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When, in 1822, Brazil declared its independence from Portugal, its vast territory was little known by the central government in Rio de Janeiro. There was a great need to create reliable maps that would delineate the new country's boundaries. This paper aims to show how a practical application of astronomy, specifically geodesy, was vital in the efforts to build the nation. We follow the professional life of an astronomer, Luis Cruls, director of the National Observatory, professor at the Military School and chief researcher of several expeditions, to discuss the strength of geodesic and cartographic activities in Brazil at the end of the 19th century. [ABSTRACT FROM AUTHOR]

This study presents an optimized gravity-sparse inversion method. The proposed method minimizes the global objective function using interior-point method for boundary constraints and a general weighting function comprising the depth, compactness, and kernel weighting functions of the density models. For the compactness weighting function, practical experiments demonstrate that the recovered model becomes more compact with an increasing value for the relative exponential factor β. However, if no appropriate boundary-constraint method is applied, the inversion results cannot be controlled within the designated constraint bounds when β needs to be set to a large value to obtain compact inversion results. The interior-point method allows the use of a larger β to obtain more compact inversion results without violating the boundary constraints. Additionally, models in close proximity can more clearly be recognized using this method. To improve the computational efficiency and obtain a more accurate regularization parameter, the preconditioned conjugate gradient and L-curve, or line search methods, were also applied. The proposed method was applied for three synthetic examples: two positive bodies adjacent to each other at different depths inverted using noise-free gravity anomaly data, three bodies (positive or negative) at different depths inverted using noise-free or contaminated gravity anomaly data, and three bodies (positive or negative) characterized by a certain dip angle inverted using contaminated gravity anomaly data. This method was also applied for the inversion of a Woodlawn sulfide body, Missouri iron ore body, and granitoid rock body in the Rio Maria region in the state of Para, Brazil. In all six test cases, larger β values were used and the density models were recovered with sharper boundaries within the designated bounds. [ABSTRACT FROM AUTHOR]

The article presents information on a number of datum origins that are readily identifiable through archived imagery using Google Earth™. Córrego Alegre is the origin for the primary mapping datum of Brazil. Carthage is the origin for the Tunesian 1925 datum. Mirador Tower is the origin for the Belvedere Datum of Vietnam.