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https://github.com/leouieda/egu2014

Talk given at the European Geosciences Union General Assembly 2014
https://github.com/leouieda/egu2014

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Talk given at the European Geosciences Union General Assembly 2014

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README 

        
Talk given at the European Geosciences Union General Assembly 2014



Slides are in the `presentation` folder.

There is a LibreOffice `.odt` file as well as a PDF version.



Results were generated using open-source software [Fatiando a

Terra](http://www.fatiando.org).



The `notebooks` folder contains

the [IPython notebooks](http://ipython.org/notebook.html)

used to run the inversions and generate the figures:



* [plume.ipynb](http://nbviewer.ipython.org/github/leouieda/egu2014/blob/master/notebooks/plume.ipynb):

  mantle plume model.

* [lineament-curved.ipynb](http://nbviewer.ipython.org/github/leouieda/egu2014/blob/master/notebooks/lineament-curved.ipynb):

  dense lineament model.

* [underplate.ipynb](http://nbviewer.ipython.org/github/leouieda/egu2014/blob/master/notebooks/underplate.ipynb):

  magmatic underplating model.

* [example-images.ipynb](http://nbviewer.ipython.org/github/leouieda/egu2014/blob/master/notebooks/example-images.ipynb):

  generates the images in the second slide.



You can download and run them to reproduce all figures in the presentation!



# Gravity inversion in spherical coordinates using tesseroids



**Leonardo Uieda and Valéria C. F. Barbosa**



Satellite observations of the gravity field have provided geophysicists

with exceptionally dense and uniform coverage of data over vast areas.

This enables regional or global scale

high resolution geophysical investigations.

Techniques like forward modeling and inversion of gravity anomalies

are routinely used to investigate large geologic structures,

such as large igneous provinces, suture zones, intracratonic basins, and the

Moho.

Accurately modeling such large structures

requires taking the sphericity of the Earth into account.

A reasonable approximation is to assume a spherical Earth and

use spherical coordinates.



In recent years, efforts have been made

to advance forward modeling in spherical coordinates using tesseroids,

particularly with respect to speed and accuracy.

Conversely, traditional space domain inverse modeling methods

have not yet been adapted to use spherical coordinates and tesseroids.

In the literature there are a range of inversion methods

that have been developed for Cartesian coordinates and right rectangular prisms.

These include methods for estimating the relief of an interface,

like the Moho or the basement of a sedimentary basin.

Another category includes methods

to estimate the density distribution in a medium.

The latter apply many algorithms to solve the inverse problem,

ranging from analytic solutions to random search methods

as well as systematic search methods.



We present an adaptation for tesseroids of the systematic search method

of "planting anomalous densities".

This method can be used to estimate the geometry of geologic structures.

As prior information, it requires knowledge of the approximate densities and

positions of the structures.

The main advantage of this method is its computational efficiency,

requiring little computer memory and processing time.

We demonstrate the shortcomings and capabilities of this approach using

applications to synthetic and field data.

Performing the inversion of gravity and gravity gradient data,

simultaneously or separately,

is straight forward and requires no changes to the existing algorithm.

Such feature makes it ideal for inverting

the multicomponent gravity gradient data from the GOCE satellite.



An implementation of our adaptation is freely available

in the open-source modeling and inversion package Fatiando a Terra

(http://www.fatiando.org).