ALBERT

Notes: We have employed least-squares collocation to derive a gravity field over the Reykjanes Ridge using Seasat, Geosat/ERM, ERS-1 and TOPEX/POSEIDON altimeter data combined with ship gravity. To avoid a crossover adjustment to correct for orbital errors we used mean geoid gradients, which were obtained by averaging gradients over 60, 10 and 36 repeat cycles for Geosat/ERM, ERS-1 and TOPEX/POSEIDON, respectively. The average standard deviations for the Geosat/ERM, ERS-1 and TOPEX/POSEIDON mean gradients are 1.12, 3.25 and 2.01 rad respectively. The standard deviations of the ship gravity, which were assigned based on weightings derived from an analysis of crossing differences, range from 6.72 to 20.17 mgal. The necessary covariances for the least-squares collocation computations were derived using the law of covariance propagation. Before merging with the altimeter data, the ship gravity for each leg was adjusted by removing a quadratic polynomial in time in order to match a satellite-only gravity field in a least-squares sense. The result of the adjustment suggests that most of the ship gravity data collected in the 1960s and the 1970s have average offsets of about 14 mgal, which is close to the offset of the Potsdam Datum. The rms difference between the satellite-only gravity, derived using least-squares collocation, and the adjusted ship gravity is 7.10 mgal, smaller than the rms difference of 12.47 mgal between the satellite-only gravity derived by a Fourier transform method and the adjusted ship gravity. The rms difference between the combined gravity field, derived from both altimetry and ship gravity, and the adjusted ship gravity is 2.65 mgal, suggesting that the former has successfully absorbed the high-frequency component of the gravity signal provided by the latter. The combined gravity field thus features a regionally uniform medium resolution from altimetry and a locally high resolution from ship gravity. The average accuracy estimate given by least-squares collocation for the combined gravity is 5.76 mgal. The combined gravity field reveals detailed tectonic structures over the Reykjanes Ridge related to the interaction of the Iceland hot spot and sea-floor spreading at the ridge.

Notes: 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.