利用Slepian基函数通过局域模式耦合推断次表面太阳磁性的方法
Recipe for inferring sub-surface solar magnetism via local mode-coupling using Slepian basis functions
摘要：
地表下气流、声速和磁场的直接地震成像对于预测太阳表面通量管的出现至关重要，而通量管是空间天气的一个重要组成部分。日震模式振幅互相关对$p$和$f$模式振荡的敏感性使得能够正式反演这种次光球扰动。众所周知，这样的问题是以积分方程的形式写的，该积分方程通过“灵敏度核”将扰动与观测联系起来。虽然灵敏度内核的流量和声速已经知道了几十年，并已被广泛使用，制定内核的一般磁扰动一直难以捉摸。最近的一项研究提出了相应的全球磁场的一般几何洛伦兹应力的灵敏度内核。本研究致力于提出内核推断洛伦兹应力以及螺线管磁场在太阳上的局部补丁通过笛卡尔模式耦合。此外，第一次在太阳物理学中，Slepian函数的参数化扰动的水平维度。这表明，在反问题中的数据约束的数量增加，这意味着推断参数的精度增加。这为可靠地成像次表面太阳磁特征铺平了道路，例如，超颗粒、太阳黑子和（新兴）活动区。
英文摘要：
Direct seismic imaging of sub-surface flow, sound-speed and magnetic field is crucial for predicting flux tube emergence on the solar surface, an important ingredient for space weather. The sensitivity of helioseismic mode-amplitude cross-correlation to $p$- and $f$-mode oscillations enable formal inversion of such sub-photospheric perturbations. It is well-known that such problems are written in the form of an integral equation that connects the perturbations to the observations via ``sensitivity kernels". While the sensitivity kernels for flow and sound-speed have been known for decades and have been used extensively, formulating kernels for general magnetic perturbations had been elusive. A recent study proposed sensitivity kernels for Lorentz-stresses corresponding to global magnetic fields of general geometry. The present study is devoted to proposing kernels for inferring Lorentz-stresses as well as the solenoidal magnetic field in a local patch on the Sun via Cartesian mode-coupling. Moreover, for the first time in solar physics, Slepian functions are employed to parameterize perturbations in the horizontal dimension. This is shown to increase the number of data constraints in the inverse problem, implying an increase in the precision of inferred parameters. This paves the path to reliably imaging sub-surface solar magnetic features in, e.g., supergranules, sunspots and (emerging) active regions.
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