Gradient-boosted equivalent sources
2021
|
Soler, S.R. and Uieda, L.
Geophysical Journal International,
doi:10.1093/gji/ggab297
PDF
Data
Code
Note: This research was done entirely with open-source software and open data!
This means that anyone should be able to fully reproduce our results
using the information in the paper and the material in the associated
GitHub repository. This is the final part of Santiago's PhD thesis.
Abstract
The equivalent source technique is a powerful and widely used method for
processing gravity and magnetic data. Nevertheless, its major drawback is
the large computational cost in terms of processing time and computer
memory. We present two techniques for reducing the computational cost of
equivalent source processing: block-averaging source locations and the
gradient-boosted equivalent source algorithm. Through block-averaging,
we reduce the number of source coefficients that must be estimated
while retaining the minimum desired resolution in the final processed
data. With the gradient boosting method, we estimate the sources
coefficients in small batches along overlapping windows, allowing us to
reduce the computer memory requirements arbitrarily to conform to the
constraints of the available hardware. We show that the combination of
block-averaging and gradient-boosted equivalent sources is capable of
producing accurate interpolations through tests against synthetic data.
Moreover, we demonstrate the feasibility of our method by gridding a
gravity dataset covering Australia with over 1.7 million observations
using a modest personal computer.
Cite as
Soler, S. R., & Uieda, L. (2021). Gradient-boosted equivalent sources.
Geophysical Journal International, 227(3), 1768–1783.
https://doi.org/10.1093/gji/ggab297
BibTex
@article{Soler2021,
doi = {10.1093/gji/ggab297},
url = {https://doi.org/10.1093/gji/ggab297},
year = {2021},
month = aug,
publisher = {Oxford University Press ({OUP})},
volume = {227},
number = {3},
pages = {1768--1783},
author = {Santiago R Soler and Leonardo Uieda},
title = {Gradient-boosted equivalent sources},
journal = {Geophysical Journal International}
}
Citations
Pooch: A friend to fetch your data files
2020
|
Uieda, L., Soler, S.R., Rampin, R., van Kemenade, H., Turk, M., Shapero,
D., Banihirwe, A., and Leeman, J.
open-access
Journal of Open Source Software,
doi:10.21105/joss.01943
PDF
Code
Note: This paper marks the release of
Pooch v0.7.1,
a Python library for downloading and managing data files.
Pooch is a part of the new ecosystem of packages in
Fatiando a Terra.
The peer-review at JOSS is open and can be found on GitHub issue
openjournals/joss-reviews#1943.
Abstract
Scientific software is usually created to acquire, analyze, model, and
visualize data. As such, many software libraries include sample datasets
in their distributions for use in documentation, tests, benchmarks, and
workshops. A common approach is to include smaller datasets in the GitHub
repository directly and package them with the source and binary
distributions (e.g., scikit-learn and scikit-image do this). As data
files increase in size, it becomes unfeasible to store them in GitHub
repositories. Thus, larger datasets require writing code to download the
files from a remote server to the user's computer. The same problem is
faced by scientists using version control to manage their research
projects. While downloading a data file over HTTPS can be done easily
with modern Python libraries, it is not trivial to manage a set of files,
keep them updated, and check for corruption. For example, scikit-learn,
Cartopy, and PyVista all include code dedicated to this particular task.
Instead of scientists and library authors recreating the same code, it
would be best to have a minimalistic and easy to set up tool for fetching
and maintaining data files.
Pooch is a Python library that fills this gap. It manages a data registry
(containing file names, SHA-256 cryptographic hashes, and download URLs) by
downloading files from one or more remote servers and storing them in a local
data cache. Pooch is written in pure Python and has minimal dependencies. It
can be easily installed from the Python Package Index (PyPI) and conda-forge on
a wide range of Python versions: 2.7 (up to Pooch 0.6.0) and from 3.5 to 3.8.
Cite as
Uieda, L., Soler, S., Rampin, R., van Kemenade, H., Turk, M., Shapero,
D., et al. (2020). Pooch: A friend to fetch your data files. Journal of
Open Source Software, 5(45), 1943. https://doi.org/10.21105/joss.01943
BibTex
@article{Uieda2020,
doi = {10.21105/joss.01943},
url = {https://doi.org/10.21105/joss.01943},
year = {2020},
month = jan,
publisher = {The Open Journal},
volume = {5},
number = {45},
pages = {1943},
author = {Leonardo Uieda and Santiago Soler and R{\'{e}}mi Rampin and Hugo van Kemenade and Matthew Turk and Daniel Shapero and Anderson Banihirwe and John Leeman},
title = {Pooch: A friend to fetch your data files},
journal = {Journal of Open Source Software}
}
Citations
Gravitational field calculation in spherical coordinates using variable
densities in depth
2019
|
Soler, S. R., Pesce, A., Gimenez, M. E., & Uieda, L.
Geophysical Journal International,
doi:10.1093/gji/ggz277
PDF
Data
Code
Note: This paper builds upon my work on Tesseroids and
extends the methodology to work for depth-variable densities. Santiago
led this project, did most of the work and a large part of the writing of
the paper. This is the first paper of his PhD thesis.
