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首页> 外文期刊>Surveys in Geophysics: An International Review Journal of Geophysics and Planetary Sciences >Magnetic Curvatures of a Uniformly Magnetized Tesseroid Using the Cartesian Kernels
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Magnetic Curvatures of a Uniformly Magnetized Tesseroid Using the Cartesian Kernels

机译：使用笛卡尔核的均匀磁化的Tesseroid的磁曲率

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摘要

In recent years, the gravitational curvatures, the third-order derivatives of the gravitational potential (GP), of a tesseroid have been introduced in the context of gravity field modeling. Analogous to the gravity field, magnetic field modeling can be expanded by magnetic curvatures (MC), the third-order derivatives of the magnetic potential (MP), which are the change rates of the magnetic gradient tensor (MGT). Exploiting Poisson's relations between (n + 1)th-order derivatives of the GP and nth-order derivatives of the MP, this paper derives expressions for the MC of a uniformly magnetized tesseroid using the fourth-order derivatives of the GP of a uniform tesseroid expressed in terms of the Cartesian kernel functions. Based on the magnetic effects of a uniform spherical shell, all expressions for the MP, magnetic vector (MV), MGT and MC of tesseroids have been examined for numerical problems due to singularity of the respective integral kernels (i.e., near zone and polar singularity problems). For this, the closed analytical expressions for the MP, MV, MGT and MC of the uniform spherical shell have been provided and used to generate singularity-free reference values. Varying both height and latitude of the computation point, it is found numerically that the near zone problem also exists for all magnetic quantities (i.e., MP, MV, MGT and MC). The numerical tests also reveal that the polar singularity problems do not occur for the magnetic quantity as a result of the use of Cartesian as opposed to spherical integral kernels. This demonstrates that the magnetic quantity including the newly derived MC 'inherit' the same numerical properties as the corresponding gravitational functional. Possible future applications (e.g., geophysical information) of the MC formulas of a uniformly magnetized tesseroid could be improved modeling of the Earth's magnetic field by dedicated satellite missions.
机译：近年来，在重力场建模的背景下，引入了引力曲率，引力电位（GP）的三阶衍生物，在重力场建模中引入。类似于重力场，磁场建模可以通过磁曲率（MC），磁电位（MP）的三阶导数而扩展，这是磁梯度张量（MGT）的变化率。利用Poisson之间的GP和N阶衍生物的衍生物与MP的N阶衍生物之间的关系，本文使用了使用均匀甜度的GP的第四阶衍生物的均匀磁化的Tesseroid的MC的表达式以笛卡尔内核功能表示。基于均匀球形壳的磁效应，由于各个整体核的奇异性（即，近区域和极性奇异性，已经检查了MP，磁载体（MV），MGT和MC的所有表达式，用于晶圆的唯一问题问题）。为此，已经提供了均匀球形壳体的MP，MV，MGT和MC的闭合分析表达式，并用于产生奇异性的基准值。计算点的高度和纬度不同，在数字上发现近区域问题也存在所有磁量（即，MP，MV，MGT和MC）。数值测试还揭示了由于使用笛卡尔而不是球形积分核而不会出现极性奇异性问题。这证明了包括新导出的MC'继承了与相应的重力功能相同的数字属性的磁量。均匀磁化的Tesseroid的MC公式的未来应用（例如，地球物理信息）可以通过专用卫星任务改进地球磁场的建模。

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