Normal-mode helioseismic data analysis uses observed solar oscillation spectra to infer perturbations in the solar interior due to global and local-scale flows and structural asphericity. Differential rotation, the dominant global-scale axisymmetric perturbation, has been tightly constrained primarily using measurements of frequency splittings via “a-coefficients.” However, the frequency-splitting formalism invokes the approximation that multiplets are isolated. This assumption is inaccurate for modes at high angular degrees. Analyzing eigenfunction corrections, which respect cross-coupling of modes across multiplets, is a more accurate approach. However, applying standard inversion techniques using these cross-spectral measurements yields a-coefficients with a significantly wider spread than the well-constrained results from frequency splittings. In this study, we apply Bayesian statistics to infer a-coefficients due to differential rotation from cross-spectra for both f-modes and p-modes. We demonstrate that this technique works reasonably well for modes with angular degrees ℓ = 50–291. The inferred a ₃-coefficients are found to be within 1 nHz of the frequency-splitting values for ℓ > 200. We also show that the technique fails at ℓ < 50 owing to the insensitivity of the measurement to the perturbation. These results serve to further establish mode-coupling as an important helioseismic technique with which to infer internal structure and dynamics, both axisymmetric (e.g., meridional circulation) and non-axisymmetric perturbations.

常模日震数据分析使用观测到的太阳振荡光谱来推断太阳内部由于全球和局部尺度流动以及结构非球面性引起的扰动。微分旋转是主要的全球尺度轴对称扰动，主要使用通过“ a系数”测量频率分裂的方法受到严格限制。然而，分频形式调用了多重态被隔离的近似。对于高角度的模式，这种假设是不准确的。分析本征函数校正，尊重跨多重模式的交叉耦合，是一种更准确的方法。然而，使用这些交叉光谱测量应用标准反演技术会产生一个-系数具有比频率分裂的良好约束结果显着更广泛的扩展。在这项研究中，我们应用贝叶斯统计来推断a系数，这是由于f模式和p模式的交叉光谱的差分旋转。我们证明了这种技术对于角度为ℓ = 50-291 的模式非常有效。发现推断的a ₃系数在ℓ > 200的分频值的 1 nHz 以内。我们还表明该技术在ℓ 处失败< 50 由于测量对扰动不敏感。这些结果有助于进一步将模式耦合确立为一种重要的日震技术，用于推断内部结构和动力学，包括轴对称（例如，经向环流）和非轴对称扰动。