Assessment of discontinuities of Helmert’s gravity anomalies on the geoid

English Abstract:

Downward continuation of gravity anomalies has been always one of the most problematic steps in geoid computation, which in that, gravity anomalies on topography are transformed down to the geoid. The area of computation is broken down typically into 1°×1° cells, as the Poisson’s formulation -the rigorous formulation of the downward continuation problem- is very demanding on computer resources and the solution is sought separately for each cell. The results in individual cells are then fused together. That can be reliably done if there are no discontinuities between the downward continued values in adjacent cells. This implies that continuity of results should be checked and topic of this contribution is one possible approach to such checking.

The proposed method is assessing differences between overlapping adjacent 1°×1° cells; instead of downward continuing gravity anomaly to a 1°×1° cell on geoid, the cell area is increased by 1’ strip on each side. Such that cells on the geoid will have 1' overlap on each side, which then offer an opportunity to compare the results from adjacent 1° cells in two adjacent 1’-wide strips. Theoretically the differences should be either zero, or at least negligible if they are less than a low multiple of the standard deviation of observed data. We note that this approach can be used in a variety of problems encountered not only in geodesy but also in other experimental sciences.

Numerical assessment of the potential of this method has been done for mean Helmert gravity anomalies in Auvergne, France. The area limits to -1°<λ<7° and 43°<ϕ<49°, with standard deviation of about 40 μGal. Discontinuities between downward continued Helmert anomalies are between ±120 μGal. The general behavior of differences suggests that they are random in origin, but more detailed examination shows some biases which may be coming from topography, neglected far zone contributions or differences in the number of iterations in downward continuation process.