太阳内部流场的全波形反演
Full Waveform Inversion of Solar Interior Flows
摘要：
太阳内部物质流动的推断是日震学的一个主要研究课题。在这里，我们应用技术的全波形反演（FWI）的合成数据来测试流动反演。在这个理想化的设置中，我们不对地震实现噪声进行建模，训练的重点完全放在所选择的超颗粒流模型是否可以被地震恢复的问题上。我们将失配函数定义为预测和观测之间的旅行时间的L_2范数偏差之和，如使用短距离f和p_1滤波和大距离未滤波的$p$模式测量的。FWI允许引入选择的测量并迭代地改进背景模型，同时监控所有期望类别中的失配的演变。虽然失配在所有类别中均匀减少，但收敛到真正的模型非常缓慢，可能是因为它陷入了局部最小值。误差的主要来源是不准确的深度定位，由于密度分层，导致水平和垂直流速的错误比率（“串扰”）。在本公式中，缺乏足够的时间频率和空间分辨率使得难以准确地定位深度处的流动剖面。因此，我们建议，发现全局最小值的最有效方法是执行概率向前搜索，包括计算与广泛的模型（例如，由蒙特卡洛算法生成）相关的失配，并定位最深的最小值。这种技术具有能够量化模型不确定性以及实现噪声（数据不确定性）的额外优势。
英文摘要：
The inference of flows of material in the interior of the Sun is a subject of major interest in helioseismology. Here we apply techniques of Full Waveform Inversion (FWI) to synthetic data to test flow inversions. In this idealized setup, we do not model seismic realization noise, training the focus entirely on the problem of whether a chosen supergranulation flow model can be seismically recovered. We define the misfit functional as a sum of L_2 norm deviations in travel times between prediction and observation, as measured using short-distance f and p_1 filtered and large-distance unfiltered $p$ modes. FWI allows for the introduction of measurements of choice and iteratively improving the background model, while monitoring the evolution of the misfit in all desired categories. Although the misfit is seen to uniformly reduce in all categories, convergence to the true model is very slow, possibly because it is trapped in a local minimum. The primary source of error is inaccurate depth localization, which, owing to density stratification, leads to wrong ratios of horizontal and vertical flow velocities (`cross talk'). In the present formulation, the lack of sufficient temporal frequency and spatial resolution makes it difficult to accurately localise flow profiles at depth. We therefore suggest that the most efficient way to discover the global minimum is to perform a probabilistic forward search, involving calculating the misfit associated with a broad range of models (generated, for instance, by a Monte-Carlo algorithm) and locating the deepest minimum. Such techniques possess the added advantage of being able to quantify model uncertainty as well as realization noise (data uncertainty).
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