Downward continuation of airborne gravity data by means of the change of boundary approach

Abstract

Within the modelling of gravity data, a common practice is the upward/downward continuation of the signal, i.e. the process of continuing the gravitational signal in the vertical direction away or closer to the sources, respectively. The gravity field, being a potential field, satisfies the Laplace’s equation outside the masses and this means that it allows to unambiguously perform this analytical continuation only in a source-free domain. The analytical continuation problem has been solved both in the space and spectral domains by exploiting different algorithms. As well known, the downward continuation operator, differently from the upward one, is an unstable operator, due to its spectral characteristics similar to those of a high-pass filter, and several regularization methods have been proposed in order to stabilize it. In this work, an iterative procedure to downward/upward continue the gravity field observations, acquired at different altitudes, is proposed. This methodology is based on the change of boundary principle and it has been expressively thought for aerogravimetric observations for geophysical exploration purposes. Within this field of application, usually several simplifications can be applied, basically due to the specific characteristics of the airborne surveys which are usually flown at almost constant altitude as close as possible to the terrain. For instance, these characteristics, as shown in the present work, allow to perform the downward continuation without the need of any regularization. The goodness of the proposed methodology has been evaluated by means of a numerical test on real data, acquired in the South of Australia. The test shows that it is possible to move the aerogravimetric data, acquired along tracks with a maximum height difference of about 250 m, with accuracies of the order of 10 $$^{-3}$$ mGal.