Reconstruction of basal properties in ice sheets using iterative inverse methods
Reconstruction of basal properties in ice sheets using iterative inverse methods
复制标题
使用迭代逆方法重建冰盖的基本特性
DOI：
10.3189/2012jog11j168
复制
发表时间：
2012
影响因子：
3.4
通讯作者：
M. Truffer
中科院分区：
文献类型：
--
作者：
Marijke Habermann;D. Maxwell;M. Truffer
摘要反问题用于从观测值估计模型参数。许多反问题是不适定的，因为它们缺乏稳定性，这意味着不可能找到相对于输入数据的微小变化稳定的解决方案。正则化技术是稳定的问题。对于非线性反问题，迭代反方法可以用作正则化方法。这些方法从模型参数的初始估计开始，在首先调整大规模空间特征的迭代过程中更新参数以匹配观测，并使用停止标准来防止数据的过拟合。这个标准决定了解的光滑性，从而决定了正则化的程度。在这里，迭代逆方法实现的具体问题，重建的基础粘性的冰盖，通过使用浅架近似作为正演模型和合成导出的表面速度作为输入数据。介绍了不完全高斯-牛顿（IGN）方法，并与常用的最速下降法和非线性共轭梯度法进行了比较。两种不同的停止准则，差异原则和最近改进的阈值，进行了比较。IGN方法是受欢迎的，因为它是快速收敛，它结合了差异原则，这导致最佳解决方案。
Abstract Inverse problems are used to estimate model parameters from observations. Many inverse problems are ill-posed because they lack stability, meaning it is not possible to find solutions that are stable with respect to small changes in input data. Regularization techniques are necessary to stabilize the problem. For nonlinear inverse problems, iterative inverse methods can be used as a regularization method. These methods start with an initial estimate of the model parameters, update the parameters to match observation in an iterative process that adjusts large-scale spatial features first, and use a stopping criterion to prevent the overfitting of data. This criterion determines the smoothness of the solution and thus the degree of regularization. Here, iterative inverse methods are implemented for the specific problem of reconstructing basal stickiness of an ice sheet by using the shallow-shelf approximation as a forward model and synthetically derived surface velocities as input data. The incomplete Gauss-Newton (IGN) method is introduced and compared to the commonly used steepest descent and nonlinear conjugate gradient methods. Two different stopping criteria, the discrepancy principle and a recent- improvement threshold, are compared. The IGN method is favored because it is rapidly converging, and it incorporates the discrepancy principle, which leads to optimally resolved solutions.