Abstract The morphologies of craters on planetary surfaces reveal clues about the geologic mechanisms by which they originate and subsequently evolve, as well as the materials and physical variables inherent to the environment in which they formed. We carried out a quantitative multivariate analysis of shape descriptors derived from the outlines of craters formed by volcanic processes on Mars, Io, and Earth and by impact cratering on the Moon using elliptic Fourier analysis (EFA) and the Zahn-Roskies (Z-R) shape function. Canonical variate analysis (CVA) was used to construct a statistical model of differences between the crater groups to classify craters produced by various volcanic and impact processes. The classification model from canonical variate analysis of EFA shape descriptors yielded a 90% rate of success for the assignment of group membership among 406 examined craters. It correctly classified 138 of 154 (90%) ionian paterae,154 of 155 (99%) lunar impact craters, 31 of 35 (89%) terrestrial basaltic shield calderas, 32 of 38 (84%) terrestrial ash-flow calderas, and 12 of 24 (50%) martian basaltic shield calderas. The classification model from canonical variate analysis of Z-R shape function descriptors classified 84% of the total population of the examined craters correctly. The analysis correctly classified 96% of ionian paterae, 100% lunar impact craters, 51% terrestrial basaltic shield calderas, and 63% martian calderas, but only 16% of the terrestrial ash-flow calderas were correctly classified. Canonical variate analysis of EFA and Z-R results shows that the shapes of ash-flow calderas and paterae on Io differ the least of all groups included in this study, and basaltic shield calderas and martian calderas analyzed together also have few differences. The Z-R model successfully classifies more ionian patera and impact craters than the EFA classification model but performs poorly at classifying the other crater groups. This result shows that the descriptors convey different shape information. The Z-R model is robust in its ability to classify end-member differences in complexity while the EFA model is robust in its ability to reliably classify among more groups. These differences and similarities in shape confirm previously understood commonalities related to the origin and evolution of various types of craters. In general, basalt shield calderas on Earth and Mars are morphologically similar and are thought to have similar origins; this study confirms that the 2-D shapes of their craters are quantitatively correlated. Similarities have been noted between terrestrial ash-flow calderas and paterae on Io, principally in their large sizes, shallow magma chambers and complex evolution; this study confirms their shapes are also similar. Impact craters and ionian paterae are most dissimilar, as are their evolutions. This study demonstrates rigorous landform shape analysis can greatly increase our understanding of the diversity in craters and the processes involved in their formation.

中文翻译：

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使用基于轮廓的形态测量学对行星陨石坑进行分类

摘要 行星表面陨石坑的形态揭示了陨石坑起源和演化的地质机制，以及陨石坑形成环境所固有的材料和物理变量的线索。我们使用椭圆傅里叶分析 (EFA) 和 Zahn-Roskies (ZR) 形状对形状描述符进行了定量多变量分析，这些描述符源自火星、艾欧和地球上的火山过程以及月球上的撞击坑的轮廓。功能。典型变量分析（CVA）用于构建火山口组之间差异的统计模型，以对由各种火山和撞击过程产生的火山口进行分类。EFA 形状描述符的规范变量分析的分类模型在 406 个检查的陨石坑中分配组成员的成功率为 90%。它正确分类了 154 个 (90%) ionian paterae 中的 138 个、155 个 (99%) 月球撞击坑中的 154 个、35 个 (89%) 陆地玄武岩盾构火山口中的 31 个、38 个 (84%) 陆地火山灰流火山口中的 32 个、 24 个 (50%) 火星玄武岩盾牌火山口中的 12 个。ZR 形状函数描述符的规范变量分析的分类模型正确分类了所检查陨石坑总数的 84%。该分析正确分类了 96% 的爱奥尼亚火山口、100% 的月球撞击坑、51% 的陆地玄武岩盾状火山口和 63% 的火星火山口，但只有 16% 的陆地火山灰流火山口被正确分类。对 EFA 和 ZR 结果的典型变量分析表明，Io 上的灰流火山口和 paterae 的形状在本研究包括的所有组中差异最小，玄武岩盾状火山口和火星火山口一起分析也几乎没有差异。ZR 模型比 EFA 分类模型成功地分类了更多的 ionian patera 和撞击坑，但在对其他火山口组进行分类时表现不佳。该结果表明描述符传达了不同的形状信息。ZR 模型在对终端成员复杂性差异进行分类的能力方面很稳健，而 EFA 模型在对更多组进行可靠分类的能力方面很稳健。这些形状上的差异和相似之处证实了先前理解的与各种类型陨石坑的起源和演化相关的共性。一般来说，地球和火星上的玄武岩盾形火山口在形态上相似，并且被认为具有相似的起源；这项研究证实了它们陨石坑的二维形状是定量相关的。已经注意到艾欧上的陆地灰流火山口和 paterae 之间的相似之处，主要是它们的大尺寸、浅岩浆房和复杂的演化；这项研究证实它们的形状也相似。撞击坑和 ionian paterae 最为不同，它们的演化也是如此。这项研究表明，严格的地形形状分析可以大大增加我们对陨石坑多样性及其形成过程的理解。已经注意到艾欧上的陆地灰流火山口和 paterae 之间的相似之处，主要是它们的大尺寸、浅岩浆房和复杂的演化；这项研究证实它们的形状也相似。撞击坑和 ionian paterae 最为不同，它们的演化也是如此。这项研究表明，严格的地形形状分析可以大大增加我们对陨石坑多样性及其形成过程的理解。已经注意到艾欧上的陆地灰流火山口和 paterae 之间的相似之处，主要是它们的大尺寸、浅岩浆房和复杂的演化；这项研究证实它们的形状也相似。撞击坑和 ionian paterae 最为不同，它们的演化也是如此。这项研究表明，严格的地形形状分析可以大大增加我们对陨石坑多样性及其形成过程的理解。