Alternative Estimation Techniques for Global High-Degree Gravity Modeling

High-degree (Nmax=360) gravitational models require surface gravity data to resolve the fine structure of the field. Given a global gravity anomaly data set, one can extract this information using either quadrature formulæ (orthogonality relations) or by solving a system of observation equations. Under certain conditions such a system yields a normal matrix of block-diagonal structure. To determine accurately the lower part of the spectrum requires the least-squares combination of the surface gravity information with a satellite-only gravity model. Depending on the technique employed to develop the surface gravity solution, the estimation of a combined model can be performed in different ways.We have used a global set of 30’ mean gravity anomalies and a satellite-only model to produce combination solutions using both quadratures and the block-diagonal adjustment technique. In both cases the complete covariance matrix of the satellite-only model was used. Global geoid height difference (to Nmax=360) between the two types of solution is at the ± 20 cm level. The error spectra obtained from the two techniques are in excellent agreement. The models from the two techniques perform equally well in orbit fit tests. Absolute comparisons with GPS/Leveling-derived undulations over British Columbia and the US indicated that the block-diagonal technique yields slightly better results. However, relative GPS/Leveling undulation comparisons seem to indicate a problem with the higher degree harmonics obtained from the block-diagonal technique which requires further study.