Spectral methods in gravity inversion: the geopotential field and its derivatives

The 3D spectral analysis of the gravitational potential field for a given mass distribution is studied. The derived quantities, the gravitational force field and the gravity gradient tensor are computed in frequency space. As an example, the fields are theoretically and numerically evaluated for a right rectangular prism. The spectral approach finds several geophysical applications, as, e.g., in inversion processes. Gravity inversion for deep seated masses, as for instance at Moho level, are treated with an iterative inversion process, in which the downward continuation is alternated with the classical calculation of the gravity field. The theory is applied to the inversion of the gravity data in the SE-Alps, regarding only the long-period field, generated by Moho undulations. The results are used for the evaluation of the equipotential lines, the gravity field, and the gravity gradient tensor in a vertical section of the Alpine crustal root