Presentations

Abstract

The Fatiando a Terra project is a collection of open-source Python libraries for geophysics which cover a range of functionalities, from data download and processing to modeling and inversion. Many of our tools are general purpose but we also focus on gravimetry and magnetometry. Development on the projected started in 2010 and has gone through several iterations as the team matured and established best practices for maintaining software projects in the open. This talk is an overview of the history and current iteration of the project, including a short demonstration of our current capabilities for downloading and processing gravity data. We will then move on to our plans for future directions of the projects and information of how you can get involved. Finally, we will briefly discuss some of the challenges and opportunities of adopting open-science practices.

Citations

Abstract

The Fatiando a Terra project is a collection of open-source Python libraries for geophysics which cover a range of functionalities, from data download and processing to modeling and inversion. In this opportunity we will present the two libraries that are focused on potential fields: Harmonica and Boule. Boule implements reference ellipsoids (including oblate ellipsoids, spheres, and soon triaxial ellipsoids), conversions between ellipsoidal and geocentric spherical coordinates, and normal gravity calculations. The latter are performed using analytical expressions for gravity fields at any point outside of the ellipsoid. Harmonica provides tools for processing, forward modelling, and inversion of gravity and magnetic data. We will demonstrate its use to compute Bouguer gravity disturbances by forward modelling the topography with prisms, removing a 2nd order regional trend, and interpolating it onto a regular grid at a constant height using the equivalent layer technique. Both libraries are still evolving as we continue to refine their goals and scopes. We invite everyone to get involved in the development, whether it's through coding, writing documentation, or giving feedback.

Abstract

This was another online version of the talk. It was really nice to connect with the geophysicists at Kiel since Prof. Jörg Ebbing's group uses Tesseroids and was involved in the generation of the GOCE gravity gradient grids cited in the talk. They have also used the Moho inversion code and are getting involved in Fatiando. I added some bits to the end about getting involved in open-source software projects and finding online communities of practice (with a shout out to the Software Underground).

Abstract

I was really delighted to get an invitation to speak at my alma mater (roughly 10 years after my graduation). The talk was also delivered online. This was the first time delivering this talk in Portuguese, which was a struggle since I had the words prepared in English already (slides are still in English, though). I added the latest news of the successful reproduction of the Ferguson COVID-19 modelling results. Funny enough, this talk is heavily inspired on the last talk I gave there in 2015.

Abstract

This is the second version of this talk and it was delivered online because of the COVID-19 pandemic. I changed it a bit to reflect current research presented at EGU2020 and focus less on the technical side of development. The online delivery was new to me but it worked out well. Even though it can be strange to talk to a screen for 50 minutes, the great questions afterwards more than made up for it.

Abstract

This is the first version of this talk, delivered at the GDSL group seminars. It was about my path through geophysics guided by my interests in making open-source software: how I got started with coding, the various projects I'm developing, how that's shaped my research, and plans for the future.

Abstract

In this talk, I'll go over some of my work on open-source geophysics software (Python and GMT), how we're building communities around them, and how this ties into my current research and efforts towards reproducibility.

Citations

Abstract

Machine learning is the new trend sweeping across the Earth Sciences. From the oil and gas industry to oceanography, these algorithms are being trained to solve previously unsolvable (or extremely tedious) problems. But what exactly is "machine learning" and what can be done with it? In this talk, I will present a brief high-level overview of some of the core concepts and interesting applications of machine learning methods to geoscience data. I will also explore some of the best practices and techniques that can be applied to geophysical inversion and interpolation methods, including a new method for gridding 3-component GPS data.

Citations

Abstract

The inner density distribution of the Earth can be inferred from disturbances in its gravitational field. However, accomplishing this is never easy. There are many possible parameterizations for the mathematical model, which is often non-linear. To make matters worse, gravity data alone do not contain enough information to obtain a unique and stable solution. One must add independent information to constrain the solution space, often in the form of regularization. Many different methods for performing this inference have been developed and research in this field is still active. Investigating new methodologies implies developing complex software, which often must be able to deal with sparse matrices and parallelism. I’ll present the open-source Python library Fatiando a Terra. It implements many of the components required for developing inversion methods, such as forward modeling, data processing and I/O, and regularization. I’ll also show how I used this library to develop a computationally efficient method for estimating the Moho depth from gravity data using a spherical approximation of the Earth.

