Studies of glacial isostatic adjustment (GIA) often use paleoshorelines and present-day deformation to constrain the viscosity of the mantle and the thickness of the elastic lithosphere. However, several studies focused on similar locations have resulted in different estimates of these physical properties. We argue that these different estimates infer apparent viscosities and apparent lithospheric elastic thicknesses, dependent on the timescale of deformation. We use recently derived relationships between these frequency dependent apparent quantities and the underlying thermodynamic conditions to produce predictions of viscoelastic properties and lithospheric thickness across a broad spectrum of geophysical timescales for two Antarctic locations (Amundsen Sea Embayment and the Antarctic Peninsula). Our predictions are constrained by input from seismic tomography, require the self-consistent consideration of elastic, viscous, and transient rheological behavior and also include non-linear steady state viscosity, which have been determined by several laboratories. We demonstrate that when the full spectrum of viscoelasticity is considered, lithospheric thickness displays a significant range across frequency and that transient creep may play an important role across the timescales relevant for the GIA studies we explore. We suggest that observational studies could move toward a framework of determining the frequency dependence of viscoelastic quantities—rather than single, frequency independent values of viscosity. There remains much work to accomplish this both theoretically and observationally, but the eventual result would provide deeper insight into the rheological behavior of Earth.

中文翻译：

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通过复粘度的频率相关地幔粘弹性：来自南极洲的案例

冰川均衡调整 (GIA) 的研究通常使用古海岸线和现代变形来限制地幔的粘度和弹性岩石圈的厚度。然而，针对相似位置的几项研究导致了对这些物理特性的不同估计。我们认为，这些不同的估计可以推断出表观粘度和表观岩石圈弹性厚度，这取决于变形的时间尺度。我们使用这些频率相关的表观量与潜在热力学条件之间最近推导出的关系来预测两个南极地区（阿蒙森海海湾和南极半岛）在广泛的地球物理时间尺度上的粘弹性特性和岩石圈厚度。我们的预测受到地震层析成像输入的限制，需要对弹性、粘性和瞬态流变行为进行自洽的考虑，还包括非线性稳态粘度，这已由多个实验室确定。我们证明，当考虑全范围的粘弹性时，岩石圈厚度在整个频率范围内显示出很大的范围，并且瞬态蠕变可能在与我们探索的 GIA 研究相关的时间尺度上发挥重要作用。我们建议观察性研究可以转向确定粘弹性量的频率依赖性的框架——而不是单一的、与频率无关的粘度值。在理论上和观察上还有很多工作要做，