Abstract
We present a new methodology to compute the gravitational fields
generated by tesseroids (spherical prisms) whose density varies with
depth according to an arbitrary continuous function. It approximates the
gravitational fields through the Gauss-Legendre Quadrature along with two
discretization algorithms that automatically control its accuracy by
adaptively dividing the tesseroid into smaller ones. The first one is a
preexisting two dimensional adaptive discretization algorithm that
reduces the errors due to the distance between the tesseroid and the
computation point. The second is a new density-based discretization
algorithm that decreases the errors introduced by the variation of the
density function with depth. The amount of divisions made by each
algorithm is indirectly controlled by two parameters: the distance-size
ratio and the delta ratio. We have obtained analytical solutions for a
spherical shell with radially variable density and compared them to the
results of the numerical model for linear, exponential, and sinusoidal
density functions. These comparisons allowed us to obtain optimal values
for the distance-size and delta ratios that yield an accuracy of 0.1% of
the analytical solutions. The resulting optimal values of distance-size
ratio for the gravitational potential and its gradient are 1 and 2.5,
respectively. The density-based discretization algorithm produces no
discretizations in the linear density case, but a delta ratio of 0.1 is
needed for the exponential and the sinusoidal density functions. These
values can be extrapolated to cover most common use cases. However, the
distance-size and delta ratios can be configured by the user to increase
the accuracy of the results at the expense of computational speed.
Lastly, we apply this new methodology to model the Neuquén Basin, a
foreland basin in Argentina with a maximum depth of over 5000 m, using an
exponential density function.
Cite as
Soler, S. R., Pesce, A., Gimenez, M. E., & Uieda, L. (2019).
Gravitational field calculation in spherical coordinates using variable
densities in depth. Geophysical Journal International, 218(3), 2150–2164.
https://doi.org/10.1093/gji/ggz27
BibTex
@article{Soler2019,
doi = {10.1093/gji/ggz277},
url = {https://doi.org/10.1093/gji/ggz277},
year = {2019},
month = jun,
publisher = {Oxford University Press ({OUP})},
volume = {218},
number = {3},
pages = {2150--2164},
author = {Santiago R Soler and Agustina Pesce and Mario E Gimenez and Leonardo Uieda},
title = {Gravitational field calculation in spherical coordinates using variable densities in depth},
journal = {Geophysical Journal International}
}
Citations
The Generic Mapping Tools Version 6
2019
|
Wessel, P., Luis, J. F., Uieda, L., Scharroo, R., Wobbe, F., Smith, W. H.
F., & Tian, D.
open-access
Geochemistry, Geophysics, Geosystems,
doi:10.1029/2019GC008515
PDF
Data
Code
Note: This paper marks the release of GMT version 6. Most of the work done for
this release had the goal of reducing barriers to entry for new users.
The user experience as a whole has been improved and these changes are
the foundation for my work on PyGMT. The development of the new modern
mode was funded by our NSF EarthScope grant.
Abstract
The Generic Mapping Tools (GMT) software is ubiquitous in the Earth and
Ocean sciences. As a cross-platform tool producing high quality maps and
figures, it is used by tens of thousands of scientists around the world.
The basic syntax of GMT scripts has evolved very slowly since the 1990s,
despite the fact that GMT is generally perceived to have a steep learning
curve with many pitfalls for beginners and experienced users alike.
Reducing these pitfalls means changing the interface, which would break
compatibility with thousands of existing scripts. With the latest GMT
version 6, we solve this conundrum by introducing a new "modern mode" to
complement the interface used in previous versions, which GMT 6 now calls
"classic mode". GMT 6 defaults to classic mode and thus is a recommended
upgrade for all GMT 5 users. Nonetheless, new users should take advantage
of modern mode to make shorter scripts, quickly access commonly used
global data sets, and take full advantage of the new tools to draw
subplots, place insets, and create animations.
Cite as
Wessel, P., Luis, J. F., Uieda, L., Scharroo, R., Wobbe, F., Smith, W. H.
F., & Tian, D. (2019). The Generic Mapping Tools Version 6. Geochemistry,
Geophysics, Geosystems, 20(11), 5556–5564.
https://doi.org/10.1029/2019gc008515
BibTex
@article{Wessel2019,
doi = {10.1029/2019gc008515},
url = {https://doi.org/10.1029/2019gc008515},
year = {2019},
month = nov,
publisher = {American Geophysical Union ({AGU})},
volume = {20},
number = {11},
pages = {5556--5564},
author = {P. Wessel and J. F. Luis and L. Uieda and R. Scharroo and F. Wobbe and W. H. F. Smith and D. Tian},
title = {The Generic Mapping Tools Version 6},
journal = {Geochemistry, Geophysics, Geosystems}
}
Citations
Efficient 3D large-scale forward-modeling and inversion of gravitational
fields in spherical coordinates with application to lunar mascons
2019
|
Zhao, G., Chen, B., Uieda, L., Liu, J., Kaban, M. K., Chen, L., & Guo, R.
Journal of Geophysical Research: Solid Earth,
doi:10.1029/2019JB017691
PDF
Data
Note: This new collaboration that came about in an unexpected way. Leo reviewed
an initial version of this paper and it ended up being rejected by the
journal. After which, the authors reached out and kindly asked if he
wanted to help improve the paper further. We worked on this for the
better part of a year, adding the inversion and lunar mascon application.
