Gravity gradiometry

Abstract: SUMMARY The fast Fourier transform (FFT) technique is a very powerful tool for the efficient evaluation of gravity field convolution integrals It can handle heterogeneous and noisy data, and thus presents a very attractive alternative to the classical, time consuming approaches, provided gridded data are available This paper reviews the mathematics of the FFT methods as well as their practical problems, and presents examples from physical geodesy where the application of these methods is especially advantageous The spectral evaluation of Stokes’, Vening Meinesz’ and Molodensky’s integrals, least-squares collocation in the frequency domain, integrals for terrain reductions and for airborne gravity gradiometry , and the computation of covariance and power spectral density functions are treated in detail Numerical examples illustrate the efficiency and accuracy of the FFT methods Key words: FFT, physical geodesy, spectral methods 1 INTRODUCTION Physical geodesy is the branch of geodesy which uses measured gradients of the anomalou6gravity potential T to determine a unique and coherent representation of the terrestrial gravity field at the Earth’s surface and in outer space The anomalous potential T is the difference between the actual gravity potential of the Earth and the reference potential of an ellipsoid with the same mass, flattening, and angular rotation rate as the Earth An approximation of T is needed to model geodetic measurements, to predict perturbations of satellite orbits, to determine global ocean circulation patterns, to assist global geophysics, and to support oil and mineral exploration In recent years, the amount of data available for the solution of this problem has increased dramatically, both in quantity and in type This has made the data processing problems more severe and has created a demand for efficient numerical solutions Since much of the data is available in gridded form, the use of fast spectral techniques was clearly appropriate Progress in the application of these methods to geodetic problems has been rapid during the last three years and it is almost certain that, because of their efficiency and accuracy, they will become standard procedures for a number of applications However, it has also become clear that geodetic and, more generally, geophysical data often present specific problems not usually encountered in typical electrical engineering applications The problems are with the heterogeneity of the data, the complicated surface on which they are given, the uneven spatial distribution, and the non-uniformity of the data noise This paper will discuss the use of

Abstract: The earliest history of the Moon is poorly preserved in the surface geologic record due to the high flux of impactors, but aspects of that history may be preserved in subsurface structures. Application of gravity gradiometry to observations by the Gravity Recovery and Interior Laboratory (GRAIL) mission results in the identification of a population of linear gravity anomalies with lengths of hundreds of kilometers. Inversion of the gravity anomalies indicates elongated positive-density anomalies that are interpreted to be ancient vertical tabular intrusions or dikes formed by magmatism in combination with extension of the lithosphere. Crosscutting relationships support a pre-Nectarian to Nectarian age, preceding the end of the heavy bombardment of the Moon. The distribution, orientation, and dimensions of the intrusions indicate a globally isotropic extensional stress state arising from an increase in the Moon's radius by 0.6 to 4.9 kilometers early in lunar history, consistent with predictions of thermal models.

Abstract: Topographic and isostatic mass anomalies affect the external gravity field of the Earth. Therefore, these effects also exist in the gravity gradients observed, e.g., by the satellite gravity gradiometry mission GOCE (Gravity and Steady-State Ocean Circulation Experiment). The downward continuation of the gravitational signals is rather difficult because of the high-frequency behaviour of the combined topographic and isostatic effects. Thus, it is preferable to smooth the gravity field by some topographic-isostatic reduction. In this paper the focus is on the modelling of masses in the space domain, which can be subdivided into different mass elements and evaluated with analytical, semi-analytical and numerical methods. Five alternative mass elements are reviewed and discussed: the tesseroid, the point mass, the prism, the mass layer and the mass line. The formulae for the potential, the attraction components and the Marussi tensor of second-order potential derivatives are provided. The formulae for different mass elements and computation methods are checked by assuming a synthetic topography of constant height over a spherical cap and the position of the computation point on the polar axis. For this special situation an exact analytical solution for the tesseroid exists and a comparison between the analytical solution of a spherical cap and the modelling of different mass elements is possible. A comparison of the computation times shows that modelling by tesseroids with different methods produces the most accurate results in an acceptable computation time. As a numerical example, the Marussi tensor of the topographic effect is computed globally using tesseroids calculated by Gauss–Legendre cubature (3D) on the basis of a digital height model. The order of magnitude in the radial-radial component is about ± 8 E.U.