Robust 3D gravity gradient inversion by planting anomalous densities

Leonardo Uieda, Valéria C. F. Barbosa



This talk and expanded abstract present the second version of what would eventually become my first publication "Robust 3D gravity gradient inversion by planting anomalous densities" and Masters dissertation.

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 inversion method for estimating a 3D density-contrast distribution defined on a grid of prisms. Our method consists of an iterative algorithm that does not require the solution of a large equation system. Instead, the solution grows systematically around user-specified prismatic elements called "seeds". Each seed can be assigned a different density contrast, allowing the interpretation of multiple bodies with different density contrasts and that produce interfering gravitational effects. The compactness of the solution around the seeds is imposed by means of a regularizing function. The solution grows by the accretion of 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, which greatly reduces the demand of computer memory and processing time. Tests on synthetic data and on real data collected over an iron ore province of Quadrilátero Ferrífero, southeastern Brazil, confirmed the ability of our method in detecting sharp and compact bodies.


Uieda, L., and V. C. F. Barbosa (2011), Robust 3D gravity gradient inversion by planting anomalous densities, SEG Technical Program Expanded Abstracts, vol. 30, pp. 820–824, doi:10.1190/1.3628201

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