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# Robust 3D gravity gradient inversion by planting anomalous densities

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

## Info

## About

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`

.

## Abstract

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.

## Citation

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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