Abstract
An efficient forward modeling algorithm for calculation of gravitational
fields in spherical coordinates is developed for 3D large‐scale gravity
inversion problems. 3D Gauss‐Legendre quadrature (GLQ) is used to
calculate the gravitational fields of mass distributions discretized into
tesseroids. Equivalence relations in the kernel matrix of the
forward‐modeling are exploited to decrease storage and computation time.
The numerical tests demonstrate that the computation time of the proposed
algorithm is reduced by approximately two orders of magnitude, and the
memory requirement is reduced by N'λ times compared with the traditional
GLQ method, where N'λ is the number of the model elements in the
longitudinal direction. These significant improvements in computational
efficiency and storage make it possible to calculate and store the dense
Jacobian matrix in 3D large‐scale gravity inversions. The equivalence
relations can be applied to the Taylor series method or combined with the
adaptive discretization to ensure high accuracy. To further illustrate
the capability of the algorithm, we present a regional synthetic example.
The inverted results show density distributions consistent with the
actual model. The computation took about 6.3 hours and 0.88 GB of memory
compared with about a dozen days and 245.86 GB for the traditional 3D GLQ
method. Finally, the proposed algorithm is applied to the gravity field
derived from the latest lunar gravity model GL1500E. 3D density
distributions of the Imbrium and Serenitatis basins are obtained, and
high‐density bodies are found at the depths 10‐60 km, likely indicating a
significant uplift of the high‐density mantle beneath the two mascon
basins.
Cite as
Zhao, G., Chen, B., Uieda, L., Liu, J., Kaban, M. K., Chen, L., & Guo, R.
(2019). Efficient 3‐D Large‐Scale Forward Modeling and Inversion of
Gravitational Fields in Spherical Coordinates With Application to Lunar
Mascons. Journal of Geophysical Research: Solid Earth, 124(4), 4157–4173.
https://doi.org/10.1029/2019jb017691
BibTex
@article{Zhao2019,
doi = {10.1029/2019jb017691},
url = {https://doi.org/10.1029/2019jb017691},
year = {2019},
month = apr,
publisher = {American Geophysical Union ({AGU})},
volume = {124},
number = {4},
pages = {4157--4173},
author = {Guangdong Zhao and Bo Chen and Leonardo Uieda and Jianxin Liu and Mikhail K. Kaban and Longwei Chen and Rongwen Guo},
title = {Efficient 3-D Large-Scale Forward Modeling and Inversion of Gravitational Fields in Spherical Coordinates With Application to Lunar Mascons},
journal = {Journal of Geophysical Research: Solid Earth}
}
Citations
Giving software its due through community-driven review and publication
2019
|
Barba, L. A., Bazán, J., Brown, J., Guimera, R. V., Gymrek, M., Hanna,
A., et al.
preprint
OSF Preprints,
doi:10.31219/osf.io/f4vx6
PDF
Abstract
A recent editorial in Nature Methods, "Giving Software its Due",
described challenges related to the development of research software and
highlighted, in particular, the challenge of software publication and
citation. Here, we call attention to a system that we have developed that
enables community-driven software review, publication, and
citation: The Journal of Open Source Software (JOSS) is an open-source
project and an open access journal that provides a light-weight
publishing process for research software. Focused on and based in open
platforms and on a community of contributors, JOSS evidently satisfies a
pressing need, having already published more than 500 articles in
approximately three years of existence.
Cite as
Barba, L. A., Bazán, J., Brown, J., Guimera, R. V., Gymrek, M., Hanna,
A., et al. (2019). Giving software its due through community-driven
review and publication. OSF Preprints. doi:10.31219/osf.io/f4vx6
BibTex
@article{Barba2019,
doi = {10.31219/osf.io/f4vx6},
url = {https://doi.org/10.31219/osf.io/f4vx6},
year = {2019},
month = apr,
publisher = {Center for Open Science},
author = {Lorena A. Barba and Juanjo Baz{\'{a}}n and Jed Brown and Roman Valls Guimera and Melissa Gymrek and Alex Hanna and Lindsey Justine Heagy and Kathryn D. Huff and Daniel S. Katz and Christopher R Madan and Kevin Mattheus Moerman and Kyle Evan Niemeyer and Jack L. Poulson and Pjotr Prins and Karthik Ram and Ariel Rokem and Arfon M. Smith and George K. Thiruvathukal and Kristen M. Thyng and Leonardo Uieda and Bruce E. Wilson and Yo Yehudi},
title = {Giving software its due through community-driven review and publication}
}
Citations
Verde: Processing and gridding spatial data using Green's functions
2018
|
Uieda, L.
open-access
Journal of Open Source Software,
doi:10.21105/joss.00957
PDF
Code
Note: This paper marks the release of
Verde v1.0.0,
a Python library for processing and gridding spatial data.
Verde is a part of the new ecosystem of packages in
Fatiando a Terra.
The peer-review at JOSS is open and can be found on GitHub issue
openjournals/joss-reviews#957.