Citations

Abstract

O Fatiando a Terra é uma biblioteca feita na linguagem Python que tem como objetivo facilitar o trabalho de pesquisadores e professores na área geofísica. Os módulos da biblioteca foram planejados para facilitar a combinação de seus componentes de diversas formas. Por exemplo, o mesmo módulo de modelagem direta pode ser usado para produzir dados sintéticos, desenvolver um método de inversão ou como parte de uma interface gráfica interativa. Além disso, as funções da biblioteca podem ser combinadas com funções desenvolvidas pelo usuário e com as muitas bibliotecas científicas da linguagem Python. O módulo de problemas inversos automatiza grande parte da implementação de um novo método de inversão. O pesquisador implementa somente o cálculo de dados preditos e da matriz de sensibilidade, ambos reutilizando os diversos módulos de modelagem direta. Com essas duas funções, o usuário pode escolher livremente entre diversos métodos de optimização e regularização para executar sua inversão. Para o ensino de geofísica, a biblioteca pode ser combinada com a interatividade de outros programas, particularmente o IPython notebook (www.ipython.org). Conceitos difíceis de serem transmitidos em aula podem ser explorados pelos alunos de forma interativa, com botões, gráficos e animações. Por exemplo, para ensinar a reflexão e refração de ondas sísmicas, o professor pode utilizar simulações numéricas da propagação de ondas para produzir animações em tempo real. Outro exemplo é permitir aos alunos explorar como o campo geomagnético interage com um corpo geológico a diferentes latitudes para produzir uma anomalia magnética de campo total. Dessa forma, os alunos ganham experiência e intuição ao interagir com os resultados. A implementação de diversos métodos geofísicos em uma única biblioteca fornece a base necessária para a rápida criação de novas metodologias e material didático interativo. A maior parte da funcionalidade atual é para gravimetria e magnetometria, embora já exista um núcleo de sísmica e sismologia que está sendo desenvolvido. O projeto necessita de usuários e desenvolvedores para crescer e abranger os demais ramos da geofísica. O projeto é software livre e contribuições de qualquer forma são bem vindas.

Citations

Poster

Abstract

Gravimetry is a routine part of the geophysicists toolset, historically used in geophysics following the geodetic definitions of gravity anomalies and their related “reductions”. Several authors have shown that the geodetic concept of a gravity anomaly does not align with goals of gravimetry in geophysics (the investigation of anomalous density distributions). Much of this confusion likely stems from the lack of widely available tools for performing the corrections needed to arrive at a geophysically meaningful gravity disturbance. For example, free-air corrections are completely unnecessary since analytical expressions for theoretical gravity at any point have existed for over a decade. Since this is not easily done in a spreadsheet or short script, modern tools for processing and modelling gravity data for geophysics are needed. These tools must be trustworthy (i.e., extensively tested) and designed with software development and geophysical best practices in mind. We present the Python libraries Harmonica and Boule, which are part of the Fatiando a Terra project. Both tools are open-source under the permissive BSD license and are developed in the open by a community of geoscientists and programmers. Harmonica provides tools for processing, forward modelling, and inversion of gravity and magnetic data. The first release of Harmonica was focused on implementing methods for processing and interpolation with the equivalent source technique, as well as forward modelling with right-rectangular prisms, point sources, and tesseroids. Current work is directed towards implementing a processing pipeline for gravity data, including topographic corrections in Cartesian and spherical coordinates, atmospheric corrections, and more. The software is still in early stages of development and design and would benefit greatly from community involvement and feedback. Boule implements reference ellipsoids (including oblate ellipsoids, spheres, and soon triaxial ellipsoids), conversions between ellipsoidal and geocentric spherical coordinates, and normal gravity calculations using analytical solutions for gravity fields at any point outside of the ellipsoid. It includes ellipsoids for the Earth as well as other planetary bodies in the solar system, like Mars, the Moon, Venus, and Mercury. This enables the calculation of gravity disturbances for Earth and planetary data without the need for free-air corrections. Boule was created out of the shared needs of Harmonica, SHTools, and pygeoid and is developed with input from developers of these projects. We welcome participation from the wider geophysical community, irrespective of programming skill level and experience, and are actively searching for interested developers and users to get involved in shaping the future of these projects.

