Structure functions, which represent the moments of the increments of a stochastic process, are essential complementary statistics to power spectra for analysing the self-similar behaviour of a time series. However, many real-world environmental datasets, such as those collected by spacecraft monitoring the solar wind, contain gaps, which inevitably corrupt the statistics. The nature of this corruption for structure functions remains poorly understood - indeed, often overlooked. Here we simulate gaps in a large set of magnetic field intervals from Parker Solar Probe in order to characterize the behaviour of the structure function of a sparse time series of solar wind turbulence. We quantify the resultant error with regards to the overall shape of the structure function, and its slope in the inertial range. Noting the consistent underestimation of the true curve when using linear interpolation, we demonstrate the ability of an empirical correction factor to de-bias these estimates. This correction, "learnt" from the data from a single spacecraft, is shown to generalize well to data from a solar wind regime elsewhere in the heliosphere, producing smaller errors, on average, for missing fractions >25%. Given this success, we apply the correction to gap-affected Voyager intervals from the inner heliosheath and local interstellar medium, obtaining spectral indices similar to those from previous studies. This work provides a tool for future studies of fragmented solar wind time series, such as those from Voyager, MAVEN, and OMNI, as well as sparsely-sampled astrophysical and geophysical processes more generally.

翻译：结构函数作为随机过程增量的矩，是分析时间序列自相似行为时功率谱的重要补充统计量。然而，许多现实环境数据集（如监测太阳风的航天器所采集数据）存在数据缺失，这不可避免地会破坏统计特性。这种缺失对结构函数造成的统计偏差本质至今尚未被充分理解——事实上常被忽视。本文通过模拟帕克太阳探测器大量磁场数据段中的缺失，以表征太阳风湍流稀疏时间序列结构函数的行为特征。我们量化了由此产生的误差，包括结构函数整体形态及其惯性区间斜率的偏差。针对线性插值法持续低估真实曲线的现象，我们证明经验校正因子能够有效消除这些估计偏差。该校正因子从单一航天器数据中"学习"得到，并被证明能良好推广至日球层其他区域的太阳风数据，在缺失比例大于25%的情况下平均产生更小的误差。基于此成功验证，我们将该校正方法应用于受数据缺失影响的旅行者号数据段（来自内日球鞘和局地星际介质），获得了与既往研究相近的谱指数。本研究为未来分析碎片化太阳风时间序列（如旅行者号、MAVEN和OMNI数据）以及更广泛的稀疏采样天体物理与地球物理过程提供了实用工具。