Abstract
Verde is a Python library for gridding spatial data using different
Green's functions. It differs from the radial basis functions in
scipy.interpolate by providing an API inspired by
scikit-learn. The Verde API should be familiar to scikit-learn users but
is tweaked to work with spatial data, which has Cartesian or geographic
coordinates and multiple data components instead of an X
feature matrix and y label vector. The library also includes
more specialized Green's functions, utilities for trend estimation and
data decimation (which are often required prior to gridding), and more.
Some of these interpolation and data processing methods already exist in
the Generic Mapping Tools (GMT), a command-line program popular in the
Earth Sciences. However, there are no model selection tools in GMT and it
can be difficult to separate parts of the processing that are done
internally by its modules. Verde is designed to be modular, easily
extended, and integrated into the scientific Python ecosystem. It can be
used to implement new interpolation methods by subclassing the
verde.base.BaseGridder class, requiring only the
implementation of the new Green's function. For example, it is currently
being used to develop a method for interpolation of 3-component GPS data.
Cite as
Uieda, L. (2018). Verde: Processing and gridding spatial data using
Green's functions. Journal of Open Source Software, 3(30), 957.
https://doi.org/10.21105/joss.00957
BibTex
@article{Uieda2018,
doi = {10.21105/joss.00957},
url = {https://doi.org/10.21105/joss.00957},
year = {2018},
month = oct,
publisher = {The Open Journal},
volume = {3},
number = {30},
pages = {957},
author = {Leonardo Uieda},
title = {Verde: Processing and gridding spatial data using Green's functions},
journal = {Journal of Open Source Software}
}
Citations
Step-by-step NMO correction
2017
|
Uieda, L.
open-access
The Leading Edge,
doi:10.1190/tle36020179.1
PDF
Code
Note: This is a part of The Leading Edge
geophysics tutorials series.
All tutorials are open-access and include open-source code examples.
The text is also included on the SEG Wiki!
The code and idea for this tutorial came from my Introduction to
Geophysics courses at UERJ. I came across the problem of implementing NMO
correction while preparing my lecture and practical exercises on this
topic. This is a clear example of how learning happens both ways in a
classroom.
Abstract
Open any text book about seismic data processing and you will inevitably
find a section about the normal moveout (NMO) correction. When applied to
a common midpoint (CMP) section, the correction is supposed to turn the
hyperbola associated with a reflection into a straight horizontal line.
What most text books won't tell you is how, exactly, do you apply
this equation to the data?
Read on and I'll explain step-by-step how the algorithm for NMO
correction from Yilmaz (2001) works and how to implement it in Python.
The accompanying Jupyter notebook contains the full source code, with
documentation and tests for each function.
Cite as
Uieda, L. (2017), Step-by-step NMO correction, The Leading Edge, 36(2),
179-180, doi:10.1190/tle36020179.1
BibTex
@article{Uieda2017,
doi = {10.1190/tle36020179.1},
url = {https://doi.org/10.1190/tle36020179.1},
year = {2017},
month = feb,
publisher = {Society of Exploration Geophysicists},
volume = {36},
number = {2},
pages = {179--180},
author = {Leonardo Uieda},
title = {Step-by-step {NMO} correction},
journal = {The Leading Edge}
}
Citations
Fast non-linear gravity inversion in spherical coordinates with
application to the South American Moho
2017
|
Uieda, L., and V. C. F. Barbosa
Geophysical Journal International,
doi:10.1093/gji/ggw390
PDF
Data
Code
Note: This paper is one of the chapters of my PhD thesis. It describes a new
gravity inversion method to estimate the depth of the crust-mantle
interface (the Moho). The inversion builds upon my work on tesseroid
modelling.
Abstract
Estimating the relief of the Moho from gravity data is a computationally
intensive non-linear inverse problem. What is more, the modeling must take the
Earths curvature into account when the study area is of regional scale or
greater. We present a regularized non-linear gravity inversion method that has
a low computational footprint and employs a spherical Earth approximation. To
achieve this, we combine the highly efficient Bott's method with smoothness
regularization and a discretization of the anomalous Moho into tesseroids
(spherical prisms). The computational efficiency of our method is attained by
harnessing the fact that all matrices involved are sparse. The inversion
results are controlled by three hyper-parameters: the regularization parameter,
the anomalous Moho density-contrast, and the reference Moho depth. We
estimate the regularization parameter using the method of hold-out
cross-validation. Additionally, we estimate the density-contrast and the
reference depth using knowledge of the Moho depth at certain points. We apply
the proposed method to estimate the Moho depth for the South American
continent using satellite gravity data and seismological data. The final Moho
model is in accordance with previous gravity-derived models and seismological
data. The misfit to the gravity and seismological data is worse in the Andes
and best in oceanic areas, central Brazil and Patagonia, and along the
Atlantic coast. Similarly to previous results, the model suggests a thinner
crust of 30-35 km under the Andean foreland basins. Discrepancies with the
seismological data are greatest in the Guyana Shield, the central Solimões
and Amazonas Basins, the Paraná Basin, and the Borborema province. These
differences suggest the existence of crustal or mantle density anomalies that
were unaccounted for during gravity data processing.
Cite as
Uieda, L., & Barbosa, V. C. F. (2016). Fast nonlinear gravity inversion
in spherical coordinates with application to the South American Moho.