Citations

Abstract

We investigate the use of cross-validation (CV) techniques to estimate the accuracy of equivalent-source (also known as equivalent-layer) models for interpolation and processing of potential-field data. Our preliminary results indicate that some common CV algorithms (e.g., random permutations and k-folds) tend to overestimate the accuracy. We have found that blocked CV methods, where the data are split along spatial blocks instead of randomly, provide more conservative and realistic accuracy estimates. Beyond evaluating an equivalent-source model's performance, cross-validation can be used to automatically determine configuration parameters, like source depth and amount of regularization, that maximize prediction accuracy and avoid over-fitting. Widely used in gravity and magnetic data processing, the equivalent-source technique consists of a linear model (usually point sources) used to predict the observed field at arbitrary locations. Upward-continuation, interpolation, gradient calculations, leveling, and reduction-to-the-pole can be performed simultaneously by using the model to make predictions (i.e., forward modelling). Likewise, the use of linear models to make predictions is the backbone of many machine learning (ML) applications. The predictive performance of ML models is usually evaluated through cross-validation, in which the data are split (usually randomly) into a training set and a validation set. Models are fit on the training set and their predictions are evaluated using the validation set using a goodness-of-fit metric, like the mean square error or the R² coefficient of determination. Many cross-validation methods exist in the literature, varying in how the data are split and how this process is repeated. Prior research from the statistical modelling of ecological data suggests that prediction accuracy is usually overestimated by traditional CV methods when the data are spatially auto-correlated. This issue can be mitigated by splitting the data along spatial blocks rather than randomly. We conducted experiments on synthetic gravity data to investigate the use of traditional and blocked CV methods in equivalent-source interpolation. We found that the overestimation problem also occurs and that more conservative accuracy estimates are obtained when applying blocked versions of random permutations and k-fold. Further studies need to be conducted to generalize these findings to upward-continuation, reduction-to-the-pole, and derivative calculation. Open-source software implementations of the equivalent-source and blocked cross-validation (in progress) methods are available in the Python libraries Harmonica and Verde, which are part of the Fatiando a Terra project.

Citations

Poster

Abstract

For almost 30 years, the Generic Mapping Tools (GMT) have provided the Earth, Ocean, and Planetary Sciences with an open-source toolbox for processing and visualizing spatial data (bathymetry, gravity, magnetic, earthquake focal mechanisms, and more). In many fields, GMT is the de facto standard for creating high-resolution publication quality maps, figures, and animations. Since version 5, GMT has provided a C language Application Programming Interface (API) that allows other programs to access its core functionality. We are using this bridge to develop PyGMT (formerly GMT/Python), an open-source library that allows users of the Python programming language to leverage the almost thirty years of continuous GMT development. PyGMT is designed to integrate with the existing scientific Python ecosystem, including popular packages such as numpy, pandas, and xarray. PyGMT integrates seamlessly with the Jupyter notebook, allowing high-quality figures to be generated interactively both in a personal computer and in cloud computing environments compatible with Jupyter. We will present the design and usage of the software package, latest developments and updates, and lessons learned during its implementation.

Citations

Poster

Abstract

GPS/GNSS measurements of deformation have high accuracy and temporal resolution but are spatially sparse. Conversely, InSAR provides great spatial resolution but is limited by the satellite look angle, atmospheric noise, and the delay between repeat passes. The sparse GPS data often need to be interpolated on regular grids to be used as constraints during InSAR processing or to calculate strain rates. The interpolation is routinely done separately for each component of the velocity field using minimum curvature or specialized geostatistical algorithms. Recently, a joint interpolation of the horizontal components has been proposed. It estimates forces on a thin elastic sheet that fit the observed data and subsequently uses the estimated model to predict data on regular grids or arbitrary points. The Green’s functions for the physical model serve as a coupling between the two vector components through elasticity theory. We propose an extension of this method to 3D, using the elastic Green’s functions to couple the horizontal and vertical components. This enables the inclusion of vector data projected in arbitrary directions, such as InSAR line-of-sight velocities. The degree of coupling can be controlled through the Poisson’s ratio of the medium. We apply damping regularization to smooth the model and avoid instabilities in the inverse problem. Furthermore, we automatically select optimal values for the Poisson’s ratio and regularization parameter through cross-validation, which is common in machine learning applications. We compare the performance of the coupled model with uncoupled alternatives to grid 2- and 3-component GPS velocities and calculate derivatives through finite-differences approximations. We will present preliminary results from applications to GPS data from the Himalayas and the calibration of InSAR data products. A future goal is to integrate InSAR line-of-sight velocities in a joint interpolation with GPS velocities.

