An optimal procedure for deriving marine gravity from multi-satellite altimetry

Abstract

An optimal procedure is developed for deriving gravity anomalies from sea-surface height measurements obtained by a number of different satellites, the inclinations of which may vary. We begin by recasting the problem of the conversion of the deflection of the vertical to gravity in the frequency domain. We show that a deterministic approach based on the Vening-Meinesz integral is equivalent in the frequency domain to the stochastically based method of least-squares collocation. A new method for gridding the deflection of the vertical is developed that uses the fact that satellite tracks of the same type (ascending or descending) are nearly parallel, so that values at grid points can be estimated by first performing along-track interpolations, followed by one cross-track interpolation, both using Akima's spline. This gridding method is very efficient compared with methods such as that of fitting minimum curvature surfaces, especially for dense data such as for the 168 day cycles of ERS-1. A weighted least-squares method is then employed to obtain the north and east components of deflection-of-the-vertical components using the gridded along-track components from all of the individual satellite missions. Finally, gravity anomalies are computed from the two deflection-of-the-vertical components in the frequency domain with truncated kernel functions, the use of which is related to the prior removal of a high-degree reference gravity field. This new procedure is more than 100 times faster than least-squares collocation, and yields gravity anomalies with errors that are comparable to those derived by least-squares collocation and smaller than those derived by other recent applications of spectral techniques, as judged by comparisons with ship-gravity measurements. The case of gravity computation for a single altimetric satellite is handled separately, and a method is given to estimate the noise spectra of deflection of the vertical and reduce the numerical problems caused by satellites with high inclination angles. The new procedures make possible quick, yet accurate, global updates of the marine gravity field.