Optimal forward calculation method of the Marussi tensor due to a geologic structure at GOCE height
by Leonardo Uieda, Everton P. Bomfim, Carla Braitenberg, and Eder Molina
Abstract, code, poster and proceedings presented at the 4th International GOCE User Workshop in Munich, Germany.
Poster is available on figshare: doi:10.6084/m9.figshare.92624
A PDF of the proceedings is available from: leouieda.com
Results were generated using open-source software Tesseroids.
Uieda, L., E. P. Bomfim, C. Braitenberg, and E. Molina (2011), Optimal forward calculation method of the Marussi tensor due to a geologic structure at GOCE height, Proc. of 4th International GOCE User Workshop, pp. 1-5
The new observations of GOCE present a challenge to develop new calculation methods that take into account the sphericity of the Earth. We address this problem by using a discretization with a series of tesseroids. There is no closed formula giving the gravitational fields of the tesseroid and numerical integration methods must be used, such as the Gauss Legendre Cubature (GLC). A problem that arises is that the computation times with the tesseroids are high. Therefore, it is important to optimize the computations while maintaining the desired accuracy. This optimization was done using an adaptive computation scheme that consists of using a fixed GLC order and recursively subdividing the tesseroids. We have obtained an optimum ratio between the size of the tesseroid and its distance from the computation point. Furthermore, we show that this size-to-distance ratio is different for the gravitational attraction than for the gravity gradient tensor.