Numerical Examples for Downward Continuation of Gravity Anomalies

摘要

To compute gravity anomalies at the surface of the earth from airborne gravity measurements Poisson's integral for the plane applied to gravity anomalies is regarded as an integral equation of the first kind, whose solution gives the sought anomalies. In the practical application the integration is replaced by a summation, so that a system of linear equations is obtained. This system is solved by successive approximations. Several examples are computed to continue anomalies downward in the centers of 5 min. x 5 min., 15 min. x 15 min., and 1 deg. x 1 deg. blocks at elevations of 6 km and 8 km. The results show that the successive approximations converge fast. In case of flight elevations between 6 km and 10 km, however, the use of 5 min. x 5 min. blocks and of smaller blocks should be excluded from the downward continuation of airborne gravity measurements to avoid ill-conditioned matrices. (Author)