This poster and conference proceedings present the results and methods after
the 1.0 release of my open-source
software (http://www.tesseroids.org).
Version 1.0 was a complete re-write of the
original Python code in the C
language.
This work was made possible by professor
Carla Braitenberg.
She funded me to spend a month at the University of Trieste, Italy, and
re-write the software from scratch.
What followed was a much faster and more robust program.
This version also featured the first iteration of the adaptive discretization
presented in the paper Tesseroids: forward modeling gravitational fields in spherical coordinates and my PhD
thesis.

Abstract

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.

Citation

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

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