On some methods of downward continuation of mean free-air gravity anomaly

Abstract

This paper investigates four methods of downward continuation of free-air gravity anomalies to sea-level, an iterative process based on the Poisson's integral, a linear simple formula, a method based on the Pellinen approximation and the one based on the topographic-isostatic potential proposed by Sjoberg. Mean free-air gravity anomalies in 6' X 10' cells from a test area with topographical heights between 71-396 metres have been successfully downward continued to sea-level. The effect of the downward continuation is everywhere positive on the geoid, while it is negative and positive on gravity anomalies. The results show some differences between these methods. The methods based on the Poisson's integral and topographic-isostatic potential have the smallest difference among the methods. A mean difference of 0.97 cm for the downward continuation effect on the geoid is computed between these two methods. In the Poissons' integral, long-wavelength contributions have been evaluated using a global gravity model and in the method based on topographic-isostatic potential, 30' X 30' heights information over the world are used to consider the long-wavelength contributions. They are missing in the other two methods. The correctness of the solution has then been checked by back substitution of the gravity values at the geoid to estimate them at the surface of the Earth. The Poisson's integral uses the gravity anomalies, directly, for the downward continuation of them to the geoid, while the Sjoberg's method implies the height data. Also, because some approximation made in the latter, the iterative process of the Poisson's integral is preferred.

On some methods of downward continuation of mean free-air gravity anomaly