Uncertainties in field-line tracing in the magnetosphere. Part I: the axisymmetric part of the internal geomagnetic field
Uncertainties in field-line tracing in the magnetosphere. Part I: the axisymmetric part of the internal geomagnetic field
复制标题
磁层中场线追踪的不确定性。
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
Jacqueline Comer
中科院分区：
文献类型：
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作者：
David M. Willis;David M. Willis;J. R. Singh;J. R. Singh;Jacqueline Comer;Jacqueline Comer
在磁层物理学中，沿磁力线追踪技术被广泛应用于提供一个“磁参照系”，以方便实验计划和观测结果的解释。任何这样的磁参照系的精度关键取决于磁层中各种磁场源的准确表示。为了系统地考虑这一重要问题，首先进行了一项研究，以估计磁层中磁场线追踪的不确定性，这些不确定性仅仅是由内源地磁场规范中已公布的（标准）误差引起的。由于计算完整的内源地磁场的这些不确定度比较复杂，本文主要关注的是由内源地磁场轴对称部分的标准误差引起的磁场线追踪中的不确定度。存在轴对称多极子的任意线性组合的磁力线的精确解析方程。该方程用于导出磁场线追踪中不确定性的数值估计，这些不确定性是由于轴对称球面谐波系数（即gn0±δgn0）的公布标准误差引起的。将解析方程的数值计算结果与沿磁力线逐步数值积分的计算结果进行了比较。在轴对称情况下，分析方法与计算方法的一致性很好，这为沿磁力线逐步数值积分的计算机程序的准确性提供了很大的信心。然后，在下面的文章中使用该计算机程序来估计磁层中磁场线追踪的不确定性，这些不确定性是由已发表的定义完整（非轴对称）内源地磁场的全套球谐系数的标准误差引起的。这里对内部地磁场的轴对称部分计算的磁层中磁场线追踪的不确定性的数值估计应被视为“第一近似”，因为这种估计仅与轴对称球调和系数集中已发表的标准误差一样精确。然而，在确定更精确的球谐系数标准误差方面取得进一步进展之后，本初步论文中开发的所有程序都可以应用于推导更现实的磁层中磁场线追踪不确定性的估计。
The technique of tracing along magnetic field lines is widely used in magnetospheric physics to provide a “magnetic frame of reference” that facilitates both the planning of experiments and the interpretation of observations. The precision of any such magnetic frame of reference depends critically on the accurate representation of the various sources of magnetic field in the magnetosphere. In order to consider this important problem systematically, a study is initiated to estimate first the uncertainties in magnetic-field-line tracing in the magnetosphere that arise solely from the published (standard) errors in the specification of the geomagnetic field of internal origin. Because of the complexity in computing these uncertainties for the complete geomagnetic field of internal origin, attention is focused in this preliminary paper on the uncertainties in magnetic-field-line tracing that result from the standard errors in just the axisymmetric part of the internal geomagnetic field. An exact analytic equation exists for the magnetic field lines of an arbitrary linear combination of axisymmetric multipoles. This equation is used to derive numerical estimates of the uncertainties in magnetic-field-line tracing that are due to the published standard errors in the axisymmetric spherical harmonic coefficients (i.e. gn0 ± δgn0). Numerical results determined from the analytic equation are compared with computational results based on stepwise numerical integration along magnetic field lines. Excellent agreement is obtained between the analytical and computational methods in the axisymmetric case, which provides great confidence in the accuracy of the computer program used for stepwise numerical integration along magnetic field lines. This computer program is then used in the following paper to estimate the uncertainties in magnetic-field-line tracing in the magnetosphere that arise from the published standard errors in the full set of spherical harmonic coefficients, which define the complete (non-axisymmetric) geomagnetic field of internal origin. Numerical estimates of the uncertainties in magnetic-field-line tracing in the magnetosphere, calculated here for the axisymmetric part of the internal geomagnetic filed, should be regarded as “first approximations” in the sense that such estimates are only as accurate as the published standard errors in the set of axisymmetric spherical harmonic coefficients. However, all procedures developed in this preliminary paper can be applied to the derivation of more realistic estimates of the uncertainties in magnetic-field-line tracing in the magnetosphere, following further progress in the determination of more accurate standard errors in the spherical harmonic coefficients.