Citations

Abstract

We are building a Python wrapper for the Generic Mapping Tools (GMT), a set of command-line programs used across the Earth, Atmospheric, and Ocean Sciences to process and visualize geographic data. At SciPy 2017, we presented the project goals and an initial prototype. The feedback received led to improvements in the design of the library, mainly the creation of an object-oriented API. We will present the newest developments including support for numpy arrays and pandas Dataframes, interactive visualization in the Jupyter notebook using NASA WorldWind, and more. Once again, we seek feedback from the community to guide us moving forward.

Citations

About

This talk is about some early results from a collaboration me and Paul have with David Sandwell. The project was started by Paul and Dave as a follow up to their 2016 paper about interpolating 2D vector data. We're expanding it into 3D and ironing out some kinks in the methodology. I picked it up at the beginning of the year and have been slowly trying things out. It was a great chance to play with some tools from machine learning since this is a supervised prediction problem. Unlike most geophysical inversion, we're not really interested in the estimated parameters themselves. They are only a means to predict new values (on a regular grid in the case of gridding). I started implementing the tools I would need in a Python library called Verde, which served as the basis for the results shown in the presentation.

Abstract

Vertical ground motion at fault systems can be difficult to detect due to their small amplitude and contamination from non-tectonic sources, such as ground water loading. However, it may play an important role in our understanding of the earthquake cycle and the associated seismic hazards. Ground motion measurements from GPS are often sparse and must be interpolated onto a regular grid (e.g., for computing strain rate), ideally taking into account the varying degrees of uncertainty of the data. Traditionally, each vector component is interpolated separately using minimum curvature or biharmonic spline methods. Recently, a joint interpolation of the two horizontal components has been developed using the Green's functions for a point force deforming a thin elastic sheet. The elasticity constraints provide a coupling between the two vector components and lead to improved results because the underlying physics of the method approximately matches that of the GPS observations. We propose an expansion of this method into 3D in order to incorporate vertical GPS velocity measurements. To smooth the model and avoid singularities, we formulate the interpolation as a weighted least-squares inverse problem with damping regularization. Optimal values of the regularization parameter and the Poisson's ratio of the elastic medium are determined through K-fold cross-validation, a technique often used in machine learning for model selection. Additionally, the cross-validation provides a measure of the accuracy of model predictions and eliminates the need for manual configuration. The computational load of the inversion is lessened by imposing a cutoff distance to the Green's functions computations, which makes the sensitivity matrix sparse. We will present preliminary results from an application to EarthScope GPS data from the San Andreas Fault system. In the future, we aim to develop a joint inversion of 3D GPS and InSAR line-of-sight velocities to improve data coverage.

Citations

Poster

Abstract

The Generic Mapping Tools (GMT) are used throughout the geosciences to processes spatial data and create publication quality data visualizations, such as contour maps, earthquake focal mechanism solutions, and animations. The software is programmed in the C language and is accessed through a command-line interface. Recent versions of GMT also provide an Application Programming Interface (API) that allows access to the core functionality from other programming languages, potentially expanding the reach of GMT far beyond the current user base. A GMT toolbox for Matlab using the API has already been released, and an experimental interface from the Julia language is being developed. We are building a software library to interface GMT with the Python programming language. Popularity of Python has grown steadily in the Earth Sciences due to its simplicity and powerful set of scientific libraries. However, there is still great need for the geospatial processing and mapping capabilities of GMT. The GMT/Python library integrates with the scientific Python ecosystem through the support of common Python data types: numpy "ndarrays" and Pandas "DataFrames" for tabular data and xarray "Datasets" for grids. We have also implemented support for the Jupyter notebooks, a web-based interactive computing environment. These features will help make GMT more accessible to students and professional geoscientists who lack an extensive background in Unix tools and shell scripting. GMT/Python is an open-source project in early stages of development. The current focus is on the implementation of a robust set of core routines that implement the bridge between Python and GMT. Later, we will expand the library to cover the entire functionality of GMT. A first release is predicted for the late 2018. The latest documentation and source code can be accessed through the website www.pygmt.org.

