Measurements of elastic wave velocities enable non-destructive estimation of the mechanical properties, elastic moduli and density of snow and firn. The variation of elastic moduli with porosity in dry snow and firn is modeled using a differential effective medium scheme modified to account for the critical porosity above which the bulk and shear moduli of the ice frame vanish. A comparison of predicted and measured elastic moduli indicates that the shear modulus of ice in snow is lower than that computed from single crystal elastic stiffnesses of ice. This may indicate that the bonds between snow particles are more deformable under shear than under compression. A partial alignment of ice crystals also may contribute. Good agreement between elastic stiffnesses of the ice frame obtained from elastic wave velocity measurements and the predictions of the theory is observed. The approach is simple and compact, and does not require the use of empirical fits to the data. Owing to its simplicity, this model may prove useful in a variety of potential applications such as construction on snow, interpretation of seismic measurements to monitor and locate avalanches and estimation of density within compacting snow deposited on glaciers and ice sheets.

中文翻译：

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雪花弹性模量的孔隙度依赖性

弹性波速度的测量能够无损估计雪和冷杉的机械特性、弹性模量和密度。干雪和冷杉中弹性模量随孔隙度的变化是使用差分有效介质方案来模拟的，该方案被修改以考虑临界孔隙度，在该临界孔隙度之上冰架的体积和剪切模量消失。预测和测量的弹性模量的比较表明，雪中冰的剪切模量低于从冰的单晶弹性刚度计算的值。这可能表明雪粒之间的键在剪切作用下比在压缩作用下更易变形。冰晶的部分排列也可能有所贡献。观察到从弹性波速度测量获得的冰架的弹性刚度与理论预测之间的良好一致性。该方法简单紧凑，不需要对数据使用经验拟合。由于其简单性，该模型可能在各种潜在应用中证明是有用的，例如在雪地上建造、解释地震测量以监测和定位雪崩以及估计沉积在冰川和冰盖上的压实​​雪的密度。