Geophysical Journal International, 208(1), 162–176.
https://doi.org/10.1093/gji/ggw390
BibTex
@article{Uieda2016,
doi = {10.1093/gji/ggw390},
url = {https://doi.org/10.1093/gji/ggw390},
year = {2016},
month = oct,
publisher = {Oxford University Press ({OUP})},
volume = {208},
number = {1},
pages = {162--176},
author = {Leonardo Uieda and Val{\'{e}}ria C.F. Barbosa},
title = {Fast nonlinear gravity inversion in spherical coordinates with application to the South American Moho},
journal = {Geophysical Journal International}
}
Citations
Tesseroids: forward modeling gravitational fields in spherical coordinates
2016
|
Uieda, L., V. Barbosa, and C. Braitenberg
Geophysics,
doi:10.1190/geo2015-0204.1
PDF
Code
Note: This paper describes the algorithms used in version 1.2.0 of the
open-source software Tesseroids.
It's also one of the chapters of my PhD thesis.
Abstract
We present the open-source software Tesseroids, a set of command-line
programs to perform the forward modeling of gravitational fields in
spherical coordinates. The software is implemented in the C programming
language and uses tesseroids (spherical prisms) for the discretization of
the subsurface mass distribution. The gravitational fields of tesseroids
are calculated numerically using the Gauss-Legendre Quadrature (GLQ). We
have improved upon an adaptive discretization algorithm to guarantee the
accuracy of the GLQ integration. Our implementation of adaptive
discretization uses a "stack" based algorithm instead of recursion to
achieve more control over execution errors and corner cases. The
algorithm is controlled by a scalar value called the distance-size ratio
(D) that determines the accuracy of the integration as well as the
computation time. We determined optimal values of D for the
gravitational potential, gravitational acceleration, and gravity gradient
tensor by comparing the computed tesseroids effects with those of a
homogeneous spherical shell. The values required for a maximum relative
error of 0.1% of the shell effects are D = 1 for the gravitational
potential, D = 1.5 for the gravitational acceleration, and D = 8 for the
gravity gradients. Contrary to previous assumptions, our results show
that the potential and its first and second derivatives require different
values of D to achieve the same accuracy. These values were incorporated
as defaults in the software.
Cite as
Uieda, L., Barbosa, V. C. F., & Braitenberg, C. (2016). Tesseroids:
Forward-modeling gravitational fields in spherical coordinates.
GEOPHYSICS, 81(5), F41–F48. https://doi.org/10.1190/geo2015-0204.1
BibTex
@article{Uieda2016,
doi = {10.1190/geo2015-0204.1},
url = {https://doi.org/10.1190/geo2015-0204.1},
year = {2016},
month = sep,
publisher = {Society of Exploration Geophysicists},
volume = {81},
number = {5},
pages = {F41--F48},
author = {Leonardo Uieda and Val{\'{e}}ria C. F. Barbosa and Carla Braitenberg},
title = {Tesseroids: Forward-modeling gravitational fields in spherical coordinates},
journal = {{GEOPHYSICS}}
}
Citations
How two gravity-gradient inversion methods can be used to reveal
different geologic features of ore deposit — A case study from the
Quadrilátero Ferrífero (Brazil)
2016
|
Carlos, D. U., L. Uieda, and V. C. F. Barbosa
Journal of Applied Geophysics,
doi:10.1016/j.jappgeo.2016.04.011
PDF
Abstract
Airborne gravity gradiometry data have been recently used in mining
surveys to map the 3D geometry of ore deposits. This task can be achieved
by different gravity-gradient inversion methods, many of which use a
voxel-based discretization of the Earth's subsurface. To produce a unique
and stable solution, an inversion method introduces particular
constraints. One constraining inversion introduces a depth-weighting
function in the first-order Tikhonov regularization imposing a smoothing
on the density-contrast distributions that are not restricted to
near-surface regions. Another gravity-gradient inversion, the method of
planting anomalous densities, imposes compactness and sharp boundaries on
the density-contrast distributions. We used these two inversion methods
to invert the airborne gravity-gradient data over the iron-ore deposit at
the southern flank of the Gandarela syncline in Quadrilátero Ferrífero
(Brazil). Because these methods differ from each other in the particular
constraint used, the estimated 3D density-contrast distributions reveal
different geologic features of ore deposit. The depth-weighting smoothing
inversion reveals variable dip directions along the strike of the
retrieved iron-ore body. The planting anomalous density inversion
estimates a compact iron-ore mass with a single density contrast, which
reveals a variable volume of the iron ore along its strike increasing
towards the hinge zone of the Gandarela syncline which is the zone of
maximum compression. The combination of the geologic features inferred
from each estimate leads to a synergistic effect, revealing that the
iron-ore deposit is strongly controlled by the Gandarela syncline.
Cite as
Carlos, D. U., L. Uieda, and V. C. F. Barbosa (2016), How two
gravity-gradient inversion methods can be used to reveal different
geologic features of ore deposit — A case study from the Quadrilátero
Ferrífero (Brazil), Journal of Applied Geophysics,
doi:10.1016/j.jappgeo.2016.04.011.
