A commercial finite element approach to modelling Glacial Isostatic Adjustment on spherical self-gravitating compressible earth models
A commercial finite element approach to modelling Glacial Isostatic Adjustment on spherical self-gravitating compressible earth models
复制标题
在球形自重力可压缩地球模型上模拟冰川等静压调整的商业有限元方法
DOI：
10.1093/gji/ggad354
复制
发表时间：
2023
影响因子：
2.8
通讯作者：
Huang P
中科院分区：
文献类型：
--
作者：
Huang P
本文提出了一种方法，修改商业工程为导向的有限元软件包的冰川均衡调整（GIA）的建模自引力，可压缩和球形地球的3-D结构。该方法称为迭代有限元体和表面力（FEMIBSF）方法，使用ABAQUS有限元软件包求解变形平衡方程，并计算与有限元理论一致的潜在扰动，避免使用球谐函数。这种方法的关键在于计算地球内部每个有限元的平均外体力以及地球表面和核幔边界（CMB）上的压力。这些数量，驱动变形和应力扰动的GIA，但不包括在商业有限元软件包的运动方程，实现。该方法还演示了如何直接在空间域和土荷载系统中计算GIA模型的1度变形。为了验证FEMIBSF方法的有效性，计算了均质和层状地球模型的荷载Love数，并与三种独立的GIA方法：简正模态法、迭代体力法和谱有限元法进行了比较。结果表明，FEMIBSF方法可以准确地再现均匀可压缩模型的不稳定模态，并与其他方法的Love数结果相当吻合。结果表明，FEMIBSF方法的精度随着分辨率的提高而提高，但由于产生了所谓的悬挂节点，因此应避免非共形网格。在CMB的势的作用也进行了研究，发现只影响长波长的表面势扰动和变形的粘性时间制度。总之，FEMIBSF方法已准备好用于现实的GIA研究中，模拟的垂直和水平位移率在一个光盘负载的情况下，显示协议与其他两个GIA方法内的GNSS测量的不确定性水平。
This paper presents a method that modifies commercial engineering-oriented finite element packages for the modelling of Glacial Isostatic Adjustment (GIA) on a self-gravitating, compressible and spherical Earth with 3-D structures. The approach, called the iterative finite element body and surface force (FEMIBSF) approach, solves the equilibrium equation for deformation using the ABAQUS finite element package and calculates potential perturbation consistently with finite element theory, avoiding the use of spherical harmonics. The key to this approach lies in computing the mean external body forces for each finite element within the Earth and pressure on Earth's surface and core–mantle boundary (CMB). These quantities, which drive the deformation and stress perturbation of GIA but are not included in the equation of motion of commercial finite element packages, are implemented therein. The method also demonstrates how to calculate degree-1 deformation directly in the spatial domain and Earth-load system for GIA models. To validate the FEMIBSF method, loading Love numbers (LLNs) for homogeneous and layered earth models are calculated and compared with three independent GIA methodologies: the normal-mode method, the iterative body force method and the spectral-finite element method. Results show that the FEMIBSF method can accurately reproduce the unstable modes for the homogeneous compressible model and agree reasonably well with the Love number results from other methods. It is found that the accuracy of the FEMIBSF method increases with higher resolution, but a non-conformal mesh should be avoided due to creating the so-called hanging nodes. The role of a potential force at the CMB is also studied and found to only affect the long-wavelength surface potential perturbation and deformation in the viscous time regime. In conclusion, the FEMIBSF method is ready for use in realistic GIA studies, with modelled vertical and horizontal displacement rates in a disc load case showing agreement with other two GIA methods within the uncertainty level of GNSS measurements.