Citations

Poster

Abstract

Figures generated by The Generic Mapping Tools (GMT) are present in countless publications across the Earth sciences. The command-line interface of GMT lends the tool its flexibility but also creates a barrier to entry for beginners. Meanwhile, adoption of the Python programming language has grown across the scientific community. This growth is largely due to the simplicity and low barrier to entry of the language and its ecosystem of tools. Thus, it is not surprising that there have been at least three attempts to create Python interfaces for GMT: gmtpy, pygmt, and PyGMT. None of these projects are currently active and, with the exception of pygmt, they do not use the GMT Application Programming Interface (API) introduced in GMT 5. The two main Python libraries for plotting data on maps are the matplotlib Basemap toolkit (matplotlib.org/basemap) and Cartopy (scitools.org.uk/cartopy), both of which rely on matplotlib (matplotlib.org) as the backend for generating the figures. Basemap is known to have limitations and is being discontinued. Cartopy is an improvement over Basemap but is still bound by the speed and memory constraints of matplotlib. We present a new Python interface for GMT (GMT/Python) that makes use of the GMT API and of new features being developed for the upcoming GMT 6 release. The GMT/Python library is designed according to the norms and styles of the Python community. The library integrates with the scientific Python ecosystem by using the “virtual files” from the GMT API to implement input and output of Python data types (numpy “ndarray” for tabular data and xarray “Dataset” for grids). Other features include an object-oriented interface for creating figures, the ability to display figures in the Jupyter notebook, and descriptive aliases for GMT arguments (e.g., “region” instead of “R” and “projection” instead of “J”). GMT/Python can also serve as a backend for developing new high-level interfaces, which can help make GMT more accessible to beginners and more intuitive for Python users. GMT/Python is an open-source project hosted on GitHub and is in early stages of development. A first release will accompany the release of GMT 6, which is expected for early 2018.

Citations

Abstract

The Generic Mapping Tools (GMT) is an open-source software package widely used in the geosciences to process and visualize time series and gridded data. Maps generated by GMT are ubiquitous in scientific publications in areas such as seismology and oceanography. We present a new GMT Python wrapper library built by the GMT team. We will show the design plans, internal implementations, and demonstrate an initial prototype of the library. Our wrapper connects to the GMT C API using ctypes and allows input and output using data from numpy ndarrays and xarray Datasets. The library is still in early stages of design and implementation and we are eager for contributions and feedback from the SciPy community.

Citations

Poster

Abstract

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.

Citations

Abstract

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.

Citations

Abstract

Solid Earth geophysics is the science of using physical observations of the Earth to infer its inner structure. Generally, this is done with a variety of numerical modeling techniques and inverse problems. The development of new algorithms usually involves copy and pasting of code, which leads to errors and poor code reuse. Added to this is a modeling pipeline composed of various tools that don't communicate with each other (Fortran/C for computations, large complicated I/O files, Matlab/VTK for visualization, etc). Fatiando a Terra is a Python library that aims to unify the modeling pipeline inside of the Python language. This allows users to replace the traditional shell scripting with more versatile and powerful Python scripting. Together with the new IPython notebook, Fatiando a Terra can integrate all stages of the geophysical modeling process, like data pre-processing, inversion, statistical analysis, and visualization. However, the library can also be used for quickly developing stand-alone programs that can be integrated into existing pipelines. Plus, because functions inside Fatiando a Terra use a common data and mesh format, existing algorithms can be combined and new ideas can build upon existing functionality. This flexibility facilitates reproducible computations, prototyping of new algorithms, and interactive teaching exercises. Although the project has so far focused on potential field methods (gravity and magnetics), some numerical tools for other geophysical methods have been developed as well. The library already contains: fast implementations of forward modeling algorithms (using Numpy and Cython), generic inverse problem solvers, unified geometry classes (prism meshes, polygons, etc), functions to automate repetitive plotting tasks with Matplotlib (automatic griding, simple GUIs, picking, projections, etc) and Mayavi (automatic conversion of geometry classes to VTK, drawing continents, etc). In the future, we plan to continuously implement classic and state-of-the-art algorithms as well as sample problems to help teach geophysics.

