An Inverse Gravimetric Problem with GOCE Data
Satellite missions dedicated to the estimation of the gravity field and its variation, like GRACE and GOCE, have drawn new attention on inverse gravimetric problems and, in particular, on the capability of these satellite data sets to describe nature and
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An Inverse Gravimetric Problem with GOCE Data M. Reguzzoni and D. Sampietro
Abstract Satellite missions dedicated to the estimation of the gravity field and its variation, like GRACE and GOCE, have drawn new attention on inverse gravimetric problems and, in particular, on the capability of these satellite data sets to describe nature and geographical location of the gravimetric signal. In this paper a semi-analytical method to detect Earth’s density anomalies, based on Fourier analysis and Wiener filter, has been developed. The method has been tested on simulated observations of the gravitational potential and its second radial derivatives with the aim of assessing the capability of the GOCE mission to detect the shape of the oceanic floor from satellite data only. Despite the simplistic hypotheses involved in our example, positive results have been obtained, showing that the shape of the oceanic floor can be estimated with a reasonable accuracy at a resolution consistent with the expected GOCE performance.
60.1 The Problem and Proposed Solution The determination of the structure of the Earth’s interior, based on the inversion of Newton’s gravitational potential (gravimetry problem), has been studied in various publications (see for example Ballani and
M. Reguzzoni () Italian National Institute of Oceanography and Applied Geophysics (OGS), c/o Politecnico di Milano, Polo Regionale di Como, Como 22100, Italy e-mail: [email protected]
Stromeyer, 1982, 1990; Hein et al., 1989; Vajda, 2006). Since the purpose of this paper is not to implement an inverse algorithm but rather to study the sensitivity of GOCE (ESA, 1999) data to local mass anomalies, we will work on such a problem, accepting very simplified hypotheses. So we try to detect and reconstruct a sea floor feature (mountain chain), orthogonally crossed by the GOCE orbits. First of all we neglect the Earth curvature; note that for some geophysical problems this is a frequently used approach (see Kirchner, 1997; Gangui, 1998; Lessel, 1998). Furthermore if the mountain chain is developing with homogeneous characteristics in the cross-track direction, the problem of reconstructing its shape can be considered essentially as a two dimensional problem and can be formulated and solved by a suitable application of the Fourier Transform. We basically suppose that the feature generating the gravity signal is a two-layer structure with one layer at 1 g cm−3 density (water) and the other at 2.67 g cm−3 (rocks), with a density contrast σ of 1.67 g cm−3 . We assume that at the altitude of h = 250 km from the sea surface a GOCE-like satellite “observes” the anomalous potential T and its second radial derivatives Tzz . In this study the z axis has the origin at the satellite altitude and is downlooking (the geometry of the problem is represented in Fig. 60.1). Since the ocean floor can be described by a function D(x) = D + δD(x) with D = const and δD < 0,, the deterministic model we have to invert is given by (Heiskanen and Moritz, 1967):
h+D+δD(ξ)
T(x)
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