of the free boundary value problem is derived. The specialization to the gravitational potential of the earth shows that this determinant does not vanish. This proves the uniqueness of the problem. This is valid as long as the spherically symmetric part of the gravitational field prevails and, to a first approximation, in gravimetric considerations the mass of the earth can be assumed to be concentrated in its centre of gravity.
 Publication:

Gerlands Beitraege zur Geophysik
 Pub Date:
 1979
 Bibcode:
 1979GBzG...88..179A
 Keywords:

 Boundary Value Problems;
 Geodesy;
 Geopotential;
 Spherical Harmonics;
 Earth Surface;
 Series (Mathematics);
 Geophysics