Cartesian Meshing Spherical Earth (CMSE): A Code Package to Incorporate the Spherical Earth in SPECFEM3D Cartesian Simulations

The SPECFEM3D_Cartesian code package is widely used in simulating seismic wave propagation on local and regional scales due to its computational efficiency compared with the one-chunk version of the SPECFEM3D_Globe code. In SPECFEM3D_Cartesian, the built-in meshing tool maps a spherically curved cube to a rectangular cube using the Universal Transverse Mercator projection (UTM). Meanwhile, the geodetic east, north, and up directions are assigned as the local x–y–z directions. This causes coordinate orientation issues in simulating waveform propagation in regions larger than 6° × 6° or near the Earth’s polar regions. In this study, we introduce a new code package, named Cartesian Meshing Spherical Earth (CMSE), that can accurately mesh the 3D geometry of the Earth’s surface under the Cartesian coordinate frame, while retaining the geodetic directions. To benchmark our new package, we calculate the residual amplitude of the CMSE synthetics with respect to the reference synthetics calculated by SPECFEM3D_Globe. In the regional scale simulations with an area of 1300 km × 1300 km, we find a maximum of 5% amplitude residual for the SPECFEM3D_Cartesian synthetics using the mesh generated by the CMSE, much smaller than the maximum amplitude residual of 100% for the synthetics based on its built-in meshing tool. Therefore, our new meshing tool CMSE overcomes the limitations of the internal mesher used by SPECFEM3D_Cartesian and can be used for more accurate waveform simulations in larger regions beyond one UTM zone. Furthermore, CMSE can deal with regions at the south and north poles that cannot be handled by the UTM projection. Although other external code packages can be used to mesh the curvature of the Earth, the advantage of the CMSE code is that it is open-source, easy to use, and fully integrated with SPECFEM3D_Cartesian.

Back to the Drawing Board: Creative Mapping Methods for Inclusion and Connection

The most well-known representation of the globe, the Mercator Projection, often provokes surprise for its considerable distortions: despite appearances, Greenland is almost five times smaller than Canada, and Russia is, in fact, approximately half the size it appears. Since the oldest civilizations, maps have relied on shifting knowledges to become more accurate and efficient, a process accelerated with science and technological development. But the unrealistic proportions of the Mercator map point to a critical reflection: maps show no absolute truths, nor are they neutral. Maps tell stories; they represent ideas as much as spaces, and exactitude is no synonym for neutrality. On the contrary, mapping is a cultural and political act. In the 1990s, geographers started to defy the power relationships of mapmaking with critical cartography. This critique, strongly supported by activists, opened new debates and representational possibilities in which scientific principles started to matter less than social and environmental justice, political participation, and storytelling. Within this framework, this chapter reflects on two alternative mapping methods used in the humanities and social sciences: social cartography and deep mapping. Each section introduces origins, theoretical frameworks, reception, and applications. Because these methods aim to rectify the abuse of power often enabled by scientific mapping, they use non-prescriptive mapmaking to legitimize neglected perspectives. Social Cartography is intrinsically participatory and uses mapping as a collaborative and critical practice. It challenges the role of traditional cartography in socio-political spheres, creating opportunities for new narratives and communities to be heard and understood. Deep maps represent abstract characteristics of a place. They can transcend the boundaries of bi-dimensional and pictorial representation, and consequently, reach different publics. The method is flexible, combining literature and immersive experiences to convey personal or subjective qualities of a place. Other expressions of deep mapping include audio and performative documentations. Social cartography and deep mapping operate against traditional mapmaking by reinforcing the notion that non-institutionalized maps are just as valid in guiding public actions and projects. As participatory practices within communities, these methods promote dialogue, empowerment, and transformation. Therefore, they are indispensable in ensuring democratic research and decision-making.

Web Mercator Projection – One of Cylindrical Projections of an Ellipsoid to a Plane

The Web Mercator projection is a projection of a relatively recent date. There has been a lot of controversy about its application. Some believe that this projection is not a projection of either the sphere or the surface of the ellipsoid. Therefore, in this paper, several projections of the surface of a rotational ellipsoid into a plane are investigated and it is shown that the Web Mercator projection is one of such projections. Namely, although the equations of this projection are identical to the equations for the projection of the sphere, the basic difference is in the choice of the area of definition, i.e., the domain of the projection. Furthermore, we have shown that the Web Mercator projection can also be interpreted as double mapping: mapping an ellipsoid to a sphere according to the normals and then mapping the sphere to the plane according to the formulas of the Mercator projection for the sphere. The Web Mercator projection is not a conformal projection, but it is close in properties to the Mercator projection.

DETERMINING THE LOCATION OF AN UNMANNED AERIAL VEHICLE BASED ON VIDEO CAMERA IMAGES

The paper deals with the problem of determining the location of an unmanned aerial vehicle from video and photo images taken by surveillance cameras. As the observation area is considered to be sufficiently limited, the area under consideration can be taken as part of a plane. The solution to the problem is based on the construction of a bijective mapping between the known geographic coordinates of three different objects recognized in the images and their coordinates relative to the monitor plane. To this end, the geographical coordinates of the objects (latitude and longitude) are first converted to the Mercator projection, and a bijective mapping is built between the coordinates of the objects calculated in the Mercator projection and the coordinates relative to the camera monitor plane. Then, based on the current orientation angles of the unmanned aerial vehicle, the coordinates of the projection of its position on the monitor plane are calculated, and the geographical coordinates are found by applying the inverse of the constructed bijective mapping.

