Vector magnetogram data are often used as photospheric boundary conditions for force-free coronal magnetic field extrapolations. In general, however, vector magnetogram data are not consistent with the force-free assumption. In this article, we demonstrate a way to deal with inconsistent boundary data, by generalizing the "self-consistency procedure" of Wheatland & Regnier (2009). In that procedure, the inconsistency is resolved by an iterative process of constructing two solutions based on the values of the force-free parameter alpha on the two polarities of the field in the boundary (the P and N polarities), and taking uncertainty-weighted averages of the boundary alpha values in the P and N solutions. When the alpha values in the P and N regions are very different, the self-consistent solution may lose high alpha values from the boundary conditions. We show how, by altering the weighting of the uncertainties in the P or N boundary conditions, we can preserve high alpha values in the self-consistent solution. The weighted self-consistent extrapolation method is demonstrated on an analytic bipole field and applied to vector magnetogram data taken by the Helioseismic and Magnetic Imager (HMI) instrument for NOAA active region AR 12017 on 2014 March 29.

中文翻译：

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基于加权边界条件的自洽非线性无力场重建

矢量磁图数据通常用作无力日冕磁场外推的光球边界条件。然而，一般而言，矢量磁图数据与无力假设不一致。在本文中，我们通过推广 Wheatland & Regnier (2009) 的“自洽程序”，展示了一种处理不一致边界数据的方法。在该过程中，通过基于边界中场的两个极性（P 和 N 极性）上的无力参数 alpha 的值构造两个解的迭代过程来解决不一致问题，并采用不确定性加权P 和 N 解中边界 alpha 值的平均值。当 P 和 N 区域的 alpha 值相差很大时，自洽解可能会从边界条件中丢失高 alpha 值。我们展示了如何通过改变 P 或 N 边界条件中不确定性的权重，我们可以在自洽解中保持高 alpha 值。加权自洽外推法在解析双极场上得到证明，并应用于日震和磁成像仪 (HMI) 仪器于 2014 年 3 月 29 日为 NOAA 活动区 AR 12017 拍摄的矢量磁图数据。