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.

We have developed the open-source software Tesseroids, a set of command-line programs to perform 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 have 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 homogenous 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.

Estimating the relief of the Moho from gravity data is a computationally intensive nonlinear inverse problem. What is more, the modelling must take the Earths curvature into account when the study area is of regional scale or greater. We present a regularized nonlinear 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 hyperparameters: 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.

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.

Measurements made on the surface of the Earth are often sparse and unevenly distributed. For example, GPS displacement measurements are limited by the availability of ground stations and airborne geophysical measurements are highly sampled along flight lines but there is often a large gap between lines. Many data processing methods require data distributed on a uniform regular grid, particularly methods involving the Fourier transform or the computation of directional derivatives. Hence, the interpolation of sparse measurements onto a regular grid (known as gridding) is a prominent problem in the Earth Sciences.

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.