Uncertainties in field-line tracing in the magnetosphere. brPart I: the axisymmetric part of the internal geomagnetic field

摘要

The technique of tracing along magnetic fieldlines is widely used in magnetospheric physics to provide a "magnetic frameof reference'' that facilitates both the planning of experiments and theinterpretation of observations. The precision of any such magnetic frame ofreference depends critically on the accurate representation of the varioussources of magnetic field in the magnetosphere. In order to consider thisimportant problem systematically, a study is initiated to estimate first theuncertainties in magnetic-field-line tracing in the magnetosphere that arisesolely from the published (standard) errors in the specification of thegeomagnetic field of internal origin. Because of the complexity in computingthese uncertainties for the complete geomagnetic field of internal origin,attention is focused in this preliminary paper on the uncertainties inmagnetic-field-line tracing that result from the standard errors in just theaxisymmetric part of the internal geomagnetic field. An exact analytic equationexists for the magnetic field lines of an arbitrary linear combination ofaxisymmetric multipoles. This equation is used to derive numerical estimates ofthe uncertainties in magnetic-field-line tracing that are due to the publishedstandard errors in the axisymmetric spherical harmonic coefficients (i.e.g_n0 ± δg_n0). Numerical results determinedfrom the analytic equation are compared with computational results based onstepwise numerical integration along magnetic field lines. Excellent agreementis obtained between the analytical and computational methods in the axisymmetriccase, which provides great confidence in the accuracy of the computer programused for stepwise numerical integration along magnetic field lines. Thiscomputer program is then used in the following paper to estimate theuncertainties in magnetic-field-line tracing in the magnetosphere that arisefrom the published standard errors in the full set of spherical harmoniccoefficients, which define the complete (non-axisymmetric) geomagnetic field ofinternal origin. Numerical estimates of the uncertainties in magnetic-field-linetracing in the magnetosphere, calculated here for the axisymmetric part of theinternal geomagnetic field, should be regarded as "first approximations''in the sense that such estimates are only as accurate as the published standarderrors in the set of axisymmetric spherical harmonic coefficients. However, allprocedures developed in this preliminary paper can be applied to the derivationof more realistic estimates of the uncertainties in magnetic-field-line tracingin the magnetosphere, following further progress in the determination of moreaccurate standard errors in the spherical harmonic coefficients.