Estimation of the total magnetization direction of approximately spherical bodies

Vanderlei C. Oliveira Jr, Daiana P. Sales, Valéria C. F. Barbosa, Leonardo Uieda


Open-source implementation

The method described in this article has been implemented in the open-source geophysics library Fatiando a Terra. The method was first introduced in version 0.3 as the fatiando.gravmag.magdir.DipoleMagDir class (see PR 87 for the full development history of this implementation). See the project documentation and the code repository of this paper (pinga-lab/Total-magnetization-of-spherical-bodies) for more information about using this class.

Open peer-review

This paper has undergone open peer-review. The original submission, reviews, and replies can be viewed at doi:10.5194/npgd-1-1465-2014.


We have developed a fast total-field anomaly inversion to estimate the magnetization direction of multiple sources with approximately spherical shapes and known centres. Our method is an overdetermined inverse problem that can be applied to interpret multiple sources with different but homogeneous magnetization directions. It requires neither the prior computation of any transformation-like reduction to the pole nor the use of regularly spaced data on a horizontal grid. The method contains flexibility to be implemented as a linear or non-linear inverse problem, which results, respectively, in a least-squares or robust estimate of the components of the magnetization vector of the sources. Applications to synthetic data show the robustness of our method against interfering anomalies and errors in the location of the sources' centre. Besides, we show the feasibility of applying the upward continuation to interpret non-spherical sources. Applications to field data over the Goiás alkaline province (GAP), Brazil, show the good performance of our method in estimating geologically meaningful magnetization directions. The results obtained for a region of the GAP, near to the alkaline complex of Diorama, suggest the presence of non-outcropping sources marked by strong remanent magnetization with inclination and declination close to −70.35 and −19.81°, respectively. This estimated magnetization direction leads to predominantly positive reduced-to-the-pole anomalies, even for other region of the GAP, in the alkaline complex of Montes Claros de Goiás. These results show that the non-outcropping sources near to the alkaline complex of Diorama have almost the same magnetization direction of those ones in the alkaline complex of Montes Claros de Goiás, strongly suggesting that these sources have been emplaced in the crust within almost the same geological time interval.


    title = {Estimation of the total magnetization direction of approximately spherical bodies},
    volume = {22},
    issn = {1607-7946},
    doi = {10.5194/npg-22-215-2015},
    number = {2},
    journal = {Nonlin. Processes Geophys.},
    author = {Oliveira Jr., V. C. and Sales, D. P. and Barbosa, V. C. F. and Uieda, L.},
    year = {2015},
    pages = {215--232},


Oliveira Jr., V. C., D. P. Sales, V. C. F. Barbosa, and L. Uieda (2015), Estimation of the total magnetization direction of approximately spherical bodies, Nonlin. Processes Geophys., 22(2), 215-232, doi:10.5194/npg-22-215-2015.

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