Bubble distributions as markers for deformation in polar ice

对极地冰芯中被气泡包围的空气的分析提供了关于过去几个世纪大气成分的宝贵信息。然而，由于缺乏将冰和观测到的空气与某一特定时期联系起来的绝对测年工具，对这一信息来源的利用受到了阻碍。最近的测年方法依赖于需要测量冰的累积变形量作为输入的模型。到目前为止，还没有办法直接从观测到的冰芯中获得这些信息。在建议的项目中，我们建议使用气泡中心的位置作为变形的标记。主要目的是建立从气泡中心点状图直接估计变形参数的方法。为此，我们的跨学科研究小组将结合冰川学和点过程统计的方法。气泡中心的位置将通过对来自不同深冰芯的冰样品进行核尺度x射线微聚焦计算机断层扫描来测量（EDC， EDML, Renland）。我们分析的主要思想是基于变形在气泡中心模式中引入各向异性的假设。因此，对主轴和各向异性程度的估计可以提供有关主要变形方向和变形强度的信息。虽然点过程统计是当前研究的一个活跃领域，但目前还没有合适的通用方法来分析三维点图形的各向异性。因此，该项目提出的冰川学问题要求在空间统计领域取得进展。特别是，必须找到三维点加工中优选方向和变形参数的估计方法。此外，在冰松弛过程中形成的噪声气泡也必须考虑在内。利用估计的变形参数，将验证和改进用于预测冰的变形参数和定年的冰川学模型。测量的累积应变将有助于了解冰的微观结构（晶粒尺寸、纹理和结构、杂质含量）对冰的变形行为的潜在影响。对来自Renland冰芯的气泡冰的分析将首次提供关于极地冰盖基岩附近变形的信息。

The analysis of air entrapped in bubbles in polar ice cores yields valuable information on the composition of the atmosphere during the last centuries. However, exploitation of this source of information is hampered by the lack of absolute dating tools linking the ice and the observed air to a certain period in time. Recent dating approaches rely on models which require a measure for the cumulated deformation of the ice as input. Up to now, there is no means for obtaining this information directly from an observed ice core. In the proposed project, we suggest using the locations of bubble centres as markers for the deformation. The main goal is to establish methods for the direct estimation of deformation parameters from the point pattern of bubble centres. To this end, our interdisciplinary research group will combine approaches from glaciology and point process statistics.The locations of bubble centres will be measured by means of core-scale X-ray-microfocus computer tomography on ice samples from different deep ice cores (EDC, EDML, Renland). The main idea of our analysis is based on the assumption that deformation introduces an anisotropy in the bubble centre patterns. Hence, estimates for the main axes and the degree of anisotropy may provide information on the main deformation directions and the strength of deformation. Although point process statistics is an active field of current research, suitably general methods for the anisotropy analysis of 3D point patterns are not available up to now. Hence, the glaciological problems posed in this project ask for advancements in the field of spatial statistics. In particular, methods for the estimation of preferred directions and deformation parameters in 3D point processes have to be found. Additionally, the presence of noise bubbles forming during relaxation of the ice must be taken into account. Using the estimated deformation parameters, models from glaciology for prediction of deformation parameters and dating of the ice will be validated and improved. The measured cumulated strain will give insights to the potential effect of microstructure (grain size, texture and fabric, impurity content) on the deformation behaviour of ice. The analysis of bubbly ice from the Renland ice core will provide information on deformation close to bedrock of a polar icecap for the first time.