星际云的结构分析：I。Delta方差法的改进
Structure analysis of interstellar clouds: I. Improving the Delta-variance method
摘要：
Delta方差分析已被证明是一种有效和准确的星际湍流功率谱特征的方法。然而，目前使用的实施方式具有若干缺点。我们提出并测试了一种改进的Delta方差算法的二维数据集，这是适用于可变误差条的地图，它可以快速计算傅立叶空间。我们校准的Δ方差谱的空间分辨率。新的Δ方差算法是基于傅立叶空间中的数据的适当滤波。它使我们能够区分变量噪声的影响，从实际的小尺度结构的地图，它有助于处理非周期性和/或不规则有界的地图的边界问题。我们尝试了几个小波和测试他们的空间灵敏度使用人工地图与众所周知的结构尺寸。结果表明，不同的小波在检测特征结构和谱指数方面表现出不同的优势，即地图结构的不同方面。作为一个合理的普遍妥协的最佳Δ方差滤波器，我们提出了墨西哥帽滤波器的核心和环的直径之间的比率为1.5。
英文摘要：
The Delta-variance analysis, has proven to be an efficient and accurate method of characterising the power spectrum of interstellar turbulence. The implementation presently in use, however, has several shortcomings. We propose and test an improved Delta-variance algorithm for two-dimensional data sets, which is applicable to maps with variable error bars and which can be quickly computed in Fourier space. We calibrate the spatial resolution of the Delta-variance spectra. The new Delta-variance algorithm is based on an appropriate filtering of the data in Fourier space. It allows us to distinguish the influence of variable noise from the actual small-scale structure in the maps and it helps for dealing with the boundary problem in non-periodic and/or irregularly bounded maps. We try several wavelets and test their spatial sensitivity using artificial maps with well known structure sizes. It turns out that different wavelets show different strengths with respect to detecting characteristic structures and spectral indices, i.e. different aspects of map structures. As a reasonable universal compromise for the optimum Delta-variance filter, we propose the Mexican-hat filter with a ratio between the diameters of the core and the annulus of 1.5.
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