Improving the Accuracy of Analytical Downward Continuation of Terrestrial Gravity Anomalies

The determination of the geoid using the Stokes integral involves transforming gravity data from their measurement altitude to the geoid/ellipsoid surface. This study focuses on improving the accuracy of analytical downward continuation (ADC) for reducing terrestrial gravity anomalies to the geoid. The ADC method uses the Taylor series and successive vertical gradients of the gravity anomalies. The Moritz integral formula, which is based on Poisson's integral, is used to derive the vertical gravity gradient. To enhance its accuracy, a mean vertical gradient is proposed by introducing an analytical formula based on planar approximation. This formula improves accuracy by 50%. Numerical analysis, using simulated free air anomalies up to harmonic degree/order 5540/5540, reveals that the difference between mean and point ADC results in geoidal height can be several decimeters. The study also finds that the ADC of 2'×2' anomalies remains stable even with different levels of noise, while the Taylor series of 1'×1' gravity anomalies diverges.