March 13, 2015 Software Open Access

Tesseroids v1.2.0: Forward modeling of gravitational fields in spherical coordinates

Uieda, Leonardo

A collection of command-line programs for modeling the gravitational potential, acceleration, and gradient tensor. Tesseroids supports models and computation grids in Cartesian and spherical coordinates.

Official website and documentation: http://tesseroids.leouieda.com/

Changes to version 1.2.0:

* General improvements to the adaptive discretization (described in the upcoming method paper)

* Better error messages when there is a stack overflow (computation point too close to the tesseroid).

* Replace the recursive algorithm with a stack-based algorithm for adaptive discretization of tesseroids. This makes the computations faster, specially for gravity acceleration and gradient tensor components.

* Divide the tesseroids only along the necessary dimensions. This provides speedups when dealing with flattened or elongated tesseroids.

* Speedup tesseroid computations by moving some trigonometric functions out of loops.

* BUG fix: Singularities when calculating around a prism. Due to wrong quadrant returned by atan2 and log(0) evaluations. Fix by wrapping atan2 in a safe_atan2 that corrects the result. log(0) error happened only in cross components of the gravity gradient when the computation is aligned with the vertices of a certain face (varies for each component. Fix by displacing the point a small amount when that happens.