BibTex
@article{Carlos2016,
doi = {10.1016/j.jappgeo.2016.04.011},
url = {https://doi.org/10.1016/j.jappgeo.2016.04.011},
year = {2016},
month = jul,
publisher = {Elsevier {BV}},
volume = {130},
pages = {153--168},
author = {Dion{\'{\i}}sio U. Carlos and Leonardo Uieda and Valeria C.F. Barbosa},
title = {How two gravity-gradient inversion methods can be used to reveal different geologic features of ore deposit {\textemdash} A case study from the Quadril{\'{a}}tero Ferr{\'{\i}}fero (Brazil)},
journal = {Journal of Applied Geophysics}
}
Citations
Estimation of the total magnetization direction of approximately
spherical bodies
2015
|
Oliveira Jr., V. C., D. P. Sales, V. C. F. Barbosa, and L. Uieda
open-access
Nonlinear Processes in Geophysics,
doi:10.5194/npg-22-215-2015
PDF
Data
Code
Note: This paper has undergone open peer-review. The original submission,
reviews, and replies can be viewed at
the journal website.
Abstract
We have developed a fast total-field anomaly inversion to estimate the
magnetization direction of multiple sources with approximately spherical
shapes and known centres. Our method is an overdetermined inverse problem
that can be applied to interpret multiple sources with different but
homogeneous magnetization directions. It requires neither the prior
computation of any transformation-like reduction to the pole nor the use
of regularly spaced data on a horizontal grid. The method contains
flexibility to be implemented as a linear or non-linear inverse problem,
which results, respectively, in a least-squares or robust estimate of the
components of the magnetization vector of the sources. Applications to
synthetic data show the robustness of our method against interfering
anomalies and errors in the location of the sources' centre. Besides, we
show the feasibility of applying the upward continuation to interpret
non-spherical sources. Applications to field data over the Goiás alkaline
province (GAP), Brazil, show the good performance of our method in
estimating geologically meaningful magnetization directions. The results
obtained for a region of the GAP, near to the alkaline complex of
Diorama, suggest the presence of non-outcropping sources marked by strong
remanent magnetization with inclination and declination close to −70.35
and −19.81°, respectively. This estimated magnetization direction leads
to predominantly positive reduced-to-the-pole anomalies, even for other
region of the GAP, in the alkaline complex of Montes Claros de Goiás.
These results show that the non-outcropping sources near to the alkaline
complex of Diorama have almost the same magnetization direction of those
ones in the alkaline complex of Montes Claros de Goiás, strongly
suggesting that these sources have been emplaced in the crust within
almost the same geological time interval.
Cite as
Oliveira Jr., V. C., D. P. Sales, V. C. F. Barbosa, and L. Uieda (2015),
Estimation of the total magnetization direction of approximately
spherical bodies, Nonlin. Processes Geophys., 22(2), 215-232,
doi:10.5194/npg-22-215-2015.
BibTex
@article{Oliveira2015,
doi = {10.5194/npg-22-215-2015},
url = {https://doi.org/10.5194/npg-22-215-2015},
year = {2015},
month = apr,
publisher = {Copernicus {GmbH}},
volume = {22},
number = {2},
pages = {215--232},
author = {V. C. Oliveira and D. P. Sales and V. C. F. Barbosa and L. Uieda},
title = {Estimation of the total magnetization direction of approximately spherical bodies},
journal = {Nonlinear Processes in Geophysics}
}
Citations
Imaging iron ore from the Quadrilátero Ferrífero (Brazil) using
geophysical inversion and drill hole data
2014
|
Carlos, D. U., L. Uieda, and V. C. F. Barbosa
Ore Geology Reviews,
doi:10.1016/j.oregeorev.2014.02.011
PDF
Abstract
The Quadrilátero Ferrífero in southeastern Brazil hosts one of the
largest concentrations of lateritic iron ore deposits in the world. Our
study area is over the southern flank of the Gandarela syncline which is
one of the regional synclines of the Quadrilátero Ferrífero. The
Gandarela syncline is considered the Brazilian megastructure with the
highest perspectives for iron ore exploration. Most of the iron-ore
deposits from the Quadrilátero Ferrífero are non-outcropping bodies
hosted in the oxidized, metamorphosed and heterogeneously deformed banded
iron formations. Therefore, the assessment of the 3D geometry of the
iron-ore body is of the utmost importance for estimating reserves and
production development planning. We carried out a quantitative
interpretation of the iron-ore deposit of the southern flank of the
Gandarela syncline using a 3D inversion of airborne gravity-gradient data
to estimate the shape of the iron-ore mineralization. The retrieved body
is characterized by a high-density zone associated with the
northeast-elongated iron formation. The thickness and the width of the
retrieved iron-ore body vary along its strike increasing southwestward.
The presence of a large volume of iron ore in the southwest portion of
the study area may be due to the hinge zone of the Gandarela syncline,
which is the zone of maximum compression. Our estimated iron-ore mass
reveals variable dip directions. In the southernmost, central and
northernmost portions of the study area, the estimated iron body dips,
respectively, inwards, vertically and outwards with respect to the
syncline axis. Previous geological mapping indicated continuous
mineralization. However, our result suggests a quasi-continuous iron-ore
body. In the central part of the study area, the estimated iron-ore body
is segmented into two parts. This breakup may be related to the
northwest-trending faults, which are perpendicular to the
northeast-trending axis of the Gandarela syncline. Our estimated iron-ore
mass agrees reasonably well with the information provided from the
lithologic logging data of drill holes. In this geophysical study, the
estimated iron-ore reserves are approximately 3 billion tons.
