Departures from standard spherically symmetric solar models, in the form of perturbations such as global and local-scale flows and structural asphericities, result in the splitting of eigenfrequencies in the observed spectrum of solar oscillations. Drawing from prevalent ideas in normal-mode coupling theory in geophysical literature, we devise a procedure that enables the computation of sensitivity kernels for general Lorentz stress fields in the Sun. Mode coupling due to any perturbation requires careful consideration of self- and cross-coupling of multiplets. Invoking the isolated-multiplet approximation allows for limiting the treatment to purely self-coupling, requiring significantly less computational resources. We identify the presence of such isolated multiplets under the effect of Lorentz stresses in the Sun. Currently, solar missions allow precise measurements of self-coupling of multiplets via "$a$-coefficients" and the cross-spectral correlation signal which enables the estimation of the "structure coefficients". We demonstrate the forward problem for both self-coupling ($a$-coefficients) and cross-coupling (structure coefficients). In doing so, we plot the self-coupling kernels and estimate $a$-coefficients arising from a combination of deep-toroidal and surface-dipolar axisymmetric fields. We also compute the structure coefficients for an arbitrary general magnetic field (real and solenoidal) and plot the corresponding "splitting function", a convenient way to visualize the splitting of multiplets under 3D internal perturbations. The results discussed in this paper pave the way to formally pose an inverse problem, and infer solar internal magnetic fields.

中文翻译：

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从太阳中的常模频率分裂推断洛伦兹应力的灵敏度核

偏离标准球对称太阳模型，以全球和局部尺度流动以及结构非球面等扰动的形式，导致观测到的太阳振荡光谱中的特征频率分裂。借鉴地球物理文献中常模耦合理论的流行思想，我们设计了一个程序，可以计算太阳中一般洛伦兹应力场的灵敏度核。由于任何扰动导致的模式耦合需要仔细考虑多重态的自耦合和交叉耦合。调用隔离多重近似允许将处理限制为纯粹的自耦合，需要的计算资源显着减少。我们在太阳中的洛伦兹应力的影响下确定了这种孤立的多重态的存在。现在，太阳任务允许通过“$a$-coefficients”和交叉光谱相关信号对多重峰的自耦合进行精确测量，从而能够估计“结构系数”。我们展示了自耦合（$a$-coefficients）和交叉耦合（结构系数）的前向问题。在这样做时，我们绘制自耦合核并估计由深环面和表面偶极轴对称场组合产生的 $a$-系数。我们还计算了任意通用磁场（实数和螺线管）的结构系数，并绘制了相应的“分裂函数”，这是一种在 3D 内部扰动下可视化多重态分裂的便捷方法。本文讨论的结果为正式提出逆问题铺平了道路，