Time-distance helioseismology is a set of powerful tools to study features below the Sun's surface. Inverse methods are needed to interpret time-distance measurements, with many examples in the literature. However, techniques that utilize a more statistical approach to inferences, and broadly used in the astronomical community, are less-commonly found in helioseismology. This article aims to introduce a potentially powerful inversion scheme based on Bayesian probability theory and Monte Carlo sampling that is suitable for local helioseismology. We describe the probabilistic method and how it is conceptually different from standard inversions used in local helioseismology. Several example calculations are carried out to compare and contrast the setup of the problems and the results that are obtained. The examples focus on two important phenomena studied with helioseismology: meridional circulation and supergranulation. Numerical models are used to compute synthetic observations, providing the added benefit of knowing the solution against which the results can be tested. For demonstration purposes, the problems are formulated in two and three dimensions, using both ray- and Born-theoretical approaches. The results seem to indicate that the probabilistic inversions not only find a better solution with much more realistic estimation of the uncertainties, but they also provide a broader view of the range of solutions possible for any given model, making the interpretation of the inversion more quantitative in nature. Unlike the progress being made in fundamental measurement schemes in local helioseismology that image the far side of the Sun, or have detected signatures of global Rossby waves, among many others, inversions of those measurements have had significantly less success. Such statistical methods may help overcome some of these barriers to move the field forward.

中文翻译：

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时距日震学的概率反演

时间-距离日震学是一套研究太阳表面以下特征的强大工具。需要逆方法来解释时间-距离测量，文献中有很多例子。然而，利用更多统计方法进行推论并在天文学界广泛使用的技术在日震学中并不常见。本文旨在介绍一种适用于局部日震学的基于贝叶斯概率论和蒙特卡罗采样的潜在强大的反演方案。我们描述了概率方法以及它在概念上与当地日震学中使用的标准反演有何不同。执行了几个示例计算来比较和对比问题的设置和获得的结果。这些例子侧重于用日震学研究的两个重要现象：经向环流和超粒化。数值模型用于计算综合观察，提供了额外的好处，即了解可以测试结果的解决方案。出于演示目的，这些问题使用射线和玻恩理论方法在二维和三个维度上进行了表述。结果似乎表明，概率反演不仅找到了更好的解决方案，对不确定性的估计更加现实，而且还为任何给定模型的可能解决方案范围提供了更广阔的视野，使反演的解释更加定量在自然界。与对太阳远端成像的局部日震学的基本测量方案取得的进展不同，或者已经检测到全球罗斯比波的特征，除此之外，这些测量的反演成功率要低得多。这种统计方法可能有助于克服其中一些障碍，推动该领域向前发展。