A Comparison of Direct and Indirect Numerical Methods for the Downward Continuation of Airborne Gravity Data

Abstract

The continuous downward continuation of the gravity field has been classified as an inverse, ill-posed problem. The practical evaluation of the harmonic Poisson downward continuation integral requires, however, the reformulation of the problem into discrete summations or convolution forms. Although this can be considered as regularization by discretization, it is not sufficient for practical downward continuation with current airborne data, because round-off errors and noise in the data are amplified. Sophisticated regularization, filtering or iteration methods have to be applied, which act on the signal to noise ratio and take the property of large sparse linear equation system into account during the downward continuation process.

The numerical comparison of direct and indirect methods for solving the discrete, inverse Poisson integral is the topic of this paper. Using high-frequency synthetic data sets at a typical flight height and with a characteristic noise level, the performance of the different methods is evaluated with respect to the reference gravity field generated at the reference sphere. The result is a detailed characterization of the behaviour of the algorithms for large sparse systems and includes the investigation of their behaviour for different applications, such as geoid determination and resource exploration. The methods that showed the most promising results for the synthetic data set were also used on a real data set.