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https://github.com/leouieda/scipy2014

Poster presentation given at the 2014 Scipy Conference
https://github.com/leouieda/scipy2014

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Poster presentation given at the 2014 Scipy Conference

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# Using Fatiando a Terra to solve inverse problems in geophysics



[Leonardo Uieda](http://www.leouieda.com),

[Vanderlei C. Oliviera Jr](http://fatiando.org/people/oliveira-jr),

[Valéria C. F. Barbosa](http://lattes.cnpq.br/0391036221142471)



Inverse problems haunt the nightmares of geophysics graduate students.

I'll demonstrate how to conquer them using Fatiando a Terra.

The new machinery in Fatiando

contains many ready-to-use components

and automates as much of the process as possible.

You can go from zero to regularized gravity inversion

with as little as 30 lines of code.

I'll walk through an example to show you how.



## Poster



![The poster.](https://raw.githubusercontent.com/leouieda/scipy2014/master/poster-low-res.png)



The notebook

[gravity_inversion.ipynb](http://nbviewer.ipython.org/github/leouieda/scipy2014/blob/master/gravity_inversion.ipynb)

was used to create all figures and code in the poster.



A PDF of this poster is permanently archived at figshare: [doi:10.6084/m9.figshare.1089987](http://dx.doi.org/10.6084/m9.figshare.1089987)



[poster_summary.ipynb](http://nbviewer.ipython.org/github/leouieda/scipy2014/blob/master/poster_summary.ipynb)

is a short version of the above notebook.



## Scipy2014



The notebook

[scipy_hashtag.ipynb](http://nbviewer.ipython.org/github/leouieda/scipy2014/blob/master/hashtag/scipy_hashtag.ipynb)

uses the finite-difference wave propagation module of Fatiando to make an

animated gif of #Scipy2014.



![#Scipy2014](https://raw.githubusercontent.com/leouieda/scipy2014/master/hashtag/scipy2014.gif)



## Abstract



The inner properties of the Earth

can usually only be inferred

through indirect measurements of their effects.

For example,

density variations

cause disturbances in the gravity field

and seismic velocity variations

affect the path of seismic waves.

From a mathematical point of view,

this inference is an inverse problem.

To complicate things, geophysical inverse problems are usually ill-posed,

meaning that a solution:



* doesn't exist;

* exists but is non-unique;

* exists and is unique but is unstable;



These problems can usually be resolved

through least-squares estimation and regularization.



Research in geophysical inverse problems

involves the development of:

new methodologies for parametrization,

different approaches to regularization,

new algorithms to handle large-scale problems,

combinations of existing methods,

etc.

All of the aforementioned developments

require the creation of software,

usually from scratch.

Furthermore,

most scientific software

are not designed with reuse in mind,

making remixing published methods difficult,

if not impossible.



We tackled these problems

by developing `fatiando.inversion`,

a framework for solving inverse problems

in [Fatiando a Terra](http://www.fatiando.org).

The goals of `fatiando.inversion` are:



* Enable writing code that

  intuitively maps to the theory (equations);

* Provide a consistent interface for all solvers

  (similar to that adopted by [scikit-learn](http://scikit-learn.org/));

* Automate the process of implementing a new inverse problem;

* Allow reuse and remixing with as little code as possible;



In this talk,

I'll briefly cover

the mathematics involved

and the design of our new API.

I'll walk through the process of

implementing a new inverse problem

(in about 30 lines of code)

using the example of

estimating the relief of a sedimentary basin

from its gravity anomaly.

Finally,

I'll conclude by outlining

how we are using this framework in our own research,

what we are currently working on,

and our plans for the future.