Approximate continuation of harmonic functions in geodesy: A spline based least squares approach with regularization

This paper is concerned with the approximate reconstruction of the earth’s potential field from geometric and gravimetric data. This is an ill-posed problem involving typically large amounts of data which are to be continued by a harmonic function. The standard approach in geodesy is based on spherical harmonics which are globally supported. Thus, a least squares approach for the data fitting yields a linear system of equations with a fully populated system matrix. This becomes computationally prohibitive for large amounts of data and, therefore, presents the biggest bottleneck for fast and efficient computations.