BSc thesis: Cálculo do tensor gradiente gravimétrico utilizando tesseroides

Thesis for my Bachelor's degree in Geophysics from the Universidade de São Paulo.

Abstract

The GOCE satellite mission has the objective of measuring the Earths gravitational field with an unprecedented accuracy through the measurement of the gravity gradient tensor (GGT). The data provided by this mission could be used to study large areas, where the flat Earth approximation can have its  limitations. In these cases the modeling could be done with tesseroids, also called spherical prisms, in order to take the Earths curvature into account. The GGT caused by a tesseroid can be calculated with numerical integration methods, such as the Gauss-Legendre Quadrature (GLQ). In the current project, a computer program was developed for the direct calculation of the GGT using the GLQ. The accuracy of this implementation was evaluated by comparing its results with the result of analytical formulas for the special case of a spherical cap. Next, the developed program was used to calculate the differences in the GGT caused by the flat Earth approximation. These differences reach are up to 30% in the Tzz component for a 50 deg x 50 deg x 10 km model. Finally, the computer program was used to calculate the effect caused by the topographic masses on the GGT at 250 km altitude for the Paraná basin region. In regions of large topographical variations, the components of the GGT due to the topographic masses have amplitudes of the same order of magnitude as the GGT components due to density anomalies in the interior of the crust and mantle.