Tesseroids: Forward-modeling gravitational fields in spherical coordinates



Uieda, Leonardo ORCID: 0000-0001-6123-9515, Barbosa, Valeria CF and Braitenberg, Carla
(2016) Tesseroids: Forward-modeling gravitational fields in spherical coordinates. GEOPHYSICS, 81 (5). F41 - F48.

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Abstract

We have developed the open-source software Tesseroids, a set of command-line programs to perform forward modeling of gravitational fields in spherical coordinates. The software is implemented in the C programming language and uses tesseroids (spherical prisms) for the discretization of the subsurface mass distribution. The gravitational fields of tesseroids are calculated numerically using the Gauss-Legendre quadrature (GLQ). We have improved upon an adaptive discretization algorithm to guarantee the accuracy of the GLQ integration. Our implementation of adaptive discretization uses a “stack-based” algorithm instead of recursion to achieve more control over execution errors and corner cases. The algorithm is controlled by a scalar value called the distance-size ratio (D) that determines the accuracy of the integration as well as the computation time. We have determined optimal values of D for the gravitational potential, gravitational acceleration, and gravity gradient tensor by comparing the computed tesseroids effects with those of a homogenous spherical shell. The values required for a maximum relative error of 0.1% of the shell effects are D ¼ 1 for the gravitational potential, D ¼ 1.5 for the gravitational acceleration, and D ¼ 8 for the gravity gradients. Contrary to previous assumptions, our results show that the potential and its first and second derivatives require different values of D to achieve the same accuracy

Item Type: Article
Depositing User: Symplectic Admin
Date Deposited: 04 Oct 2019 12:05
Last Modified: 06 Dec 2021 12:04
DOI: 10.1190/GEO2015-0204.1
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3057019