Tesseroids: forward modeling gravitational fields in spherical coordinates

by Leonardo Uieda, Valéria C. F. Barbosa, Carla Braitenberg (2016)

Thumbnail image for publication.

Info

Article Level Metrics

Main article

About

This paper is a chapter of my PhD thesis. It describes the algorithms used in version 1.2.0 of the open-source software Tesseroids: gravity forward modeling in spherical coordinates. The software is a suite of C coded command-line programs that calculate the gravitational field of a tesseroid (spherical prism) model. There is also a separate Python implementation of the same algorithm in the fatiando.gravmag.tesseroid module of the open-source library Fatiando a Terra: modeling and inversion for geophysics (introduced in version 0.3).

Presentations about the modeling methods and previous versions of the software:

Abstract

We present the open-source software Tesseroids, a set of command-line programs to perform the 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 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 homogeneous spherical shell. The values required for a maximum relative error of 0.1% of the shell effects are D = 1 for the gravitational potential, D = 1.5 for the gravitational acceleration, and D = 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. These values were incorporated as defaults in the software.

Citation

Uieda, L., V. Barbosa, and C. Braitenberg (2016), Tesseroids: Forward-modeling gravitational fields in spherical coordinates, GEOPHYSICS, F41–F48, doi:10.1190/geo2015-0204.1.