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Tesseroids; forward-modeling gravitational fields in spherical coordinates

Leonardo Uieda, Valeria C. F. Barbosa and Carla Braitenberg
Tesseroids; forward-modeling gravitational fields in spherical coordinates
Geophysics (September 2016) 81 (5): F41-F48


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 = 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.

ISSN: 0016-8033
EISSN: 1942-2156
Coden: GPYSA7
Serial Title: Geophysics
Serial Volume: 81
Serial Issue: 5
Title: Tesseroids; forward-modeling gravitational fields in spherical coordinates
Affiliation: Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil
Pages: F41-F48
Published: 201609
Text Language: English
Publisher: Society of Exploration Geophysicists, Tulsa, OK, United States
References: 26
Accession Number: 2016-074666
Categories: Applied geophysics
Document Type: Serial
Bibliographic Level: Analytic
Illustration Description: illus. incl. 1 table
Secondary Affiliation: Observatorio Nacional, BRA, BrazilUniversity of Trieste, ITA, Italy
Country of Publication: United States
Secondary Affiliation: GeoRef, Copyright 2017, American Geosciences Institute. Reference includes data from GeoScienceWorld, Alexandria, VA, United States. Reference includes data supplied by Society of Exploration Geophysicists, Tulsa, OK, United States
Update Code: 201636
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