Citations

Abstract

We present a new 3D magnetic inversion algorithm based on the computationally efficient method of planting anomalous densities. The algorithm consists of an iterative growth of the anomalous bodies around prismatic elements called "seeds". These seeds are user-specified and have known magnetizations. Thus, the seeds provide a way for the interpreter to specify the desired skeleton of the anomalous bodies. The inversion algorithm is computationally efficient due to various optimizations made possible by the iterative nature of the growth process. The control provided by the use of seeds allows one to test different hypothesis about the geometry and magnetization of targeted anomalous bodies. To demonstrate this capability, we applied our inversion method to the Morro do Engenho (ME) and A2 magnetic anomalies, central Brazil (Figure 1a). ME is an outcropping alkaline intrusion formed by dunites, peridotites and pyroxenites with known magnetization. A2 is a magnetic anomaly to the Northeast of ME and is thought to be a similar intrusion that is not outcropping. Therefore, a plausible hypothesis is that A2 has the same magnetization as ME. We tested this hypothesis by performing an inversion using a single seed for each body. Both seeds had the same magnetization. Figure 1b shows that the inversion produced residuals up to 2000 nT over A2 (i.e., a poor fit) and less than 400 nT over ME (i.e., an acceptable fit). Figure 1c shows that ME is a compact outcropping body with bottom at approximately 5 km, which is in agreement with previous interpretations. However, the estimate produced by the inversion for A2 is outcropping and is not compact. In summary, the estimate for A2 provides a poor fit to the observations and is not in accordance with the geologic information. This leads to the conclusion that A2 does not have the same magnetization as ME. These results indicate the usefulness and capabilities of the inversion method here proposed.

Citations

Abstract

We have interpreted the airborne gravity gradiometry data from Carajás Mineral Province (CMP), Brazil, by using two different 3D inversion methods. Both inversion methods parameterized the Earth's subsurface into prismatic cells and estimate the 3D density-contrast distribution that retrieves an image of geologic sources subject to an acceptable data misfit. The first inversion method imposes smoothness on the solution by solving a linear system that minimizes an depth weighted L2 model objective function of density-contrast distribution. The second imposes compactness on the solution by using an iterative growth algorithm solved by a systematic search algorithm that accretes mass around user-specified prisms called “seeds”. Using these two inversion methods, the interpretation of full tensor gravity gradiometry data from an iron ore deposit in the area named N1 at CMP shows the consistent geometry and the depth of iron orebody. To date, the maximum depth of the iron orebody is assumed to be 200 m based on the maximum depth attained by the deepest well drilled in this study area. However, both inversion results exhibit a source whose maximum bottom depth is greater than 200 m. These results give rise two interpretations: i) the iron orebody may present its depth to the bottom greater than the maximum depth of 200 m attained by the deepest borehole; or ii) the iron orebody may be 200 m deep and the rocks below may be jaspilite whose density is close to that of soft hematite.

Citations

Abstract

We present an improvement to the method of 3D gravity gradient inversion by planting anomalous densities. This method estimates a density-contrast distribution defined on a grid of right-rectangular prisms. Instead of solving large equation systems, the method uses a systematic search algorithm to grow the solution, one prism at a time, around user-specified prisms called "seeds". These seeds have known density contrasts and the solution is constrained to be concentrated around the seeds as well as have their density contrasts. Thus, prior geologic and geophysical information are incorporated into the inverse problem through the seeds. However, this leads to a strong dependence of the solution on the correct location, density contrast, and number of seeds used. Our improvement to this method consists of using the "shape-of-anomaly" data-misfit function in conjunction with the l2-norm data-misfit function. The shape-of-anomaly function measures the different in shape between the observed and predicted data and is insensitive to differences in amplitude. Tests on synthetic and real data show that the improved method not only has an increased robustness with respect to the number of seeds and their locations, but also provides a better fit of the observed data.

