About me

About

After 2.5 years in Hawaiʻi, I was offered a position to join the Geophysics group of the University of Liverpool's Department of Earth, Ocean and Ecological Sciences. This was an exciting opportunity to start my own research group and navigate the UK system, which was entirely new to me.

About

After my initial leave from UERJ was done, I decided to quit that job and stay in Hawaiʻi a bit longer. I transitioned into this soft-money position to be able to apply for grants that could sustain myself and the GMT project beyond the funding we had available.

About

This was a mix of a sabbatical from UERJ and a postdoc position. I took a leave of absence for 1 year to work with the Generic Mapping Tools team to create PyGMT, a widely-used Python library for processing and visualizing geophysical data.

About

This was my first academic position, which I got while still working on my PhD thesis. It was a great opportunity to gain some experience, particularly in teaching, which turned out to be the thing I like the most about the job.

Thesis: Forward modeling and inversion of gravitational fields in spherical coordinates

Advisor: Valéria C. F. Barbosa

About

After my Master's degree, I stayed at the Observatório Nacional for my PhD, also with Valéria C. F. Barbosa. In 2016, I defended my thesis, which was submitted for publication in 3 parts:

• Modeling the Earth with Fatiando a Terra (2013)
• Tesseroids: forward modeling gravitational fields in spherical coordinates (2016)
• Fast non-linear gravity inversion in spherical coordinates with application to the South American Moho (2017)

During my PhD, I presented the following yearly seminars:

• leouieda/seminario-on-2012
• leouieda/qualify (qualification exam)
• leouieda/seminario-on-2014
• leouieda/seminario-on-2015

Abstract

We present methodological improvements to forward modeling and regional inversion of satellite gravity data. For this purpose, we developed two open-source software projects. The first is a C language suite of command-line programs called Tesseroids. The programs calculate the gravitational potential, acceleration, and gradient tensor of a spherical prism, or tesseroid. Tesseroids implements and extends an adaptive discretization algorithm to automatically ensure the accuracy of the computations. Our numerical experiments show that, to achieve the same level of accuracy, the gravitational acceleration components require finner discretization than the potential. In turn, the gradient tensor requires finner discretization still than the acceleration. The second open-source project is Fatiando a Terra, a Python language library for inversion, forward modeling, data processing, and visualization. The library allows the user to combine the forward modeling and inversion tools to implement new inversion methods. The gravity forward modeling tools include an implementation of the algorithm used in the Tesseroids software. We combined the inversion and tesseroid forward modeling utilities of Fatiando a Terra to develop a new method for fast non-linear gravity inversion. The method estimates the depth of the crust-mantle interface (the Moho) based on observed gravity data using a spherical Earth approximation. We extended the computationally efficient Bott's method to include smoothness regularization and use tesseroids instead right rectangular prisms. The inversion is controlled by three hyper-parameters: the regularization parameter, the density-contrast between the real Earth and the reference model (the Normal Earth), and the depth of the Moho of the Normal Earth. We employ two cross-validation procedures to automatically estimate these parameters. Tests on synthetic data confirm the capability of the proposed method to estimate smoothly varying Moho depths and the three hyper-parameters. Finally, we applied the inversion method developed to produce a Moho depth model for South America. The estimated Moho depth model fits the gravity data and seismological Moho depth estimates in the oceanic areas and the central and eastern portions of the continent. We observe large misfits in the Andes region, where Moho depth is largest. In Amazon, Solimões, and Paraná Basins, the model fits the observed gravity but disagrees with seismological estimates. These discrepancies suggest the existence of density-anomalies in the crust or upper mantle, as has been suggested in the literature.

Thesis: Robust 3D gravity gradient inversion by planting anomalous densities

Advisor: Valéria C. F. Barbosa

About

I did my Master's degree in Geophysics at the Observatório Nacional in Rio de Janeiro, Brazil, under the supervision of Valéria C. F. Barbosa. I started in March 2010 and defended my dissertation in October 2011. The method that we developed is implemented in the software Fatiando a Terra. The dissertation was later published as the paper:

• Robust 3D gravity gradient inversion by planting anomalous densities (2012)

During my MSc, I presented the following yearly seminars:

• leouieda/seminario-on-2010
• leouieda/seminario-on-2011

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.

About

In the fourth year of my BSc degree, I went on an international exchange program to York University to study in their Geomatics Engineering degree. I spent the year learning about geodesy, gravimetry, positioning, and least-squares adjustment, all of which I still use to this day. I also had a great time in Toronto and got to make a bunch of international friends.

Thesis: Cálculo do tensor gradiente gravimétrico utilizando tesseroides

Advisor: Naomi Ussami

About

My Bachelor's degree in Geophysics is from the Universidade de São Paulo, Brazil, where I studied from 2004 until 2009. I did an undergraduate research project and eventually my thesis under the supervision of Naomi Ussami. This was when I started development of the software Tesseroids and the research that lead to the paper which is the first part of my PhD thesis:

• Tesseroids: forward modeling gravitational fields in spherical coordinates (2016)

Abstract

The GOCE satellite mission has the objective of measuring the Earths gravitational field with an unprecedented accuracy through the measurement of the gravity gradient tensor (GGT). The data provided by this mission could be used to study large areas, where the flat Earth approximation can have its limitations. In these cases the modeling could be done with tesseroids, also called spherical prisms, in order to take the Earths curvature into account. The GGT caused by a tesseroid can be calculated with numerical integration methods, such as the Gauss-Legendre Quadrature (GLQ). In the current project, a computer program was developed for the direct calculation of the GGT using the GLQ. The accuracy of this implementation was evaluated by comparing its results with the result of analytical formulas for the special case of a spherical cap. Next, the developed program was used to calculate the differences in the GGT caused by the flat Earth approximation. These differences reach are up to 30% in the Tzz component for a 50 deg x 50 deg x 10 km model. Finally, the computer program was used to calculate the effect caused by the topographic masses on the GGT at 250 km altitude for the Paraná basin region. In regions of large topographical variations, the components of the GGT due to the topographic masses have amplitudes of the same order of magnitude as the GGT components due to density anomalies in the interior of the crust and mantle.

Award: IES\R3\213141

Amount: £10,500

Abstract

The magnetization that is locked in certain minerals at the time of their formation is one of the few gateways we have to the Earth's distant past. By measuring the magnetization of certain rocks we are able to determine properties about the Earth's magnetic field in the past, which provides crucial information about our planet's climate history and the movement of the plates that make up the outermost layer of the Earth. For decades, researchers have only been able to make measurements of the average magnetic field of each rock sample, which can lead to large uncertainties in our estimates or even having to discard entire samples. Recent advances in technology are allowing us to make measurements in such detail that we may soon be able to distinguish the magnetic fields of the individual minerals that make up the rock sample. This new technology opens the door to using methods normally applied to national or continental scale geophysical surveys to micrometer scale data. There is still much to be explored and refined before this can be achieved. This collaboration will bring together experts from both large scale geophysics and micrometer scale paleomagnetism to explore the possibilities and help define future directions of research.