Cite as
Carlos, D. U., L. Uieda, and V. C. F. Barbosa (2014), Imaging iron ore
from the Quadrilátero Ferrífero (Brazil) using geophysical inversion and
drill hole data, Ore Geology Reviews, 61, 268-285,
doi:10.1016/j.oregeorev.2014.02.011
BibTex
@article{Carlos2014,
doi = {10.1016/j.oregeorev.2014.02.011},
url = {https://doi.org/10.1016/j.oregeorev.2014.02.011},
year = {2014},
month = sep,
publisher = {Elsevier {BV}},
volume = {61},
pages = {268--285},
author = {Dion{\'{\i}}sio U. Carlos and Leonardo Uieda and Valeria C.F. Barbosa},
title = {Imaging iron ore from the Quadril{\'{a}}tero Ferr{\'{\i}}fero (Brazil) using geophysical inversion and drill hole data},
journal = {Ore Geology Reviews}
}
Citations
Geophysical tutorial: Euler deconvolution of potential-field data
2014
|
Uieda, L., V. C. Oliveira Jr, and V. C. F. Barbosa
open-access
The Leading Edge,
doi:10.1190/tle33040448.1
PDF
Data
Code
Note: This article is part of the
Geophysical Tutorials
series in The Leading Edge,
started by Matt Hall.
All tutorials are open-access and include open-source code examples.
The February 2016 tutorial
by Matt provides an introduction to the series.
The tutorial is also available at the
SEG wiki
where it can edited and improved.
Abstract
In this tutorial we'll talk about a widely used method of interpretation
for potential-field data called Euler deconvolution. Our goal is to
demonstrate its usefulness and, most importantly, call attention to some
pitfalls encountered in the interpretation of the results. The code and
synthetic data required to reproduce our results and figures can be found
in the accompanying IPython notebooks. The notebooks also expand
the analysis presented here. We encourage you to download the data and
try it on your software of choice. For this tutorial we'll use the
implementation in the open-source Python package Fatiando a Terra.
Cite as
Uieda, L., V. C. Oliveira Jr, and V. C. F. Barbosa (2014), Geophysical
tutorial: Euler deconvolution of potential-field data, The Leading Edge,
33(4), 448-450, doi:10.1190/tle33040448.1
BibTex
@article{uieda2014,
title = {Geophysical tutorial: {Euler} deconvolution of potential-field data},
volume = {33},
issn = {1070-485X, 1938-3789},
doi = {10.1190/tle33040448.1},
number = {4},
journal = {The Leading Edge},
author = {Uieda, Leonardo and Oliveira Jr., Vanderlei C. and Barbosa, Valéria C. F.},
month = apr,
year = {2014},
pages = {448--450}
}
Citations
Estimating the nature and the horizontal and vertical positions of 3D
magnetic sources using Euler deconvolution
2013
|
Melo, F. F., V. C. F. Barbosa, L. Uieda, V. C. Oliveira Jr, and J. B. C. Silva
Geophysics,
doi:10.1190/geo2012-0515.1
PDF
Data
Abstract
We have developed a new method that drastically reduces the number of the
source location estimates in Euler deconvolution to only one per anomaly.
Our method employs the analytical estimators of the base level and of the
horizontal and vertical source positions in Euler deconvolution as a
function of the x- and y-coordinates of the observations. By assuming any
tentative structural index (defining the geometry of the sources), our
method automatically locates plateaus, on the maps of the horizontal
coordinate estimates, indicating consistent estimates that are very close
to the true corresponding coordinates. These plateaus are located in the
neighborhood of the highest values of the anomaly and show a contrasting
behavior with those estimates that form inclined planes at the anomaly
borders. The plateaus are automatically located on the maps of the
horizontal coordinate estimates by fitting a first-degree polynomial to
these estimates in a moving-window scheme spanning all estimates. The
positions where the angular coefficient estimates are closest to zero
identify the plateaus of the horizontal coordinate estimates. The sample
means of these horizontal coordinate estimates are the best horizontal
location estimates. After mapping each plateau, our method takes as the
best structural index the one that yields the minimum correlation between
the total-field anomaly and the estimated base level over each plateau.
By using the estimated structural index for each plateau, our approach
extracts the vertical coordinate estimates over the corresponding
plateau. The sample means of these estimates are the best depth location
estimates in our method. When applied to synthetic data, our method
yielded good results if the bodies produce weak- and mid-interfering
anomalies. A test on real data over intrusions in the Goiás Alkaline
Province, Brazil, retrieved sphere-like sources suggesting 3D bodies.
Cite as
Melo, F. F., V. C. F. Barbosa, L. Uieda, V. C. Oliveira Jr, and J. B. C.
