The nonstationarity of the terrestrial bow shock is analyzed in detail from in situ magnetic field measurements issued from the fluxgate magnetometer (FGM) experiment of the Cluster mission. Attention is focused on statistical analysis of quasi-perpendicular supercritical shock crossings. The present analysis stresses for the first time the importance of a careful and accurate methodology in the data processing, which can be a source of confusion and misunderstanding if not treated properly. The analysis performed using 96 shock front crossings shows evidence of a strong variability of the microstructures of the shock front (foot and ramp), which are analyzed in great detail. The main results are that (i) most statistics clearly show that the ramp thickness is very narrow and can be as low as a few $c/{\mathit{\omega }}_{\mathrm{pe}}$ (electron inertia length); (ii) the width is narrower when the angle ${\mathit{\theta }}_{B_n}$ (between the shock normal and the upstream magnetic field) approaches 90^∘; (iii) the foot thickness strongly varies, but its variation has an upper limit provided by theoretical estimates given in previous studies (e.g., Schwartz et al., 1983; Gosling and Thomsen, 1985; Gosling and Robson, 1985); and (iv) the presence of foot and overshoot, as shown in all front profiles, confirms the importance of dissipative effects. Present results indicate that these features can be signatures of the shock front self-reformation among a few mechanisms of nonstationarity identified from numerical simulation and theoretical studies.A comparison with 2D particle-in-cell (PIC) simulation for a perpendicular supercritical shock (used as reference) has been performed and shows the following: (a) the ramp thickness varies only slightly in time over a large fraction of the reformation cycle and reaches a lower-bound value on the order of a few electron inertial length; (b) in contrast, the foot width strongly varies during a self-reformation cycle but always stays lower than an upper-bound value in agreement with the value given by Woods (1971); and (c) as a consequence, the time variability of the whole shock front is depending on both ramp and foot variations.Moreover, a detailed comparative analysis shows that many elements of analysis were missing in previous reported studies concerning both (i) the important criteria used in the data selection and (ii) the different and careful steps of the methodology used in the data processing itself. The absence of these precise elements of analysis makes the comparison with the present work difficult; worse, it makes some final results and conclusive statements quite questionable at the present time. At least, looking for a precise estimate of the shock transition thickness presents nowadays a restricted interest, since recent results show that the terrestrial shock is rather nonstationary, and one unique typical spatial scaling of the microstructures of the front (ramp, foot) must be replaced by some “variation ranges” (with lower-bound and upper-bound values) within which the spatial scales of the fine structures can extend.

中文翻译：

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来自多航天器观测的地球弓形激波非平稳性的证据：方法、结果以及与细胞内粒子 (PIC) 模拟的定量比较

从集群任务的磁通门磁力计 (FGM) 实验发出的原位磁场测量结果详细分析了地面弓形激波的非平稳性。注意力集中在准垂直超临界激波交叉的统计分析上。目前的分析首次强调了在数据处理中采用谨慎和准确方法的重要性，如果处理不当，这可能会导致混淆和误解。使用 96 个激波前沿交叉点进行的分析表明激波前沿（足部和斜坡）的微观结构存在很大的可变性，对此进行了非常详细的分析。主要结果是 (i) 大多数统计数据清楚地表明斜坡厚度非常窄，可以低至几个$C/{\mathit{\omega }}_{\mathrm{聚乙烯}}$ （电子惯性长度）；(ii) 角度变窄时宽度变窄 ${\mathit{\theta }}_{{乙}_n}$（在冲击法线和上游磁场之间）接近 90 ^∘; (iii) 足部厚度变化很大，但其变化具有由先前研究中给出的理论估计值提供的上限（例如，Schwartz 等，1983；Gosling 和 Thomsen，1985；Gosling 和 Robson，1985）；(iv) 足部和过冲的存在，如所有前部轮廓所示，证实了耗散效应的重要性。目前的结果表明，这些特征可能是从数值模拟和理论研究中确定的几种非平稳机制中激波前缘自我改造的特征。 与垂直超临界激波的二维细胞内粒子 (PIC) 模拟的比较（使用作为参考）已执行并显示以下内容：(a) 在重整周期的大部分时间里，斜坡厚度仅随时间略有变化，并达到几个电子惯性长度数量级的下限值；(b) 相比之下，脚宽在自我改造周期中变化很大，但始终低于上限值，与 Woods (1971) 给出的值一致；(c) 因此，整个激波前沿的时间可变性取决于斜坡和足部的变化。此外，详细的比较分析表明，之前报告的关于 (i) 重要的研究中缺少许多分析要素数据选择中使用的标准以及 (ii) 数据处理本身使用的方法的不同和谨慎的步骤。缺少这些精确的分析要素，使得与目前的工作进行比较变得困难；更糟糕的是，它使目前的一些最终结果和结论性陈述相当可疑。至少，现在寻找对激波过渡厚度的精确估计是一个有限的兴趣，因为最近的结果表明地球激波是相当不稳定的，并且必须是前部（斜坡，脚部）微观结构的一个独特的典型空间尺度由一些“变化范围”（具有下限和上限值）代替，在这些范围内精细结构的空间尺度可以扩展。