An improved solution for the problem of upward continuation of gravity field data in rugged topography

The problem of upward continuation of potential field data measured on rugged topography has been tackled by several authors. Its importance lies in the fact that gravity data, and to a certain extent also magnetic and aeromagnetic data, are not measured on a plane, whereas all algorithms for signal analysis and inversion are designed to work with data reduced to a plane surface. On the other hand, the need of properly prepared gravity and magnetic data does not permit careless solutions of this problem. The method proposed in this paper is based on the principle of equivalent-sources. In our method, the equivalent-source layer has a specific geometry and depth. Therefore, only the density distribution has to be inverted. The upward continuation is then performed by means of a stepwise foreward computation procedure which minimizes edge effects. The method provides a well-conditioned system of linear equations and is, therefore, quite stable and produces high-quality results (errors less than 0.04% using the whole grid to invert for the density distribution) even in the case of very rough topography, which is its main advantage.