An iterative spectral solution method for thin elastic plate flexure with variable rigidity
An iterative spectral solution method for thin elastic plate flexure with variable rigidity
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DOI：
10.1093/gji/ggu449
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发表时间：
2015-02-01
影响因子：
2.8
通讯作者：
Luttrell, Karen M.
中科院分区：
文献类型：
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作者：
Garcia, Emmanuel S.;Sandwell, David T.;Luttrell, Karen M.
薄板挠曲理论为岩石圈在水平长度范围从几十公里到几百公里的垂直载荷下的响应提供了一个精确的模型。例子包括海山、断裂带、沉积盆地和俯冲带的弯曲。当将该理论应用于实际情况时，大多数研究假设板的局部厚度均匀，以实现简单的傅里叶变换解。然而，在弯曲幅度明显的情况下，如俯冲带，或海底年龄快速变化的情况下，如裂缝带，这些模型是不充分的。本文提出了一种求解非均匀板厚和任意垂直载荷下薄板挠曲方程的高效算法。该迭代方案利用二维快速傅立叶变换在空间域和谱域进行计算，从而得到精确且计算效率高的解。我们通过与已知解析解的比较来说明该方法的准确性。最后，我们给出了三个简单模型的结果，表明当考虑板刚度和应用弯矩的二维变化时，沟槽外上升挠度的差异。虽然我们的分析重点是海沟挠曲，但该方法也适用于其他具有空间刚度变化的二维挠曲问题，如热侵蚀岩石圈的海山载荷或跨大陆-海洋地壳边界的挠曲。
Thin plate flexure theory provides an accurate model for the response of the lithosphere to vertical loads on horizontal length scales ranging from tens to hundreds of kilometres. Examples include flexure at seamounts, fracture zones, sedimentary basins and subduction zones. When applying this theory to real world situations, most studies assume a locally uniform plate thickness to enable simple Fourier transform solutions. However, in cases where the amplitude of the flexure is prominent, such as subduction zones, or there are rapid variations in seafloor age, such as fracture zones, these models are inadequate. Here we present a computationally efficient algorithm for solving the thin plate flexure equation for non-uniform plate thickness and arbitrary vertical load. The iterative scheme takes advantage of the 2-D fast Fourier transform to perform calculations in both the spatial and spectral domains, resulting in an accurate and computationally efficient solution. We illustrate the accuracy of the method through comparisons with known analytic solutions. Finally, we present results from three simple models demonstrating the differences in trench outer rise flexure when 2-D variations in plate rigidity and applied bending moment are taken into account. Although we focus our analysis on ocean trench flexure, the method is applicable to other 2-D flexure problems having spatial rigidity variations such as seamount loading of a thermally eroded lithosphere or flexure across the continental-oceanic crust boundary.