3D gravity gradient inversion by planting density anomalies

by Leonardo Uieda, Valéria C. F. Barbosa (2011)

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The poster


This poster and expanded abstract present the first version of what would be my first publication "Robust 3D gravity gradient inversion by planting anomalous densities" and eventually Masters dissertation. The inversion method was developed along a few iterations after this (in order):

I have added an open-source implementation of the method to the Python library Fatiando a Terra. In version 0.1 to 0.4, the code is in module fatiando.gravmag.harvester.


We present a new gravity gradient tensor inversion for estimating a 3D density-contrast distribution defined on a user-specified grid of prisms. Our method consists of an iterative algorithm that does not require the solution of large equation system. Instead, the solution grows systematically around user-specified prismatic elements called “seeds”. Each seed can have a different density contrast, allowing the interpretation of multiples bodies with different density contrasts. The compactness of the solution is imposed by means of a regularizing function that favors compact bodies closest to the priorly specified seeds. The solution grows by accreting neighboring prisms of the current solution. The prisms for the accretion are chosen by systematically searching the set of current neighboring prisms. Therefore, this approach allows that the columns of the Jacobian matrix be calculated on demand. This is a known technique from computer science called “lazy evaluation”, which greatly reduces the demand of computer memory and processing time. Test on synthetic data from multiple buried sources at different depths and on real data collected over iron deposits located in the Quadrilátero Ferrífero, southeastern region of Brazil, confirmed the ability of our method in detecting sharp and compact bodies.


Uieda, L., and V. C. F. Barbosa (2011), 3D gravity gradient inversion by planting density anomalies, 73th EAGE Conference & Exhibition incorporating SPE EUROPEC, pp. 1-5