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.
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.
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