The availability of high-resolution global digital elevation data sets has raised a growing interest in the feasibility of obtaining their spherical harmonic representation at matching resolution, and from there in the modelling of induced gravity perturbations. We have therefore estimated spherical Bouguer and Airy isostatic anomalies whose spherical harmonic models are derived from the Earth's topography harmonic expansion. These spherical anomalies differ from the classical planar ones and may be used in the context of new applications. We succeeded in meeting a number of challenges to build spherical harmonic models with no theoretical limitation on the resolution. A specific algorithm was developed to enable the computation of associated Legendre functions to any degree and order. It was successfully tested up to degree 32,400. All analyses and syntheses were performed, in 64 bits arithmetic and with semi-empirical control of the significant terms to prevent from calculus underflows and overflows, according to IEEE limitations, also in preserving the speed of a specific regular grid processing scheme. Finally, the continuation from the reference ellipsoid's surface to the Earth's surface was performed by high-order Taylor expansion with all grids of required partial derivatives being computed in parallel. The main application was the production of a 1 × 1 equiangular global Bouguer anomaly grid which was computed by spherical harmonic analysis of the Earth's topographybathymetry ETOPO1 data set up to degree and order 10,800, taking into account the precise boundaries and densities of major lakes and inner seas, with their own altitude, polar caps with bedrock information, and land areas below sea level. The harmonic coefficients for each entity were derived by analyzing the corresponding ETOPO1 part, and free surface data when required, at one arc minute resolution. The following approximations were made: the land, ocean and ice cap gravity spherical harmonic coefficients were computed up to the third degree of the altitude, and the harmonics of the other, smaller parts up to the second degree. Their sum constitutes what we call ETOPG1, the Earth's TOPography derived Gravity model at 1 resolution (half-wavelength). The EGM2008 gravity field model and ETOPG1 were then used to rigorously compute 1 × 1 point values of surface gravity anomalies and disturbances, respectively, worldwide, at the real Earth's surface, i.e. at the lower limit of the atmosphere. The disturbance grid is the most interesting product of this study and can be used in various contexts. The surface gravity anomaly grid is an accurate product associated with EGM2008 and ETOPO1, but its gravity information contents are those of EGM2008. Our method was validated by comparison with a direct numerical integration approach applied to a test area in Morocco-South of Spain (Kuhn, private communication 2011) and the agreement was satisfactory. Finally isostatic corrections according to the Airy model, but in spherical geometry, with harmonic coeffi...

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A new model of Mars gravity field in spherical harmonics up to eighteenth degree and order has been computed from all available Doppler tracking data of Mariner 9 and Viking 1 and 2 orbiters. It represents an achievement in the knowledge of Mars global gravitational potential, since no more data will be available for such a derivation before the next mission to the planet. The model has been extensively tested from the point of view of orbit representation over periods of time ranging from a few hours to 12 days, and it is currently used for geophysical studies of the Martian lithosphere.

Abstract. We present a new 180th degree and order model of and order L = 40 (Sjogren et al., 1997), instead of L = 90, as the Venus gravity field directly derived from line of sight suggested by sensitivity studies relative to the cycle 4 Magellan residual Doppler data instead of usual line of sight Magellan orbits. This lower threshold also has the advantage residual acceleration data. We discuss the influence of the a to enhance the signal-to-noise ratio in the Doppler residuals. priori covariance matrices on the deconvolution process, and The second major difference is that we directly processed the compare our results with previous solutions.