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 ([Formula: see text]) that determines the accuracy of the integration as well as the computation time. We have determined optimal values of [Formula: see text] 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 [Formula: see text] for the gravitational potential, [Formula: see text] for the gravitational acceleration, and [Formula: see text] for the gravity gradients. Contrary to previous assumptions, our results show that the potential and its first and second derivatives require different values of [Formula: see text] to achieve the same accuracy. These values were incorporated as defaults in the software.

The Python code that produces the results presented here is available under a BSD 3-clause open-source license at github.com/pinga-lab/paper-moho-inversion-tesseroids Moho model and data: The Moho depth model for South America and the data used to generate it are available under a Creative Commons Attribution 4.0

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. Fatiando a Terra is a Python library that aims to automate common tasks and 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. The library can also be used as an API for developing stand-alone programs. Algorithms implemented in Fatiando a Terra can be combined to build upon existing functionality. This flexibility facilitates prototyping of new algorithms and quickly building interactive teaching exercises. In the future, we plan to continuously implement sample problems to help teach geophysics as well as classic and state-of-the-art algorithms.

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An efficient forward modeling algorithm for calculation of gravitational fields in spherical coordinates is developed for 3-D large-scale gravity inversion problems. The 3-D 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 2 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 3-D 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 hr and 0.88 GB of memory compared with about a dozen days and 245.86 GB for the traditional 3-D GLQ method. Finally, the proposed algorithm is applied to the gravity field derived from the latest lunar gravity model GL1500E. Three-dimensional 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.

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 userspecified 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 Ferrí-fero, southeastern Brazil, we estimated a compact iron ore body that is in agreement with geologic information and previous interpretations.

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