Search Results (3)

With the rapid advancement of satellite remote sensing technology, many scientists and organizations, including NASA, ESA, NAOC, and Roscosmos, observe and study significant changes in the geomagnetic field, which has greatly promoted research on the geomagnetic field and made it an important research direction in Earth system science. In traditional geomagnetic field research, tesseroid cells face degradation issues in high-latitude regions and accuracy limitations. To overcome these limitations, this paper introduces the Discrete Global Grid System (DGGS) to construct a geophysical model, achieving seamless global coverage through multi-level grid subdivision, significantly enhancing the processing capability of multi-source and multi-temporal spatial data. Addressing the challenges of the lack of analytical solutions and clear integration limits for DGGS cells, a method for constructing shape functions of arbitrary isoparametric elements is proposed based on the principle of isoparametric transformation, and the shape functions of isoparametric DGGS cells are successfully derived. In magnetic vector forwarding, considering the potential error amplification caused by Poisson’s formula, the DGGS grid is divided into six regular triangular sub-units. The triangular superconvergent point technique is adopted, and the positions of integration points and their weight coefficients are accurately determined according to symmetry rules, thereby significantly improving the calculation accuracy without increasing the computational complexity. Finally, through the forward modeling algorithm based on tiny tesseroid cells, this study comprehensively compares and analyzes the computational accuracy of the DGGS-based magnetic vector forwarding algorithm, verifying the effectiveness and superiority of the proposed method and providing new theoretical support and technical means for geophysical research. Full article

For regional or even global geophysical problems, the curvature of the geophysical model cannot be approximated as a plane, and its curvature must be considered. Tesseroids can fit the curvature, but their shapes vary from almost rectangular at the equator to almost triangular at the poles, i.e., degradation phenomena. Unlike other spherical discrete grids (e.g., square, triangular, and rhombic grids) that can fit the curvature, the Discrete Global Grid System (DGGS) grid can not only fit the curvature but also effectively avoid degradation phenomena at the poles. In addition, since it has only edge-adjacent grids, DGGS grids have consistent adjacency and excellent angular resolution. Hence, DGGS grids are the best choice for discretizing the sphere into cells with an approximate shape and continuous scale. Compared with the tesseroid, which has no analytical solution but has a well-defined integral limit, the DGGS cell (prisms obtained from DGGS grids) has neither an analytical solution nor a fixed integral limit. Therefore, based on the isoparametric transformation, the non-regular DGGS cell in the system coordinate system is transformed into the regular hexagonal prism in the local coordinate system, and the DGGS-based forwarding algorithm of the gravitational field is realized in the spherical coordinate system. Different coordinate systems have differences in the integral kernels of gravity fields. In the current literature, the forward modeling research of polyhedrons (the DGGS cell, which is a polyhedral cell) is mostly concentrated in the Cartesian coordinate system. Therefore, the reliability of the DGGS-based forwarding algorithm is verified using the tetrahedron-based forwarding algorithm and the tesseroid-based forwarding algorithm with tiny tesseroids. From the numerical results, it can be concluded that if the distance from observations to sources is too small, the corresponding gravity field forwarding results may also have ambiguous values. Therefore, the minimum distance is not recommended for practical applications. Full article

Parameterization is the key property of a parametric surface and significantly affects many kinds of applications. To improve the quality of parameterization, equiareal parameterization minimizes the equiareal energy, which is presented as a measure to describe the uniformity of iso-parametric curves. With the help of the binary Möbius transformation, the equiareal parameterization is extended to the triangular Bézier surface on the triangular domain for the first time. The solution of the corresponding nonlinear minimization problem can be equivalently converted into solving a system of bivariate polynomial equations with an order of three. All the exact solutions of the equations can be obtained, and one of them is chosen as the global optimal solution of the minimization problem. Particularly, the coefficients in the system of equations can be explicitly formulated from the control points. Equiareal parameterization keeps the degree, control points, and shape of the triangular Bézier surface unchanged. It improves the distribution of iso-parametric curves only. The iso-parametric curves from the new expression are more uniform than the original one, which is displayed by numerical examples. Full article