Ziheng Yu, David Al-Attar, Frank Syvret, Andrew J. Lloyd
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引用次数: 0
摘要
本文重温并扩展了 Crawford 等人(2018 年)的冰川等静力调整(GIA)邻接理论。现在纳入了旋转反馈,并首次描述了二阶积分法的应用。一阶积分法为计算选定目标函数的灵敏度核提供了一种高效方法,而二阶积分法则以黑森核的形式提供了二阶衍生信息。高效的牛顿优化方案和非线性逆问题的不确定性量化方法都需要后一种核。最重要的是,对整个理论进行了重新表述,以简化 GIA 社区其他成员的实施。特别是,Crawford 等人(2018 年)提出的 GIA 前向问题的速率公式已被用于模拟横向异质地球模型中 GIA 的常规方程所取代。在现有和新的 GIA 代码中,一阶和二阶邻接问题的实现相对容易,只需包含更多的一般力项。
Application of first- and second-order adjoint methods to glacial isostatic adjustment incorporating rotational feedbacks
This paper revisits and extends the adjoint theory for glacial isostatic
adjustment (GIA) of Crawford et al. (2018). Rotational feedbacks are now
incorporated, and the application of the second-order adjoint method is
described for the first time. The first-order adjoint method provides an
efficient means for computing sensitivity kernels for a chosen objective
functional, while the second-order adjoint method provides second-derivative
information in the form of Hessian kernels. These latter kernels are required
by efficient Newton-type optimisation schemes and within methods for
quantifying uncertainty for non-linear inverse problems. Most importantly, the
entire theory has been reformulated so as to simplify its implementation by
others within the GIA community. In particular, the rate-formulation for the
GIA forward problem introduced by Crawford et al. (2018) has been replaced with
the conventional equations for modelling GIA in laterally heterogeneous earth
models. The implementation of the first- and second-order adjoint problems
should be relatively easy within both existing and new GIA codes, with only the
inclusions of more general force terms being required.