The Spread of the Mercator Projection in Western European and United States Cartography

En 1569, le cartographe hollandais Gérard Mercator publiait une projection qui allait révolutionner la navigation maritime. Bien que l’importance de la projection de Mercator soit soulignée dans la documentation existante, la façon dont elle en est venue à jouer un rôle prépondérant dans la production de cartes du monde en cartographie thématique et en cartographie de référence n’a pas retenu l’attention. L’institutionnalisation de la projection de Mercator dans la cartographie de l’Europe occidentale et des États-Unis découle du rôle joué par les navigateurs, les sociétés et les organismes scientifiques, ainsi que les producteurs de cartes de référence et de cartes thématiques de même que d’atlas à l’usage du public. Les données, que l’auteure soumet à une analyse de contenu, proviennent du registre de publication de cartes du monde individuelles et apparaissant dans les atlas, et elles sont comparées et confrontées aux données historiques de sources complémentaires. L’étude révèle que l’utilisation impropre de la projection de Mercator a commencé après 1700, au moment où elle a été rattachée aux travaux des scientifiques auprès des navigateurs et à la création de la cartographie thématique. Au cours du dix-huitième siècle, la projection de Mercator a été diffusée dans les publications et les rapports destinés aux sociétés de géographie qui décrivaient les explorations financées par l’État. Au dix-neuvième siècle, l’influence de scientifiques bien connus faisant usage de la projection de Mercator a filtré dans les publications destinées au grand public. L’utilisation de la projection de Mercator dans la production de cartes du monde en cartographie de référence et en cartographie thématique est un choix qui résultait de la validation indirecte de cette projection par les milieux scientifique et universitaire depuis le dix-huitième siècle jusque tard au dix-neuvième siècle.

Interference Identification for Time-Varying Polyhedra

Identification of when and where moving areas intersect is an important problem in maritime operations and air traffic control. This problem can become particularly complicated when considering large numbers of objects, and when taking into account the curvature of the earth. In this paper, we present an approach to conflict identification as a series of stages where the earlier stages are fast, but may result in a false detection of a conflict. These early stages are used to reduce the number of potential conflict pairs for the later stages, which are slower, but more precise. The stages use R-trees, polygon intersection, linear projection and nonlinear programming. Our approach is generally applicable to objects moving in piece-wise straight lines on a 2D plane, and we present a specific case where the Mercator Projection is used to transform objects moving along rhumb lines on the earth into straight lines to fit in our approach. We present several examples to demonstrate our methods, as well as to quantify the empirical time complexity by using randomly generated areas.

Interference Identification for Time-Varying Polyhedra

Identification of when and where moving areas intersect is an important problem in maritime operations and air traffic control. This problem can become particularly complicated when considering large numbers of objects, and when taking into account the curvature of the earth. In this paper, we present an approach to conflict identification as a series of stages where the earlier stages are fast, but may result in a false detection of a conflict. These early stages are used to reduce the number of potential conflict pairs for the later stages, which are slower, but more precise. The stages use R-trees, polygon intersection, linear projection and nonlinear programming. Our approach is generally applicable to objects moving in piece-wise straight lines on a 2D plane, and we present a specific case where the Mercator Projection is used to transform objects moving along rhumb lines on the earth into straight lines to fit in our approach. We present several examples to demonstrate our methods, as well as to quantify the empirical time complexity by using randomly generated areas.

Study of an Elliptic Partial Differential Equation Modeling the Ocean Flow in Arctic Gyres

We study the ocean flow in Arctic gyres using a recent model for gyres derived in spherical coordinates on the rotating sphere. By projecting this model onto the plane using the Mercator projection, we obtain a semi-linear elliptic partial differential equation in an unbounded domain, difficulty which is then overcome by projecting the PDE onto the unit disk via a conformal map. We then study existence, regularity and uniqueness of solutions for constant and linear vorticity functions.

Methodology of mapping of historical and cultural heritage objects by GIS technologies using archival cartographic and aerial materials

Aim. The purpose of the work is to process archival cartographic materials and remote sensing data for the interpretation of objects of historical and cultural heritage (OHCH) of Cherkasy, including those that have not been preserved. Method. One of the possible technological schemes for research is offered. According to her, the first step was to analyze the input data of the study, among which were: a map of Cherkasy in 1895 at a scale of 1:42000; German aerial image of 1944; a fragment of a space image of Cherkasy obtained from the GeoEye-1 satellite in 2018. Geometric correction of the input materials was performed in the Mercator projection and the WGS84 coordinate system, in which the transformed image was obtained. The next step was to vectorize the objects of historical and cultural heritage of Cherkasy, according to the list obtained on the city’s website. There are two types of objects: point and polygonal. When vectorizing polygonal objects, the historical boundaries were specified with the help of archival maps and aerial images. Special symbols have been developed for each of the types of historical and cultural heritage sites, according to the proposed classification. In addition, an attributive database of these objects was created, which had the following structure: number of the passport of object, the name of the object, the address of the OHCH, the number of the decision to take under protection, information about the OHCH. Also, the obtained vector data was exported to the exchange format with the extension kmz and an online version of the thematic map was created on the basis of the free GISFile resource. Results. As a result of the conducted researches, the thematic GIS of the objects of historical and cultural heritage of Cherkasy was created, which are plotted on the space image of high spatial resolution, obtained in 2018. An on-line version of the GIS of Cherkasy historical and cultural heritage sites has been created on the basis of the free GISFile cartographic service, with the possibility of analyzing the location of these objects and building optimal tourist routes. Scientific novelty. Possible algorithms for creating offline and on-line versions of thematic GIS are proposed. Practical value. The obtained results of mapping the objects of historical and cultural heritage of Cherkasy can be used by the structures of protection of objects of historical and cultural heritage of Cherkasy at the Ministry of Culture.