Knowledge Bank

The subject of the present report is downward continuation of gravity from flying altitudes to a reference surface. This is done by a numerical inversion of the upward continuation integral, which leads to the inversion of an ill-conditioned matrix. The first part considers computational and numerical problems such as the discretization of the upward continuation integral, the improvement of convergence of the iterative inversion by using the knowledge of the spectrum to obtain convergence factors, and the improvement of the stability of the linear system. In the second part, downward continuation of gravity is discussed theoretically as an improperly posed problem using Tykhonov's regularization, and various solutions proposed in the literature are compared.