Silva (2013), Estimating the nature and the horizontal and vertical
positions of 3D magnetic sources using Euler deconvolution, Geophysics,
78(6), J87-J98, doi:10.1190/geo2012-0515.1
BibTex
@article{melo2013,
title = {Estimating the nature and the horizontal and vertical positions of 3D magnetic sources using {Euler} deconvolution},
volume = {78},
issn = {0016-8033, 1942-2156},
doi = {10.1190/geo2012-0515.1},
number = {6},
journal = {GEOPHYSICS},
author = {Melo, Felipe F. and Barbosa, Valeria C. F. and Uieda, Leonardo and Oliveira, Vanderlei C. and Silva, João B. C.},
month = oct,
year = {2013},
pages = {J87--J98}
}
Citations
Polynomial equivalent layer
2013
|
Oliveira Jr, V. C., V. C. F. Barbosa, and L. Uieda
Geophysics,
doi:10.1190/geo2012-0196.1
PDF
Abstract
We have developed a new cost-effective method for processing
large-potential-field data sets via the equivalent-layer technique. In
this approach, the equivalent layer is divided into a regular grid of
equivalent-source windows. Inside each window, the physical-property
distribution is described by a bivariate polynomial. Hence, the
physical-property distribution within the equivalent layer is assumed to
be a piecewise polynomial function defined on a set of equivalent-source
windows. We perform any linear transformation of a large set of data as
follows. First, we estimate the polynomial coefficients of all
equivalent-source windows by using a linear regularized inversion.
Second, we transform the estimated polynomial coefficients of all windows
into the physical-property distribution within the whole equivalent
layer. Finally, we premultiply this distribution by the matrix of Green's
functions associated with the desired transformation to obtain the
transformed data. The regularized inversion deals with a linear system of
equations with dimensions based on the total number of polynomial
coefficients within all equivalent-source windows. This contrasts with
the classical approach of directly estimating the physical-property
distribution within the equivalent layer, which leads to a system based
on the number of data. Because the number of data is much larger than the
number of polynomial coefficients, the proposed polynomial representation
of the physical-property distribution within an equivalent layer
drastically reduces the number of parameters to be estimated. By
comparing the total number of floating-point operations required to
estimate an equivalent layer via our method with the classical approach,
both formulated with Cholesky's decomposition, we can verify that the
computation time required for building the linear system and for solving
the linear inverse problem can be reduced by as many as three and four
orders of magnitude, respectively. Applications to synthetic and real
data show that our method performs the standard linear transformations of
potential-field data accurately.
Cite as
Oliveira Jr, V. C., V. C. F. Barbosa, and L. Uieda (2013), Polynomial
equivalent layer, Geophysics, 78(1), G1–G13, doi:10.1190/geo2012-0196.1
BibTex
@article{oliveira2013,
title = {Polynomial equivalent layer},
volume = {78},
issn = {0016-8033, 1942-2156},
doi = {10.1190/geo2012-0196.1},
number = {1},
journal = {GEOPHYSICS},
author = {Oliveira Jr., Vanderlei C. and Barbosa, Valéria C. F. and Uieda, Leonardo},
month = jan,
year = {2013},
pages = {G1--G13},
}
Citations
Robust 3D gravity gradient inversion by planting anomalous densities
2012
|
Uieda, L., and V. C. F. Barbosa
Geophysics,
doi:10.1190/geo2011-0388.1
PDF
Data
Code
Note: This was my first publication in a scientific journal and the topic of my
Masters dissertation. The inversion method proposed in this paper is
implemented in the open-source Fatiando a Terra Python library as the
fatiando.gravmag.harvester module, introduced in version
0.1.
Abstract
We have developed a new gravity gradient inversion method for estimating
a 3D density-contrast distribution defined on a grid of rectangular
prisms. Our method consists of an iterative algorithm that does not
require the solution of an equation system. Instead, the solution grows
systematically around user-specified prismatic elements, called “seeds,”
with given density contrasts. Each seed can be assigned a different
density-contrast value, allowing the interpretation of multiple sources
with different density contrasts and that produce interfering signals. In
real world scenarios, some sources might not be targeted for the
interpretation. Thus, we developed a robust procedure that neither
requires the isolation of the signal of the targeted sources prior to the
inversion nor requires substantial prior information about the
nontargeted sources. In our iterative algorithm, the estimated sources
grow by the accretion of prisms in the periphery of the current estimate.
In addition, only the columns of the sensitivity matrix corresponding to
the prisms in the periphery of the current estimate are needed for the
computations. Therefore, the individual columns of the sensitivity matrix
can be calculated on demand and deleted after an accretion takes place,
greatly reducing the demand for computer memory and processing time.
Tests on synthetic data show the ability of our method to correctly
recover the geometry of the targeted sources, even when interfering
signals produced by nontargeted sources are present. Inverting the data
from an airborne gravity gradiometry survey flown over the iron ore
province of Quadrilátero Ferrífero, southeastern Brazil, we estimated a
compact iron ore body that is in agreement with geologic information and
previous interpretations.
Cite as
Uieda, L., and V. C. F. Barbosa (2012), Robust 3D gravity gradient
inversion by planting anomalous densities, Geophysics, 77(4), G55-G66,
doi:10.1190/geo2011-0388.1
BibTex
@article{uieda2012,
title = {Robust 3D gravity gradient inversion by planting anomalous densities},
volume = {77},
issn = {00168033},
doi = {10.1190/geo2011-0388.1},
number = {4},
journal = {Geophysics},
author = {Uieda, Leonardo and Barbosa, Valéria C. F.},
year = {2012},
pages = {G55--G66},
}
Citations