Citations

Abstract

Forward modeling of potential fields is a useful way to incorporate the interpreter's knowledge about the geology of the interpretation area into the model. However, this can be a very tedious task. This is specially true when modeling in 3D and trying to fit multiple components, e.g., in gravity gradiometry. The interpreter is required to simultaneously supervise the data fit and the construction of geologically realistic 3D bodies. This problem is partially solved by methods of geophysical inversion, which automatically fit the data. Conversely, inverse problems introduce other challenges of their own. Most geophysical inverse problems are ill-posed because their solutions are neither unique nor stable. Thus, they require the introduction of prior information, usually through regularizing functions. Moreover, 3D inverse problems are very computationally expensive. Recent developments in potential field inversion have proposed different regularizing functions to transform the ill-posed problem into a well-posed one. Also, several techniques, like data compression and parallel computation, have been applied to overcome the computational complexity. We call attention to the method of potential field inversion by planting anomalous densities. This method uses an iterative algorithm to automatically grow the anomalous bodies around user-specified prismatic elements called "seeds", which have fixed density contrasts and positions. These seeds provide a first estimate of the skeletal outlines of the presumed anomalous bodies. Then, the inversion iteratively concentrates mass around this "skeleton" in a way that both fits the observed data and yields compact bodies. Therefore, the interpreter can easily impose prior information on the inversion through the seeds. The interpreter needs only to supply a few seeds that specify the sources' skeleton, eliminating the exhaustive task of specifying the complete geometry of multiple sources. Moreover, the interpreter is liberated from the time- consuming procedure of yielding a reasonable fit to the data. Due to its high computational efficiency, the method of planting anomalous densities can be used to quickly test geologic hypothesis of different locations and density contrasts for presumed sources. To test a hypothesis, one would choose the locations and density contrasts of the seeds accordingly and verify if the inversion result is able to fit the observed data. If it is not able, then the hypothesis can be rejected and a new one can be formulated and tested. Otherwise, there is no reason to reject the hypothesis on the basis of the geophysical data. Thus, the method can be viewed as a an enhanced forward modeling. The method of planting anomalous densities can be used with both gravity and gravity gradient data. This makes it an ideal tool to interpret compact geologic bodies using the new generation GOCE data. We present applications to synthetic and real data that illustrate the usefulness of our method.

Citations

Abstract

We present a new gravity gradient inversion method for estimating a 3D density-contrast distribution defined on a grid of prisms. Our method consists of an iterative algorithm that does not require the solution of a large equation system. Instead, the solution grows systematically around user-specified prismatic elements called "seeds". Each seed can be assigned a different density contrast, allowing the interpretation of multiple bodies with different density contrasts and that produce interfering gravitational effects. The compactness of the solution around the seeds is imposed by means of a regularizing function. The solution grows by the accretion of neighboring prisms of the current solution. The prisms for the accretion are chosen by systematically searching the set of current neighboring prisms. Therefore, this approach allows that the columns of the Jacobian matrix be calculated on demand, which greatly reduces the demand of computer memory and processing time. Tests on synthetic data and on real data collected over an iron ore province of Quadrilátero Ferrífero, southeastern Brazil, confirmed the ability of our method in detecting sharp and compact bodies.

Citations

Abstract

This paper presents a novel gravity inversion method for estimating a 3D density-contrast distribution defined on a grid of prisms. Our method consists of an iterative algorithm that does not require the solution of a large equation system. Instead, the solution grows systematically around user-specified prismatic elements called "seeds". Each seed can have a different density contrast, allowing the interpretation of multiple bodies with different density contrasts and interfering gravitational effects. The compactness of the solution around the seeds is imposed by means of a regularizing function. The solution grows by the accretion of neighboring prisms of the current solution. The prisms for the accretion are chosen by systematically searching the set of current neighboring prisms. Therefore, this approach allows that the columns of the Jacobian matrix be calculated on demand. This is a known technique from computer science called "lazy evaluation", which greatly reduces the demand of computer memory and processing time. Test on synthetic data and on real data collected over the ultramafic Cana Brava complex, central Brazil, confirmed the ability of our method in detecting sharp and compact bodies.

Citations

Poster

Abstract

The new observations of GOCE present a challenge to develop new calculation methods that take into account the sphericity of the Earth. We address this problem by using a discretization with a series of tesseroids. There is no closed formula giving the gravitational fields of the tesseroid and numerical integration methods must be used, such as the Gauss Legendre Cubature (GLC). A problem that arises is that the computation times with the tesseroids are high. Therefore, it is important to optimize the computations while maintaining the desired accuracy. This optimization was done using an adaptive computation scheme that consists of using a fixed GLC order and recursively subdividing the tesseroids. We have obtained an optimum ratio between the size of the tesseroid and its distance from the computation point. Furthermore, we show that this size-to-distance ratio is different for the gravitational attraction than for the gravity gradient tensor.

