In the Computer-Oriented Geoscience Lab we create and use open-source software to
undertake research into geophysical inversion, modelling, and data processing.

## Inverse problems

Our ultimate goal as geophysicists is to infer the physical properties of the inner
Earth and its processes from surface observations. This is an ill-posed inverse problem,
to which a solution might not exist or be non-unique and unstable. We develop methods
for solving different kinds of inverse problems using several sets of constraints to
overcome the instability of the solution.

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Distribution of an iron ore deposit in Brazil estimated from gravity
gradient data.
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## Forward modeling

A key component for solving an inverse problem is first solve the "forward problem".
This is jargon for predicting data given a set of model parameters. One of the main
research problems on which we work is developing a method for forward modeling
gravitational fields caused by a tesseroid (a spherical prism).

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A tesseroid discretized using our adaptive algorithm.
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## Data processing

There is no turning back from the machine learning frenzy that has taken over the world.
Geoscientists have been doing similar things for decades but with different names and
objectives. One of these things is called the "equivalent layer technique" in gravity
and magnetics. Similar methods in different fields have many different names, for
example radial basis functions or Green's functions interpolation. All of these methods
are linear regressions in which we fit a linear model to some data and then use the
model to predict new data. Given the many similarities, we are applying other machine
learning techniques to these geophysical problems.

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Spatial data has uncertainties which need to be handled properly. There are different
ways to use uncertainties as data weights for different algorithms, like interpolation
and blocked statistics.
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