CMG Research: The Basal Velocity Field of a Glacier: An Inverse Approach

冰川和冰盖的底部边界通常无法通过观测到达。 这给冰川建模研究带来了一个主要问题，因为基底边界条件是适定问题的重要组成部分。 然而，地面、空中和卫星测量都可以到达表面。 现在可以测量大面积的表面地形、冰厚和表面速度。 这在数学中建立了一个经典的反问题，在顶部有太多的边界条件，而在底部没有足够的边界条件。 提供的资金用于应用地球物理学和其他领域常见的反演方法来推断地下冰川流动的问题。 已经完成了一维线性正演模型的第一步。资助的努力将扩大这项工作的非线性二维和三维问题。 逆理论和最优控制的强有力的方法将被应用于解决这些问题。 研究目标将需要在这两个数学领域以及数值分析中获得新的成果。 由此产生的方法将适用于现有数据，因此不需要额外的实地工作。

The basal boundary of glaciers and ice sheets is generally not observationally accessible. This poses a major problem for glacier modeling studies, because the basal boundary condition is an essential part of a well-posed problem. The surface, however, is accessible to ground based, airborne, and satellite measurements. It is now possible to measure surface topography, ice thickness, and surface velocities over large areas. This sets up a classic inverse problem in mathematics with too many boundary conditions at the top and not enough at the bottom. Funds are provided to apply inverse methods, common in geophysics and other areas, to the problem of inferring subsurface glacier flow. A first step with a one-dimensional linear forward model has been accomplished. The funded effort will expand that work to non-linear two- and three-dimensional problems. Powerful methods of inverse theory and optimal control will be applied to solving these problems. The research goals will require obtaining new results in these two fields of mathematics as well as in numerical analysis. The resulting methods will be applied to existing data and thus no additional field work is required.