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Poster

Abstract

We present a new gravity gradient tensor inversion for estimating a 3D density-contrast distribution defined on a user-specified grid of prisms. Our method consists of an iterative algorithm that does not require the solution of large equation system. Instead, the solution grows systematically around user-specified prismatic elements called “seeds”. Each seed can have a different density contrast, allowing the interpretation of multiples bodies with different density contrasts. The compactness of the solution is imposed by means of a regularizing function that favors compact bodies closest to the priorly specified seeds. The solution grows by accreting neighboring prisms of the current solution. The prisms for the accretion are chosen by systematically searching the set of current neighboring prisms. Therefore, this approach allows that the columns of the Jacobian matrix be calculated on demand. This is a known technique from computer science called “lazy evaluation”, which greatly reduces the demand of computer memory and processing time. Test on synthetic data from multiple buried sources at different depths and on real data collected over iron deposits located in the Quadrilátero Ferrífero, southeastern region of Brazil, confirmed the ability of our method in detecting sharp and compact bodies.

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Abstract

The GOCE satellite mission has the objective of measuring the Earth's gravitational field with an unprecedented accuracy through the measurement of the gravity gradient tensor (GGT). One of the several applications of this new gravity data set is to study the geodynamics of the lithospheric plates, where the flat Earth approximation may not be ideal and the Earth's curvature should be taken into account. In such a case, the Earth could be modeled using tesseroids, also called spherical prisms, instead of the conventional rectangular prisms. The GGT due to a tesseroid is calculated using numerical integration methods, such as the Gauss-Legendre Quadrature (GLQ), as already proposed by Asgharzadeh et al. (2007) and Wild-Pfeiffer (2008). We present a computer program for the direct computation of the GGT caused by a tesseroid 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 with computation point located at one of the poles. The GGT due to the topographic masses of the Parana basin (SE Brazil) was estimated at 260km altitude in an attempt to quantify this effect on the GOCE gravity data. The digital elevation model ETOPO1 (Amante and Eakins, 2009) between 40º W and 65º W and 10º S and 35º S, which includes the Paraná Basin, was used to generate a tesseroid model of the topography with grid spacing of 10' x 10' and a constant density of 2670 kg/m3. The largest amplitude observed was on the second vertical derivative component (-0.05 to 1.20 Eötvos) in regions of rough topography, such as that along the eastern Brazilian continental margins. These results indicate that the GGT due to topographic masses may have amplitudes of the same order of magnitude as the GGT due to density anomalies within the crust and mantle.

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Abstract

Presentation for a short workshop about open science practices for the SPIN: Seismological Parameters and INstrumentation doctoral training network.

Abstract

Palestra e bate papo com o National Observatory Greenstone Belt (SEG-EAGE Student Chapter do Observatório Nacional) sobre minha carreira e dicas para os alunos que quiserem trilhar um caminho parecido.

Poster

Abstract

A ESA (European Space Agency) planeja lançar no outono de 2008 a missão GOCE (Gravity field and steady-state Ocean Circulation Explorer). A missão foi planejada para medir o campo gravitacional da Terra com acurácia e resolução sem precedentes. Para isso, fará uso de um gradiômetro de gravidade eletrostático que consiste de três pares de acelerômetros idênticos mutuamente ortogonais. O GOCE fornecerá dados do tensor gradiente da gravidade (TGG) a uma altitude de órbita de aproximadamente 250 km. Está sendo desenvolvido um programa computacional para analisar dados do TGG sobre as bacias sedimentares brasileiras. O programa utilizará o método da Quadratura Gauss-Legendre para efetuar a modelagem direta do TGG gerado por feições ou corpos geológicos com geometria esférica. A modelagem será feita discretizando o corpo por tesseróides, também denominados prismas esféricos. Os tesseróides são segmentos de uma casca esférica de espessura finita limitados por linhas de grade geográficas. A geometria dos tesseróides possibilita a construção de modelos levando em conta a curvatura da Terra. Isto se torna importante na modelagem de corpos geológicos com grande extensão lateral, como por exemplo, a bacia do Paraná. Será criado um modelo de densidade desta bacia a partir de dados de poços e dados sísmicos e utilizaremos o programa desenvolvido para obter estimativas do TGG. As estimativas serão comparadas com os futuros dados do GOCE na tentativa de separar o componente gravimétrico associado às variações de densidade na parte mais profunda da bacia.

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Poster

Abstract

I can't even find an abstract for this but I like to share it anyway. It's kind of nostalgic.

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